Load Fonto.ttf into your font directory to see all ... - of Boris Haase

Index
Current
Version 6.6 of 25.11.2012: Proposition concerning the simplex method proved.
Introduction (revised: 25.09.2011)
What is the aim of this homepage?
Informatics (revised: 25.09.2011)
Radio computing, internet and co, programming with Stair and sorting and searching
Linguistics (revised: 09.04.2011)
Binary font, font Fonto, ambisexuality, planned language Lango and language of science
Mathematics (revised: 25.11.2012)
Geometry, equitable distributing, set theory, nonstandardanalysis, optimisation, representations,
transcendent numbers and calculation of times
Philosophy (revised: 10.05.2011)
Consciousness, reference theory, interview, problem solutions and knowledge representation
Physics (revised: 30.10.2011)
Oscillations and universe
Politics (revised: 11.04.2009)
The political site of the religion of love on www.relil.org
Religion (revised: 21.02.2011)
Description of www.relil.eu, www.relil.net and www.relil.de
About me (revised: 06.09.2009)
Boris Haase
Bibliography (revised: 21.11.2012)
Books used
Subject catalogue (revised: 25.09.2011)
Central terms
Definitions and glossary (revised: 13.02.2011)
Terms used differently
Private (revised: 05.12.2008)
Admission only by user and password
Revisional history:
25.11.2012: Optimisation improved and mathematics extended. #44
12.06.2012: Nonstandardanalysis and mathematics completed. #43
07.04.2012: Nonstandardanalysis improved. #42
06.04.2012: Transcendent numbers and mathematics improved. #41
05.04.2012: Set theory improved. #40
30.10.2011: Formulas in oscillations prettified.
29.10.2011: Nonstandardanalysis altered resp. completed. #39
25.10.2011: Mathematics, set theory and transcendent numbers altered resp. extended. #38
© 1983-2012 by Boris Haase page 1 of 154

25.09.2011: Radio computing inserted. #37
22.09.2011: Sorting and searching extended. #36
09.07.2011: Sorting and searching as well as nonstandardanalysis completed. #35
07.06.2011: Transcendent numbers completed. #34
10.05.2011: Reference theory and universe extended. #33
09.04.2011: Language of science extended. #32
07.03.2011: Language of science inserted, introduction and linguistics completed. #31
13.02.2011: Programming with Stair inserted, introduction and informatics completed. #30
11.01.2011: Consciousness extended. #29
07.12.2010: Introduction changed, philosophy rephrased and consciousness inserted as well
as carried over from reference theory. #28
12.11.2010: Geometry inserted and introduction and mathematics extended. #27
06.11.2010: Problem solutions completed. #26
05.11.2010: Problem solutions completed. #25
09.10.2010: Reference theory extended. #24
17.09.2010: Sorting and searching extended. #23
13.09.2010: Reference theory completed. #22
11.09.2010: Reference theory completed. #21
03.06.2010: Nonstandardanalysis inserted and introduction and mathematics extended. #20
30.05.2010: Set theory extended. #19
11.04.2010: Introduction, informatics and sorting completed by searching. #18
21.03.2010: Introduction, informatics and sorting completed. #17
13.03.2010: Oscillations extended. #16
07.03.2010: Problem solutions inserted and introduction and philosophy extended. #15
16.01.2010: Set theory completed. #14
27.12.2009: Knowledge representation completed. #13
23.11.2009: Physics renamed oscillations, universe inserted and physics rewritten. #12
01.10.2009: Transcendent numbers improved and extended. #11
06.09.2009: Mathematics extended and with introduction plus About me amended. #10
03.09.2009: Set theory, transcendent numbers and informatics improved and extended. #9
11.07.2009: Reference theory extended. #8
28.06.2009: Representations inserted. #7
30.05.2009: Informatics extended. #6
24.05.2009: Mathematics and set theory fundamentally reworked. #5
25.04.2009: Pages migrated to XHTML 1.1, search function improved and used files more
uniformly renamed.
25.02.2009: Interview completed. #4
22.02.2009: Subject catalogue improved and homepage from HTML migrated to XHTML.
25.01.2009: Politics completed by election procedure. #3
11.01.2009: Set theory amended and transcendent numbers inserted. #2
05.12.2008: Size- and colour change and also RSS feed inserted.
21.11.2008: Planned language Lango improved and extended. #1
09.11.2008: Set theory improved.
28.09.2008: Linguistics finelier subdivided into binary font, font Fonto, ambisexuality (new)
and planned language Lango.
24.08.2008: Optimisation inserted.
05.07.2008: Internet and co extended.
20.06.2008: Knowledge representation completed.
04.05.2008: Introduction and politics completed.
03.05.2008: Definitions and glossary inserted.
29.04.2008: Error site set up and language independent code programmed.
20.04.2008: Statistics inserted and politics extended.
13.04.2008: Homepage after W3C validated and PHP code as text inserted.
06.04.2008: Introduction and mathematics extended and politics newly inserted.
05.04.2008: Informatics reworked and internet and co and sorting newly inserted.
24.02.2008: Linguistics completed.
© 1983-2012 by Boris Haase page 2 of 154

17.02.2008: Linguistics and introduction completed.
11.02.2008: About me changed.
05.01.2008: Linguistics and calculation of times (outlook) extended.
16.12.2007: Linguistics changed.
01.12.2007: Religion inserted.
06.11.2007: Linguistics extended.
26.10.2007: Bibliography inserted and introduction completed.
16.09.2007: Calculation of times completed.
09.09.2007: Letters in linguistics changed.
19.08.2007: Linguistics extended by letters.
29.07.2007: Reference theory extended.
17.06.2007: Linguistics completed.
05.05.2007: Linguistics completed by grammar for verbs.
01.05.2007: Linguistics corrected and extended.
20.04.2007: Linguistics extended.
15.04.2007: Reference theory completed.
30.03.2007: Linguistics changed and completed.
29.03.2007: Linguistics and introduction changed and extended.
24.02.2007: Reference theory extended.
18.02.2007: Reference theory completed.
11.02.2007: Numbers/set theory shortened to set theory.
29.01.2007: Physics inserted.
23.01.2007: Numbers/set theory extended.
22.01.2007: Numbers/set theory completed.
07.01.2007: Numbers/set theory changed.
02.01.2007: Numbers/set theory completed by more examples.
01.01.2007: Numbers/set theory extended by considerations concerning the approximation
order.
31.12.2006: Mathematics completed.
30.12.2006: Informatics completed with considerations to the n-dimensional space.
23.12.2006: Reference theory completed.
05.11.2006: About me revised.
04.11.2006: Reference theory extended.
02.10.2006: Reference theory completed.
09.09.2006: Reference theory extended.
03.09.2006: Complete revision of the sites.
01.09.2006: I found the religion of love.
27.08.2006: Reference theory, God, God and man and theodicy extended.
20.08.2006: Prayers by dependence prayer extended.
12.08.2006: Theodicy extended.
06.08.2006: God and theodicy completed.
30.07.2006: Private sector with Web log as diary set up.
25.07.2006: Reference theory extended.
20. and 23.07.2006: Virtue doctrine completed.
16.07.2006: Theodicy extended.
13.07.2006: Basics completed.
09.07.2006: Linguistics completed by Braille, keywords and descriptions updated.
08.07.2006: Linguistics written.
07.07.2006: Theodicy extended, Website search inserted.
© 1983-2012 by Boris Haase page 3 of 154

Current
25.11.2012: Proposition concerning the simplex method proved.
12.06.2012: Riemann hypothesis disenchanted.
20.10.2011: Publication of the e-book "Relil - Religion und Lebensweg".
25.09.2011: Presenting the idea of radio computing.
13.02.2011: Presentation of the programming concept Stair.
07.12.2010: Definition and localisation of consciousness.
12.11.2010: Challenge of several axioms of the Euclidean geometry.
05.11.2010: Depiction that the right measure and world view are necessary.
09.10.2010: Evidence that each being-entity is infinite-dimensional and can be imagined from
arbitrarily small as any-dimensional spheres.
11.09.2010: Proof of the theoretical equivalence and infinity of all worlds and the previous
finiteness of our world.
30.05.2010: Definition of the complex and real numbers.
11.04.2010: Elucidation of fast indexing and of searching in O(1).
21.03.2010: Presentation of the sorting procedure immediate sort.
07.03.2010: Solution of the mind-body, qualia, determinism and causality problem.
16.01.2010: Proof of the minimax-proposition for sets.
27.12.2009: Description of the knowledge representation.
23.11.2009: Presentation of two models of the universe.
24.05.2009: Numbers of algebraic numbers now proved.
11.01.2009: Sensational breakthrough in the field of transcendent numbers achieved.
15.10.2008: Ambisexuality established and English translation improved.
28.09.2008: I solve the problem of the ambisexual personal pronoun in the third person singular.
24.08.2008: I consider how God solves optimisation problems.
20.06.2008: I consider how knowledge is stored.
06.04.2008: I consider details to the qualified democracy.
01.12.2007: I convert the homepage into PHP and MySQL.
06.11.2007: I build the font fonto.ttf.
16.09.2007: I consider new letters to the International Phonetic Alphabet.
09.09.2007: I read "Mind Time" by Benjamin Libet.
19.08.2007: I consider n-dimensional letters.
29.07.2007: I consider further issues about the multidimensional time.
17.06.2007: I improve further details of the planned language.
05.05.2007: I consider the application of the octal principle to the planned language.
01.05.2007: I consider the grammar for verbs.
© 1983-2012 by Boris Haase page 4 of 154

Introduction
What is the aim of this homepage?
This homepage is result of my independent considerations. The ideas come almost exclusively
from L, for what I gave thanks by service to zer. It is to a large extent not scientifically
oriented, but shall address a market as wide as possible. The individual web pages are
rather skimped.
Citations of other authors are missing. If an author should think, my considerations are zis
then I will insert appropriate citations if ze wants. But it is a bibliography specified that includes
literature in my possession, not the few that I have borrowed.
The homepage attends to informatics, linguistics, mathematics, philosophy, physics, politics
and religion.
In the informatics part, I show how radix sort can sort by appropriate storage support in two
steps and apply it to simpler and simpler architectures. Furthermore, the sorting procedure
bitsort is presented as well as fast searching and indexing. Knowledge of informatics studies
is helpful. Radio computing enables, by simultaneous radioing on different frequencies, parallel
computing through parallel communication of each memory cell with each other one.
Programming with Stair presents a programming concept for development environments,
with which source codes can be converted into ones of other programming languages, or
rule-based into freely chosen notations. Internet and Co outlines what role the internet could
play in the future, what the multifunction device strap could serve for and what could apply
for transport and machines.
Below linguistics, a binary font is presented that goes without keyboard. Furthermore, the
appurtenant planned language Lango is outlined and the font Fonto for the International
Phonetic Alphabet presented. The ambisexual grammar for English and German is elucidated
below ambisexuality. The language of science offers a linguistically correct and futureoriented
expression of scientific results.
Mathematics treats geometry, equitable distributing, nonstandardanalysis, optimisation, infinite
sets, representations, transcendent numbers and calculation of times. The set theory
clarifies how many elements important infinite sets have. The nonstandardanalysis offers
new definitions to obtain more precise mathematical statements. For the transcendent numbers
necessary and sufficient criteria are specified. The geometry challenges several axioms.
Below optimisation I present how L solves optimisation problems. For understanding, knowledge
of mathematics studies is necessary. Below representations simplification and exactitude
of expressions are weighed against each other. Moreover, there are some examples of
use for probability calculation at school. Concerning calculation of times, I present a new calendar
and a new calculation of times based on the octal system and give examples for
whose application to length specifications.
Below philosophy, one finds the beginning of the reference theory that represents the radix
for the description of our world. Below consciousness, this is defined, described and it is outlined,
of what we should be aware. In the interview I explain briefly what fascinates me by
philosophy, what I contributed there and how should be philosophised. The problem solutions
contain solutions to important philosophical problems. The knowledge representation
happens with information methods on mathematical radix using the substance term.
Below physics in the context of youth research 1983, I dealt with selected oscillations of
mass points in the plane. Here their period time is determined approximately on the basis of
radius of curvature, initial height and backwards pushing force without integration. To under-
© 1983-2012 by Boris Haase page 5 of 154

stand, a study of mathematics or physics is helpful. There is a test for the mathematical pendulum.
Furthermore, two models of the universe are presented and their experimental verifiability
is discussed.
Concerning the issues politics and religion as well as lectures, see the sites www.relil.org,
www.relil.eu. www.relil.de and the wiki on www.relil.net.
The sitemap contains also a revisional history; the definitions and the glossary list only terms
that are new or are used differently than usual.
And now much pleasure with my homepage!
(It does not depend on the pictures: From the texts peace shall emanate.)
© 1983-2012 by Boris Haase page 6 of 154

Informatics
Internet and Co deals with some aspects of the future internet: How can examinations be
conducted with the aid of the internet? How can an identification (number), the ID, assigned
uniquely to each person, usefully be applied in connection with the internet? What types of
content will be on the internet? How can information user profiles simplify search processes
on the internet?
What tasks could a multifunction device called strap fulfil? What can modern clothes achieve
(for deafblind people)? How can virtual reality be realised (in rooms and in the brain)? How
can goods be transported quickly in future? What are the consequences for professions in
the future? What must be in future considered for intelligent machines?
Programming with Stair presents a programming concept for development environments,
with which source codes can be converted into ones of other programming languages, or
rule-based into freely chosen notations. The programming language Clare provided in it is
capable of learning (by adding rules and meta-rules) and has activatable (self-) optimisation
algorithms that adapt themselves nearer the time to the individual circumstances.
Below sorting and searching an O(1)-sorting algorithm with two steps is presented if the
hardware is not limited. This procedure is adapted to different real conditions. By simple
hardware adaption (organisation of memory locations preferably as tree of degree 2 t with
natural t) an O(n)-procedure (bitsort) can be specified for n successively read input values.
Furthermore is described how one can fast index and search in O(1).
Radio computing enables, by simultaneous radioing on different frequencies, parallel computing
through parallel communication of each memory cell with each other one. Thus, n values
can be sorted in O(1), the indexing of database tables becomes widely obsolete. Networking
and cloud computing solve with radio technology various problems much faster than
before, what can be accessed comfortably at home.
L can solve all problems of any world in a higher world at one go by singling out those from
all possible solutions with recording the solution formations by (comparative) sorting that satisfy
the solution criteria. On substantial comparisons can largely be foregone by gödelisation.
Consequently, all problems are for zer in the same complexity class O(1).
Ze does not get around the formation of all possibilities, since crucial problems are irreducible
in terms of complexity. For our (finite) world, this means that in it crucial problems are not
solvable. This does not mean, however, that we cannot solve the problems important for us,
but only, that we cannot answer all scientific questions.
Theorem: All problems of a finite world can be solved in O(1).
Proof: Conditions are checked by inserting the complete solution space into the conditions at
once, possibly by parallel processing. Calculations are accelerated by summarising calculation
steps. Continued summarising yields an overall calculation step. Hence the claim follows,
since every finite solution space can also be constructed in one step.
© 1983-2012 by Boris Haase page 7 of 154

Radio Computing
How can a memory cell communicate with as many other ones by radio chips at different
frequencies in order to support parallel computing? How can in this way sorting of n values
be improved from O(n log n) to O(1) and thus the indexing of tables in databases become
obsolete?
If each radio chip transmits (simultaneously) at the frequency that corresponds to the value,
transformed into the smallest positive natural interval valid for all values, of the associated
memory cell, then the counterpart stations receive these new values sorted in O(1) and they
can output them in O(1), if they are hierarchically organised as a binary tree, while first the 0node
and then the 1-node sends to its parent node.
If the parent node is still not taken, it stores the value of the 0-node. For each free further
parent node, the procedure is the same and the 1-node is pulled behind. This is altogether
possible in O(log n), thus enabling an output of all nodes by traversing the resulting binary
tree in O(n). Equal values are first made different by appending a sequence number in O(n).
It is clear that the radio distances depend only on the size of the radio chips and that the radio
must not be disturbed from the outside. Here weak (if need be shielded) signals and a
predetermined frequency range are advisable. Possibly, first an implementation in datacentres
is provided, as long as the radio chips are still relatively large, but this is for example not
a big problem because of the increasing cloud computing.
For fewer frequencies than values to be transmitted, use FSO or microwaves, or double the
number of transmission runs for each additional bit. If the frequency values are smaller than
the values to be transmitted, so another transmission run for the subsequent sorting is necessary,
for every transcending by a further frequency range. If applicable, for additionally
occurring values, overflow areas are advisable (e.g. for table queries).
If one arranges the radio chips in a straight line, and puts in each case two of these lines
crosswise one above the other, they can, if they are confronted with, send without intersection,
and one gets along with one or few frequencies. Thus, k + 1 tables can be joined in a
query in O(1) instead of O(n log k n). However, the necessity for serial processing sets limits
to the parallel (radio) computing.
The radio technology can also be used to implement parallel transmission of parallel adders
or other (linear) arithmetic operations (e.g. comparisons). In conjunction with networks and
fast data transmission (e.g. DSL), it can be parallel calculated in combination (e.g. to solve
(linear) optimisation problems in linear time). Also associative problems can be parallel
solved (better than in the brain).
© 1983-2012 by Boris Haase page 8 of 154

Internet and Co
Exams
To guaranty the authenticity of information (e.g. for exams), appropriate safety mechanisms
are necessary. The authentication can be done by biometric procedures. Supervised computers
are suitable as the only foreseeable inexpensive solutions. Unsupervised computers
can be easily outwitted since information can be channelled in from unwanted side (e.g. human
or computer).
The supervised computers must be able to identify, store and display for usage the brought
along allowed additive information as such and to prevent or to channel the access to the
internet specifically. For this purpose, both appropriate standards and intelligent verification
methods are to develop if one wants to accomplish a certain comfort.
A simple way is to specify the allowed URLs for the browser. Automatic image recognition
procedures that can filter out undesirable sites are not suitable because the sites can be
coded and the velocity of decoding is the problem. Thus, only sites that have a fixed incorruptible
authorship and no hidden areas come into question.
A reliable control can only be ensured if the assignment of URL and content can not be manipulated
(beware of generic URLs). The brought along additional information may be protected
by appropriate passwords (exam on the internet) and decrypted before the exam. The
customising of programs for additional information must not take up too much time.
For this purpose, profiles of the programs should be able to be safely stored passwordprotected
that will only need to be imported (requires appropriate programming of the programmes).
If the internet should evolve to the extent that there every program is available,
this problem is omitted. This is certainly desirable since special knowledge is to test as a rule
by special programmes, too.
Programmes that cannot be called up via internet may, however, be called up via appropriate
controlled remote connections (velocity should be no longer a problem in the future). It is
more difficult when the exam situation requires special hardware (such as surgery). There
will always be exams that are to be conducted only at certain places. Most exams can be yet
realised with standard equipment.
Is knowledge from certain time units in demand, a questionnaire is appropriate that, varied at
given times, the examinees have to answer at the same time. For the success, a certain percentage
of correct answers for individual fields may be demanded, which can vary depending
on the field. Multiple-choice questions facilitate the evaluation on the computer, as long as
the automatic language comprehension is limited.
For exams via internet, the result of the automatic evaluation can be made public immediately
after the end of the exam time. The exam possibilities and fairness require in any case
sometime the internet: Nobody can be expected to have retained all needed knowledge in
memory. The irreplaceable accomplishment of man is in the creative and information connecting
field.
To protect the personality of the examinee, it may be necessary to conduct exams on the
internet anonymously. For this purpose, the testing centre should offer signatures on the
internet that are available after selection by the examinee only to this to identify himself. Furthermore,
the testing centre should offer anonymous (temporary) email accounts under that
the examinee can view the exam result with the signature and a password.
© 1983-2012 by Boris Haase page 9 of 154

Email
Votings on the internet are also easily possible if the identity of the voter can be uniquely
clarified. Everybody should get assigned at birth a free e-mail account to that all emails are
sent, needing a unique identification of the recipient. This email account would have even a
higher status than the letterbox, concerning security aspects.
It could be (also) managed till the early infancy by the legal guardians. For this purpose,
every person would have to have internet access in case of need. This could be installed in
public authorities. Their employees would then have to help those in the operating that alone
are not in a position to do so. The operating must be possible voice-operated in the future
without a keyboard having to be used.
Each person should also be assigned at birth a worldwide unique identification (number) that
can be pronounced as a name (see linguistics) and serves officially as such. This also serves
as a signature of important documents. It is to consider whether this ID is uniquely generated
from biometric data that do not change during life. Simpler is the query in a safe database.
The consequential use of the ID also allows finding certain contents about oneself quickly
and reliably on the internet. With increasing improvement of spam protection the email account
assigned at birth can be linked to the ID uniquely and for everybody recognisably: e.g.
[ID]@mail.world. Each person should be provided with a free web space where ze can present
zerself.
Contents
This should, for example, be accessible at www.[ID].net.world and free of unwanted content.
Over this administrators watch that are appointed by the future world government. Each
presentation should be drafted in the future world language, so that everybody can easily
and quickly get an idea. For the official part an obligatory profile can be made. It may be
linked to unobjectionable private home pages.
People who do not want to position own content are represented by minimal content as they
among others e. g. can be found in an identity card. Everybody is to be enlightened about zis
stored data and their location. When creating one’s own content the authorities assist within
their means. What can be listed by a uniform questionnaire everybody can demand (even in
part) as content.
A worldwide valid law determines the volume of the minimum contents. It is conceivable, for
example, that publicly only ID and nationality may be published. Since nationality in the future
plays a less and less important role in view of the world civil society, it is quite conceivable
that the law only the ID views as liable to publication. One only knows then that this ID
exists, but no more.
The principle of equality has no bite here since each person must be able to determine by
himself to what extent ze wants to represent zerself in the public. Authorities are entitled to
attend their duties by storing much more data concerning an ID. Everybody can only demand
within the valid laws to view the data stored about zer. Sufficient data privacy is always to
guarantee.
Who publishes data on www.[ID].net.world assents explicitly that the data may be used for all
legal purposes. This includes in particular the automated processing. Each person is to be
informed about what can be done with zis data theoretically and practically, so that ze receives
a comprehensive idea and can realise the scope of zis decision.
© 1983-2012 by Boris Haase page 10 of 154

The right to freedom of self-expression includes that the published data have not to be truthful.
This should be clear to everybody. Nobody can demand a correction. Nobody can also
demand that somebody corrects the truthful data published elsewhere if the privacy rights of
the described are not violated.
Is somebody public figure, ze can defend zerself to a lesser extent against depictions of
zerself since the legitimate interest of the general public can conflict with zis personality
rights. A core of individual rights but always remains inviolable since the dignity of man must
be respected. The laws of world government regulate particulars and this is not to be subject
here.
A person may reply fictitious statements about facts concerning zerself with a counter statement,
which has to be published also on the internet, regardless of its truthfulness at the
place of its occurrence. It does not matter how many times the homepage is called. Will the
depiction be sufficiently corrected or be withdrawn, the right to publish the counter statement
expires.
The freedom of publication allows that publications about a described person have not to be
notified to this person, since ze can easily browse the internet because of zis ID for depictions
of zis person by zerself. If the described person wants to be informed about this, one
should be in keeping with this wish by mailing to zis wished email address since this does not
represent a significant expense.
Mobile internet reception should be possible: via satellite or sufficiently densely distributed
hotspots etc. The control of the internet should be possible by language (headset), data
gloves and eye movements. The monitor is replaced by semi-transparent to switch data
glasses (with prompter), whereby for each eye contents of various kinds can be seen - even
for 3D representations of the same content.
On the internet one can arrange radio broadcasts in future on one’s own. Newscasts can be
specifically read to (by a female, male or child's voice). In so doing, one can select specifically
the speaker's voice (e.g. of the partner). Pieces of music can be selected specifically or
pools. The cost is comparable to that of sound radio or television broadcasting. One can create
programs for others.
These can be combined with own broadcasts (going live with a microphone or webcam). Examples
are own concerts or play stagings, art exhibitions with virtual tours and explanations,
(collective) karaoke, commercial spots for own products, workshops or conference circuits.
Since the future on the internet is multimedia, much is thinkable right up to the 3D film.
With the increasing development of speech recognition and translation programs automatic
simultaneous translations via internet are imaginable – by being delayed introduction of the
worldwide uniform planned language. The more intelligent the programs are, the more likely
they can correct an error in speaking, and, if necessary, interpose explanations. It remains of
course reserved to the internet user what ze permits or initiates autonomously.
In order to simplify the search processes, the existing idea of autonomously seeking agents
is extended to (standardised) information user profiles that specify the wishes of the user for
a site, and to which then each site can react by corresponding queries and displaying only or
primarily the desired contents. For this purpose, the programming language PHP, for example,
or the browser could be extended.
The web site content would be to categorise smartly and could be queried by these categories.
The browser should be able to summarise the contents that are scattered across several
sites, on one site to obtain a clear representation. Ontology concepts should be included
© 1983-2012 by Boris Haase page 11 of 154

meaningfully (e.g. through on terms formulated query rules that browser and PHP then
evaluate).
The advantages of this approach are in the free determination of categories that have not to
occur in the site and also can consist of whole sentences and of rules that can be complex,
without extending the search time significantly. Since queries are based on searching in
sorted data, suitable data storage is to choose, as sorting and reference theory with substances
and references suggest.
Strap, clothes and virtual reality
Portable computers can be connected to the so-called strap, which as a multi-function device
serves for authentication, is worn like a watch and takes over whose functions with display,
option to telephone and key function. The functions of the strap can be currently (partly) enabled
or disabled: through language or touch. The strap has integrated a simple computer.
It works even without a computer connection, replacing an implanted chip. When it is laid
down, an alarm can be prepared that is triggered when it is not activated in a specified period
again in a certain way. Certain functions should be always disabled for security reasons if the
strap is laid down. The alarm can let send the integrated transmitter messages to the security
forces.
One can also justify the strap so that the events of the last few hours around its wearer are
recorded (black-box function). This recording can be sent out when an alarm occurs or at the
request of the wearer. In order that criminals have no possibility to stop the transfer process,
a running transfer to a secure computer can happen or the transmission must be sufficiently
quick.
Since the coordinates of the wearer are also transferred, the last place of residence prior to a
possible kidnapping is always known. Versions of the strap may also be used as an electronic
tag. Everyone should consider precisely what functions of the strap are enabled or
disabled, since many conclusions regarding his behaviour are possible – be the (encrypted)
transfer even so secure.
Modern clothes can also contribute to the information transfer: So information can be absorbed
with the body surface as a pattern of different pressures or different temperatures.
Thus, images and language become easily transferable to deafblind. If the habiliment is connected
with rangefinder or correspondent image analysis software, even the white cane can
be dropped.
Connecting the habiliment with other measuring devices, e.g. magnetic fields, pollutant concentrations
can be inconspicuously evaluated and everything else, what can be measured as
scaled substance or evaluated by programmes (for example fluctuations in the voice or skin
or eye contact of the counterpart, which can give hints on certain emotional states).
If the habiliment is programmable - input via voice, touch or evaluation of the viewing direction,
the measured variables can be easily changed. Imagination about what can be measured
has no limits. A connection to the internet and databases increases the information
available again. However, prices also will rise with the requirements - and decrease with a
high number of units again.
The path to virtual reality can lead in rooms (CAVE) in addition to projection procedures onto
suitable coated surfaces - whereby a computer computes the image to project for objects
existing in the room (compensation of distortion) - also via programmable wallpaper that can
© 1983-2012 by Boris Haase page 12 of 154

e operated like the clothes above. Even 3D effects can be achieved by this (higher dimensions
as a projection).
The surfaces of the room can be segmented at work for different contents and can be individually
addressed. Given these possibilities, the inability of man for parallel processing becomes
displeasingly noticeable. As long as ze is not a cyborg, ze remains reliant on computer
assistance. Direct influence on the brain is therefore so attractive because impressions
have not to be communicated materially (sensory organs).
Transport and machines
In order to transport goods quickly and reliably from warehouses and collecting points to the
consumers, partly underground express connections are established. The volume of goods is
not more than 0.125 cubic metres (0.5 m) 3 since bigger goods can be transported slower.
Computers compute optimal network utilisation and collision avoidance. They also inform
technicians about occurred jams.
Type of transport could be for example magnetic suspension technology in combination with
vacuum tunnels. The goods may be collected and posted at easily accessible shipping
points. Whether will be transported partly (with a different technology) to the households
must be reconsidered. Foods can be, for example, centrally prepared at the collecting points.
By centralising also unusual wishes can be fulfilled.
The individual containers for the transport can be streamlined. Integrated chips control the
unmanned system. Only a few minutes pass by between order and delivery. The transport
fees are low in relation to the value of the goods if the containers are filled well: driving
should be more expensive. Many occupations that we know today will vanish or are performed
by robots or computers.
Only where complicated conversations with people arise, where creative performance, years
of experience and special skills are needed, where must be complexly organised and coordinated,
man is still in demand. Physical work and everything, for what rules can be laid down,
is vulnerable to replacement. Our world will be to manage with much less people. However,
the needs will considerable increase.
The differences between man and machine will wane more and more: human beings will
have properties of machines and vice versa. Man will die if ze wants to: to get into the subsequent
world - at a point of time which ze has chosen. Fatal accidents will continue to occur
- but more rarely. The question for the domination through the machines will arise: concerning
this, man, however, will find a solution.
The solution is control and monitoring. The information that accumulates in a machine is
checked by appropriate programs. Certain functions in a machine may not be disabled without
disabling the machine itself. With this, an interdiction of coding in certain areas is associated,
respectively that what is coded, must be able to be decoded simultaneously by certain
programs.
Machines need a central, unforgeable and by rota to renew approval that can be checked up
at any time - like the overall status of the machine. Simpler checkups must be possible by
owner and police, complex ones may be reserved for specialists. There have to be enacted
laws against criminality committed by machines that hold manipulators and owners responsible.
© 1983-2012 by Boris Haase page 13 of 154

Programming with Stair
Stair is a programming concept for development environments and stands for standardised
transformation after individual rules. It provides a programming language Clare (coding language
after rule environment), which is capable of learning (by adding rules and meta-rules)
and where activatable (self-) optimisation algorithms are available that adapt themselves
nearer the time to the individual circumstances and are so complex as their intelligence
yields, or a reasonable behaviour of the running time and an acceptable effort suggests.
Its rule-based individual notation can be, within the feasible scope, freely chosen and is recorded
in (per programming language used) exchangeable modules, which are collected in a
rule environment. It can be, as far as possible, transformed into any other feasible notation
(also into a general standard), comfortably after individually selected rules, in order to share
it with others. Coding suggestions can be easily selected in the IDE.
By appropriate selecting its modules, it can be kept lean. The use of sample code of the target
programming language, which can be, for example, received via the internet, enables
also realising code, for that (yet) no favourable rules exist. Since source code is used, the
string operations insert, delete and replace are sufficient as basic operations. Modularisation
and text editing can also be automated in the target programming language.
Discussion: Stair is interesting if source code is to be converted (on a large scale) at pace
into other programming languages, for example, because these have advanced concepts, if
the own notation is to be maintained for different programming languages, as possible, for
example, because they are shorter, or in order to do not need to adjust oneself, or to optimise
code, or to prove its correctness with further tools.
© 1983-2012 by Boris Haase page 14 of 154

Sorting and Searching
Is sorting of values in O(1) possible? Yes it is, in two steps.
Suppose we had no hardware restrictions: The memory be organised in the form of a tree of
degree k and have k m+1 memory locations with k m+1 = 2 h with natural h. Each memory location
can store every value to be sorted completely. Do values exist multiply, be a consecutive
index attached to every value, both constituting the new value. Each value be coded in the ksystem
and let w. l. o. g. maximum k m values to be sorted.
K m data lines branch from the root, each k m-1 from the two successors, each k m-2 from whose
successors etc. Each z-th intermediate node corresponds hierarchically with the z-th digit in
the k-system of the value to be sorted. In the leaves alternatively the addresses of the values
instead of the values themselves can be stored. Then, in one step, all the values can be
stored in the leaves and in a further one fetched back sorted in the root. It is sufficient to
move the values so far into the tree until they separate.
Have we now a limit of one data line per memory location, the values must be read in succession.
The attaching of an index for multiple values can now be dropped since multiple
values can be managed in a separate list. Every intermediate node memorises which values
went through it by setting the corresponding bit for each value to 1. This bit is set to 0 if the
intermediate node has no successors to read anymore. One starts with the smallest value at
a time for ascending sorting order, with the largest for a descending one.
It results the complexity O(n) (storing, testing the successor, masking the bits, reading). If an
additional value is to sort, an additional complexity of O(log n) arises (binary search in a
sorted list). If d data lines are used, decreases the complexity of sorting by a factor 1/d. If the
values are g-times as long as a memory location can contain, the complexity increases by a
factor g.
If the memory is not organised as a tree of degree k, the complexity increases by a factor
logkn because then each intermediate node to a value must be read. The more one can find
of a tree of degree k in the memory organisation, the lower is the complexity. If the first k p
memory locations should be used otherwise, so all intermediate nodes of the p-th level are to
search. The complexity increases thereby marginally if the memory is filled good, but otherwise
accordingly more with the worst-case factor O(k p ).
Currently viable, non-parallel sorting algorithms, based on the swapping of the n input values,
have a complexity of O(n log n). This value can be significantly underbid as described
by the procedure following radix sort.
In the following the optimal sort algorithm bitsort is presented. It sorts stable with at all times
equal time complexity O(n) and needs O(n) additional storage space. Here is assumed that
the comparison of two values needs the time complexity O(1), the values are present as bit
sequence and all bits of a value can be also processed in O(1). It is furthermore presupposed
that the storage is realised as binary tree and the path from root to leaf can be run through
also in O(1). If p is the number of parallel steps for parallel bitsort, so the time complexity is
O(n/p).
Once a value has been processed, the values inserted so far are available sorted. Inserting
an additional value has the time complexity O(1). After each insertion, the m values can be
output with time complexity O(m). The storage must be provided with a certain own intelligence:
Each storage node must be able to store the value that reaches it independently and
© 1983-2012 by Boris Haase page 15 of 154

to pass it to the next storage node, if it was already visited, resp. to give it back to the central
unit, if it was still not visited, after it stored the value. The next storage node at each time results
from the corresponding bit of the value within the storage hierarchy.
The bits of a value are at each time - beginning with the leading bit - processed as long until
a difference to the compared value or equality is certain. Every value is compared with a binary
tree whose root represents the most significant bit of the value. In each leaf of the binary
tree reached by comparison, the most significant bit is set 1. At the end of the comparisons
with the value, a leaf stores either the number of the values for this leaf, the address of
a list that contains the addresses for this value, or, if the bits of the value were still not processed
completely, the value itself or the bit rest. The bit chain is always then broken up at the
position where a leaf is built. Very many bits of the same value can be stored with their number.
This is advisable, for example, for floating point numbers in exponential representation.
The lists can be summarised to one list, if every entry refers to its successor (predecessor) of
the same value resp. to null, if there is none.
In all the sorting procedures in that values are sorted with a bit length of l = q a with address
length a, the time complexity increases per value from O(1) to O(q). If O(r) is the average
value of O(q), thus in the time complexity of the sorting procedure at least one O(n) is to be
replaced by O(r n). If s is the average of the number of different (!) values that end up in a
bucket after sorting up to bit length a and whose bit length is greater than a, then the time
complexity of the sorting procedure is O((log s + r) n). The mentioned values of a bucket are
stored per bucket in an AVL tree (or in a B-tree, if they are stored in a relatively slower external
memory with respect to the main memory). There is worked each time always only with
the significant part value of address length of a value.
If one forgoes that the values of each processing of a value are present completely sorted,
then the time complexity O(r n) can be maintained for the complete sorting by using two areas
of main memory. The values are first sorted up to address length into buckets and then
further sorted address length for address length (i.e. part value for part value), bucket for
bucket. The processing of the values whose part value previously processed is equal is
counted as one run. It is presupposed here that reading and writing of the part values of a
value and its address on all runs are on average completely counted as O(r).
The second area of main memory is deleted after each run to be available for the next run,
until the bucket is processed. Into the first area of main memory, always only the addresses
in the current sort sequence are written back, before the values with equal part value just
processed are further sorted. Each value is to be stored contiguously in memory, so that can
be accessed quickly to any part value. About the time complexity can be admittedly argued.
The values of a bucket and all the addresses should fit into the main memory to avoid relatively
long loading times.
Both procedures can be combined well: First the O(r n)-procedure for master data, then the
O((log s + r) n)-procedure for transaction data. Sorted data can be stored in O(n) in main
memory and AVL- resp. B-tree. Thus especially indices can be quickly built for non-indexed
columns in database queries. For large tables, it makes a significant difference, whether an
index is built in O(r n) instead of O(r n log n), and then a value can be searched on average
in O(log s + r) instead of O(log n + r) or worse. Using skilfully a sufficiently large main memory
several indexes can easily be kept simultaneously. For numbers, r is usually quite small,
depending on the accuracy, and s also for a corresponding distribution. The same is true for
(compressed) words, if the memory size corresponds to that of today commercially available
computers. Sorting by merging of arbitrarily many sorted lists is also possible in O(r n).
© 1983-2012 by Boris Haase page 16 of 154

Discussion of bitsort: It is well suited for parallel programming and stable. It is optimal under
the presuppositions made. Bitsort does only what is absolutely required, it is optimal for the
rapid ongoing building of indices in (relatively fast growing) databases and for searching (see
below). Search trees need not to be balanced. It beats for values with relatively few bits
(maximally address length) and corresponding hardware all sorting procedures known to me,
if the values have to be read successively. One should consider carefully whether an adaptation
of the hardware pays off to achieve the described time complexity. The implementation
of an appropriate memory with relatively low intelligence is admittedly simple and saves more
complex processors, but by using sufficiently many of these or parallel processing (e.g. parallel
use of memory areas) the term log r in O(r n) can be made less than 1.
In support of sorting and searching in heterogeneous (distributed) databases (for instance of
different database models), a database query language can be used that allows a unified
data manipulation, with the aid of dynamically generated data structures from these (e.g.
under a uniform interface), as long as the records have a somehow similar structure. It can
decide dynamically, based on corresponding demands (possibly anticipatorily), which manipulation
steps are to be performed. It must be provided only with the corresponding memory
information of the databases with the setup of the database structures.
Changes of the programme code and data (such as the integration of further databases) at
run time can be provided, if sufficient security mechanisms (including authorisation checking
and setting locks) are available. The indices may be built up, for example parallel or on times
of low charge, depending on their size, with different data structures - adapted to the individual
presentation of the problem or optimised. Possibly a temporary merging or parallel accessing
is sufficient. High-octane standards can facilitate the implementation of such a database
language clearly.
Outlook on the graph theory: Let n be the number of nodes of a finite simple connected
graph. (If it is not simple, allow by sorting out in O(n) only the smallest parallel edge and no
loops. If it is not connected, remove in O(n) all isolated nodes.) Since sorting and parallel
adding and comparing is possible in O(1), Dijkstra's algorithm yields each time a shortest
path in it in at most O(n), if negative weights are excluded. How can we compute in it a minimum
and a maximum spanning tree in O(n log n) or even in O(log n)?
Let each node correspond to a different natural number. Then the edges that spring from it
can be each time parallel sorted in at most O(n) or O(1). Let be all edges coloured white at
the beginning. Each node adds the smaller and then the greater number of the nodes involved
of the edge with the smallest weight of all white-coloured edges to this bit by bit as
value that spring from it and stores the smallest value that reaches it. This is at most O(n) or
O(1) possible. Then, each node has one nearest adjacent node and the edges, each consisting
of two nodes of the same minimum spanning tree, are coloured black. This is also at
most O(n) or O(1) possible.
Now the process continues with the white-coloured edges in at most O(log n) steps, where
the smallest value of a minimum spanning tree can be determined in at most O(n) or O(1),
until an overall minimum spanning tree is created in at most O(n log n) or O(log n). An overall
maximum spanning tree can be calculated by subtracting each time edge weights from a
sufficiently large constant as new edge weights.
By calculating the shortest paths, e.g. a traffic control system can be simulated in the computer
that responds to changing conditions by modifying the edge weights. Packet collisions
can be prevented if the nodes are numbered consecutively, and each time the packet gets
the first chance that passes through the previous node with the smallest number. Hereby
collisions can be minimised by presetting road users interim targets on less-loaded routes.
© 1983-2012 by Boris Haase page 17 of 154

© 1983-2012 by Boris Haase page 18 of 154

Linguistics
The linguistics devotes itself to the diverse linguistic issues.
Below binary font without keyboard, a font keyboard without letters to be entered is presented
that is based on the binary system.
The font Fonto contains newly-designed letters for the International Phonetic Alphabet and is
the basis for the planned language Lango.
Below ambisexuality in each case a new ambisexual personal pronoun for the third person
singular for the English resp. German language and further grammatical changes are proposed,
as they are applied in the word of L.
The planned language Lango is a future world language whose root words are determined
through a democratic computerised voting. The related grammar is stated.
The language of science offers a linguistically correct and future-oriented expression of scientific
results. In addition, a trenchant picture of present science is drawn.
© 1983-2012 by Boris Haase page 19 of 154

Binary font without keyboard
The past fonts appeared rather illogical in the structure and needed a keyboard for the input.
Here a new phonetically accurate font with 36 phonetic characters is presented that can represent
16 * 1024 * 1024 different characters by one sign. Some of them can represent whole
words. It is in the following about suggestions, from which can be deviated naturally. Therefore
little is concretised, since it concerns the idea.
The characters of the primary system consist of ten bits of that four stand for the vowels in
the middle part, three for the hierarchic consonants in the left part and three for the grammatical
consonants in the right part. The bits are arranged on a circle (top, bottom, left, right)
and the circles are abreast. The bits can be arranged also differently.
If one or two of the three parts remain empty, one dot is set above beside or over the remaining
part in a condensed representation for the identification of the part that is missing in each
case, so that one can recognise which parts are missing. However, only the bits are entered
that can be set. No sounds are assigned to the dots. All this can be managed by a programme.
Each bit is assigned to a finger respectively the thenar. This assignment can be chosen unrestricted,
should be however standardised. So thumbs and index fingers for the vowels can
be used, the remaining fingers and the thenar for the consonants. If a finger or the thenar is
lowered on the desk top, then the associated bit is set.
In the primary system, 16 syllables can be represented. To the vowels belong a (corresponds
to 4, right), e (1, left), i, o (2, top) and u (bottom), the umlauts ae (5), oe (3), ue and ao (6 as
in law) and the diphthongs ai, au, ei, oi, ui (7) and ou (as in low), because these occur frequently.
The i consists of a complete circle, for the diphthongs with i the bit of the associated
vowel is omitted. The 0 corresponds to y, which is spoken without opening the lips (like hm
without m).
The (grammatical) consonants in the initial sound are k (1, nouns, personal pronouns), p (2,
adverbs, prepositions), l (3, plural), w (4, accusative like ch in German teich), t (5, adjectives),
f (6, verbs), s (7, accusative plural) and c (0, links like sh in shoe). The final sound is
the same and the real grammatical consonant. The fourth bit is represented by m, which follows
in the initial sound after and in the final sound before the consonants.
The sounds that cannot be represented with twelve bits are represented with further four bits
within the circles (horizontally, perpendicularly and two diagonals). The consonants read g
(1), b (2), r (3), x (4 like ch in German buch), d (5), v (6), z (7) and j (0 like j in journal). They
correspond to the primary system in the order. The fourth bit is n, which follows in the initial
sound after and in the final sound before the consonants. So we have again twelve bits, to
which one switches, as all ten fingers respectively the thenars are lowered on the desk top.
If the bits should not be sufficient, further ones can be added. They can be "written" with the
feet or elbows or knees. Ersatz consonants are h (like th in thin) and q (like th in the). Bit
combinations with m or n can be spoken also as other sounds: e.g. xn like the hitherto h, dn
such as English th and so on.
If mankind should succeed to be able to use the thoughts in the brain, - it is with additional
technology - this is omitted. Then less characters than complete pictures are thought, and
these are converted in characters. Since whole words can be written at once, a clear speed
increase is to be expected. However, the complete character set cannot be exploited completely,
since, because of the danger of mix-ups, sufficient gaps must remain (thin allocation).
© 1983-2012 by Boris Haase page 20 of 154

The conversion for blind persons is likewise simple. Additionally deaf-mutes can communicate
with the hands (and fingertips). Since one is substantially faster with the keyboard, as
long as parallel processing is too difficult for man, it is to focus in the following on the keyboard
and the dependence on the phonetic transcription (a character - a sound). The conventional
characters are more eidetic than the bit combinations and thus easier catchy (maintaining
of history).
The "keyboard" could consist of a "data glove" that determines the correct "key" from the
relative movement of the fingers. So substantially more "keys" could be mapped. Furthermore,
the "keys" could be rearranged by considering the frequency of the characters and/or
letters. As long as there is no unitary language, customisable country versions are here useful.
The "keyboard" can be specified by three-dimensional holography or two-dimensional
laser light.
© 1983-2012 by Boris Haase page 21 of 154

Font Fonto
To the International Phonetic Alphabet, there is in the future an own new font: fonto.ttf. Thus,
the language of the future can be formed in such a way that each sound corresponds to a
letter and vice versa. There are uniform letters: one does not distinguish between upper and
lower case. All letters are horizontal symmetrical and have two heights. Similar sounds are in
principle also similarly written.
The more seldom vowels get, compared to the more frequent vowels, one more line, the
voiced consonants, compared to the voiceless, a close form. In the n-dimensional representation,
the two-dimensional letters are laid on the surfaces of an n-dimensional cube. Since
no two unequal letters can be transformed by rotation into another, they are always good to
recognise.
Plosives contain a v, nasals a point, trills consist of a circle with a horizontal bar at the top,
taps/flaps have additionally a horizontal bar at the bottom, lateral fricatives contain an E,
whose upper and lower end point to the middle crossbar, approximants can be identified by
two parallel lines and lateral approximants consist at least of a circle, from which two bars
diverge.
Load Fonto.ttf into your font directory to see all
characters properly!
Digits: 0 (0), 1 (1), 2 (2), 3 (3), 4 (4), 5 (5), 6 (6), 7 (7), 8 (8), 9 (9).
Vowels:
Opening Location Roundness Unicode IPA Alt ISO Fonto
close front unrounded U+0069 i Alt+0105 i i
close front rounded U+0079 y Alt+0121 y y
close central unrounded U+0268 ɨ Alt+0073 I I
close central rounded U+0289 ʉ Alt+0089 Y Y
close back unrounded U+026F ɯ Alt+0085 U U
close back rounded U+0075 u Alt+0117 u u
near-close near-front unrounded U+026A ɪ Alt+0239 ï ï
near-close near-front rounded U+028F ʏ Alt+0207 Ï Ï
near-close near-back rounded U+028A ʊ Alt+0216 Ø Ø
close-mid front unrounded U+0065 e Alt+0101 e e
close-mid front rounded U+00F8 ø Alt+0248 ø ø
close-mid central unrounded U+0258 ɘ Alt+0069 E E
close-mid central rounded U+0275 ɵ Alt+0244 ô ô
© 1983-2012 by Boris Haase page 22 of 154

close-mid back unrounded U+0264 ɤ Alt+0079 O O
close-mid back rounded U+006F o Alt+0111 o o
mid central U+0259 ə Alt+0212 Ô Ô
open-mid front unrounded U+025B ɛ Alt+0232 è è
open-mid front rounded U+0153 œ Alt+0246 ö ö
open-mid central unrounded U+025C ɜ Alt+0200 È È
open-mid central rounded U+025E ɞ Alt+0214 Ö Ö
open-mid back unrounded U+028C ʌ Alt+0193 Á Á
open-mid back rounded U+0254 ɔ Alt+0225 á á
near-open front unrounded U+00E6 æ Alt+0230 æ æ
near-open central U+0250 ɐ Alt+0198 Æ Æ
open front unrounded U+0061 a Alt+0097 a a
open front rounded U+0276 ɶ Alt+0224 à à
open back unrounded U+0251 ɑ Alt+0065 A A
open back rounded U+0252 ɒ Alt+0192 À À
Consonants:
Manner Place Voice Unicode IPA Alt ISO Fonto
Plosive bilabial voiceless U+0070 p Alt+0112 p p
Plosive bilabial voiced U+0062 b Alt+0080 P P
Plosive alveolar voiceless U+0074 t Alt+0116 t t
Plosive alveolar voiced U+0064 d Alt+0084 T T
Plosive retroflex voiceless U+0288 ʈ Alt+0100 d d
Plosive retroflex voiced U+0256 ɖ Alt+0068 D D
Plosive palatal voiceless U+0063 c Alt+0099 c c
Plosive palatal voiced U+025F ɟ Alt+0067 C C
Plosive velar voiceless U+006B k Alt+0107 k k
Plosive velar voiced U+0067 g Alt+0075 K K
Plosive uvular voiceless U+0071 q Alt+0113 q q
Plosive uvular voiced U+0262 ɢ Alt+0081 Q Q
Plosive glottal voiceless U+0294 ʔ Alt+0202 Ê Ê
© 1983-2012 by Boris Haase page 23 of 154

Nasal bilabial voiced U+006D m Alt+0109 m m
Nasal labiodental voiced U+0271 ɱ Alt+0077 M M
Nasal alveolar voiced U+006E n Alt+0110 n n
Nasal retroflex voiced U+0273 ɳ Alt+0241 ñ ñ
Nasal palatal voiced U+0272 ɲ Alt+0209 Ñ Ñ
Nasal velar voiced U+014B ŋ Alt+0078 N N
Nasal uvular voiced U+0274 ɴ Alt+0234 ê ê
Trill bilabial voiced U+0299 ʙ Alt+0062 b b
Trill alveolar voiced U+0072 r Alt+0114 r r
Trill uvular voiced U+0280 ʀ Alt+0082 R R
Tap/Flap labiodental voiced U+? ? Alt+0223 ß ß
Tap/Flap alveolar voiced U+027E ɾ Alt+0226 â â
Tap/Flap retroflex voiced U+027D ɽ Alt+0194 Â Â
Fricative bilabial voiceless U+0278 ɸ Alt+0118 v v
Fricative bilabial voiced U+03B2 β Alt+0086 V V
Fricative labiodental voiceless U+0066 f Alt+0102 f f
Fricative labiodental voiced U+0076 v Alt+0070 F F
Fricative dental voiceless U+03B8 θ Alt+0103 g g
Fricative dental voiced U+00F0 ð Alt+0071 G G
Fricative alveolar voiceless U+0073 s Alt+0115 s s
Fricative alveolar voiced U+007A z Alt+0083 S S
Fricative postalveolar voiceless U+0283 ʃ Alt+0122 z z
Fricative postalveolar voiced U+0292 ʒ Alt+0090 Z Z
Fricative retroflex voiceless U+0282 ʂ Alt+0252 ü ü
Fricative retroflex voiced U+0290 ʐ Alt+0220 Ü Ü
Fricative palatal voiceless U+00E7 ç Alt+0231 ç ç
Fricative palatal voiced U+029D ʝ Alt+0074 J J
Fricative velar voiceless U+0078 x Alt+0120 x x
Fricative velar voiced U+0263 ɣ Alt+0088 X X
Fricative uvular voiceless U+03C7 χ Alt+0243 ó ó
© 1983-2012 by Boris Haase page 24 of 154

Fricative uvular voiced U+0281 ʁ Alt+0211 Ó Ó
Fricative pharyngeal voiceless U+0127 ħ Alt+0240 ð ð
Fricative pharyngeal voiced U+0295 ʕ Alt+0208 Ð Ð
Fricative glottal voiceless U+0068 h Alt+0104 h h
Fricative glottal voiced U+0266 ɦ Alt+0072 H H
Lateral Fricative alveolar voiceless U+026C ɬ Alt+0238 î î
Lateral Fricative alveolar voiced U+026E ɮ Alt+0206 Î Î
Approximant labiodental voiced U+028B ʋ Alt+0245 õ õ
Approximant alveolar voiced U+0279 ɹ Alt+0213 Õ Õ
Approximant retroflex voiced U+027B ɻ Alt+0199 Ç Ç
Approximant palatal voiced U+006A j Alt+0106 j j
Approximant velar voiced U+0270 ɰ Alt+0066 B B
Lateral Approx. alveolar voiced U+006C l Alt+0108 l l
Lateral Approx. retroflex voiced U+026D ɭ Alt+0076 L L
Lateral Approx. palatal voiced U+028E ʎ Alt+0227 ã ã
Lateral Approx. velar voiced U+029F ʟ Alt+0195 Ã Ã
Klick bilabial non-pulm. U+0298 ʘ Alt+0210 Ò Ò
Klick dental non-pulm. U+01C0 ǀ Alt+0253 ý ý
Klick (post)alveolar non-pulm. U+01C3 ǃ Alt+0221 Ý Ý
Klick palatoalveolar non-pulm. U+01C2 ǂ Alt+0254 þ þ
Klick alveolar lateral non-pulm. U+01C1 ǁ Alt+0222 Þ Þ
Implosive bilabial voiced U+0253 ɓ Alt+0237 í í
Implosive dental/alveolar voiced U+0257 ɗ Alt+0205 Í Í
Implosive palatal voiced U+0284 ʄ Alt+0236 ì ì
Implosive velar voiced U+0260 ɠ Alt+0204 Ì Ì
Implosive uvular voiced U+029B ʛ Alt+0242 ò ò
Other symbols:
Manner Place Voice Unicode IPA Alt ISO Fonto
Fricative labiovelar voiceless U+028D ʍ Alt+0119 w w
Approximant labiovelar voiced U+0077 w Alt+0087 W W
© 1983-2012 by Boris Haase page 25 of 154

Approximant labiopalatal voiced U+0265 ɥ Alt+0203 Ë Ë
Fricative epiglottal voiceless U+029C ʜ Alt+0235 ë ë
Fricative epiglottal voiced U+02A2 ʢ Alt+0233 é é
Plosive epiglottal voiceless U+02A1 ʡ Alt+0201 É É
Fricative alveolopalatal voiceless U+0255 ɕ Alt+0228 ä ä
Fricative alveolopalatal voiced U+0291 ʑ Alt+0196 Ä Ä
Flap lateral alveolar voiced U+027A ɺ Alt+0229 å å
Fricative velopalatal voiceless U+0267 ɧ Alt+0197 Å Å
© 1983-2012 by Boris Haase page 26 of 154

Ambisexuality
L gave me the idea to introduce the following ambisexual personal pronouns in the third person
singular for the word of L, and to propose them to be taken over into the German resp.
English language: ze in English and zie in German.
The letter z is to found an own root word, which is also to apply in other languages, provided
that this does not lead to a collision with present words. Letters like j (declinable too badly) or
x (too un-German) are ineligible and were also considered. There should be no confusion
with words of the in each case other language and a basic similarity be observed.
The declination in English is ze (subjective), zer (objective), zerself (reflexive) and zis (possessive).
The suffix for nouns is -rel. The preponderance of the female deduction reflects the
fact that the male personal pronoun was hitherto predominant and thus a poetic justice is to
establish.
The declination in German is zie (nominative), zihrer (genitive), zihr (dative and the beginning
of the associated possessive pronoun) and zihn (accusative). The related articles read don,
doren, dor and don; the relative pronouns don, doren, dor and don. The suffixes for adjectives,
substantives, pronouns and the indefinite article read -on, -or, -or and -on in the singular
and -onen in the plural. The declination of the adjectives in connection with the articles
and substantives reads: einon/don -e -on (nominative and accusative) and einor/dor -en -or
(genitive and dative). Man is replaced by on, -mann and -frau by -on. For the preponderance
of female deduction applies the same as in English.
Examples (for the German language)
God is in the religion of love denoted with L and is ambisexual, so it reads: don L. One finds
the ambisexual form of a male noun, either by replacing the male suffix by on: don Mession
(from: der Messias) and don Prieston (from: der Priester), or by appending: don Bischöfon
(from: der Bischof). Adjectives between article and noun remain unchanged: don gute Betreuon
(from: der gute Betreuer).
Zie zeigt dor aufmerksamen Schiedsor den Brief dor Professoror (from: Er/sie zeigt dem/der
aufmerksamen Schiedsmann/Schiedsfrau den Brief des Professors/der Professorin). Einon
Vermittlon zwischen den Anwältonen, doren Weisheit zihr zum Vorteil gereichte, machte
donselbe auf zihren Fehler aufmerksam (from: ein/eine Vermittler/in zwischen den Anwälten/Anwältinnen,
dessen/deren Weisheit ihm/ihr zum Vorteil gereichte, machten denselben/dieselbe
auf seinen/ihren Fehler aufmerksam).
The changes interfere insofar little, since there are only additional words. Thus it still reads:
Niemand, dem ... and not nieond, dor ... About this the last word certainly has not yet been
spoken :-).
© 1983-2012 by Boris Haase page 27 of 154

Planned language Lango
Only capital letters are written. In adjectives is the vowel a inserted, in adverbs the vowel e
and in prepositions the vowel u and personal pronouns have the vowel of nouns (o in the
singular, i in the plural). The latter do not have a sex (also by occupations it is omitted).
There are no articles. There is no case (subject-predicate-object-rule). To place the object
first, this is preceded with a preposition in case of need. Comparisons of all words are assigned
in the positive to the numbers of 1 to 3, in the negative to the numbers of 7 to 5 (see
octal clock).
Verbs consist of the stem and inserted time. There is a question, a subjunctive and a passive
particle. The tenses are formed as follows: Present (umlaut aj), imperative (in the sentence
preceded present), future I (uj), future II (finish particle and future I), past perfect (finish particle
and past), past (oj) and perfect (finish particle and present). The directions are read off
also from the octal clock and assigned to the numbers. The modal verbs are assigned to the
verb to be and to the numbers as follows: Neutral 0, can 1, may 2, like 3, want 4, shall 5,
need 6 and must 7.
The words are formed after the languages up to now according to the following rules:
1) Priority is given to the word formation with most speakers,
2) the most frequently used words are the shortest ones - for this purpose for each word
maximum lengths are determined and if they are exceeded at the selection, alternatives are
searched for,
3) enough gaps are to mind (also for future terms): if the words are too similar (the specified
number is exceeded), also alternatives are searched for,
4) at collisions is to switch to rarer languages,
5) similar words that are not derived from each other, must have distinct meanings,
6) there is for the moment only one meaning, as precisely determined as possible, per word,
7) if a word has in a previous language several meanings, so a ranking of the meanings is
specified, which determines what meaning gets a chance, if the word is the winner,
8) the order of the determination is: noun, adjective, adverb, verb, remaining lexical categories,
i.e. starting from the noun, the remaining lexical categories are determined by specifying
for each word the corresponding meaning,
9) diacritics, suprasegmentals, pitches, stress and intonation are not recorded and lead to no
difference in meaning (principle of licence of dialect),
10) the standard emphasis is on every second syllable of the word measured from the end.
The vocabulary of the planned language Lango is democratically determined: First, all the
words of the existing languages coming into question are filed in a database. To be able to
concentrate on the main languages, the language with the most root words is identified.
Then, the total population number is divided by the number of root words of the language
with the most root words.
Thus one obtains the minimum number of speakers that a language needs to be considered.
Proceeding more accurately, also all foreign root words in the language with the most root
words are considered. Alternatively, one can divide the total population number by the total
number of all meanings.
After the languages are identified to be taken into account, a multilingual dictionary is compiled
as a database in that the translations and meanings of all words are located. Then the
determined meanings are assigned to fields of daily life in such a way that in each field so
many meanings are located as the population divided by the smallest number of speakers to
be taken into account indicates.
© 1983-2012 by Boris Haase page 28 of 154

Then, for each language, the relative frequency of occurrence in the entire vocabulary of the
language per (presumable) meaning is determined. To have a uniform, but language individual
standard text, the most comprehensive electronic dictionary is employed as basis and
first mainstay. Missing records are translated so that each language is represented by the
same amount.
As second mainstay texts are taken into account that are of special importance in a language.
These texts are weighted by a democratic election of the speakers. For this purpose,
a list is created from that each speaker may choose maximum one-tenth. If ze chooses less
text, zis choice is weighted proportionally higher.
The third mainstay is the colloquial language. At this, newspapers, magazines, television and
radio broadcasts are determined for a representative period with the weighting of their use in
the population of speakers of a language. Each mainstay is equally considered. Untranslatable
root words are replaced by the most common foreign root word or determined by voting.
The name of the planned language is replaced by the root word for language that accepted
the bid. The grammar is determined by a working group in that the members are represented
by their strength of languages. It would be nice if my grammar proposed would be taken into
account. The same is true for my letters from the font Fonto. The grammar always has priority
over the vocabulary: All meanings are processed appropriately to the grammar.
Now, the formation of the vocabulary can start. A field is determined by random generator. A
meaning is chosen by random generator. It is chosen first the meaning with the highest number
of similarity. This arises from the number of languages resp. number of speakers, accounting
for the corresponding root words if one looks only at its similarity between the languages.
At equality the random generator decides.
With the number similarity determination the relative frequency of occurrence in the relevant
languages is determined concerning the part of the word, after all composites, based on the
part of the word, were counted and all inflection forms after the grammar. The frequency is
converted into points and multiplied with the word number. The point value is entered for all
languages involved.
Now, the language with the most speakers in the languages without points is selected and
the meaning is sought with the highest number of similarity. At equality the random generator
decides. Calculation is as above. The points are entered and the next important not considered
language is processed. The process will continue as long until each language according
to its frequency has been adequately considered.
It is ongoing paid attention to the proportional consideration of languages: Where the largest
deficits are, will be continued (difference of the actual with the percentage numbers due to). If
a field is exhausted, the random generator determines the next one. The surplus percentage
points are transferred from the previously handled field.
Languages, whose number of speakers is not enough to be percentally considered in the
language groups, are involved anyway: They may suggest words as foreign words that exist
only in their language and proper nouns that belong to their language and represent it. The
proposals are yet grammatically adapted.
Proper names such as rivers, mountains, places, buildings, etc. are always denoted in the
language that most speakers speak in the area in that the object is located. By presence of
various languages one proceeds like the main procedure (percental consideration). Personal
names are written as the owner or his legal representative intend to. The laws of other states
may provide other things: than applies the law.
© 1983-2012 by Boris Haase page 29 of 154

Each speaker decides among which languages ze wants to be counted (or the legal representative).
For this purpose, more comprehensive elections can be held: To choose are all
existing languages in descending order according to their number of speakers.
Per language a maximum of five crosses can be made. Additionally one can make a single
cross to choose all languages (offered as a single option). The crosses are converted into
percentages. Each voter has one vote, what corresponds to 100 %. Then there is the percentage
of the total electorate that includes every human being.
Election workers advise the illiterate. Invalid ballots are not counted. Who stays away from
the election is also not counted. The electoral process is fair to those that speak more than
one language or want to favour languages that they do not speak.
If it comes to conflicts in the definition of the vocabulary, because a word was once already
assigned, alternatives within the two words are searched for: first for the new word, then for
the old one. In the unlikely event that there are more meanings than corresponding words or
root words, either artificial words are to form or meanings to assign to existing words or root
words (homonyms). In the latter case, the most common use is awarded the contract.
© 1983-2012 by Boris Haase page 30 of 154

Language of science
What language of science is appropriate? How are scientific results expressed, linguistically
correct and future-oriented? What has to be considered in this case? These questions are to
be answered in the following.
Within and outside of science applies: No appropriate text can emerge without sufficient personal
maturity. Who has this will avoid (conventional) phrases as far as possible, even if their
use is highly esteemed, to a large extent, or demanded. No one can upgrade a poor paper,
in front of a sufficiently developed reviewer by parlance or talebearing, or present it in a significantly
more favourable light.
Such behaviour is repulsive and does a disservice to science. In the future, only texts will
endure that stand clearly aloof from that, since, with the exponential growth of knowledge, no
one will bother to take note of the poor texts, in the light of the many good ones. Who does
not want to perish thus will have to think properly, and must also give zis thoughts the right
form.
The worse mistakes are the wrong, insufficient or superfluous thoughts. Who only wants to
fill the pages and publish (at any price) has them surely. Who spends much time here wastes
it, but often incentives, such as a title, are the stronger argument than the quality, even if only
expensive linguistic garbage emerges. The number of basically worthless "papers" runs unfortunately
worldwide into a few million texts.
Is it bad enough that decidedly too many superfluous and irrelevant research projects are run
in science, and, even worse, financed (at the expense of the general public), since the persuasive
power is stronger than the mind, which can be easily proven by the "results", so it is
standing to reason to use a language that allows for as many as possible, without difficulty,
to separate the wheat from the chaff.
Present science is far too often characterised to roll out weak thoughts, ranting, overprecise
and simple, leading to believe, with as many level-depressing quotes, a completeness (of the
still insufficient), yet passing the essential, since it would otherwise flinch from its own justification,
although it lost it by this, as easy reflections and back translations show.
A winning presentation is mostly sacrificed in favour of drily "scientificalness", which is accompanied
by self taboos and its formalised unimaginativeness, since scientific wit wants to
contrast with the "ordinary" one. If wit would actually be made obligatory, the craftsmanship
science would be overchallenged, since this form of upgrading would contradict the cold neutrality
that makes it such an exciting experience today.
If scientists allow themselves to rate, then preferably about the stupidity of those who published
so poorly earlier, so that only the own superiority could correct this, if they want to
serve with a scientifically presentable result at all, since even the smallest new tail constitutes
scientific progress and dangles then conspicuously from the graduation cap or preliminary
to the own name.
Equally popular is to rate in a (poorly) hidden manner, because of the self-imposed value
freedom, by choosing words that (also) can be rated pejorative (and actually must be), but
what the respective author is forgiven, because oneself does not think much better, or knuckles
under to the "luminary", who is, as contrasted with a beginner, entitled to this, after the
thorny climbing the peak of science.
If one would confront a scientist with a brief, novel and fruitful text, it could be still so ingenious
and significant and ze would not accept it as such, or take note of it, if it would not meet
© 1983-2012 by Boris Haase page 31 of 154

the conventional and outdated standards, which do not reveal anything about the value of a
paper, but, on the contrary, reduce it relatively. This must be avoided and made clearly conscious.
It is outrageous, which trivial things of course are transformed into unmeaning results, under
the guise of science, by extensive and costly studies, empirically on the cusp of the predicable
at all resp. meaningless, with scarce expressiveness and slight significance multiply "secured",
and at a high price regaled as the eggs of Columbus on symposia, congresses, etc.
No subject is too absurd, as that it is not suitable for the meticulous scientific exploration and
squandering generation of (hypo-) theses, since science is at best ashamed of its impatience,
which the reality produces, but is actually an expression of its lack of restraint and
immoderateness resp. brazenness to pretty up verbosely that what is not worth knowing, and
to defend it against offences of decency.
Who dares to call the (scientific) significance of the results into question is confronted with
elusive spurious arguments, which turn every X into a U, but emphasise above all the necessity
for the survival of humanity, which enables the knowledge of science to preserve its
power. When it comes to its existence, science cannot take a joke, just as little as with the
loss of influence in society.
If the majority would trust in divine revelation and its common sense more than in the undeserved
opinion leadership of science, because of the verifiability and (seeming) objectivity of
scientific results, so it would quickly be on to science and start to give back the distinction to
it that it deserves, by defining, better and more strictly, the standards for science for the good
of all.
Who wants to experience of what science is vain needs only to follow the way it presents
itself in its publications and lectures, when it demonstrates its learnedness, in off-hook terminology,
and often bossy as overly didactic, in strict accordance with the scientific pecking
order. It is dissected and reinterpreted in endless discussions, what already comes out of
one's ears again.
In numerous animal experiments, the animals suffer for the most superfluous questions, only
because science does not want to control its insatiable curiosity, or wants to prove that for
what its reason is not sufficient, or where it is too comfortable for appropriate alternatives.
The greed for comfort, (dubious) fame and long-lasting luxury as possible incites it more than
the cognition that a happy and fulfilling life follows the divine order.
Instead of building on solid foundations, it rather erects swashbuckling theoretical buildings,
which everyone with a clear mind shuns, because of its bookish inaccessibility and insufficiency.
In doing so, it loses the essentials completely out of sight and knits with primitive scientific
manner an inextricable ball of mental aberrations that passes by life and only gives
trouble to anyone who must be concerned with it.
Quality, as well as aesthetics, suffers from the fury of publishing, and so the treatises are to
read again and again as testimonials of the personality and the character of their authors,
since their language and their content still disclose what the authors would prefer to conceal.
Who lives agreeable to L and refined zerself intensively is not concerned with things that are
unworthy for L, since ze aims at higher goals than extremely giving zerself airs.
Instead of respecting the individuality of the individual and doing justice to zer in zis uniqueness,
science makes general statements about so large groups that their significance is vanishingly
small. In doing so, it tries to reduce everything, if possible, to one principle and to
jam the diversity into a scientific corset that satisfies its drive for simplicity. But it depends on
the right amount of both.
© 1983-2012 by Boris Haase page 32 of 154

Who develops, in the relationship with L, the greatness that comes from L knows how ze
brings zer thinking, concentrated on the essentials, in the right form and spares others the
mistakes that we find in science today. One may find the drawn picture in a given case exaggerated,
but it shows how science basically is in our time. The way out of the grievance was
shown clearly. It is always worthwhile to go it for the good of all.
© 1983-2012 by Boris Haase page 33 of 154

Mathematics
The following results in the field infinity, set theory, transcendent numbers and nonstandardanalysis
have to be called sensational!
Because of the finiteness of our world, there are certain difficulties to treat the infinite. One
difficulty is the question whether one shall define the number of elements of the set of algebraic
numbers finite or infinite. The finite definition offers significant advantages of handling
and stands in the tradition. It is also shown that the set of natural, integer, rational, algebraic,
real and complex numbers is not closed. Hence, the difference of algebraic numbers is no
longer necessarily algebraic, what complicates the theory of the transcendent numbers.
A trans-rational and transcendent number can also consist of a finite continued fraction, in
which the last partial denominator is infinitely large. Would it be identified with a conventionally
rational number by setting the last partial fraction equal to zero, it would simultaneously
solve a linear equation with integer as with trans-integer coefficients. This identification leads
to contradictions, if the first equation is subtracted several times from the second one and the
solution of every newly emerged equation is determined, and is therefore incorrect. Correct is
working with approximate fractions.
One can show by (conventionally natural and trans-natural) induction that one, starting with
the set of conventionally natural numbers, can diagonalise up to any power according to
Cantor, so that all(!) infinite sets are equipotent to the set of conventionally natural numbers,
if one uses Hilbert's translations as an aid. This contradictoriness is met with the proposition
that there is for no set a bijection to its proper subset. Hence, Dedekind-infinity and Hilbert's
hotel are destroyed, since the image sets of translations of every set lead out of this.
Every number of elements of a set can be specified by reference to the set of conventionally
natural numbers. Only from the exact construction instruction it can be specified precisely.
Thus, it makes an important difference if one treats all multiples of five and constructs
thereby the associated set in such a way that one times each conventionally natural number
with five or that one deletes all numbers, up to each fifth, from the set of the conventionally
natural numbers. Cantor regarded such sets as of the same cardinal number. If one considers,
however, bijections correctly, one receives on the one hand the number of the set of the
conventionally natural numbers or on the other hand a fifth of it.
Cantor's distinction between merely countable and uncountable sets is too undifferentiated.
The correct treatment of bijections yields the statement that, concerning the number, there
are infinite many sets between the set of conventionally natural numbers and the one of conventionally
real numbers. Thus, the continuum hypothesis gets a new answer. Furthermore,
the asymptotic function of the number of algebraic numbers is determined.
Since individual n-ness belongs to every natural number n that cannot be derived from its
predecessors or successors, there is no complete system of axioms in mathematics, because
with each new number something irreducible new emerges. If one confines, however,
to selected aspects, a finite system of axioms for a finite number of entities can be specified.
Each level of infinity refuses completeness all the more.
Theories are based on presuppositions. In mathematics, they are often expressed by axioms
that may be true or false, what can possibly be proven by other considerations. Thus, all
theories are incomplete and, as the case may be, beyond that contradictory. Instead of explicit
axioms, (implicit) definitions are more suitable in that the existence of the specified is
tacitly presupposed, until refutation.
© 1983-2012 by Boris Haase page 34 of 154

Mathematics is not value-free. There can be always stated (rational) reasons why one procedure
is to choose over the other one.
The geometry gives definitions and remarks on Euclidean geometry that challenge several
axioms, using results of set theory.
The question of a fair distribution of persons deals less about the theoretical content than
about practical application. Here a spread-sheet analysis is used.
In the nonstandardanalysis, integration, differentiation, continuity, convergence and limit
value for finite and infinite (conventionally not measurable) sets are redefined and examples
given, as well as for discontinuous functions, to obtain better, more precise and more elegant
mathematical statements (also for known propositions of analysis). Two finiteness criterions
are given, one for series and one for products and the Riemann hypothesis is proved.
With the optimisation is presented how optimisation problems can be solved and which role
the best-path method could play here.
Below representations simplification and exactitude of expressions are weighed against each
other and the resulting desirable proceeding, deriving from this, is ethically outlined.
Below transcendent numbers necessary and sufficient criteria for transcendence are stated.
There are some numbers determined as transcendent from that one previously did not know
this. Transcendent numbers are essentially the sum of an algebraic and a sufficiently small
or sufficiently large number. The transcendence of a number can be furthermore characterised
via the product and sum proposition. Algebraic numbers, however, are determined by
the zeros of polynomials with conventionally integer or conventionally rational coefficients.
From this, criteria for transcendence can be directly derived from the coefficients of the polynomials.
The greatest-prime criterion is also efficient. Finally, the approximation of algebraic
numbers and their distances is treated.
In the calculation of times is shown how one can apply the octal system practically worldwide
and what the advantages are here. Besides introducing a new calendar and a new calculation
of clock time, the octal system is applied also to the SI-units metre (m) and second (s)
and some practical examples are given. There are reasons given why the octal system can
completely replace the decimal system.
© 1983-2012 by Boris Haase page 35 of 154

Geometry
Axiom: Everything possible exists – until someone finds out its impossibility.
Definition: Everything, possible, existence, something, different, whole, not and space are
substantial terms, which cannot be defined without a circle. A part is something that forms,
with something distinct from it, to wit somehow different, a whole. A point is, according to
Euclid, something that has no parts. Two points are identical, if they differ by nothing else
than their designation (otherwise non-identical). Then they coincide (otherwise they do not).
Definition: Two non-identical points are called, with two options, starting and end point and,
considered as a whole, elementary line segment or pair (of points). A chain of elementary
line segments consists of an initial elementary line segment and possibly further elementary
line segments, whose starting point each coincides with the end point of an elementary line
segment different from them, where the end points are each pairwise non-identical, as well
as starting and end point are uniquely determined.
Definition: A starting point of the chain of elementary line segments is then called, in each
case, connected with its end point. A chain of elementary line segments, for that three points
of it, chosen freely, satisfy the triangle inequality for every metric (selected in each case) always
with equality, is called line segment. Depending on its length, it is called (in-) finite. The
maximal line segment, with as many points as the number of the real numbers, defined in set
theory, is called straight line. More specifically, a line segment is only a chain of elementary
line segments that was cut out from a straight line at its starting and end point. One can define
(in-) finite line segments with (in-) finitely many points and obtains this way four different
possibilities to define line segments.
Definition: Line segments are called congruent, if their starting and end points have in each
case the same Euclidean distance. A point y of a line segment is located between two points
x and z different from it and among themselves, if for the Euclidean norm ||x - z|| = ||x - y|| +
||y - z||. If we have additionally ||x - y|| = ||y - z|| = ½ ||x - z||, it builds the middle between x
and z. If the three points are not located on a line segment, so each is located between the
two others, depending on the perspective. If two not end-point-identical line segments have
an identical starting point, and if their end points coincide with the starting resp. end point of
another line segment, so all three edge a triangle and are called sides of the triangle, whose
three starting resp. end points are called vertices of the triangle.
Definition: If we duplicate a triangle by letting coincide (combining) the two corresponding
sides so that the original (starting point) end point coincides with the duplicated (end point)
starting point, we obtain a parallelogram, if it is yet ensured that the original triangle vertex
that is not on the combined side has maximum distance from the associated duplicated vertex,
with regard to the Euclidean norm. Here, two corresponding sides and their partial line
segments are called parallel.
Definition: A point of a line segment is called its inner point, if it is not identical with its starting
and end point. Two line segments intersect at a point, if they have only an inner point in
common. The geometry is called free of point identity, if we permit in their overall result of the
point-set no identical points, otherwise open for point identity.
Remark: Angles are defined via scalar product, Euclidean norm and cosine function as usual,
hyperplanes, circles, spheres, etc. by the sufficiently known equations. This can also happen
otherwise (for example as by Hilbert). It is generally useful to specify maximum distances of
the points. In the non-Euclidean geometry, the definitions partially vary.
Result: For shorter defined straight lines, arbitrarily many counter-examples, with the above,
can easily be given for the parallel axiom, Pasch's axiom, the axiom of line completeness
© 1983-2012 by Boris Haase page 36 of 154

and several other axioms and their equivalents. This was to be shown. The parallel axiom is
redundant in Euclidean geometry, since a parallel straight line through a further point is
uniquely determined by its maximality. Any other straight line through this point has a point
that has another distance as that to the original straight line, and can therefore not be parallel
to it. The Archimedean axiom is to extend to a trans-natural number of ablations of a line
segment, which cannot be done beyond the starting and end point of a straight line, or to
replace by the Archimedean proposition (in the finite case). Pasch's axiom is also dispensable
if one considers that a straight line must completely pass the interior of a triangle because
of its maximality, including its boundary. There must be only enough inner points per
side. Maximality means here that longer straight lines than the real numbers define are not to
be considered.
© 1983-2012 by Boris Haase page 37 of 154

Equitable Distributing
In life, there is often distribution unfairness. Although the following is not new, equitable distributing
is to be demonstrated by examples that occur daily at school:
1. How are work-results distributed equitably?
2. How does one channel groups equitably through the cafeteria?
3. How does one form equitably groups in physical instruction?
To 1.: The work results are put down first alphabetically, arranged according to the names of
the present pupils (in trays, on the table or the like). The names are or will be put down alphabetically
in a spread-sheet analysis (except the missing pupils). Behind each name a
random number is produced. The names are arranged according to the random number. The
pupils are called according to this order (possibly in groups) so that they can receive their
work results.
To 2.: At the beginning, groups with members are formed that would like to dine together or
are to do this. These groups (-names) become arranged as under 1. described. Then for
each group (the available output time) * group size/diners is computed. The second group
goes into the cafeteria if the time determined for the first group is past. The third group follows
if additionally the time for the second group has elapsed and so on. If necessary, the
points in time have to be computed rounded. If singular groups can do only to certain time
intervals, they are distributed first on the time intervals. Then the procedure continues with
the remainder time for the remaining.
To 3.: At the beginning, groups of same capacity are formed and the individual names are
written in a firm sequence one below the other and after an assigned group number numbered
serially. If group members are missing, they are first filtered, as e.g. the entry "missing"
is noted behind their name and afterwards is selected after the empty entries.
The group size should be a multiple of the number of groups that can be formed. The sequence
of the names should be firm, for reasons of the probability. Changes of the capacity
are considered in changed groups. Behind each name, the numbering is divided by the number
of groups. If the numbering does not begin with 0, a number must be subtracted before
accordingly. The decimal places of the received values are truncated. This can be attained
also by a rounding of the values reduced by 1/2. In a further column, now random numbers
are registered.
Whereupon the three columns are only arranged according to the values determined first,
then additionally according to the random numbers. In a fourth column, beginning from
above, the numbers from 1 to number of groups are registered. After the last value, it is
again continued with 1 up to the number of groups and so on. Now the numbers are sorted
again according to names. Finally the group assignments can be announced in alphabetical
order.
If the number of pupils who can be divided is not a multiple of the number of groups, proxies
from the same group should be formed to each name. The names that have the smallest
time absent by sitting out are intended for sitting outs. They deputise for their deputies (e.g.,
if there are several runs in an instruction unit). The time absent is credited accordingly.
A simple procedure with a dice (instead of a computer) functions as follows: The pupils are
set up ordered according to their (self-determined or over-directed) capacity on a line. The
one with the highest capacity is assigned to one of the groups by throwing the dice. The next
one is determined under the remaining groups by the dice and so on. If each group has a
member, it is continued as with the one with the highest capacity now with the one with the
henceforth highest capacity.
© 1983-2012 by Boris Haase page 38 of 154

Without considerable aids, groups can be formed also as follows: All pupils are requested to
move respectively in a circle after their capacity coincidentally. Couple formation is prevented
with the request "A and B apart to the circle line!". After the command "stop!" everyone remains
at his place. One of the pupils is now requested to leave its place and move on an
approximate circle line around the remaining or around in each case a group.
After a further command "stop!" the pupils are divided by imaginary straight lines into groups.
First, the intersection is build the straight line forms through the break point of the one who
stands on the circle line and the respective centre of the circle with the group circle line. The
groups are defined by parallel straight lines that go parallel to the straight line through the
respective intersection and the respective centre of the circle.
These procedures are more equitable than the judging selection by individual pupils. Three
capacities are sufficient according to experience.
© 1983-2012 by Boris Haase page 39 of 154

Set theory
Preliminary remark: Sufficiently known axioms define the conventionally real numbers ℝ (as
totally ordered field) and conventionally complex numbers ℂ (with additional imaginary unit i),
all numbers ≠ 0 with absolute value ≤ � resp. ≥ 1/� and � := ⌊1 + max ℝ⌋ - ⌊max ℝ⌋/� ⌊max ℝ⌋
(see transcendent numbers and below), which can be continued in all infinity with the same
operators and is realised this way in the following. Hereby, the completeness axiom can be
relinquished (see below). The conventionally natural numbers ℕ* are defined therein as all
emerging sums by adding 1 to 0 (with 0 as ℕ), conventionally integer numbers ℤ by adding
the additive inverses of ℕ, the conventionally rational numbers ℚ by fractions with conventionally
integer numerator and conventionally natural denominator ≠ 0.
Definition: A complex number whose absolute value is greater than � is called infinite. A
complex number different from zero whose absolute value of its reciprocal is infinite is called
infinitesimal. Conventionally real numbers that are not conventionally rational are called irrational.
Definition: The sum p(x) = amx m + am-1x m-1 + ... + a1x + a0 is called polynomial. Here m ∈ ℕ* is
the degree of the polynomial if am ≠ 0, and the ak ∈ ℤ with k ∈ ℕ≤m are called coefficients (of
the polynomial). The conventional complex numbers x that let the sum become zero (socalled
zeros of the polynomial) are called algebraic. The corresponding sets are Aℝ in the
real case and Aℂ in the complex one. In the special case am = 1 one speaks of algebraic integers.
Conventionally complex numbers x that let no polynomial become zero are called transcendent.
Definition: Algebraic numbers that are denoted by finitely many concrete figures are called
concretely given, the ones that can be denoted this way concretely specifiable. Both together
form the subset of concrete numbers, which is symbolised as well as for the subsets of algebraic
numbers with the prefix c . Infinitesimal numbers and those in that the absolute value is
maximally a concretely specifiable number are called finite. The remaining algebraic numbers
are called inconcrete, and the prefix symbol is u . They form an interstage between the
(in any case finite) concrete and the infinite numbers.
Definition: Algebraic numbers can be denoted by (am, am-1, ..., a1, a0; g, h; #l, Mv; w, p)s,
whereby the number 0 is represented with g = h = a0 = 0, with g ∈ ℕ* (ℤ 0 (< 0), with g = 0, h ∈ ℕ* (ℤ 0 (<
0), and the remaining algebraic numbers are so correspondingly. #l specifies the number l ∈
ℕ* of zeros if at least for one ak, a variable is used, Mv the number v ∈ ℕ of multiple zeros.
With a minimal polynomial (with a0 = 0 only for the polynomial x = 0) for the specification s
the letter m is denoted, otherwise the letter n. The numeric value is represented by w with
precision p.
Remark: In this way the zeros of a polynomial with integer or rational coefficients can be
strictly totally ordered, if multiple zeros are not distinguished. The particulars g, h, # l, Mv, s,
w and p can be omitted as the case may be (e.g. for rational numbers). The (|ℕ|+2)-tuple (0,
..., 0, am, ..., a0, g, h)m with natural ak form a lexical strict well-ordering for the algebraic numbers.
Remark: The sets continued into infinity are preceded by ~ , numbers residing in infinity by
trans- and their corresponding sets by T . The conventional notation is used for the conventional
and trans-conventional numbers. If the conventional numbers are meant, this is indicated
by the preceding word conventional. The number of all elements of a set M is denoted
with |M|. If the carrier of an interval is unclear, it follows the interval.
© 1983-2012 by Boris Haase page 40 of 154

Examples: The concretely specifiable numbers (1, 0, 0, 0, -1)n are given as 1, -1, i, -i. The
concretely given golden number (1 + √5)/2 is denoted as (1, -1, -1; 1, 0; 1.618033, 10 -6 )m.
The number 0.⥘ = 0.11...11 with |ℕ*| ones after the comma is inconcrete and different from
the concretely given number1/9, since 9 × 0.⥘ = 0.99...99 = 1 - 10 -| ℕ *| ≠ 1. Hence it is transcendent
(cf. transcendent numbers) and would have to be denoted for instance as (9 ×
10 | ℕ *| , 1 - 10 | ℕ *| ).
Definition: A number a + bi with a, b ∈ ℚ is called conventionally complex-rational. A number
±b1/b2 ± ib3/b4 is called trans-complex-rational if for k ∈ {1, 2, 3, 4} with b2b4 ≠ 0 for at least
one bk |bk| ∈ ~ ℕ≥|ℕ| applies - with conventionally integer bk else. The complex numbers that
satisfy polynomial equations p(x) = 0 of degree or with integer coefficients of absolute value ≥
|ℕ| form with the algebraic ones the field of hyper-algebraic numbers with infinitely many subfields.
The proofs and results are obtained as for the algebraic numbers. Analogously there
are also hyper-transcendent numbers.
Remark: The assertion that |ℝ| should equal 2 | ℕ | states that all conventionally real numbers
can be developed into dual numbers. Against this speaks, on the one hand, that many conventionally
rational numbers can be represented only approximately as dual numbers and
much more that conventionally real numbers may be also sums with smaller exponents of 2
than the 2 -n set minimal. For example, the number ⅓ is only approximately included as
0.01010101... and must be distinguished from it.
Proposition: For no set, there is a bijection to its proper subset.
Proof: We prove this by (conventionally natural and trans-natural) induction, starting with the
singleton and progressing over multi-element sets by successively adding an element. The
same result is obtained if one removes an element from a set and wants to find a bijection for
the resulting set: There is none, because the missing element cannot be replaced. The natural
induction again proves the claim.
Conclusion: Thus especially Dedekind-infinity and Cantor's diagonal argument are discounted,
since ℕ is a proper subset of ℚ. A translation of an infinite set always leads out of
this set. Thus Hilbert's hotel is destroyed. Concerning the continuum hypothesis is to say that
there is an infinite number of sets whose number of elements lies between that of ℕ and that
of ℝ.
Completion lemma: The set of conventionally natural numbers is not closed concerning addition.
Proof: If one forms by bijection to ℕ the set 2ℕ, so this contains elements that cannot be contained
in ℕ, since the odd numbers are missing in 2ℕ. On the other hand, for all k ∈ ℕ also k
+ k must be included in ℕ. This contradiction implies the assertion.
Conclusion: The conventionally rational, algebraic, real and complex numbers as well as
their supersets are also not closed concerning addition, because they are based on the addition
of conventionally natural numbers, resp. then the addition for some elements cannot be
anymore be appropriately defined, because it cannot go beyond | ~ ℕ|. The lack of completion
is also transferable to multiplication and inversion, since they build on the addition. Sum, difference,
product and quotient of two concretely given numbers are always concretely specifiable.
All this results especially from the following
Minimax proposition: In every non-empty partially ordered set, each chain contains exactly
one minimal and one maximal element, and thus the set itself at least one each.
Proof: For finite sets, the claim is clear. Infinite chains and such with inconcretely naturally
many elements are isomorphic to sets consisting only of consecutive ordinal numbers - start-
© 1983-2012 by Boris Haase page 41 of 154

ing with 0. Consider now the set [0, 2 | ℕ | ] ~ ℕ. This is isomorphic to the homogeneous set ([0,
2 | ℕ | ] ~ ℕ)/2 | ℕ | , which that consists of the numbers {0, 1, ½, ¼, ¾, ⅛, ⅜, ⅝, ⅞, ...}, emerged by
successively bisecting the distances of the elements, by dint of the mapping k ↦ k / 2 | ℕ | for k
∈ [0, 2 | ℕ | ] ~ ℕ. It has exactly the minimal element 0 and the maximal element 1. By thinning, the
assertion holds also for the set ℕ by dint of the mapping 2 k ↦ k, with what the notation |ℕ|,
with the maximum element |ℕ*|, is justified. The assertion now follows by natural induction
for all smaller ordinal number sets by removing elements from ([0, 2 | ℕ | ] ~ ℕ)/2 | ℕ | with 1/2 | ℕ | -
steps, and for all bigger ordinal number sets by successively still increasing the exponent |ℕ|.
Indefiniteness lemma: About the minimal and maximal elements of an inconcrete or infinite
set, only a more precise statement can be made if there are decision criteria present. This
particularly applies to the element with the smallest or the greatest absolute value of the real
and complex numbers.
Proof: Clear.
Definition: The greatest concrete or finite element max c Aℝ is denoted as �, the smallest inconcrete
one greater than � as �+ and the smallest infinite one greater than � as �+ as well
as the absolutely greatest one max ~ ℝ as �∞.
Example: It is undecidable whether |ℕ| is even or not, since who examines the middle of ℕ
as homogeneous isomorphic interval [0, 1]ℕ/|ℕ| = ℕ/|ℕ| can only find something (extensive)
and not nothing, which would be, contradictorily, divisible, what makes the argument circular.
Therefore we cannot say, whether being or non-being is attributed to the middle, whether it is
element or not. For | c ℕ|, we would need also more precise information.
Remark: ℕ is uniquely determined, but not in every respect. From ℕ = {0} ∪ {n + 1 finite : n ∈
ℕ} and 1 + max ℕ ∉ ℕ, no contradiction can be construed, since from the assumption ∃ n ∈ ℕ
(n + 1 ∉ ℕ) only follows, without contradiction, n = max ℕ. In all subsets of ~ ℂ, the operators
permitted in all subsets of ℂ can be used in the same way (transfer principle), which is to be
shown in individual cases, but remains undone here because of their number.
Remark: The symbol ∞ can be adjoined to the complex and real numbers, with which can be
calculated as with a variable and whose value is to be greater than �∞. Since division by 0 is
not defined, due to the lack of uniqueness in calculations, one can manage this with replacing,
wherever it is opportune, for example, ±0 by ±1/∞, depending on which direction one is
interested in, and calculating with ∞ as described above. Then calculating is again unique
and consistent. Considering vague limits can be avoided, but every replacement should be
carefully considered where it makes sense, and it should not be arbitrarily switched between
the symbols. In this way, integral and differential for each operation on the complex and real
numbers can be defined such that each function is everywhere integrable and differentiable -
at least as a directional derivative (see nonstandardanalysis).
Definition: Let the circular constant � be defined as area or the half circumference of the unit
circle. Let Euler's number e be defined as solution of the equation x i� = -1. Then, let a logarithm
function ln be defined by e ln z = z and the corresponding power function by z s s ln z
= e
with complex s and z. In this way, the exponentiation can be defined (symbolically). Computationally,
one will usually have to be content with approximations.
Lemma: The Archimedean property does not apply for infinitely many real numbers.
Proof: Let a ∈ ℝ>1 and b = 1/|ℕ*|. Then applies b n ≤ 1 < a for all n ∈ ℕ.
© 1983-2012 by Boris Haase page 42 of 154

Archimedean proposition: There is a n ∈ (c) ℕ with b n > a, iff for a > b with a, b ∈ ℝ>0 a/b <
| (c) ℕ*| applies.
Proof: If a/b ≥ | (c) ℕ*| applies, then also a/b ≥ n is valid for all n ∈ (c) ℕ.
In the following, the behaviour for inconcrete n ∈ ℕ is considered.
Remark: Let be m ∈ ℕ the maximum allowable degree of the polynomial and n the maximum
absolute value that the conventionally integer coefficients ak of the polynomials amx m + am-1x m-
1 + ... + a1x + a0 with k ∈ ℕ≤m are to take. This is justified since the ak are not distinguished
against each other. The number of conventionally algebraic numbers corresponds to the
number of zeros of the so defined normalised irreducible polynomials: The greatest common
divisor gcd of their coefficients is 1 and it applies am > 0 and a0 ≠ 0.
Theorem: For the number Am of conventionally algebraic numbers (of the polynomial degree
m, and thus in general) applies the asymptotical equation
m
� �� � �
��m�1� m
m
� � �� � �
z m 2n 1 n
A � � O z m 2n � 1 ln n ,
where � is the Riemann zeta function and z(m) the (average) number of zeros of a polynomial.
Proof: To determine the number of the reducible polynomials, multiply a left polynomial factor,
with coefficients whose absolute value is maximally one, successively by two and check
how great the coefficients of a right polynomial may maximally become when building the
product. For this O(ln n) steps are necessary and the multiplications by two are neutralised in
each step by the divisions by two. The factor 1/�(m+1) provides for the elimination of polynomials
with gcd(a0, a1, ..., am) ≠ 1. To eliminate multiples of the prime p, the multiplication of
the number of polynomials with (1-p -m-1 ) is required. Building the product over all the primes
and developing the factors into geometric series yields, after multiplying, the factor of
1/�(m+1). If exactly one coefficient is 0, �(m+1) would be to be replaced by �(m). This replacement
is, however, equally covered by the correction term as the polynomials that have
more than one coefficient equal to 0. In the case m = 1, the correction term O(n ln n) is necessary
if one calculates the number of the conventionally rational numbers via Euler's totient
function as
n
�
4 �(k) �1.
For m > 1, the correction term O(z(m)(2n+1) m ln n) cannot be ex-
k�1 ceeded because of the divisibility circumstances, so that it is justified and the claim follows.
Remark: In the complex case, according to the fundamental theorem of algebra applies z(m)
= m. In the real case, z(m) is asymptotically equal to 2/� ln m + O(1) after (Mark Kac, "On the
average number of real roots of a random algebraic equation. II.", Proc. London Math. Soc.
50 (1949), 390-408. MR 11:40e).
Examples: For m = 1 one obtains 12n 2 /� 2 + O(n ln n) conventionally rational solutions. For m
= 2 one obtains 4n 3 /�(3) + O(n 2 ln n) conventionally real solutions, since a conventionally real
polynomial of degree 2 has two conventionally real zeros with probability ½. For am = 1 one
obtains z(m)(2n+1) m + O(z(m)(2n+1) m-1 ln n) conventionally algebraic integer solutions. That
what was said above about z(m) here also applies.
Examples: For m = n = |ℕ|, we obtain in the real case
© 1983-2012 by Boris Haase page 43 of 154

and in the complex case
* 2 � �
ln
A � �O
ln
�
* 2
� �
A � �O ln .
Examples: The set of conventionally algebraic numbers contains no numbers whose absolute
value is less than 1/(|ℤ| | ℕ* | |ℕ| 2 ) or greater than |ℤ| | ℕ* | |ℕ| 2 . The number of the set of complex
(real) numbers includes as many elements as one allows. These can be created, among
other techniques, by continued exponentiation.
Remark: The determination of the number of elements of any constructed (in-) finite set must
consider exactly its construction before it can be related to the number of conventionally
natural numbers. This should be, due to its simple construction, used as basis. Without
knowing the construction of a set, their number cannot be (uniquely) determined. If there are
several construction options, the most plausible should be used, i.e. it should represent (in-)
finiteness in the best possible way, in the sense of differentiation. Since this requires a value
judgement, it has not to be uniquely determined. If one does not agree on a single construction
option, despite rational reasoning, so the calculated number of elements of the set is to
state with its construction.
© 1983-2012 by Boris Haase page 44 of 154

Nonstandardanalysis
Preliminary remark: In the following, the notations from the set theory are applied and let be
always m, n ∈ ℕ*. The integration and differentiation on arbitrary always non-empty subsets
A of the sets ℂ n or ℝ n with arbitrary n are studied (especially for conventionally nonmeasurable,
inconcrete and infinite sets, as well as discontinuous functions). A generalisation
to other sets is easily possible.
Definition: For z0 ∈ ℂ n and the Euclidean norm ||z0|| z ∈ ℂ n with the set of neighbourhood relations
B ⊆ ℂ n ×ℂ n is called neighbour ñB(z0) of z0 ≠ z with (z0, z) ∈ B if there is no w ∈ ℂ n with z
≠ w ≠ z0 and (z0, w) ∈ B, as well as (w, z) ∈ B with
||z0 - w|| + ||w - z|| = ||z0 - z||.
The set ÑB(z0) of all neighbours of z0 with respect to B is called neighbourhood of z0 with
respect to B. The irreflexive, but not necessarily symmetric neighbourhood relations in B are
noted always as (predecessor, successor) in the form (z0, �z0) or (�z0, z0), whereby � and
� are pronounced "suc" and "pre". Let be z0 ∈ A and f: A → ℂ m . In the following, the proofs
with predecessors are usually omitted, since they run similarly to those with successors.
Then f is called �B-successor-continuous in z0 if for infinitesimal � ∈ ℝ>0 applies:
||f(�B z0) - f(z0)|| < �.
If f is for all �B z0 ∈ ÑB(z0) �B-successor-continuous, then one speaks simply of �B-
continuity. If the inequality applies only for � = 1/�, one speaks simply of (B-successor-) continuity.
If one writes x0 for each z0, x for each z, and ℝ for each ℂ, we obtain the conventionally
real case. The �B-predecessor-continuity results analogously.
Remark: In practice, we will determine � by estimating (after consideration of any jump discontinuities
of f). If B is obvious or unimportant, it can be omitted. This is in the following always
the case if B = B1×...×Bn with Bk ∈ {ℂ, ℝ} for k ∈ [1, n]ℕ applies.
Definition: Let f be a (uniquely) defined function f: A → ℂ m . Then
d �B zBf(z) := f(�B z) - f(z)
is called B-differential towards �B z of f in z ∈ A. If f is the identity, that is f(z) = z, we write
d �B zBz instead of d �B zf(z). If A or �B z are obvious or unimportant, they can be omitted.
The conventionally real case results analogously as above.
Definition: The function �B: A → ~ ℝ≥0 with dBxk, dByk ∈ ℝ>0 for all k ∈ [1, n]ℕ and all z = x + iy
∈ A ⊆ ℂ n with x, y ∈ ℝ n as well as
� �� �
B(A) dBx dBy
z�A1�k�n k k
with �B(∅) = |∅| = 0 is called exact B-measure of A and A B-measurable, provided there is for
no w ∈ A with xk ≤ Re wk ≤ xk + dBxk and yk ≤ Im wk ≤ yk + dByk for all k ∈ [1, n]ℕ for a z ∈ A a
j ∈ [1, n]ℕ, so that xj < Re wj < xj + dBxj or yj < Im wj < yj + dByj is fulfilled. For A ⊆ ℝ n , the
formula can be analogously simplified to
© 1983-2012 by Boris Haase page 45 of 154

� �� �
B(A) dBx .
x�A1�k�n Remark: Obviously, �B(A) is additive and uniquely determined, i. e., if A is a union of pairwise
disjoint sets Ak with k ∈ ~ ℕ, so we have
�
~
k�
© 1983-2012 by Boris Haase page 46 of 154
k
� �
�B(A) � �B
A .
It is moreover strictly monotone, i.e. for sets A, D ⊆ ℂ n (ℝ n ) with A ⊂ D applies
�B(A) < �B(D). Thus, it measures more accurately than other measures and is optimal, since
it turns out neither smaller nor greater than the individual distances of the points parallel to
the coordinate axes amount, because it merely considers the neighbourhood of a point. Concepts
such as �-algebra or null sets are not needed here, since the empty set is the only null
set here.
Definition: With the notations above, the B-derivative towards �B z of the function f, then
towards �B z exactly B-differentiable, in A at the position � ∈ A ⊆ ℂ is defined as
dBf( �) f( B �) � f( �)
f� B�B(
�) : � �
,
dB� B�
� �
provided the difference quotient in the middle is defined.
If A or �B z are obvious or unimportant, they can be omitted. The conventionally real case
results analogously as above, and one speaks for �B w > w ∈ ℝ of the right-sided exact
B-derivative fr′B(w), and for �Bw < w one does of the left-sided exact derivative fl′B(w).
If the derivatives match towards all neighbours, one speaks correspondingly of the exact derivative
f′B(�) (f is then in ℂ conventionally regarded as holomorphic).
Remark: Differentiability thus can be easily established. One can define the exact derivative
in the conventionally real case alternatively also everywhere there as
f( B w) � f( B w)
f� bB(w):
�
B w� B w
where the quotient is defined. This has the advantage that fb′B(w) can be regarded more as
"tangent slope" in the point w, which can become rather zero for a local extremum, especially
if f is �B-continuous in w. This is convenient, for example, if one wants to characterise the
exact values of �B w and �B w only as arbitrarily close to w, or wants to round the exact
derivatives suitably, in order to provide simple derivation rules, if necessary. The transfer to
the conventionally complex is done analogously.
Definition: With z ∈ A ⊆ ℂ and f: A → ℂ as well as where dBz resp. �B z is defined,
�
z�A �
f(z)dBz : � f(z)( B z �z)
z�A is called the exact B-integral in A over f(z) and f(z) is called B-integrable. For �: [a, b[A → ℂ,
A ⊆ ~ ℝ and f: ℂ → ℂ,
k

� �
f( �)dB � : � f( �(t)) � �D(t)dDt
� t �[a,b[A
with dDt > 0, �D t ∈ ]a, b]A and �B �(t) = �(�Dt) (so especially for A = ℝ, B maximal in ℂ 2
and D maximal in ℝ 2 ) is called the exact path integral of f along the path �. The conventionally
real case results analogously as above. We write specifically for
�: [a, b[ℝ → ℝ and x ∈ D = ℝ:
b
f(x)dx � f(x)dx.
� �
�
Remark: Obviously, the exact integration is a special case of summation. The exact integral
coincides on the conventional ℂ or ℝ widely with conventional integrals; f must yet not be
continuous and also else the conditions are significantly weaker, in order that the integral
exists. For A = ℂ or ℝ, A can be omitted. Obviously, the exact integral is linear and, in the
conventionally real case, monotone. The art of integrating consists in correctly summarising
the addends.
Definition: The exact B-integral in A ⊆ B1×...×Bn over a function f: A → C1×...×Cm, then
B-integrable, with Bk, Cj ∈ {ℂ, ℝ} and k ∈ [1, n]ℕ, j ∈ [1, m]ℕ, z ∈ A is defined by
� 1 1 n m 1 n
� �
z�A �zn�Bnz1�B1zn�Bnz1�B1�z�A © 1983-2012 by Boris Haase page 47 of 154
a
� �
f(z)dBz : � ... f (z)dBz ...dBz ,..., ... f (z)dBz ...dBz � .
� � � � �
Remark: Obviously, we have
�
x�A dBx ��B(A),
if dBxk > 0 is fulfilled for all x ∈ A ⊆ ℝ n and all k ∈ [1, n]ℕ as well as the conditions mentioned
for the exact B-measure.
Remark: Analogously, the exact integral can be alternatively defined. But the original definitions
are to handle the easiest way. If applicable, there is an appropriate Landau notation. If
the result of differentiation lies outside of the domain, it should be replaced by the number
lying closest to it, within the domain. If the number is not uniquely determined, the result is to
consist of all these numbers, or one may choose one (e.g. after a uniform rule).
Definition: If
dB(F(z))
F�B z : � � f z
dBz
� � � �
applies for all z ⊆ A ⊆ ℂ and all dBz ∈ ℂ with f: A → ℂ, so F(z) is called B-antiderivative of f in
A. In the conventionally real, left-sided and right-sided B-antiderivatives Fl(x) and Fr(x) with
x ∈ ℝ can be distinguished, depending on whether we face the left-sided or right-sided
B-derivative.
Remark: Obviously, the B-antiderivatives of a function differ from each other only by a conventionally
complex or real addend. B-antiderivatives of discontinuous functions can usually
only be obtained by adding them up and skilfully combining them, such of piecewise �Bcontinuous
functions easier (for example, by reversing the rules of derivation).
r
T

Definition: A set A ⊆ B1×...×Bn with Bp ∈ {ℂ, ℝ} for all p ∈ [1, n]ℕ and h ∈ ~ ℝ>0 is called
h-homogeneous, if �B zj = xj + h + iyj + ih applies for all zj ∈ Bj = ℂ and �B xk = xk + h for all
xk ∈ Bk = ℝ with j, k ∈ [1, n]ℕ.
Example: Let be [a, b[h[1, n] ~ ℤ a non-empty h-homogeneous subset of [a, b[ℝ with B = ]a,
b]h[1, n] ~ ℤ. For infinitesimal h and � = -a = b - h, [a, b[h[1, n] ~ ℤ is comparable with the conventional
ℝ. Let be Tr furthermore a right-sided B-antiderivative of a taylor series t, not necessarily
convergent in [a, b[h[1, n] ~ ℤ, and f(x) := t(x) + �(-1) x/h with conventionally real x and �
≥ 1/�. For infinitesimal h, f is nowhere continuous, and can therewith nowhere be conventionally
differentiated and integrated in [a, b[h[1, n] ~ ℤ, but it applies exactly for all h:
and
�
~
x �[a,b[h
2 ( 1)
f �
��
rB(x) �t� rB(x)
�
dBx
© 1983-2012 by Boris Haase page 48 of 154
x
h
a b
h h
� �
�
f(x)dBx � T r(b) � T r(a)
� ( �1) � ( �1)
.
2
Remark: ℝ is, however, not h-homogenous, as long from x ∈ ℝ always is to follow 1/x ∈ ℝ: If
it is assumed h-homogenous for x in the interval ]0, 1[, so applies 1/x - 1/(x + h) = h/(x (x +
h)) > h. Something similar is true, if ℝ is assumed h-homogenous for values > 1 and their
reciprocals are considered. It is thus precisely to specify, with which definition and construction
of ℝ it is dealt, e.g. with a h-homogenised ℝh. Analogously, there is also the
h-homogenous set ℚh of rational numbers with max ℚh = -min ℚh = |ℕ| and h = min |w| =
1/max kgV(1, 2, ..., m), with |ℚh| = kgV(1, 2, ..., m) (|ℤ| - 1) + 1 ≤ |ℚ| for w ∈ ℚ. Obviously,
calculating in the conventional ℝ corresponds to calculating in ℚh. If the set Aℝ of the real
algebraic numbers is h-homogenised, it is just at least as dense as the conventional ℝ, as
one can easily realise with the h-homogenisation of the set ℕ ∪ {√2}.
Remark: Much more important, interesting and relevant, for computers, are the hhomogeneous
sets Bk with natural k that emerge by continued halving of the unit distance. If
one agrees on an accuracy of representation 2 -k , so it can be calculated with this maximal
accuracy of calculating. The h-homogenised ℝh should also be isomorphic to such an infinite
set, where h = 2 -k is to be assumed minimal possible for x ∈ Bk and now trans-natural k. For
every additional number x, concerning a h-homogenous underlying set, the newly emerged
set can then be h-homogenised, if one agrees on an accuracy of representation for x.
Example: The middle thirds Cantor set C has the measure µ(C) = (⅔) | ℕ* | . Let the function c:
[0, 1] → {0, (⅔) | ℕ* | } be defined by c(x) = (⅔) -| ℕ* | for x ∈ C and c(x) = 0 for x ∈ [0, 1] \ C. Then it
applies:
�
x�C 1
�
x�0 2 � �
c(x)dx � c(x)dx � �(C) � 1.
Example: For the classes a + ℚ with a ∈ ℝ of the equivalence relation x ~ y ⇔ x - y ∈ ℚ with
x, y ∈ ℝ, their representatives can be specified by the set R = [0, 1/|ℕ*|[ with the measure
�(R) = 1/|ℕ*|. Let the function r: ℝ → {0, 1} be defined by r(x) = 1 for x ∈ ℤ + R and r(x) = 0
for x ∈ ℝ \ (ℤ + R). Then it applies:
�
x�
1
r(x)dx � �(R) � 2 � � 2.
*
3
�
*

Example (cf. set theory): Let A1 = [0, 1[ ∩ Aℝ and the function q: A1 → {0, 1} be defined by
q(x) = 1 for x ∈ A1 and q(x) = 0 for x ∈ A1 ∩ ℚ. The exact integral over q(x)dx has then in A1
the transcendent value
1
�
0
A �
3
q(x)dx � � 1� � 1.
A � 1 �2 �3
2
� ln �Oln
� �
Remark: The sets C, R and ℚ are conventionally not measurable. Thus, the exact integral is
more generally valid than Riemann, Lebesgue (-Stieltjes) integral and other integrals, since
the latter exist only in conventionally measurable sets. The functions were chosen so easy
only because of the clearness and may be, of course, more complicated.
Definition: A sequence (ak) with members ak is a map of [1, p] ~ ℕ to ℂ m : k ↦ ak. A series is a
sequence (sk) with the partial sums
k
sk � � a j.
The smallest index in sk for j can be defined differently (e.g. 0 or -k).
j�1 Remark: Since sums can be arbitrarily added otherwise, because of the associative, commutative
and distributive law, if is calculated correctly resp. with the Landau symbols, Fubini's
theorem results for exact B-integrals, which allows to change the order of integration arbitrarily.
Remark: Thus, in particular, the Riemann series theorem is invalid, since one is coerced,
when summing up the positive summands to a value aimed at, to add so many negative
ones, until one obtains again the original sum of the series, and vice versa. With a smaller
resp. greater value than the sum of the positive resp. negative summands, the same applies,
since the rest is almost annulled, and so on. Also infinity must not be dealt with arbitrarily, if
one wants to avoid going astray. Who moves something into infinity must not lend zerself to
the illusion that it would no longer exist.
Finiteness criterion for series: The Euclidean norm of the partial sum with the greatest index
of a real series (sk) for infinite (trans-) natural k and j is finite, iff it can be represented as
max j
� �
�
maxk � �
j�1 j � j
j�1 s 1 a b
with finite ||aj - bj|| forming a monotonically nonincreasing sequence for aj, bj ∈ ℂ m
Proof: The assertion follows directly from the finiteness of ||a1 - b1|| and because the addends
can be added arbitrarily otherwise, sorted by size and sign, summed up or split up into sums.
Example: From the alternating harmonic series follows
2 �
� * /2�
�
�
k�1 k
1
� � � �
� � *
1� �1
�1 * � � � ln2.
k
2 *
Remark: More interesting examples are those whose limit value of (bj) and the nonincreasing
monotony of |aj - bj| cannot be so easily proven as e.g. for divergent the series
© 1983-2012 by Boris Haase page 49 of 154

� �
� � �
� �
� �
* k
*
k�1 ( �1) ( �1)k
�� �
j(k�� j 1) k
k�1 j�1 k�1 where (bj) has the limit value � (= aj for all j) and (bj+1 - bj) is monotonically nonincreasing.
Finiteness criterion (corresponds to the fundamental theorem) for products: The product
for k ∈ ~ ℕ* and ak ∈ c ℝ>0, is finite, iff
is less than a number concretely given.
maxk
�
k�1 �1�a �
max k
�
k�1 Proof: Let the factors be initially restricted to ak ∈ ]0, 0.9]. Then the assertion follows from the
logarithmic series because of
maxk maxk maxk maxk
� � � �
© 1983-2012 by Boris Haase page 50 of 154
a
k�1 ��1� k 1
a � a � a .
k k j 2 k
k�1 k�1 j�1 k�1 It does not change if the remaining factors are yet still included, since their number must be
concretely given.
Remark: Products with ak ∈ ℂ are finite, iff their absolute values are. Factors with absolute
value < 1 are to be set off against those with absolute value > 1, for example, by considering
their product of the reciprocals.
Definition: Let j, k, p and q be natural. A sequence (ak) with ak ∈ ℂ and infinitesimal � ∈ ℝ>0 is
called �-convergent, if there is a q, so that for all k and p with max k ≥ k > p ≥ q applies:
k
k
|ak - ap| < �.
If the inequality applies only for � = 1/�, so the sequence is simply called convergent. The
uniquely determined last value of the sequence is amax k and is also called 0-limit value or
simply limit value, while the �-limit values aj(�) are given by the elements of
with infinitesimal � ∈ ℝ>0.
{z ∈ ℂ : |z - amax k| ≤ �}
Remark: The conventional limit values are often only �-limit values, selected after (general)
preferences (with � often no more precise than O(1/|ℕ|)) and generally too imprecise, since
they are for example (arbitrarily) algebraic (of a certain degree), or transcendent.
Proposition about commuting �-limit values for the integration: Let be A ⊆ ℝ and (fk) a sequence
of integrable functions with (trans-) natural k and fk: A → ℝ, which �-converge to the
integrable function f: A → ℝ. Then applies for
2
,

� �
� �f (x) � f(x) �dBx
�(
� ) � � � �
� �
�
j 2 0
�x�A �
� �
f ( � )(x)dBx � � f (x)dBx �(
� ) � � �B(A) � � .
� �
� �
� �
j 1 j 2 1
x�Ax�A � �
f ( � )(x) � f(x) dBx �� f (x) � f(x) dBx �(
� ) � � dBx � � � � �B(A) � � .
� � �
� �
Proof: � � � � � �
j 1 j 2 1 1
x�Ax�Ax�A Remark: As long as one correctly calculates with Landau notation, differentiation or integration
and summation may be (also) interchanged in (divergent) series. The conventional procedure
can, however, lead to not inconsiderable error propagations, in subsequent calculations,
for example, if β1�B(A) ≥ 1/� applies.
First fundamental theorem of exact calculus: The function
�
F(z) � f( �)dB� with �: [c, x[A → ℂ, f: ℂ → ℂ, c ∈ [a, b[A and �B �(x) = �(�D x) (so especially for A = ℝ, B
�
maximal in ℂ 2 and D maximal in ℝ 2 ) is exactly B-differentiable and it applies for all x ∈ [a, b[A
and z = �(x)
dB(F(z)) = dD(F ∘ �)(x) = f(�(x))�r′D(x)dDx = f(z)dBz
Proof:
�( Dt) � �(t)
dB(F(z)) � F( B z) � F(z) � f( (t)) �D(t)dDt f( (t)) �
� � � � � � � D(t)dDt � � f( �(t))
dDt
Dt � t
r r
t �[c,x]At �[c,x[Ax
� dD(F �)(x) � f( �(x)) � �D(x)dDx
� f( �(x))( B �(x) � �(x)) � f(z)dBz.
r
Second fundamental theorem of exact calculus: If F is, instead of f as above, for t ∈ [a, b[A
right-sided exactly differentiable and its exact D-derivative Fr′B is there exactly B-integrable,
then it applies for �B �(t) = �(�D t) (so especially for A = ℝ, B maximal in ℂ 2 and D maximal
in ℝ 2 ) and �: [a, b[A → ℂ n :
Proof:
� �
�F( �(b)) � F( �(a)) � (F �) �D(t)dDt�F�B( �)dB �.
� �
F( �(b)) � F( �(a)) � F( B �(t)) � F( �(t)) �
t �[a,b[At �[a,b[A
r r
t �[a,b[A� � � �
r r r r
t �[a,b[A t �[a,b[A �
�F( B �(t)) � F( �(t)) �� �( Dt) � �(t) �� Dt � t�
� B �(t) � �(t) �� Dt � t�
� (F �) �D(t)dDt � F�B( �(t)) � �D(t)dDt � F�B( �)dB �.
Corollary (integral proposition): It applies for a closed path �: [a, b[A → ℂ and f: ℂ → ℂ
© 1983-2012 by Boris Haase page 51 of 154

iff f has an antiderivative F on �.
�
�
f( �)dB� � 0,
Proof: Every f(�) has a representation (F(�B�) - F(�))/(�B� - �), where F(�B�) is succes-
sively newly determined for each � and F(�(a)) was freely chosen. Until the last summand,
the integral has a value F(�(b)) - F(�(a)). The integral has the value 0 iff the last term is
F(�(a)) - F(�(b)). This yields the assertion.
Remark: In both fundamental theorems, the conventionally real case results analogously as
above. For v, w ∈ [a, b[A, v ≠ w and �(v) = �(w), �B �(v) ≠ �B �(w) is permitted. Notice that
continuity is not presupposed for integral and derivative. Actual integration (as inversion of
the derivative) only makes sense for continuous functions, if it is to go beyond mere summation.
However, if function values can be combined into a finite number of continuous functions,
for which each of them the antiderivative can be specified in finite time, also the integral
for discontinuous functions can be calculated in this way, possibly with the appropriate
aid of the Euler-Maclaurin sum formula and further simplification techniques.
Remark: In the same way, Stokes' theorem can be proven (also generalised for discontinuous
and non-holomorphic functions), since the integrals vanish on the inner paths. Over the
more or less elements is integrated, the greater the value of the integral can differ, even
within the same interval limits. If one uses the alternative exact derivation, then the formulas
change accordingly, and this applies the less, the more continuous the occurring functions
are. Here and in general appropriate rounding rules can be helpful.
Definition: For a close path �: [a, b[A → ℂ and z ∈ ℂ
is called the winding number or index ind�(z).
Integral formula: With f: ℂ → ℂ, it is
iff with g(�) = (f(�) - f(z))/(� - z)
1 d�
2�i � � � z
�
1 f( �)
f(z)ind �(z)
� d �,
2�i � � � z
�
�
© 1983-2012 by Boris Haase page 52 of 154
�
g( �)d� � 0
applies, thus especially if g has on � an antiderivative.
Proof: The assertion follows directly from the integral proposition.
Remark: The winding number is 0, if z is not revolved (antiderivative ln(� - z)). With n ∈ ~ ℕ, it
is n (-n) if it is revolved n times positively (negatively). This can be easily seen from the following
figure with the parametrisation � = z + r e it of the circle line � with the length 2�r for t ∈
[0, 2�[ and r ∈ ~ ℝ>0:

Fig. 1
Example: The integration on the boundary ∂ℰ of the unit circle ℰ resp. its translation by 2
yields over 1/z the values 2�i resp. 0 (antiderivative ln(z + 2) on ∂ℰ + 2), and over |z| 2 0
(antiderivative z on ∂ℰ) resp. 4�i.
Remark: The example shows that the existence of a antiderivative of the integrand of a path
integral and its value generally depend only on the integrand and path, including its orientation,
not on the property of the underlying set, the interior and exterior of a path, the holomorphy
or the homology (to zero) as in the conventional complex analysis.
Definition: The coefficient a-1 of the function f: ℂ → ℂ with
�� ���n����� � � �
j
f(z) � a (z � c) � a (z � c )
i ij i
i��� ���� i�1 j����
���
and n ∈ ℕ, ai, c, aij, ci ∈ ℂ as well as pairwisely different ci ≠ c is called the residue resc f.
Residue theorem: If f: ℂ → ℂ is represented by
n
����� ��
i�0 j�������
j
a (z � c )
ij i
with n ∈ ℕ, aij, ci ∈ ℂ and ci pairwisely different, it applies
for a closed path �: [a, b[ → ℂ.
1
2�i Proof: For all i ∈ ℕ≤n and all j ∈ ℤ \ {-1}, we have
and
�
�
�
�
n
�
f( �)d� � ind (c )res f
�
i�0 j
a ij( � � c i)
� 0
�
i
i ci
ai, �1d�
�2�iind �(c
i)rescf. i
��c
© 1983-2012 by Boris Haase page 53 of 154
�

Intermediate value theorem: Let be f: [a, b] → ℝ �-continuous in [a, b]. Then, f(x) maps to
any value between min f(x) and max f(x), for x ∈ [a, b], with an accuracy < �. If f is continuous
in ℝ, it maps to any value of the conventional ℝ between min f(x) and max f(x).
Proof: Between min f(x) and max f(x), there exists an unbroken chain of overlapping �environments,
each with f(x) as the centre, since otherwise a contradiction to the �-continuity
of f would emerge. The second part of the assertion follows from the fact that a deviation
|f(�x) - f(x)| < 1/� resp. |f(x) - f(�x)| < 1/�, in the conventional ℝ, falls below the resolution
maximally permitted.
Extremum criterion: Iff f has, as above, in the point x0 a left-sided exact derivative > 0 and a
right-sided exact derivative < 0, f has there a local maximum. Iff f has, as above, in the point
x0 a left-sided exact derivative < 0 and a right-sided exact derivative > 0, f has there a local
minimum. A derivative can then be defined there as 0.
Proof: Clear from the definitions.
Remark: The following considerations can be transferred analogously to the conventional
complex and omit the specification of set of all neighbourhood relations, since they can be
easily added.
Product, quotient and chain rule: Let be f and g right-sided (left-sided) exactly differentiable
functions and all quotients well defined, i.e. their denominator does not equal 0. Then it applies:
(fg)r′(x) = fr′(x) g(x) + f(�x) gr′(x),
and
with
Left-sided applies analogously:
and
with
� f �
�
f �
r (x)g( x) � f( x)g �
r (x)
� � (x) �
�g� g(x)g( x)
r
f(g(x))r′ = �r(x) fr′(g(x)) gr′(x)
( g(x) �g(x))(f(g( x)) �f(g(x)))
�r(x) �
.
(g( x) �g(x))(f( g(x)) �f(g(x)))
(fg)l′(x) = fl′(x) g(�x) + f(x) gl′(x),
� f �
�
f �
l (x)g(x) � f(x)g �
l (x)
� � (x) �
�g� g( x)g(x)
l
f(g(x))l′ = �l(x) fl′(g(x)) gl′(x)
(g(x) � g(x))(f(g(x)) �f(g(
x)))
�l(x) �
.
(g(x) �g( x))(f(g(x)) �f(
g(x)))
It applies �r(x) = �l(x) = 1, iff f(g(x)), f(g(�x)) and f(�g(x)) resp. f(g(x)), f(g(�x)) and f(�g(x))
are lying on a straight line.
© 1983-2012 by Boris Haase page 54 of 154

Proof: Product and quotient rule are easy to recalculate. It applies:
Thus
f( g(x)) f(g(x)) f(g( x)) f(g(x))
f �
� �
r (g(x)) � �
,
g(x) � g(x) � (x)(g( x) � g(x))
f(g( x)) f(g(x))
f(g(x)) �
�
r � � �r(x)f
�
r (g(x))g �
r (x).
x�x The last sentence is valid, because the differences of the f-values are lying anyway on a
straight line and, divided by the differences of the corresponding g-values, build a quotient of
slopes of two straight lines that share a point. Iff the slopes are equal, the quotient becomes
1, applies therefore the conventional chain rule and it follows the assertion.
Remark: In order that the product and quotient rule exactly coincides precisely enough with
the conventional one, in x0 either f or g must be (�-) continuous enough (i.e., α can be set
small enough). It can be seen from the functions f(y) = y ±2 and y = g(x) = x 2 with x0 = d0 and y
∈ ℝ that � can attain almost any value in ℝ. Thus the conventional chain rule is only usable
approximately for not infinitesimal arguments. If f is not affine-linear or g is not the identity or
a translation, it is quite unlikely that the three f-values are lying on a straight line. If f and g
are continuous, the chain rule applies at least approximately.
Remark: The right-sided resp. left-sided exact derivative of the inverse function results as
f -1 r′(y) = 1/fr′(x) bzw. f -1 l′(y) = 1/fl′(x)
from y = f(x) and the identity x = f -1 (f(x)), with the aid of the chain rule, for the same precision.
L'Hôpital's rule is useful for (�-) continuous functions f and g and results for f(w) = g(w) = 0
with w ∈ ℝ, as well as f(�w) and g(�w), not both simultaneously 0, and analogously left-
sided from
f( w) f( w) � f(w) f �
r (w)
� � .
g( w) g( w) � g(w) g �(w)
Definition: Let be f a (uniquely) defined function f: A → ℂ. Then
2
Bz
d Bf(z) f( B( B z)) �2f( B z) �f(z)
: � 2 2
(d B z) (d B z)
is called the second derivative towards �B z of f in z ∈ A. The partial derivative towards �B
zk of f in z ∈ A with k ∈ [1, n]ℕ is defined as
� f(z ,..., B z ,...,z ) � f(z)
�BzBz�z B f(z) 1 k n
: �
.
k k k
Higher (partial) derivatives are defined analogously. The number j ∈ ℕ of executed partial
derivatives is specified as exponent behind ∂; the variables, after which is differentiated, follow
each other in the denominator, each one preceded by ∂. Hereby, the same variables are
provided with an exponent, according to the number of their occurrence. Taylor series make
only sense for |ℕ*|-fold �-continuously differentiable functions, because of their approximating
and convergence behaviour.
© 1983-2012 by Boris Haase page 55 of 154
r
r

Exchange proposition: The result of multiple partial derivatives of a function f: A → ℂ is independent
from the order, whilst variables are replaced by values or limit values are considered
only finally, if necessary.
Proof: It is uniquely determined: This is clear until the second derivative, for higher ones the
assertion follows by (trans-natural) mathematical induction.
Example: Let be f: ℝ 2 → ℝ given by f(0, 0) = 0 and f(x, y) = xy 3 /(x 2 + y 2 ) else. Then it applies:
with value ½ for (0, 0), although in
2 6 2 4 4 2 2
� f y � 6x y � 3x y � f
� �
� � (x � y ) � �
2 2 3
x y y x
5 2 3 4 3 2
�f y � x y xy � 3x y �f
� � �
� (x �y ) (x �y
) �
2 2 2 2 2 2
x y
we have y for x = 0 on the left and 0 for y = 0 on the right, i.e. then, the partial derivative towards
y yields on the left 1 ≠ 0, which is the partial derivative towards x on the right.
Outlook on the complex analysis: Let be all conventionally complex functions f: A → ℂ for
A ⊆ ℂ implicitly so defined that we have f(z) = �f(z)/|f(z)| for actually |f(z)| > �. The entire
functions f(z) = z/� and g(z) = Σak z k with k ∈ ℕ and ak = 1/� k+1 disprove Liouville's theorem.
Evidence: Since we have |f(z)| ≤ 1 and |g(z)| < 1, the assertion follows directly.
Remark: Choosing sufficiently small (transcendent) constants in the generalisation of Liouville's
theorem disproves it too. Both theorems cannot be remedied by restricting them, since
the holomorphy of a function h on ℂ compels that the Laurent polynomial (the Laurent series)
of h must have coefficients ak with |ak| < O(� -|k| ) (O(� -|k|-1 )) and (trans-) integer k (to converge),
if it is not already constant. Thus, a limitation to coefficients ≥ 1/� is pointless.
The function f yields the biholomorphic, bijective mapping of the conventionally and circular
defined ℂ onto the complex unit circle ℰd, very condensed from the complex unit circle ℰ, with
|ℰd| = |ℂ| ≫ |ℰ|. Therewith, the Riemann mapping theorem would be also valid for ℂ. The
complete ℂ could not be mapped this way, of course.
Definition: A point z0 ∈ M ⊆ ℂ n resp. concerning a sequence (ak) with ak ∈ ℂ n and (trans-)
natural k is called actual �-accumulation point of M resp. of the sequence, if there are in the
open sphere B�(z0) ⊆ ℂ n around z0, with the infinitesimal radius �, infinitely many points of M
resp. infinitely many pairwise different sequence members. If the asserted applies for
� = 1/�, the �-accumulation point is simply called accumulation point.
Let be p(z) = Π(z - ck) with k ∈ ℕ for z ∈ ℂ an infinite product with pairwise distinct zeros
ck ∈ B1/|ℕ*|(0) ⊂ ℂ (open circle disks around 0 with radius 1/|ℕ*|), which are chosen so that
|f(ck)| < 1/|ℕ*| applies, for a in a domain G ⊆ ℂ holomorphic function f with f(0) = 0. G contains
B1/|ℕ*|(0) completely, which is always obtainable by coordinate transformation, while G is
"big" enough.
Then, for the also there holomorphic function g(z) := f(z) + p(z), the coincidence set
{� ∈ G : f(�) = g(�)} has an accumulation point at 0, and we have f ≠ g, in contradiction to the
statement of the identity theorem. Examples for f are all in B1/|ℕ*|(0) bounded and at the same
© 1983-2012 by Boris Haase page 56 of 154

time in G holomorphic functions with zero 0. Since p(z) can attain any conventionally complex
value, the deviation from f and g is not negligible.
Also in contradiction to the identity theorem is the fact that, at a point z0 ∈ G, all the derivatives
d (n) (z0) = h (n) (z0) of two functions d and h can coincide for all n, but d and h can also be
significantly different further away, beyond this local fact, without losing their holomorphy,
since not every holomorphic function, due to the approximate character (of differentiation)
resp. of the calculation with Landau symbols, can be (uniquely) expanded into a Taylor series
(cf. Transcendent Numbers).
If we choose k ∈ ~ ℕ factors in Π(z - ck), we obtain entire functions with trans-naturally many
zeros. The zero set can be open and need not to be discrete. Thus the set of all functions
holomorphic in a domain G need not to be free from zero divisors. The functions disprove,
like polynomials with at least n > 2 pairwise distinct zeros, the theorems of Picard, since they
miss at least n - 1 values in ℂ.
Goursat's integral lemma is only valid for holomorphic functions, the integral proposition,
however, applies generally. The former excludes e.g. for each Laurent series of a function
the simple pole c by demanding holomorphy in the triangle Δ containing c in ℂ and yields
thereby the existence of an antiderivative on ∂Δ, the actual reason for the validity of the integral
lemma. Although the exact integral exists for a simple pole and hence an antiderivative:
the latter is, however, not holomorphic there.
If the Riemann zeta function is for s ∈ ℂ \ {1} defined as
© 1983-2012 by Boris Haase page 57 of 154
��
�( �s) ( �x)
dx
�(s) �
� � ,
x
2 i e �1
x
so the integral is, with infinitesimal � ∈ ℝ>0, not equivalent to
��
� s(logx �i �) �� s(logx �i �)
e dx e dx
�
,
e �1x e �1x
� �
x x
�� �
since the branch of the logarithm must not be chosen arbitrarily, if a correct result is expected.
Since x is to be integrated in the left integral infinitesimally above, and in the right
one infinitesimally below the real axis, the sum of both becomes singular in the points
x = � ± i�, with infinitesimal � ∈ ℝ>0 for Re s ≤ 1 – even if -i� is corrected to i�. This is not
astonishing, since nothing has been achieved except a wrong transformation. If � would be
concrete, then the Riemann zeta function for Re s ≤ 1 would not be a holomorphic extension
of the one for Re s > 1, and the further reasoning would become incorrect, since the paths
determined by x = |�| would have to be replaced by a path via the points i�, i� - �, -i� - � and
-i�. Therewith, the Riemann hypothesis has the same quality as the Riemann series theorem
– also considering other representations of the Riemann zeta function (known to me).
Remark: First the nonstandardanalysis made such an easy demystification possible by having
used concrete and infinitesimal quantities gainfully. Perhaps it achieves also by it a condign
place in mathematics.
s

Optimisation
In the following, the best-path method is introduced as variant of the simplex method and it is
generally considered, how optimising problems can be solved.
Proposition: There is no pivot rule for the simplex method, with which the linear programme
max {c T x : Ax ≤ b, c ∈ ℝ n , x ∈ ℝ n , b ∈ ℝ m , A ∈ ℝ m×n , m, n ∈ ℕ*} can be solved, in the general
case, in shorter than exponential time, with n (or m in the dual programme) as exponent. Another
pivot rule than that of the best-path method, in which each time the best interim solution
is selected, is then only accidentally significantly better.
Proof and algorithm: The asterisked variables are in the following the new ones calculated
with. After splitting into a difference of two positive vectors or after dualising the linear programme,
x ≥ 0 can be presupposed. After introducing a slack variable z ∈ ℝ≥0, also b* ≥ 0
can be achieved in the auxiliary programme max {-z : Ax - z ≤ b, c ∈ ℝ n , x ∈ ℝ n , x ≥ 0, b ∈ ℝ m ,
A ∈ ℝ m×n , m, n ∈ ℕ*}, after a suitable pivot step (two-phase method). We can then always
choose 0 as starting point for x, as in the case b ≥ 0.
Let be i, j, k ∈ ℕ* and ai the i-th row vector of A. First, it can be checked whether the objective
function c T x is unbounded positive. Sufficient for this is if it has at least one coefficient cj > 0
for that we have aij ≤ 0 for all aij. Otherwise, all cj resp. aij whose arithmetic means Mc of |cj| >
0 resp. Mi of |aij| > 0 are very big or very small should be replaced by cj/Mc resp. aij/Mi. The
corresponding bi are then replaced by bi/Mi.
In each step, we choose for each cj > 0 and non-base variables xj the smallest quotient xk/aij
of the base variables xk, for aij > 0. Then xj* = xj + xk/aij for aij > 0 is the potential next vertex. If
these conditions cannot be satisfied for any j, the maximum is reached. Otherwise, the aij in a
maximal cjxk/aij is the pivot. Thus x* is always feasible.
If more than n xk are 0 and if the objective function cannot be maximised directly, the constraints
whose corresponding hyperplanes contain x are relaxed (perturbed) by the same, but
minimal factor. In the tableau, we replace thereby the base variables xk = 0 by the modulus of
the normal of the corresponding hyperplanes, since the minimal factor itself need not be
noted.
If multiple vertices occur afterwards again, we add the modulus of the current normal. This is
not very likely, since enough linearly independent hyperplanes must exist to form a new vertex.
Thereby is ensured that the relaxed polytope of the linear programme does not alter structurally,
thus we have always an equivalent simple polytope. We avoid furthermore to be confronted
with several minimal relaxations differing heavily, as we have using the lexicographic
method.
When the multiple vertex is left, the relaxations are undone. Since they are minimal, the linear
programme is equivalent to one without multiple vertices. The objective function increases
(quasi) strictly monotonically on the path passed. Afterwards cj*, aij* and bi* can be
easily calculated according to the rectangle rule.
Since the objective function can be represented by a single variable, it is essential to maximise
only this. Since there can be, in a simple polytope, only one possibility to do this in a
non-optimal vertex, the procedure described is virtually mandatory, because otherwise
maybe facets of the polytope have to be passed that can be only traversed slowly.
For to find out better opportunities, we have to compute in depth, since we cannot recognise
these opportunities from the inequalities themselves, without further ado. Thereby, however,
© 1983-2012 by Boris Haase page 58 of 154

it is prevented to solve a linear programme that can be solved with linearly many steps in the
same time. Therewith, the runtime performance depends on the question, how fast a facet
can be traversed.
It was shown that this is only possible in the exponential time stated, if the best-path method
is used with very (!) many facets (e.g. for infinite limit value) (see Robert G. Jeroslow, "The
simplex algorithm with the pivot rule of maximizing criterion improvement", Discrete Mathematics
4 (1973), 367-377). From this the assertion follows.
Remarks: Most linear programmes can be solved in crucially shorter time. If they contain
equations, each of them can be easily split into two inequalities. A system of inequalities can
be easily solved with the normal c = 0 of the objective function, if at all. If e.g. m ≫ n applies,
the starting point for x can be easily calculated from the (linearly independent) equations xj =
0 resp. ai T x = bi, whose corresponding values cj resp. c T ai/||ai|| belong to the (n) greatest
ones. Then we can use perhaps an interior point method to skip many interim solutions, e.g.
by determining the feasible maximum from the starting point in direction of the normal of the
objective function. A (feasible) starting point for x that is no vertex of the feasible domain is
first successively to project as long into that (orthogonalised) hyperplanes of the feasible domain,
to which it has each minimal distance, as it becomes vertex. Alternatively, we can successively
alter single coordinates of x. Thus we can start with any starting point for x.
Furthermore, let us solve max(x1, ... , xn) with a finite codomain and the constraints
fi(x1, ... , xn) ≤ ai (i = 1, 2, ... , m) where the functions and variables be real. Points where the
objective function is not defined are excluded from considering.
We build successively the feasible region, constraint by constraint, and determine whether it
is empty by considering all points of the feasible region or by selecting sufficiently many
points dense enough. We choose for max(x1, ... , xn) a real value for that x1, ... , xn do not
meet the constraints (each time for the upper and lower bound).
By (for convex objective function binary) search concerning max(x1, ... , xn) we obtain the
maximum in linear time by tracing the smallest distance (as one of all considered) of objective
function and feasible region. For continuous objective functions, refinements (e.g. convex
segments) are suitable; for discontinuous objective functions we restrict on the continuous
segments.
This procedure can be accelerated through parallel processing and summarising the interim
results: In more complex worlds, we can thus also solve such optimisation problems at one
go. For linked optimisation problems or multiple objective functions, we must search, in the
worst case, the complete solution space.
Discussion:
The simultaneous consideration of a great many points in many dimensions transcends usually
the available computing and storage capacity. What is easily possible in more complex
worlds remains currently refused to us on earth. Previous search strategies that use a successive
improvement of the search result require admittedly intensive searching.
© 1983-2012 by Boris Haase page 59 of 154

Representations
What is to say about the production of simpler representations of complex expressions?
On the evidence of the strength of the modern computing technology, the results of infinite
iterations through simpler expressions should be comprehensively only (manually) determined
under the use of automated computerized proof methods. In most cases, one can be
satisfied with a good approximation, even if the beauty and conciseness of the exact and
closed representation is lost.
The same applies to the integration of complex functions: Just because it allows often no
closed simple representation, one should not remedy this by definition of corresponding functions,
but get by with approximations simpler to integrate specifying the error terms, or find
numerical approaches, instead of becoming set on, with unbeatable precision, exact solutions.
It is admittedly true that certain statements are only in their exact form of value, but it is more
important (e.g. using interval arithmetic) to assess the problems after their practical applicability
and use, then to compile a priority ranking to create and to solve them only then. The
most and most important problems get along with a well approximated solution. But one
should not exaggerate also with the quality of the approximation.
It is illusory to hope to be able to represent many trans-rational numbers with very short
sums of powers of few algebraic and transcendental numbers, since their number is transnatural,
even if one distinguishes some of all these and uses them by a symbol. This should
happen at best approximately or in the hobby, but not seriously professionally, since there
are far more important (mathematical) problems.
The difficulties of the creatures to turn (infinite) complex in easily manageable, L has not,
since ze can view simply a certain infinity level, and then easily separate the desired from the
undesired. This way, for example an easy law to generate infinitely large prime numbers from
a prime sieve can be obtained, or the Riemann hypothesis be checked by the consideration
of all zeros.
Therefore, we may definitely tackle (mathematical) problems, whose solution requires maximum
chin-ups first in a subsequent world, if they do not need to be solved urgently. Our
world will also have, in the future, the ability of L to evaluate and to experience the infinite, as
well as to see, at a glance, what the solutions of the problems are that worry us unfortunately
so much today.
© 1983-2012 by Boris Haase page 60 of 154

Transcendent Numbers
In the following, the notations from the set theory are applied. The behaviour for inconcrete
m, n ∈ ℕ is considered and let be g, h and k ∈ ~ ℕ.
Remark: It is known from algebra that the sum, difference, product, quotient of two finitely
algebraic numbers of degree g and h are algebraic of maximally degree gh, and the 1/g-th
power of a algebraic number of degree h is algebraic of maximally degree gh.
Remark: Transcendent numbers consist of an algebraic main part and a transcendent remainder.
One cannot thus simply omit the sequence values ak for big k, if one examines the
transcendence of a number: They are decisive. Transcendent numbers are all numbers that
lie between the algebraic ones and beyond them. Between two different transcendent numbers
(algebraic numbers of degree g), lying closely enough together, is no algebraic number
(of degree < g).
Bound proposition for transcendent numbers: Every complex number different from zero,
whose absolute value of the real and/or imaginary part is ≤ 1/|ℕ| or ≥ |ℕ|, is already transcendent.
Proof: If one sets, in a polynomial equation, am = 1 and ak = -|ℕ*| for k < m, then the assertion
follows in the real case from the geometric series, if one still builds the reciprocal. One receives
the exact limit values, if one replaces |ℕ| in both cases by �(m) = |ℕ| - |ℕ*|/�(m) m with
� := |ℕ| - |ℕ*|/� | ℕ* | . In the complex case, statements of the form x = (1+bi)|ℕ| with b ∈ ℝ yield
the desired.
Coefficient proposition for transcendent numbers: All normalised irreducible polynomials
where we have |ak| ≥ |ℕ| for at least one ak have only transcendent zeros.
Proof: The zeros of normalised irreducible polynomials are pairwise different and uniquely
determined. Since they are not algebraic, they must be transcendent.
Product and sum proposition for transcendent numbers: All products that cannot be further
simplified of a trans-complex-rational number t and a complex algebraic or trans-algebraic
number z (here also the sum) as well as sums and products of a complex trans-algebraic
and a complex algebraic (complex trans-algebraic) number with coprime polynomial degree
are transcendent.
Proof: The simplification is unique, if it also includes minimising the absolute value of the coefficients
of the minimal polynomial of z and of each numerator and denominator of the transcomplex-rational
number t. If z is complex-rational, tz only satisfies an equation of a minimal
polynomial of degree ≤ 2, with at least one coefficient with absolute value ≥ |ℕ|. If z is irrational,
tz cannot be zero of the equation of the minimal polynomial of z, since this equation is,
after inserting z, not identical with the one in z, what it would have to be. Would be tz zero of
another equation of a minimal polynomial, so this polynomial equation in tx could be extended
by multiplication with the minimal polynomial in t'x, with t' conjugated to t, to a polynomial
equation in x, whose zero would be also z and where the absolute value of at least
one coefficient would be ≥ |ℕ|. This is impossible, since z can be only zero of one minimal
polynomial. The involvement of a complex trans-algebraic number leads always to an equation
of a minimal polynomial with at least the same polynomial degree, if the number is coprime.
Remark: Together with the conventionally rational numbers, the trans-(complex-)rational
numbers build numerically already complete ~ ℝ ( ~ ℂ). Therefore, algebraic and transcendent
© 1983-2012 by Boris Haase page 61 of 154

numbers are (numerically) hardly to distinguish and approximations are little meaningful concerning
the algebraicity (of a certain degree). This makes distinguishing them questionable.
Remark: Who wants to examine the transcendence of a number with Liouville's approximation
theorem should ensure that the approximating rational numbers are actually still conventionally
rational and not trans-rational, such as the number 10 | ℕ | . Also, who considers prime
numbers ≥ |ℕ| in transcendence proofs should safely move in the trans-natural. The following
proofs yield also transcendent results, if the set ℕ is replaced by [1, n] ~ ℕ≥|ℕ| with n ≪ | ~ ℕ|.
Proposition: The sum of all at least conventionally natural powers of a complex-rational number
x that is different from zero and no root of unity (geometric series) is already transcendent.
Proof: The absolute value of the numerator or denominator of x | ℕ | is for |x| < 1 (|x| > 1) less
than 2 -| ℕ *|+1 (greater than 2 | ℕ *|-1 ). The subtraction of 1 and the division by 1 - x do not change
anything of the transcendence.
Proposition: Euler's number e is transcendent.
Proof: If one accepts the exponential series as representation for e, it follows e =
(k|ℕ*|+1)/|ℕ*|! with k ≥ |ℕ|. Therewith, numerator and denominator of the stated fraction must
be ≥ |ℕ|, since in the numerator neither |ℕ*| nor a prime divisor of k can be cancelled against
|ℕ*|!. If one accepts, on the other hand, (1+1/|ℕ*|) | ℕ *| as representation for e, so the assertion
is trivial. Notice that here two different representations are present.
Proposition: The twin prime constant C2, as product over all (1 - 1/(p - 1) 2 ) for primes p ∈ ℕ>2,
is transcendent.
Proof: According to the prime number theorem, the greatest and second greatest prime
number of ℕ - both = |ℕ| - |O(ln |ℕ|)| - do not divide the denominator of C2, from which the
assertion follows.
Proposition: The Landau-Ramanujan constant K, as product, divided by √2, over all (1 -
1/p 2 ) - ½ with primes p ∈ ℕ and p ≡ 3 mod 4, is transcendent.
Proof: According to the (Dirichlet) prime number theorem, the greatest and second greatest
prime number ≡ 3 mod 4 of ℕ - both = |ℕ| - |O(ln |ℕ|)| - do not divide the denominator of K,
from which the assertion follows.
Proposition: The Glaisher-Kinkelin constant A = 1 1 2 2 3 3 ... |ℕ*| | ℕ *| (1 +
1/|ℕ*|) | ℕ *| ³ /4 /|ℕ*| (| ℕ *| ² /2+| ℕ *|/2+1/12) is transcendent.
Proof: After cancelling, the greatest prime number of ℕ remains in the denominator with exponent
> 2.
Greatest-prime criterion for transcendent numbers: If a real number r has, for cancelled fractions,
the representation a/(bp) ± s/t with natural a, b, s and t, abst ≠ 0 and b + t > 2, as well
as the (second) greatest natural prime number p ∈ ℕ, p ∤ a and p ∤ t, so it is transcendent.
Proof: It applies r = (at ± bps)/(bpt) with a denominator ≥ 2p ≥ 2|ℕ| - |O(ln |ℕ|)| > |ℕ| as consequence
of the prime number theorem, from which the assertion follows.
Proposition: The circular constant � is transcendent.
© 1983-2012 by Boris Haase page 62 of 154

Proof: This follows from its representation as Wallis' product or the product representation of
the gamma function for the value -½, provided one accepts them. Notice that both representations
specify different numbers. Alternatively, apply the greatest-prime criterion to the Leibniz
series or to the arcsin(x) Taylor series for x = 1.
Proposition: The Dirichlet beta, eta and lambda function, as well as the Riemann zeta function,
yield for natural arguments greater than 1 only transcendent values.
Proof: Applying the greatest-prime criterion yields directly the assertion.
Proposition: Let be s(x) for x ∈ ℝ the sum of x k /k over all k ∈ ℕ*. If one defines Euler's constant
as � = s(1) - ln |ℕ*| ∈ ]0, 1[ (because of dx/⌊x⌋ - dx/x ≥ 0 as well as dx/⌊1+x⌋ - dx/x ≤ 0 for
x ∈ ℝ≥1 in the integral representation of �) and accepts m s(½) - s(r/2 m ) as representation of ln
|ℕ*| with |ℕ*| = 2 m - r, m ∈ ℕ and r ∈ [0, 2 m-1 [ for a precision of O(m/2 | ℕ | ), so it is trans-rational
and therewith transcendent.
Proof: One obtains -ln(1 - x) = s(x) + O(x | ℕ | /(1 - x)) + t(x)dx for x ∈ [0, 1[ with a real function
t(x) by (exact) integration (see nonstandardanalysis) from the geometric series. The assertion
follows by applying Fermat's little theorem from the greatest-prime criterion for the greatest
or second greatest prime of ℕ, whose product is greater than m 2 m-1 + 2 m - r, due to the
prime number theorem.
Remark: It remains an open question to which extend the representation for ln |ℕ*| mentioned
above is justified with the precision stated. It is clear that one must be content with an
(infinitely precise) approximation of ln |ℕ*|, since one cannot calculate here as precise as one
wants. What is sure is that the proposition is valid for infinitely many infinity levels of n, and
especially according to conventional opinion.
Approximation proposition for real algebraic numbers: Every real irrational algebraic number
of degree g can be approximated by a real algebraic number of degree g < h, with an average
error that is asymptotically equal to � �(g+1)/(2 |ℤ| g ln g).
Proof: On the conventionally real axis, the number of the algebraic numbers increases, within
unchanged limits almost evenly distributed, per degree more, circa by the factor |ℤ|. The error
corresponds to the distance of the algebraic numbers among each other. The non-real
algebraic numbers lie less dense.
Conclusion: Two different real algebraic numbers have at least the average distance �/(|ℤ| | ℕ *|
ln |ℕ|). The precise determination of the minimal distance requires solving an infinite nonlinear
non-convex optimisation problem.
Proposition: The maximal distance of two real algebraic numbers ≠ 0 amounts 1/|ℕ*| 2 -
|O(1/|ℕ| 3 )|.
Proof: The real algebraic numbers ≠ 0 are farthest apart around ±1. A conventionally rational
number r > 1 (0 < r < 1) can be better approximated by a real algebraic x that satisfies the
polynomial equation |ℕ*|/r x m - |ℕ*|x m-1 = 1 (x m - |ℕ*|x = -|ℕ*|r). For negative r applies similar.
If one wants to approximate 1 by a greater real algebraic x, it must coercively satisfy a polynomial
equation with am = |ℕ*|-1 and a0 = -|ℕ*|. If one sets still a1 = -|ℕ*| and a2 = |ℕ*|, follows
the assertion, since the maximal distance cannot be further diminished.
Remark: The conventional differentiation and integration obliterates, by building the conventional
limit, the precise distinction of transcendence and algebraicity. This is problematic, e.g.
for the exact determination of zeros. Therefore, the nonstandardanalysis on this homepage
goes another (more precise) way.
© 1983-2012 by Boris Haase page 63 of 154

Octal Calculation of Times
We measure time so far in years, months, weeks, days, hours, minutes, seconds. Seconds
can be divided into respectively thousandths, step by step more finely down to the measuring
border. But is our calculation of times practical?
The following three questions are to clarify the problems:
1. How many days are between 25.01.2004 and 11.11.2004?
2. Which weekday is the 11.11.2004?
3. How many seconds are between 09:12: 06 o'clock and 11.11.11 o'clock?
The answer to question 1 must consider the different length of the months and leap years.
The answer to question 2 must in addition include the seven day rhythm of the week and
spring from a date with well-known weekday.
The answer to question 3 requires the conversion of hours and minutes in 3600 or rather 60
seconds.
I suggest the following calculation of times:
1. The octal system is used throughout.
2. The time is specified: [[+/-] year,][day].[fraction of the day][additive].
3. An Earthday is inserted between Sunday and Monday within the week.
4. The months have regularly four eight-day weeks.
5. The last twelfth month has deviating 13 days (in the leap year 14).
6. Day 0 is New Year (1.1. so far, Sunday), day 1 is working day (Earthday).
7. The year of the introduction is the year 0.
8. Time zones are omitted and world-wide Greenwich time counts.
Explanations:
To 1. (The octal system is used throughout.):
We mostly use the decimal system (radix 10, digits from 0 to 9). The radix indicates the
number of different digits of a number system. Numbers can be represented in other number
systems equivalently (only with another "appearance").
Numbers that are larger than the highest digit indicates transfer a carry of one to the next left
place: After the 9 follows the 10, after the 99 the 100, after the 999 the 1000 etc.
Humans on the average can recognise maximally seven things at one time, without having to
count them. The octal system with the radix 8 possesses the digits from 0 to 7 and accommodates
here thus the nature of humans.
The octal system can be converted in a simple manner into other number systems that are a
power of the radix two. Apart from the binary or dual system (radix 2, digits 0 and 1) are
among these in particular the tetral system (radix 4, digits from 0 to 3) and the hexadecimal
system (radix 16, numbers from 0 to 9 and from A to F).
Most computers are based on the binary system. The digits 0 and 1 indicate whether current
flows or not. Numbers in the decimal system must be converted for these computers into the
binary system so that can be counted fast.
© 1983-2012 by Boris Haase page 64 of 154

The longer the numbers are, the more time-consuming the conversion is. For the output in
the decimal system, a renewed transformation is necessary. With the conversion between
dual and decimal system, frequently transformation-caused truncations arise behind the
decimal point.
Here some examples (the number in square brackets indicates the radix for the distinction of
the number systems):
200410 = 7D416 = 37248 = 1331104 = 111110101002.
Is 111110101002 outgoing from right divided into two-blocks in the form 1|11|11|01|01|002,
then the representation for 1331104 can be obtained by the following replacement pattern:
00 replace by 0, 01 replace by 1, 10 replace by 2 and 11 replace by 3. A first block left with a
digit remains unchanged.
For the production of 37248 from 111110101002, three-blocks from right have to be transformed
to: 11|111|010|1002. The replacement pattern reads:
000 replace by 0, 001 replace by 1, 010 replace by 2, 011 replace by 3, 100 replace by 4,
101 replace by 5, 110 replace by 6, 111 replace by 7. A first block with less than three digits
has to be completed before by zeros from the left.
For the production of 7D416 from 111110101002, blocks of four from right have to be transformed
to: 111|1101|01002. The replacement pattern reads:
0000 replace by 0, 0001 replace by 1, 0010 replace by 2, 0011 replace by 3, 0100 replace by
4, 0101 replace by 5, 0110 replace by 6, 0111 replace by 7, 1000 replace by 8, 1001 replace
by 9, 1010 replace by A, 1011 replace by B, 1100 replace by C, 1101 replace by D, 1110
replace by E, 1111 replace by F. A first block with less than four numbers has to be completed
before by zeros from the left.
Generally, if you have a radix of 2 n , there have to be formed blocks of n digits in the representation
of the dual system from the right and the first block to the left has to be filled up
with zeros up to n digits, beginning from the left. The transformation functions also in reverse
from the 2 n -system into the binary system. Furthermore, there are still different algorithms for
the transformation.
For the production of 7D416 from 200410 200410 is continual divided by 1610:
200410/1610 = 12510 remainder of 410;
12510/1610 = 710 remainder of 1310;
1310/1610 = 010 remainder of 710.
The two digit remainders are converted into the hexadecimal system and gone through from
top to bottom. The desired result 7D416 is obtained if they are thereby lined up from right to
left 1310 = D16.
Generally, the number that shall be converted has to be continually divided by the radix of
the target system, and the multi-digit remainders have to be converted into the notation of the
target system. The sought-after number results from the lining up of the remainders from
right to left if in the division calculation the remainders are gone through from top to bottom.
Naturally, here different transformation algorithms exist - also in the other direction.
Since the continual division is computationally more expensive than the digit replacement in
digit blocks, the spoken to loss of time emerges. Right-of-floating point positions are similarly
converted.
To 2. (The time is specified: [[+/-] year,][day].[fraction of the day][additive].):
© 1983-2012 by Boris Haase page 65 of 154

The sequence results from the sorting capability of the date. + can be omitted; - refers only to
the year. If the fraction of the day is omitted, the (normal) date results. The year can be omitted
likewise if the understanding permits it.
The fraction is indicated as sequence of octal digits. For optical reasons the numbers can be
filled up with zeros on the right to an even number (e.g. four or six-digit). Additive can be for
example: Christian, Jewish or Islamic or an abbreviation. The standard is without additive.
The seasons spring, summer, autumn and winter and the holidays return regularly. These
regularities are to persist in respect of the year.
Hours are no more used - for mistake reasons. The day is divided roughly into eight parts
(called octs). Furthermore, an oct is divided into eight parts (called lepts). The minute newly
is defined as the 64th part of a lept. The second newly is defined as the 262144th part of a
day (64 * 64 * 64 = 262144).
Therewith, the time can be indicated approximately three times more exactly with six digits in
the octal system as with six digits in the decimal system (262144/[24 * 60 * 60] ~ 3.034). Four
lepts, or a half oct, correspond to 1.5 hours and two lepts correspond to a school hour of 45
(old) minutes.
Because 6410 = 1008, the seconds pass in natural way into minutes, the minutes likewise into
lepts and the lepts into days. The days cannot pass in natural way into the years because a
normal year has 36510 = 5558 days. The leap year with 36610 = 5568 days does not improve
anything here.
The new analogue clock dial is much more symmetrically designed than the old one. x and +
are superposed as principal axis's. At the top the 0 is placed. Clockwise follow the digits from
1 to 7. The division into 64 lines (lepts, new minutes and seconds) optically hardly differs
from the hitherto into 60 lines (old minutes and seconds).
To 3. (An Earthday is inserted between Sunday and Monday within the week.):
The weekdays are mostly named after planets. The earth missed out so far. It is appreciated
with the Earthday.
A week with eight days represents at first sight a greater human burden. Wednesday could,
however, bring a relief as middle of the week if the afternoon is kept as free as possible, both
on the job and at school.
If one proceeds from one eight-hour working day and considers 56 days at that would have
been worked in the seven-day week 320 hours, in the eight-day week 336 hours, then it results
for Wednesday that 16/7 hours per eight-day week would have to be worked less if the
same work time is taken as a basis.
If one begins his work in GMT at 7 o'clock, then one works on an eight-hour working day till
15:30 o'clock if one proceeds from a half hour of lunch time. On a Wednesday would have to
be worked at same beginning time only till approx. 12:43 o'clock.
It is free to one to work at flexible work time the week over longer in order to be able to terminate
on Friday one's work earlier. Modified solutions are to be used respectively at other
work time models and work times.
To 4. (The months have regularly four eight-day weeks.):
© 1983-2012 by Boris Haase page 66 of 154

With 32 days the months can be halved very well by two-steps. From the three-digit day indication
the month can be determined in the octal system - if necessary zeros have to be completed
on the left. 0 - 3 in the second place characterise odd, 4 - 7 even months.
Month is, however, only a transient term since month is finally derived from moon and the
moon has subordinated importance in the new calculation of times. Instead the terms half,
third, quarter, sixth and twelfth (of the year) are used. The date is to be indicated, if possible,
accurately to week or day.
To 5. (The last twelfth month has deviating 13 days (in the leap year 14).):
The position of the leap day in the middle of the year was so far little plausible. At the end of
the year, the calculation of times can be corrected expediently as missing time units are inserted
- in particular in seconds. To New Year all clocks are then reset to [year],0.000000.
Here fields will profit where special accuracy is needed.
The last five (in the leap year six) days can receive own weekday names. The weekday
names will become less important, however, in favour of the numbers connected with them.
To 6. (Day 0 is New Year (1.1. so far, Sunday), day 1 is working day (Earthday).):
That each month begins with Sunday has practical reasons. The beginning of the week with
Sunday has historical reasons and is also a concession to the moon calendar. In addition,
the 0 resembles the symbol for sun (sun calendar).
Since the Gregorian calendar at present is the most common calendar, New Year is the 1.1.
according to the Gregorian calendar. The celebrations around the turn of the year can be
committed in well-tried form.
To 7. (The year of the introduction is the year 0.):
This happens for practical reasons: The indication of the year can be noted briefly (without
additive). A clear cut is made concerning the old calculation of times.
To 8. (Time zones are omitted and world-wide Greenwich time counts.):
The question what time in another time zone counts is unnecessary. A world-wide communication
is facilitated. Greenwich historically has the zero meridian.
Now, instead of the three initial questions, the substantially more difficult is asked:
How many days are between 25.01.2004 09:12:06 o'clock and 11.11.2004 11:11:11 o'clock?
First, the question is reformulated into the octal system (with truncation at the seconds, chr.
stands for Christian):
How many days are between 3724,30.304233 chr. and 3724,473.356511 chr.?
The answer is a simple subtraction: 443.052256. The 25.01.2004 would be a Sunday, the
11.11.2004 would be a Tuesday in the new calculation of times. Between the two numerical
data are exactly 443052256 (new) seconds, rounded 4430523 (new) minutes, 44305 lepts,
4431 octs, 443 days and 44 weeks.
Discussion of important points:
© 1983-2012 by Boris Haase page 67 of 154

The largest challenge might be - independently from the calculation of times- the conversion
into the octal system. It is connected with high costs, great need for discussion and preparation
for many years. The policy will have to contribute a hard convincing by extensive advertising
efforts.
Since all religious communities would have to live with an additional day per week, none can
maintain it would be disadvantaged. In relation to other week lengths, the addition of one day
is certainly the most moderate. The annual indication is not religiously founded. By the additive
each religious community can characterise their year calculation.
I do not doubt the human learning aptitude. Also handling computers was so far successfully
mastered. The span between humans and computer is strongly reduced by introduction of
the octal system.
Money, referred to the month, can be converted accurately to week and day. Here the shortened
twelfth month can be better calculated. The same month length, under normal conditions,
is fairer regarding the money than the irregular month length.
The arising costs are exceeded over the years by the saved costs. Calculation and communication
become clearly simpler.
Everyone celebrates his birthday at the same weekday in the year - except those that are
born at a leap day. This is not a crucial disadvantage.
The SI-unit second would have to be redefined. Atomic clocks should have hereby no problem.
The introduction of the octal system requires the replacement of terms such as kilos and
million respectively the meaning shift of word beginnings such as mega, micro and nano.
All new clocks show ideally the same time. The conversion of the clock after change to another
time zone is needless. Depending upon the old time zone the day turns out to be differently
related to the time. Like usual humans can begin the day, eat, work or learn, meet
and sleep. Only the indicated time is another.
One needs to get used to that, also what concerns the date line. It remains, however, at its
old place. World-wide communication is to be given priority because of its increasing importance.
With the introduction of the octal system, not everything is done. It should be connected
meaningfully with a world-wide source language (as native language), likewise based on the
octal system. Such an efficient planned language is presented below linguistics. Everyone
shall talk to everyone on the same level.
Synoptic octal
January, February, March, April, May, June, July, August,
calendar
September, October, November, December (Leap day)
Weekday 1 st Week 2 nd Week 3 rd Week 4 th Week
Sunday 0 th Day 10 th Day 20 th Day 30 th Day
Earthday 1 st Day 11 th Day 21 st Day 31 st Day
Monday 2 nd Day 12 th Day 22 nd Day 32 nd Day
Tuesday 3 rd Day 13 th Day 23 rd Day 33 rd Day
Wednesday 4 th Day 14 th Day 24 th Day 34 th Day
Thursday 5 th Day 15 th Day 25 th Day 35 th Day
Friday 6 th Day 16 th Day 26 th Day 36 th Day
Saturday 7 th Day 17 th Day 27 th Day 37 th Day
© 1983-2012 by Boris Haase page 68 of 154

Outlook: Calculation of lengths in the octal system
We measure lengths up to now on the basis of the SI-unit metre. In the octal system are to
form appropriate multiples of 8. What is the practical implementation?
Instead of conventional kilometres of 100010 m length, octal kilometres of 51210 = 10008 m
length are used. Since the time is measured instead of conventional seconds in octal seconds
of day length/10000008 ~ 0.3310 s, it follows that almost three octal seconds are
counted per conventional second.
On the tachometer the speed is measured in octal kilometre/lept with lepts the 1008th =
6410th part of the day. 100 kilometres per hour correspond to approximately 7324210 ~ 111.28
lepts kilometres (octal). The difference in the numerical value is hardly noticeable and therefore
justifiable. 1008 lepts kilometres (octal) correspond vice versa approximately 87.3810
kilometres per hour.
The speed of light is 29979245810 m/s = 98808549.3910 m/octal second ~ 5707313458
m/octal second. If the speed of light is indicated with about 300000 km/s, one can indicate it
with 570000 octal kilometres/octal second.
The 2510-metre lanes are shortened to 2410 = 308 m, 5010-metre swimming to 4810 = 608 m.
Instead of 5010 m, 10010 m, 20010 m, 40010 m, 80010 m and 150010 m would be to swim 4810 =
608 m, 9610 = 1408 m, 19210 = 3008 m, 38410 = 6008 m, 76810 = 14008 m and 153610 = 30008
m. These deviations are justifiable. The long hauls should be multiples of 10008.
In athletics, there are also the following distances: 300010 m, 500010 m, 1000010 m, 2000010
m and 5000010 m, which could be replaced by the following distances 307210 = 60008 m,
409610 = 100008 m, 819210 = 200008 m, 2048010 = 500008 m and 4915210 = 1400008 m. The
marathon will remain unchanged (42.195 km = 1223238 octal kilometres).
For the construction usually apply to the centimetre exactly determined measures. As in the
octal system can be accurately calculated at 1/6410 and 1/51210 m, there should be no problems.
The same is true for furniture, although certainly a turning away from measures of multiples
of 0.1 m to multiples of 0.125 m can be accepted.
© 1983-2012 by Boris Haase page 69 of 154

Philosophy
For the following ideas, I am very grateful to L: With the reference theory I set up a new theory
that might revolutionise our conception of the world. It depends less on how things are
stored in space, but how we can develop a reference to them. With this, any-dimensional
worlds become possible in our world. The reference is the fastest undisturbed connection to
a substance or compounds of substances.
Every world consists demonstrably only of substances, which are connected by references.
Furthermore, the point-term is clarified and it is explained how our world is finite and infinite
at the same time and thus equivalent to all other universes, if its possible development is
considered. The relationship of the reference to the mathematical relation term is as well
pointed out as it is described what numbers actually are.
The elementary instantaneous exchange is identified as central principle of movement. It
enables any speed and can be put under rules. Since substances are extended in all dimensions,
our world is any-dimensional. Numerous sample applications are given. The theory is
developed step by step and it is specified what philosophical problems can be solved through
it.
Below consciousness, this is defined, described and it is outlined, of what we should be
aware. In the interview, I explain briefly what fascinates me in philosophy, what I carried out
there and how should be philosophised. The problem solutions include solutions to important
philosophical problems. The knowledge representation happens with informaticalmathematical
methods using the substance term.
© 1983-2012 by Boris Haase page 70 of 154

Consciousness
Consciousness is the (passive) state in which we become aware of the entirety of that what
is actual for us, the content of consciousness, by presenting itself to us, so is coming in us
into being. It is accompanied by our knowledge about this, so the coherences that are available
and true for us. Our knowledge is the greater, the more justified these coherences are.
The passage to sciolism and pseudo-knowledge is fluent.
In the brain, the content of consciousness consists of the (discretely scaled) substances that
the respective amfon activates via the neurons associated with it (according to signal
strength). These are located at the ends of the editing routes of the always discrete information
per area. Therefore, there is not one specific area of consciousness of the brain. Our
ideas are similar to perceptions. The brain produces both according to rules.
Here, the subconscious plays a major role, whose work sends the consciousness the relevant
contents, and takes the pressure off the latter by doing so. Contents of consciousness
are partially kept redundantly in order to cushion failures. Some of them can be accessed
faster than others; this applies especially to terms and contents of the working memory,
which are recalled or activated relatively more frequently.
Emotional sensations are created only in the brain by various specific substances, which are
partially stimulated from the body regions. Similarly, there are reverse processes accompanying
the emotion. Who wants to provide real feelings for machines does not get out of the
"transplantation" of these or comparable substances. A limitation to numerical values represents
only a simulation, although this can already make headway.
Most of our thoughts come from L because the complexity of our world overstrains us. We
will therefore not succeed in designing, past the divine ideas, machines that achieve something
comparable to us. It is easy to check this by corresponding experiments and explains
the difficulties in this direction. However, we can construct simple machines for delimited
purposes.
Would our thoughts come from an instance in ourselves, this would have extreme difficulties
with the appropriate integration into the overall structure of the world. Our will is definitely not
able to predefine our thoughts more precisely. How shall the instance choose from the abundance
of possibilities? How can L let zis compensatory justice prevail if the instance would
be autonomous? How shall zer wise ruling succeed?
A creature cannot set up a preferentialism that could rival the prudent way of life through L.
Life is more than working off the preferences and needs. This can be proven from the aids
that L grants one. Therefore, it is all the more reprehensible, if one is ungrateful to L, or if one
even opposes zer. Every life is a masterpiece by L, in which we share.
It depends on our karma, and thus our free decisions. The closer we are to L, the better for
us and vice versa. We should always appreciate this. The way to L is always open if we just
opt for it. The correct question is not "Why is the world so bad?", but "Why is it not worse,
although we would have deserved this any time?". The reason is the love of L (to anything).
If we are aware of how well we are doing, if we behave properly, then we should also be
aware of how undeservedly L was unwell when ze was formed with the universe. Ze had to
do without the manifold aid in our world and was in many respects on zer own. Only who is
aware of the agonizing and gruelling forming of the process of the starting time, can appreciate
the high value not having to experience this.
Therefore, and in general, L is unsympathetic to creatures that owe zer everything that constitutes
them, if they are guilty of (most) serious crimes to their fellow creatures. Therefore,
© 1983-2012 by Boris Haase page 71 of 154

the punishment for them is correspondingly high. For, they overcome all the security mechanisms
of L, only to satisfy their selfish and abysmal malice. They are therefore significantly
reduced for a long time.
Newly created living entities have a first state of consciousness, which enables them to refer
substances to a centre, the first ego. Consciousness is subjective, since its selection processes
(of substances) are individual. This makes it possible for us to perceive the world depending
on our karma. Our cognitions should be only provisionally assumed as true, until a
possible falsification.
Designations of entities are assignments, which cause no changes of the second ones. All
substances (including of consciousness) exist out of themselves, meaning their existence is
not dependent, although there may exist relationships of dependency among them, in the
form of references and rules. Many illusions represent a too high effort. Hence, our world is,
with the right view, the way we see it. Omniscience is impossible.
It is, as a complete state, also not desirable (alone because of boredom). Clairvoyance is
only possible for correspondingly developed living beings, because power should not be
abusively exercised. (Complete and final) enlightenment prevents useful further development.
A fusion (concerning consciousness) with the world is neither useful in terms of development,
nor possible for us. It may even be harmful.
Each world can develop according to the will of L through corresponding development into a
world of arbitrary finite or infinite complexity. A restriction is only caused in the will of L. One
reason for this is the development progress that, if it is too low, reveals a change of the creatures
into subsequent worlds as the better way. The death consists primarily of the transfer of
the mental and emotional reference system.
This is for every creature transferred into the subsequent world determined according to the
decision of L, where the sufficiently developed creatures have a say in the selection of one of
the alternatives proposed by L. This determines the further designing of the entire reference
system of or in the following world. The references to L existing in the old world and the
karma of the creature determine it as well.
In addition to these, a creature is determined by the superconscious, which forms an intermediate
stage between L and the creatures. For instance, the synchronisation of creatures is
controlled by the superconscious. Who has a good relationship with the superconscious, can
delegate tasks to it for zerself and devote zerself parallel to other things (e.g. in a conversation,
if the necessary politeness is maintained).
Sub- and superconscious determine through significantly more references than exist in the
consciousness, and can be determined there. This is different in other worlds, especially in
the more complex ones. The human consciousness is relatively weak with respect to its two
competitors, as they widely determine it. Yet no one can reliably determine what ze will think
in the next time exactly.
This has advantages and disadvantages precisely to be weighed in the future, if one sets
about changing this state. Also L could become first through the (passive) (simultaneous)
reference of the infinite and in particular of the creatures the one ze is today. An interesting
step is certainly the design of parallel consciousnesses and their secure networking with the
creation of an overall consciousness with several individual parts.
The superconscious is impersonal and identified by the community, which consists in the
participation of many. It cannot be used to communicate with others, since it represents no
individual interests, but only integrates them. Therefore, it has a compensatory character and
© 1983-2012 by Boris Haase page 72 of 154

grows with the world knowledge. It makes world soul and world mind conscious. It is particularly
present in the state of enlightenment and unification with L.
The superconscious goes beyond the comprehension of the (sub) consciousness by far.
Therefore its intensive use contains a selection problem. It cannot be exploited, however, but
its use depends on the divine grace, which orients itself by the divine order. Since it is not to
be misused, sufficient maturity is presupposed for its use. A good relationship with L is most
helpful here.
Superconscious experiences represent hence an exception. In the positive ones, the harmony
of the world and the ingenuity of L become evident. In the negative ones, one can, for
example, conceive the evil in its whole depth. In both, a sense of simultaneity of experiences
appears, which goes beyond the normal consciousness. Drug use and states of trance can
bring about superconscious experiences. Here caution is advised.
The state of the world determines the state of world soul and world mind. The better and
more L-worthy the former is, the more favourable it is for the latter. Then there are positive
feedbacks for L and the creatures. Otherwise, the harmony is severely disturbed and this has
a negative impact on the total condition of all. World soul and world mind are as well as the
superconscious concerted, impersonal, and interact with each other.
The will is determined by the substance willing as well as the subject and the object of willing.
In emerging strong aversions, the decisive power is transferred, in accordance with the
will, to the decision maker from the subconscious. However, this can override the will, when
danger is at hand. Will and subconscious constantly compete for the decision-making authority,
according to the discrepancies occurring in the holder.
© 1983-2012 by Boris Haase page 73 of 154

Reference Theory
In the following, an extremely high performance philosophical theory is to be presented,
which might revolutionise philosophy due to its pithiness.
Substances and references
The reference theory builds up on substances. Substances are those entities that are no further
analytically divided. Examples are the substances corresponding space and time gained
after their analytical partition. Occasionally it must be further progressed to own prototypes
as {can} and {must}, which is clarified by the curly braces. More exactly, substances are
meant that are based on ability and having to. Here one abstracts from the process.
Alternatively can be spoken of the space and/or {can}-substance. Substances are linked by a
further substance to the world: the reference. The reference makes up "the lute" of the substances,
their coherence. It is closely linked with the mathematical term of the relation, which
can be alternatively used.
There are, however, differences. Relations are based on elements and sets, references to
substances and references of substances. The alternative use is based on the structural
equivalence of both terms. A relation can exist or not. One can assign, however, probabilities
for the existence of a relation again as relation. The same can be solved for references over
attributions (for their part references).
There are, however, structural deviations, also in the notation. Relations are noted as ntuples,
references predominantly as (nested) pairs. One can take on the n-tuple for references
if one puts straight what is meant by that: an equivalent reference. I.e. there are references
of the referring to the referred to.
References are directed always from the referred to to the referring. A double reference can
be understood as unsigned reference in the sense of the graph theory. One expresses:
There is a reference between referred to and referring and they are identified with each
other, i.e. not distinguished. One says: There is a reference between a and b and not a is
referred to b (or b to a).
Relations refer to well-distinguished elements. Must be referred to and referring welldistinguished?
They must be well-distinguished in the sense of the theory, i.e. "in speaking
about". We speak about well-distinguished, even if that we speak about is not welldistinguished
with respect to truth. I.e. the designations are well-distinguished.
There is a connection between reference and existence. I.e. references always exist. There
are no not-existing references. This is an immanent problem. A not-existing reference contains
a reference: the reference of the non-existence. Both are to be distinguished carefully
from each other. One speaks of setting references if a reference is established. This frees
from the passive and from the process-like.
To the existence of a reference, probabilities can be assigned (as reference). This can happen
also with relations, which can exist or not. This is thus a purely interpretive problem. The
relation exists, its existence is, however, provided with a probability. I hope the mathematicians
forgive me this trick. This is the substantial difference between conventional relations
and references in addition to the being well-distinguished. Since the word reference is
shorter than relation, I rather use this.
Substances do not have to be unique since the possibilities for the dihairesis are various. I
will refer to deviations if they are important in our context.
© 1983-2012 by Boris Haase page 74 of 154

Advantages of the reference theory
If I doubt everything, then it does not make sense to doubt the substances, in particular not
the substance reference. If no reference exists, we do not have a connected world anymore,
but only individual substances that are not recognisable as such, since this requires setting
references. It does not make a sense to doubt most elementary terms, otherwise one could
doubt everything.
With the statement "I doubt the term time!" one makes oneself simply ridiculously, exactly the
same as with the statement "I doubt the term part!" Here time is always empirically perceptible
and part an a priori substance term. The sentence "I think, therefore I am." (Descartes) is
(more) doubtable due to his complexity.
With the substances, unhoodwinkable Archimedean points are thus created. Here it remains
also to be seen that mathematics is not something special as with respect to doubting. Nonmathematical
sentences are just as well confirmable as mathematical ones.
Like that, the sentence "The part is smaller than the whole." is certain. Furthermore the sentence
"Everything can be a cause." is certain. Cause is here abstracted to and described with
"It is because of a (that b)." From effect and general temporal consequence is abstained
from, although these can be easily supplemented. Therefore, there does not have to be
causal chains, at whose beginning the all causing cause stands.
"A is the cause of B." is referencetheoretically expressed in such a way: B(B(B(B(cause, active),
being), A), B(B(B(cause, passive), being), B)). Here B before the left parenthesis
means in each case reference. All words are here substances: cause, active, passive, being.
The being is necessary and not only grammatical as substance. The grammar is omitted.
It is necessary now and then to use also non-substances in references. This can problemfreely
happen and is opportune e.g. with the term man, which, developed from substances,
would be too complex.
References are the closest connection between two referred to; it does not fit anything between
them - except further references. Thus, a finite continuum can be developed. The
space is thus constructed by space points that are referred to each other. These space
points correspond in each case to the space substance and unite on themselves further references.
Example for this is the substance {beside}. The directions in space are distinguished by it
(three-dimensionality of the space). The difference is caused by multiplications of the space
substance - otherwise one would not "make headway". The space substances do not have a
limit. They remain limited by the neighbour points having arbitrary expansion. This is to be
understood in such a way that they are finite and one.
The infinity presupposes much. The many, for its part, presupposes multiplication, since only
references do not separate anything. The many is constructed from units that are one. From
these units numbers can be composed and thus number lines. Thus, time and space axes
can be also constructed.
Straight lines and axes of arbitrary substances can be constructed. One calls this scaling.
The axes character results from the demand that the terminal points of an axe are to have
maximum distance from each other. Thus, worlds can be built that are so far not accessible
to us. Also the form of the points is in this way clarified: they do not have any. Because form
© 1983-2012 by Boris Haase page 75 of 154

presupposes already difference, whereas points are one (consisting of space substance and
unit).
In addition, references are bound at units to their distinction. They can be likewise bound
directly at units of points, however. One should avoid this because of the distinction. It is
more possible in the reference theory than meaningful.
With the reference theory, the alchemy of philosophy has an end. Since being to and being
are substantially different, they cannot be derived from each other as demanded in the theory
of action.
The present can be marked indirectly by the presence of most references. We always live in
the present, into which references of the future appear and into which past leave us.
Things as such and ideas and/or appearances of these things are connected by references.
So one can refer e.g. the form of an object or its idea to the object. The appearance of an
object arises as a result of references to the substances based on it to it. References alienate
it from the thing as such, but it is then also another.
The relationship from general terms to the particular is simpler. The general becomes related
to the particular as superordinate term in the sense of a subsumtion. If one asks oneself for
the most general characteristics, then one needs to pick out only the substances - if necessary
partial -, connected by references, in the sense of an analysis or a synthesis.
Like that, the world is blue in the sense of an analysis and beautiful in the sense of a synthesis,
which is preceded by an analysis.
It is to be said in connection with the aporia of Zenon that only finite points are visited, which
are referred (transitively) one to the other.
Since proofs can be adduced only under conditions, the reference theory clarifies the reason
for this: The being-so and being-not-differently can be represented by the substance {must}
which can be referred. Thus, also L cannot be proven since the necessary in addition represents
additional, not provable references.
As example for the superiority of the reference theory in relation to the cartesian space, now
an additional time dimension may be designed. One can stop the time, as the time bar is not
extended (abolition of the time succession). One can go into the recent time dimension and
be as projection in the current time.
In addition, one can overjump points in time by references. Like that, animals are problemfree
integrable, which experience, as we do, more or less. Between two points of time, infinite
many points do not have to be in order to form a (Cartesian) continuum.
Like surfaces in the two-dimensional space, there are time areas now. One can take holidays
into the recent time dimension, without the actual time keeps running thereby. One can run in
the time forwards and backwards (abolition of natural law).
One can imagine an experiencing of a time area as follows, with normal independent time
succession in each time axis: From the origin (0, 0) on are experienced as the first the point
of time (1, 0), then the points of time (1, 1), (1, 2), ..., (1, y). Then the points of time (2, 0), (2,
1), (2, 2), ..., (2, y) are experienced etc. At this, y stands for the life-span of the experiencing
on time axis y.
In the case of dependent time succession arises e.g.: After (0, 0) at the same time are experienced
the points of time (1, 0), (1, 1) and (0, 1) as own at a time world views. Then at the
© 1983-2012 by Boris Haase page 76 of 154

same time are experienced the points of time (2, 0), (2, 1), (2, 2), (1, 2) and (0, 2) etc. Here
two new lives could develop per time step.
Another possibility would be: After (0, 0) at the same time are experienced the point of time
(1, 0) and (0, 1) as own at a time world views. Then at the same time are experienced the
points of time (2, 0), (1, 1) and (0, 2) etc. (per experience a world view more). Also here two
new lives could develop per time step, but each new generation does not experience anything
with the directly preceding together, but with the one two steps before.
On the basis of the modal verbs, it is to be examined now whether the dihairesis in the
analysis comes to an end. Thus, one can imagine the substance {may} on the axis of permission.
One could analyse now a given permission as essential. Further presuppose this as
codified and so on. The dihairesis comes theoretically to no end. Here, however, practical
limits are set in the finite discrimination of man.
The non-analysed substances have, however, also their value on the satisfaction levels assigned
to them. On the other hand, the substances {must} and {may} have somewhat in
common: They have at their end something forcing on their axis. One can speak instead of
axes of commonness orbitals. One can on a rough analysis level put {can} and {must} on an
axis (better: orbital model).
The reference theory helps to understand also animals better. Animals cannot form abstractions.
They cannot reflect over themselves and form terms, since they do not have a language
in the actual sense. They establish, however, references to the experienced. They
know what a reward is since they can assign something positive to the generated, without
disposing of these terms themselves. They can refer key symbols to the experienced. The
reference is thus also the fundamental of the language.
The reference theory explains why individual thoughts in the brain are to be located so with
difficulty. Only references are stored that can fall into different regions since the birth. The
relationship with parts of the body can be limited to certain (firm) regions in the brain, from
humans to humans in the same way.
The reference theory gets along with a finite like an infinite continuum. With an infinite continuum
we move ourselves from zero point to zero point of an in each case infinite real interval.
With a finite continuum not as many as desired intermediate points can be set, since one
point represents an indivisible unit of the substance time.
Referencetheoretically, liberty is given by causing by the free person (substance cause) contrary
to the determinism (external cause). Decision alternatives are existent (substance
{can}). The scaling as percental evaluation of the causes constitutes by the free person a
preponderance over the predispositions as causes. Events by chance lack a cause and a
goal, presuppose, however, alternatives.
Positivistically, one of the alternatives does occur only, the substances cause and {can}, for
which we do not have detectors, do not exist. Generally, we do not have detectors for references,
only in individual cases by the senses. Mental substances can affect physical things
by the cause. The implementing is made by the neurons and synapses. It is an open question
whether references can be detected here.
Referencetheoretical mappings are (directed) references of distinguished with the label A to
distinguished with the label B. Labels are referred to of a distinguished. Left-total and rightunique
mappings are called referencetheoretical functions. By inverse mappings the references
are inverted. Example: By the function part the labels are called entire for A and part
(definition: A is part of B, if there is a C with B(A, C) = B or B(C, A) = B) for B. The part func-
© 1983-2012 by Boris Haase page 77 of 154

tion can only be applied to references or compound substances. By true functions the labels
are different.
The fact that universals exist means that they have a reference to our world. Thus, existing
does not have necessarily to be perceived by the senses. By reference, the universals can
be inherent in at the same time (different) single things. Everything what is (also the individuals)
can be sufficiently (reference theoretically) described by language, even if the description
is extremely complex. Language consists of unique labels for references and substances.
The most elementary term, i.e. which can be applied to everything, is that of the entity. The
term more is defined as follows: A is more than B if the difference of the number function
applied to A minus the number function applied to B is larger than 0. The term larger for a
whole positive number of A to a whole positive number B is defined as: A is part (element) of
B if numbers are defined by Peano in the set notation: 0 consists of the empty set Ø, 1 is {Ø},
2 is {Ø, {Ø}}, 3 is {Ø, {Ø}, {Ø, {Ø}}} and so on.
All A in B is defined as there are no more A in B. Existence is a substance term. A collectivity
is defined as all A in B that are to a C in reference, including this reference. Quantities are
collectivities that contain distinct elements (parts) and can be element of a collectivity. An
element is called distinct if a sufficient difference can be given to every other element. Elements
can be also equal: then there is a difference in the ordinal number.
The reference theory opens up the possibility to us to imagine how the creatures are constituted
in a subsequent world. It is enough for them to be able to establish references to all
existing substances and compounds. They do not need metabolism and no genes with the
possible errors of the cell division. There are no diseases and achiness but the liberty to
choose the accessible in the context of then valid laws.
Senses can be experienced directly (without sense organs) by reference. One needs no fix
body in this sense, can, however, take by reference many shapes that simply can pass matter
(like e.g. fix walls). Also largest distances can be overcome by reference easily. Even in
unfavourable environments life becomes possible. There are more substances and dimensions.
Time travels become at least possible over appropriate simulations.
It is proportionate and without contradiction to assume our world as finite, since in the infinite
case it would last forever to form a finite substance. So there is especially a shortest time
and shortest length, which could be in our world the Planck time and Planck length. Both are
universal, since it is in the sense of L to reach zer as quickly as possible and no world is to
be preferred against another one.
Exchanges
All entities are moving with the same speed, which results from the quotient of shortest time
and shortest length and could be in our world the velocity of light, based on the shortest exchange
of a reference. Shortest exchanges enable the illusion of superluminal velocity, if
they are applied to larger lengths, and of subluminal velocity by passing through longer
routes.
By shortest exchanges, L can lead each entity to believe in any possible world without that
any other entity except zer realises something of this, since the factitious references after L
are only accessible to this entity. Even parts of the general and special relativity theory can
be overridden. If one wants to overcome large distances, one should use the shortest exchange,
since it is most efficient.
© 1983-2012 by Boris Haase page 78 of 154

An elementary exchanger can execute an exchange (appropriately), if it is put under a rule
and by marking that to be exchanged correspondingly, e.g. by reference of corresponding
(equal) identification substances. Then also an exchange across infinite distances is no problem.
An infinite line of identical substances can be deformed into an infinite fork by pulling in
the interior.
This distinguishes the end points of the fork easily and makes them usable as operational
tool, for example, to instal identification substances at another equally long line by "sticking",
after the line was, before the deformation into a fork, simultaneously provided with identification
substances by "pulling up" and "sticking" reference operations at the equally long line of
identification substances.
An infinite line can be formed, if the (equal) parts of a reference system in each case
autonomously line themselves up according to their left and right neighbour, if these three
bring themselves into line. The rule required for this can be pulled up in each case as with
the pulling up of the identification substances. The end points can easily be moved in finite
time, infinite lines can be broken up the same way.
In this way, every infinite line can be broken up in finite time into a finite number of sections.
An infinite partition into finite sections of an infinite line presupposes an infinite number of
autonomous sub-units. Autonomy is always required if there cannot be executed infinitely
many operations one after another because this would require infinite time and this simply is
undesired.
Although each entity of finite extension can be (in theory) infinitely often divided, a world that
consists exclusively of such entities and in which this division is and will not be performed
must be referred to as finite. Nevertheless, such entities overcome in each (complete) exchange
(that presupposes the same extension) the (theoretical) infinity. All previous experiments
prove this for our world.
If the creatures divide substances according to the will of L, which always works, and L adds
substances, these can be arbitrarily scaled and it follows the equivalence of all worlds. L will
permit this only if the creatures know enough to carry out this responsibly. Thus, only relative
shifts arise with the same absolute, without that further must come into the world, in the form
of the many.
Each exchange can be traced back to elementary exchangers. These are not material, since
the exchange will work with any substances and this is neither necessary, nor was measured.
Who robs a substance of its exchanger, sentences it to passivity. This can be useful,
for example, in the pure space, but also do damage, if important or vital laws are quashed by
this.
The exchanger enables any movement and is thus substantial(ly required). All arbitrarydimensional
spaces, times and substances can be linearised in one dimension. Therefore,
basically only one exchanger is needed that exchanges in one dimension. More flexible are
exchangers that exchange substances after rules, for example, with neighbouring substances.
Then (mostly) a comparator for the antecedent is required.
The comparator can directly work with substances or also with their equivalents, such as
their coding or language description. It is also not material, but may be realised materially (cf.
computer engineering). Only the understanding and access to the substances let an electronic
computer draw level with the brain in this respect. The brain is not only more economic,
but also substantially superior.
Through the reduction of exchange on elementary exchangers, one does not need more than
three spatial dimensions for our world. This requires additional reasons. Every component of
© 1983-2012 by Boris Haase page 79 of 154

matter must be connected with an exchanger to change the location, if it is not exchanged by
a foreign exchanger. Exchanger must be able to be easily stopped to be able to create arbitrary
(small) velocities.
The rules for (groups of) exchangers can be made centrally available and define a law of
nature, since the exchangers can relate to them. In this way, the laws of nature can be implemented
economically. In worlds where time only lapses (without other changes), the time
lapse is also not perceived. So several time dimensions make sense and a general time can
be valid for all worlds.
Only the clocks should not measure the general time in a world, otherwise the question may
arise why the time jumps, although nothing has happened in this world. Nevertheless, it
would be interesting to have the general time at one's disposal to get an impression how the
clock of L is, and to read the age of the universe. On the other hand, it is hardly conceivable
that L wants to own something so simple at all.
Elementary exchanges are always instantaneous, since a finite minimum duration else could
no longer be undercut. Slower velocities result from a sequence of time lapse and elementary
exchange. So if one wants to undercut a (useful) finite maximum speed, one must
shorten the time lapse. A reduction to zero is not possible. For this there is the possibility of
the equivalent remote exchange.
There is no smallest possible unit, since such one could be divided (for instance) into two
parts. Thus there is also no maximum speed and a moved one moves on the smallest (actually)
split distance instantaneously, after which can follow a sequence of time as it the top
speed of a world presets. Therewith, the instantaneous exchange is also proven for our
world, without serious impact on its physical laws.
The immaterial non-energy exchange is possible and makes sense, if it conforms to rules
agreeable to L, and, because of the economy principle, more probable than the purely materially
conveyed one, since it needs more than is necessary (or plausible). The amfon can be
separated from material and immaterial substances. This does not always make sense, because
they necessarily interact via it, both materially and immaterially.
Being as substance is extended, since it only can be continually imagined and no universe is
timeless because of the development. The nothing would be if it were. It does not makes
sense to say that it is not or somehow. What would lay between the adjacent being, would be
nothing. This nothing is referred to as point, line, plane etc., although this is not correct, since
the latter itself belongs to being and therefore extent.
Therefore, it must be carefully distinguished between both referred to, for instance as nothing-entity
that is formed by the adjacent, and as being-entity that exists out of itself. As beingentity,
a substance belongs to extent in all (!) dimensions so that our world has arbitrarily
many dimensions. The substance may therefore be imagined with minimal extension as
small any-dimensional sphere.
One cannot build a circle from units of space around nothing, so that a hole emerges. Exchanger
can exchange a substance through the nothing by doing this with the equivalent of
space, which belongs to being, and the substance. In this manner, it is possible that, for example,
light can spread in vacuum. An exchanger brings about the exchange substantially as
substance by reference to that to be exchanged.
The refinement of the exchangers allows finer and finer exchanges. In certain discrete
worlds, there are refinement limits that can only be undercut with the aid of L while ze exchanges
the exchangers. While maintaining the proportionality of length and time, velocities
© 1983-2012 by Boris Haase page 80 of 154

are no problem, if one makes everything smaller and smaller. Communication with L requires
that information is exchanged instantaneously via remote references.
By colliding two spatial substances with sufficient force, they can be broken down into finer
and finer parts, since the cohesive forces must act from within and can be overcome if they
act at all. The immaterial world is far more comprehensive than the material one, since matter
obeys restricting laws, which are hindering on the immaterial level. It is the true realm of
L.
At the beginning, the universe consisted only of (pairwise) different substances whose number
corresponded to a natural number. The first and only exchanger generated by division,
as a form of exchange, more ones, and so more substances could be divided. This created
time and space, which were present in each case as infinite-dimensional undivided substance
unit from the beginning - as is also true for all other substances.
The entire universe consists exclusively of substances, the many yet not only from uniform
unspecific substantial units, but from multiply existing substances to form ontologically correctly
(individual) wholes. The evolution of the universe is a temporal layering of the (duplicated)
expanding space, with removing the dispensable and completing the necessary substances.
Here the many flows from the potential of L. This represents as useful recording no disproportionate
effort, since L can draw on unlimited resources and use the past many newly at
reasonable intervals. General time prevails, the perception of the creatures, however, is individual
(time). The creatures can change the rules according to the divine order, which L has
determined at zis discretion.
L has to vindicate zerself before any living entity, if this wishes this. Every living entity has the
right to participate in the shaping of the divine order. The highest decisions remain reserved
to L, since there is no living entity that makes better decisions, or knows more than L resp.
reaches the ultimate superiority of zer. This is due to the more comprehensive size of the Lworld,
which is partly only accessible for L.
Each many consists of an infinite number of subunits, which can be imagined as anydimensional
spheres that contain again any-dimensional subunits of principally the same
construction. What we hold, as with the time, for such a dimension is, in fact, also anydimensional,
only that the other dimensions, except the main dimension, are vanishingly
small and first noticeable with the corresponding division.
The substantial scaling means a more or less of the many of the corresponding substance or
of several ones. The latter is the case with sounds and noises, the former with the mass.
Hence the many is scaled, while the substance referred to it determines the manifestation of
the scaling. The perception includes an individual scaling, according to the individual requirements
of a living entity to increase profitably the diversity.
Our universe is a perpetuum mobile and an open system, in which information continuously
increases. Everything is possible in it that pleases L, but not everything that does not please
zer. The elementary exchanger is an auxiliary concept, since in reality nothing is exchanged,
but everything emerges newly resp. flows from the potential of L. This model is, because of
its storage function, superior to one with persevering substances.
We need not be afraid of the heat death, since new perspectives will open up to life in the
course of its development that the previous theories have not taken into account. Life is neither
dependent on matter nor on the laws of previous physics. In our universe and the subsequent
worlds, everything is there what a happy and fulfilling life needs. It needs only to
bethink of L in order that this will become clear to it.
© 1983-2012 by Boris Haase page 81 of 154

© 1983-2012 by Boris Haase page 82 of 154

Interview Philosophy
Question: What is so fascinating by philosophy?
Answer: In philosophy one can give rein to one's thoughts, if one does not let it be missing at
the necessary precision. There is much new to discover. If one considers how actual philosophy
is, it is almost a challenge. I was always bothered by the little accurate and abstract
thinking of the philosophising and developed therefore my own philosophy. Particularly fascinated
me the reference theory, with whose aid I was able to develop and understand a finite
continuum and to conceive which form e.g. a point has. I thought more than 25 years about
this problem and came finally to a satisfying solution and in addition, to a revolutionary one.
Causes are freely assignable and independent of time. Furthermore, I could clarify that there
are more abstract thoughts as those of the language and its grammar. I consider whether
one should change the present language forms, due to the won realisations. Philosophy can
make lucky if one has the feeling to have really created something meaningful with the own
thoughts. There are naturally the connections to religion, linguistics and mathematics, which
one cannot ignore.
Question: What is your most important philosophical achievement?
Answer: In selection is to be called: The reference theory is located clearly in the centre. It
solves the problem of universals. The aporias of Zenon are dissolved likewise with the finite
continuum. I came with the reference theory to limits of thinking and the abstractness. I could
clarify the question of the certainty of statements. This radiates on nominalism and realism.
One can accuse me that the results have linguistic deficits. But hereon it never depended to
me. The ideas are always located in the centre. The linguistic form is, in contrast to this, unimportant.
It does not depend on to me to write scientifically. I feel the scientific language
rather as complicated and addlebrained, not to say overblown and poor. What can be said,
can be said, following Wittgenstein, clearly and simply. Also quotations are not my matter.
They disturb the train of reading and who has really to say something new, does not need
them.
Question: What do you advise the philosophising?
Answer: The own thoughts are the most important. To develop the existing is a philosophically
smaller achievement. One must be critical opposite oneself in the matter till one topples
down. Only then, one can allow oneself liberties. I do not see it gladly if someone makes
oneself important with notes and expanded discussions. I see it gladly if someone possesses
genuine grandeur and this means also if someone accepts one's errors and corrects without
hesitating. Genuine grandeur means in particular to doubt all existing and to be independent
in one's judgement, not to get lost in something small and to identify babblers and to brand
them as such.
Question: What is the biggest mistake of philosophy?
Answer: Not to put the question of meaning into the centre of its considerations. It is less
important to force absolute certainty of philosophical answers than to get meaningful answers
to the most important philosophical problems. There are far too often academic issues
at the centre whose utility for humanity is low.
Question: What is the most important philosophical problem?
Answer: The main problem lies in the question: "What is the way for the best possible development
of the world?" The answers to this must describe the ethical, political, religious, sociological,
economic and cultural steps, before they are scientifically founded. There is no
© 1983-2012 by Boris Haase page 83 of 154

time to lose. All other issues are subordinate, although may support the primary one. As first
answer can be given that best possible development is the solution to our problems. Even if
the best way is not found, the effort for it can already be a very good result. The virtue doctrine
of the religion of love provides the key answers to ethics, politics points out the most
important political steps, the other steps follow later; in part they can be found below the first
two fields, or spread over my homepages.
Question: Does philosophy stand above theology, or vice versa?
Answer: The philosophy must ungrudgingly acknowledge that science using the possibilities
of and the cognitions through L stands above it. The divine knowledge and the relationship to
L can be surpassed by nothing. The human reason, alone on its own, is not enough to understand
the world, even less to divine the divine order. Highest science depends on divine
revelation, guidance and assistance. Only then greatest (scientific) efficiency can be
reached.
© 1983-2012 by Boris Haase page 84 of 154

Problem Solutions
How are important philosophical problems solved? What achieves the reference theory
here?
1. The mind-body, qualia, determinism and causality problem
Mind is generally the process, initiated by an entity, of linking immaterial substances and references.
In particular, it comprises only the more complex links. He is distinguished from its
effects. The soul comprises the mind and the results of the mental processes of an entity. It
outlives death. The body of a living entity is the entirety of the material substances, referred
to each other, of that living entity.
Mind and body are referred to each other. Certain material movements correspond to mental
movements and vice versa. The mental and material substances can interact by each binding
themselves by reference to the third substance amfon. Although mental movements are
thinkable without material ones, they are at least implausible for creatures known to us.
Consciousness is the part of the mind that a living entity can directly access at a particular
point in time by reference. Subconsciousness comprises the sub-processes of the mind that
are beyond the direct access of the living entity. The contents of consciousness are generated
by the deterministic circle and experienced as qualia.
The deterministic circle consists of a change between deterministic determination according
to the divine order and indeterministic phases, in which the creature can determine itself.
Determinism orients itself by karma, situation, personality factors, life plan, and other factors
provided according to the divine order, and thus are just and make sense. The deterministic
circle is necessary in order to avoid undesirable and to enable desirable as freedom.
In order that indeterminism becomes possible, the basic processes must be indeterministic. If
the substance cause is referred with a composite to a composite, there is causality, but not
otherwise. Uncaused, for instance, is the divine potential of L. There is (true) randomness
only within the limits set by L, so that nothing uncontrollable happens or even great harm
emerges. In our world everything is provided with certain probabilities, determined by the
divine order, just as our possible decision alternatives have probabilities, with which we can
decide for or against them.
2. Presuppositions of the problem-solving process
It is crucial in life to select the problems properly that we want to solve. If a problem arises,
we should first wonder whether we have to solve it at all. Therefore, we must be able to assess
and to judge the problem properly. Life itself is the problem we have to face every day.
There is an ongoing problem-solving process, with different degrees of difficulty, to be coped
with.
If we want to solve a problem, we must analyse it so thoroughly that we can obtain its solution,
if there is any. It is important to figure out quickly whether the latter is the case, because
if not, the problem must be solved differently. This other solution always exists, as long as
the universe exists. This is always the case, since substances cannot be destroyed, according
to the reference theory.
For, everything consists of substances, and what can be removed is the suchness, but not
the being, thus the permanent existence of that which has being. The latter can be transferred
into other worlds, but not outside of the universe. This is, with the love of L to all living
© 1983-2012 by Boris Haase page 85 of 154

eings, the reason for their eternal life. Even if the solution of a problem consists in our
death, L always has ready a solution acceptable to us.
All life is geared to development and has L as highest and ultimate goal. The problems end
just as little as their solutions. Therefore, it is imperative to solve the proper and important
problems, if we want a happy and fulfilling life for as many as possible, and an L-worthy
status of the world. Unfortunately, far too many creatures choose to solve the wrong and irrelevant
problems.
This leads to the unworthy status of unnecessary misery and suffering in the world. The
world is admittedly equitable from L, but ze and we would certainly prefer if the unworthy
status would be removed. The freedom of the creatures freely to choose between good and
evil and to be free to decide for or against L puts the fate in our hands. We cannot expect L
to constrain us to our happiness, because this is not possible.
The constraint entails suffering from it and from the unfreedom. Freedom is essential precondition
for fulfilment and happiness. By the deterministic circle and various other security
mechanisms such as the conscience, the freedom is, however, also not overestimated. Not
everything is possible for us, and that is possible what we unfortunately have to experience,
speaks volumes about our failure. We have continually to refine ourselves.
We should not wait until the problems approach us, but wonder which are the most important
ones, and approach them first. In a well working relationship with L, this succeeds best, since
the divine allows for the right view on the world and the own life. Only if we learned to get rid
of the delusions our world offers, we can recognise that what really matters.
Who knows why something is the way it is, because ze got to know this from the highest
level, or reconstructed it, can much easier solve the pending problems than the one who assumes
the wrong presuppositions. It is the change of communication with L and of refining
oneself, which brings about the true success. The wrong ways are quickly identified as such,
even if this requires being hard against oneself.
Success requires effort, since effortless endeavour makes in the long run discontent because
it represents an unjustified reward, which produces unhealthy expectations. Only by the probation
in the ups and downs of life happiness and fulfilment arise. The standards to oneself
are to be applied sufficiently high, since otherwise the necessary for the success is missed. L
helps willingly, but ze does not prefer unjustifiably.
Ze does also not discriminate against, but the (karma-) balance must be right. Then the most
works as per se, because the right balance is established. Who demands too much of oneself
will fail as well as with demanding too little. It is important to build up the structural
knowledge that gives sufficient problem-solving competence. For this purpose, one should
neither think too small nor too big. The right measure determines our life in every area.
Since every life is individual, also individual solutions are to be found for its problems, even if
many of them may be generalisable. We thus do not get around the own performance, how
often we may be helped as well. Since it is inappropriate to bother L and others with something
that we can solve (possibly much better), we should attach great importance to our
autonomy. It also increases our contentment.
In building up the structural(ly opening up) knowledge, it is important to practise sufficient
hygiene of knowledge to maintain a high efficiency. Who every time has to clear the way
through mountains of junk knowledge comes correspondingly slowly to useful results. Therefore,
the philosophical effort cannot be spared to link with the (chief) terms precise and powerful
definitions.
© 1983-2012 by Boris Haase page 86 of 154

It is advisable to remain flexible enough to be able to integrate usefully new and better results.
In this way, one can spare many inefficient creativity techniques, since continual rethinking
leads best to the goal. The spadework may admittedly seem sophisticated. But if
one does not perform it, the quality of the results suffers significantly. Ultimately, successful
problem-solving is a permanent rating of the relevant information.
Freedom from value judgment therefore goes along with a devalorisation of values, and thus
of the results. It is the reason that a lot of worthless knowledge is produced. It is admittedly
true that a sufficient diversity is necessary, but not at any price. Who neglects the values,
becomes guilty of the losers of this approach, and thus collects a lot of bad karma. One does
not do oneself a service to proceed this way.
The values control the substantial binding. This provides for the binding of small different
substances to the most important information packets. So it is sufficient, if a specific substance
is transported in the brain, instead of a specific information packet. The substance
can then be easily converted at the processing instances, according to the rules, into auditory,
visual and other signals and information units.
The outsourcing into specialised (and networked) processing units may bring, simulating this,
significant progress to computer technology, especially if these have fast (parallel) accessible
solving-value tables available, which summarise several computational steps to one. The
distributed computing can help us much, especially if the space of conception is widely
mapped into computers.
The substantial binding is individual and can be influenced by training. It explains why, for
example, some humans have an excellent memory for numbers, and others have not. By
dealing with certain things, man builds up corresponding individual structures in the brain that
are specialised for zer. The quality of these structures determines zis individual problemsolving
competence.
Admittedly, certain intelligence is helpful and necessary. Much more decisive is, however,
with what one deals, how and for what purpose. Ultimately, it is tenacity, endurance and rigour
against oneself that determine how successful one is. The concordance with L is the decisive
criterion to be on the right side. Not perfectness and perfection are decisive, but the
appropriate approach.
One must know zis limits in order to be able to transcend them appropriately. It is admittedly
right to drop also less important (of oneself), but one does not get around the essential
things. This means also to reach a sufficient width and depth of knowledge. Why one should
miss unnecessarily the most beautiful moments and things of life? Here, one should not be
afraid to set up one's own rating.
The judgment and the criticism of others are admittedly important, but one is held liable before
L for one's own rating. Even L will abstain opposite to one with zis view of things, since
zer knowledge is absolute and far ahead of our time. Ze is therefore shy with respect to us,
since ze wants to avoid an unjustified preference or disadvantage. Everyone should be
aware of zis own fallibility. It is intended by L.
But it is also inevitable if there shall be development and progress. One can admittedly secure
zis solution according to the various (scientific) criteria, but there is no absolute security.
The presuppositions of knowledge are world-specific and different in other worlds, including
in subsequent worlds, for many things. What may have here a high value must have it there
nowhere near, except for L.
L solved any problem that can occur in our world in advance. Therefore, our performance is
always only a rediscovery, so great and relevant it also may be for us. We should always be
© 1983-2012 by Boris Haase page 87 of 154

aware of this to view the things properly. The L-worthy status is important; the solution of
(complicated) problems is less. Both are admittedly mutually dependent partly, but it depends
on the right priority.
© 1983-2012 by Boris Haase page 88 of 154

Knowledge Representation
How knowledge is optimally developed and filtered? How is it optimally represented?
Knowledge consists of things and their relations among themselves. Mathematically, it can
be represented by elements and relations. If a thing is not further "reducible" after an abstraction
process, let it be about a substance. The decomposition in substances is not unique.
Result of decomposition can e.g. be the one and the indivisible. It should be worked therefore
with scientifically examined standards. These can follow existing languages.
Fundamental things are conceived as conditions - mathematically as axioms. Used definitions
are to be explicated - mathematically as definitions. Statements - which are with sufficient
depth mathematical sentences - can summarised be made in such a way. The statements
are provided according to rules. The rules are likewise conditions. Mathematically is
proven by sentences according to (proof) rules.
While presuppositions should be always true, statements can be also wrong or to a certain
percentage true - mathematically probability. Generally, numbers from an interval (e.g. the
substance temperature or the day) can be assigned to things. One calls this scaling. Also the
assignment of vector spaces is meaningful (particularly with substances like e.g. space or
colour).
The scaling does not have to be made by real intervals in order to create a continuum. There
are also finite continuums. These do not have a "gap" between two (number) points. Points
are indivisible thereby and have an undifferentiated expansion. Our entire world is finally presentable.
This is not provable since we can think nor measure the infinity. Also as axiom
must apply that the world splits at each time into further ones after the laws (of nature).
The presuppositions and statements should be selected in such a way that they are as general
and comprehensive as possible, so that there are as few ones as possible and the
knowledge remains manageable. Probability of the truth should be indicated as far as possible
as a function of the main unit. Possibly it is to be estimated. As projection we receive the
usual statements. Also hypotheses can be selected as presuppositions (possibly probability
50%).
Relations can be requested by a (relational and/or object-oriented) data base. This can be
done fast if suitable indices exist (if necessary, as binary trees, as represented in "informatics").
Central and large data bases can receive inquiries after individual profiles. For the
marking out of the data, suitable ontologys can be used in order to implement methods like
e.g. inheritance.
How is knowledge stored?
There is a parallel increase and decrease of information through births and entering of new
substances and through death and elimination of substances (e.g. diseases, extinction of
species) in our world. The latter is thus an open system. Each brain builds up an individual
reference system (to substances), which can exist independently of matter: matter does not
suffice at all to describe it completely. The part of the brain, accessible to us, is the functional
one: What must be materially given so that the brain can work?
The individuality of the reference system consists in the selection and quality of the substances
and references. So the substance goal is e.g. for the one the overall goal of life, for
the other the highest individual happiness. The reference system is also languagedependent.
While a computer, up to now, knows only rules to denominate substances, man
has direct access to substances. It makes no sense to tie certain molecule forms to certain
© 1983-2012 by Boris Haase page 89 of 154

substances since substances have an own life (for example, in the form substance P is always
goal).
The real awareness is not encoded materially, although the brain regions are involved. Not
the sensual connotations, but the references and substances are crucial. The soul cannot be
destroyed materially because it is immaterial (references and substances). It cannot be located
materially. Since the potential activities of the mind are illimitable, but the awareness is
finite, the determinism is needed. The extensive orientation by the basic needs is indeed
possible, but inadequate since man wants to be satisfied mentally and emotionally.
Since man cannot determine himself due to zis insufficient skills, only L or the divine instance
are qualified for this. This is not a makeweight function, but crucial for the whole issue: Everyone
is experiencing the meaningful to zer. However, it is a mutual process in that the person
has a decisive part: Ze determines by zer behaviour how L or the divine instance can
accommodate zer. Every creature and also the divine instances orientate themselves upwards.
Only L at the top has all liberties, which also make a successful life possible to zer.
How is knowledge to represent?
It is important, first to figure out what knowledge is important at all, and one gets to know this
best in a relationship with L. Presupposition is that one views the world right and positions
oneself properly in it. Who attaches importance to too many things that have none will fail in
this world more or less. Then is to consider what contribution oneself can make to knowledge
representation. It depends on talent.
Knowledge representation presupposes always assessments on the status of knowledge.
Here should the own self should be as possible excluded and priority given to the things
themselves and the importance they have for others. If one has collected knowledge according
to priority, it is to edit and represent according to its relevance. The most important content
belongs at the beginning, the least important at the end of the whole.
Knowledge is to represent adapted to the target group. It is therefore necessary to be exactly
clear about this. The higher the level of the target group, the shorter one can make it, and
vice versa. The increasing intelligence of the population makes it possible to focus more and
more on the actual message. An appropriate comment can take over a clarifying representation
for the less intelligent.
Who works at the highest level, may also represent at the highest level. However, this must
be based on a realistic and verifiable assessment. The highest level is most condensed and
of the highest expressiveness and universality. This will be only achieved from a very good
relationship with L. Many quotations and examples cannot be found here, but an original representation,
which reflects the greatly the divinity of L.
Who works at a lower level should also try to acquit zerself as well as it goes. It is not about
creating the greatest possible extent, but as much quality as possible. Recipients take with
good reason offence when they are crushed with mass, which is of low quality. A unobjectionable
line of argument should be a matter of course. One can contribute all the qualities
from the relationship with L.
A critical self view avoids making unnecessary mistakes. Before publishing, the representation
should be carefully counter-checked and corrected, if necessary. The means of an attractive
and educationally well constructed representation should be used. A timeless representation
is preferable to a fashion-specific one, if the effect should persist for a longer period,
or a frequent adjustment is to be avoided.
© 1983-2012 by Boris Haase page 90 of 154

The more important a representation is, the larger and more carefully the circle is to choose
who should be entrusted with the publication. Only a good translation preserves the quality, if
it should be necessary. All parties involved must be well coordinated, possibly by a qualifiedly
controlled project. Who has not to live from zis publication, will also demand no price. If
ze does it anyway, it is to make as low as possible.
© 1983-2012 by Boris Haase page 91 of 154

Physics
Below oscillations, as result of Jugend forscht 1983, an approximate formula, derived by differentiation,
for the periodic time of selected oscillations of a mass point in the plane is deduced,
which avoids the exact but cumbersome integration. The periodic time for the
mathematical pendulum is experimentally checked. For the universe, the cube and the
sphere model isomorphic to it are presented.
© 1983-2012 by Boris Haase page 92 of 154

Oscillations
Youth researches 1983
Subject area physics
A novel method for the determination of the periodic time of the mathematical pendulum with
large amplitudes and the discussion for the applicability on other selected oscillations of the
plane
Compiled by Boris Haase (18),
Theodor-Heuss-Gymnasium in Göttingen
Abstract of the present paper
The oscillation period of mass points on curved oscillation ways in the vertical plane - like
e.g. the mathematical pendulum and the cycloid pendulum -, is to be computed in the present
paper in a simpler way than so far.
Most of these oscillation periods are - if the mass point on the oscillation way is far from the
rest position, whose lowest point - dependent on this distance, which makes the computation
more difficult generally.
In order to be able to compute an of this distance, the amplitude, independent periodic time,
one must know except the mass only the direction parameter, the quotient from repelling
force and corresponding amplitude respectively direction way.
This knowledge is extended and applied in this paper to the oscillation period dependent on
its amplitude.
Here partially differences result to the conventional methods - by the example of the mathematical
pendulum up to at the most one per cent with 90° of amplitude - partly do not as by
the example of the cycloid pendulum however. To the likewise treated ellipse pendulum no
literature data could be found.
In the experimental part the calculated periodic time for the mathematical pendulum in consideration
of the sources of error and the measuring accuracy could be confirmed.
The author comes to the conclusion that the independently developed procedure could by all
means be used in physics.
© 1983-2012 by Boris Haase page 93 of 154

Table of contents
1.
1.1.
1.2.
2.
2.1.
2.1.1.
2.1.2.
2.1.3.
2.1.4.
2.2.
2.2.1.
2.2.2.
2.3.
2.4.
3.
3.1.
4.
Introduction
Reason and Basic Idea
Presuppositions
Main Part
Theoretical Solution of the Problem
General Solution
The Mathematical Pendulum
The Cycloid Pendulum
The Ellipse Pendulum
Experiment to the Mathematical Pendulum
Experimental Setup
Test Procedure and Results
Calculations of Errors
Discussion
Conclusion
Critical Appreciation of the Paper
Appendix
- Figures
- Auxiliary Calculations
- Test devices
- Tables
5. Bibliography
1. Introduction
1.1. Reason and Basic Idea
The periodic time of the mathematical pendulum with large amplitudes was determined so far
by quite difficult procedures of the infinitesimal analysis and series expansion. The in the
present paper developed new procedure for the determination of the periodic time for selected
oscillations of the plane is to simplify the calculation method on the one hand, in addition
be compared regarding his accuracy by two examples with the old procedure.
Basic idea is the simultaneous simulation of the respective pendulum oscillation by a
straight-lined harmonic oscillation (spring pendulum, oscillator).
1.2. Presuppositions
All selected oscillations emanate from a mass point, which is to swing in the vertical plane at
a thread without mass around a fix point. The pendulum thread may be pulled to the side
here - seen from the rest position - at the most by 90°, since the maximally repelling force
must lie in the initial height, in which no additional acceleration is to arise.
In order to prevent a free fall, otherwise bars would have to be used instead of threads,
which could however not (as necessary) be huddled against evolutes of the oscillation ways.
© 1983-2012 by Boris Haase page 94 of 154

Despite the huddling against for simplification the length of the pendulum in rest position is
assumed.
The radius of curvature of the oscillation way must remain either constant from the rest position
or be continuously reduced, so that a free fall is likewise prevented.
Friction and damping aspects are to be neglected.
Otherwise further computations are necessary for the periodic time, which would go however
beyond the scope of this paper.
2. Main Part
2.1. Theoretical Solution of the Problem
2.1.1. General Solution
The periodic time of a harmonic oscillation is given by:
m
(a)T �2 � . D
After the principle of conservation of energy holds:
(b) ½ m v 2 = ½ D s 2 = m g h.
During an oscillation form the potential energy Wpot and the kinetic energy Wkin the constant
sum:
(c) Wpot + Wkin = Wpot 0 .
Wpot 0 is to be expressed now by the tension energy Wten, in order to determine a direction
parameter D(�0), dependent on the amplitude. D(�0) is to be inserted then into the formula
(a) for the determination of the periodic time.
In addition an ersatz movement of the mass m is necessary by force F on the direction way
s. It applies:
(d) D = F/s (Hooke's law) and
(e)F �ma �ml � �Newton �.
In the further one always harks back to the direction parameter D of the plane thread pendulum
with minimum amplitude. Here applies to the repelling and to the oscillation way tangential
force FR, since the normal force is compensated by the tension force of the thread (1, 2):
(f)FR �mgsin � �� ml � .
From this follows:
g
(g) �� sin � . l
For smallest amplitude angles � sin� can be replaced by �, and the conditions apply to the
harmonic oscillation. Therefore is:
2
(h)�� � �
and from (g) follows:
Thus applies:
g
(i) �� . l
© 1983-2012 by Boris Haase page 95 of 154

© 1983-2012 by Boris Haase page 96 of 154
2
g
l
(j)D � m� � m .
For larger amplitudes the direction parameter D must consist of the product of the direction
parameter for the harmonic oscillation with a function value f(�0) of the amplitude angle �
determining the inharmonic oscillation.
One writes:
g � l �
(k)D( � ) � m f( � ).
0 0
The function value f(�0) is not however defined for the harmonic condition of the energy theorem,
so that it must cancel itself during an introduction. With s = x l applies:
f( �0
)mxg 2
(xl)
1
(l) xl � mgh.
2 f( � )
0
Hereby the not changing direction way s can be computed by the energy theorem, if one assigns
the function value f(�0) to the repelling force FR. With
arises for the direction way:
� �
1 g 2
2 l
m s mgh �
(m)s � 2lh.
The repelling force FR must be developed thus independently of the energy theorem. It is
rather fixed by the initial oscillation as the in the initial height of the oscillation way tangential
attacking and thus maximally repelling force. From
one obtains the periodic time with (a) and (d):
(n) FR = (-) m a
2lh
(o)T �2 � .
a
Concretely the direction way s represents with (m) the chord of a circle with the radius l.
Since this circle is circle of curvature for the rest position of the oscillation way, this chord
must lead from one point of the circular path in the initial height h to the rest position.
The simplest form of an oscillation way which aligns with the circle of curvature and possesses
a punctiform evolute is those of the mathematical pendulum (fig. 1). This is to be first
treated therefore.
2.1.2. The Mathematical Pendulum
From fig. 1 one obtains for the direction way s:
�0
� 2 �
s � 2sin l.
With (f) applies to the maximally repelling force FR:

The periodic time is with (a) and (d) therefore:
2.1.3. The Cycloid Pendulum
FR = (-) m g sinφ0.
l
T �2 � .
cos g
© 1983-2012 by Boris Haase page 97 of 154
�0
� 2 �
To the common cycloid (fig. 2) the parameter equation (2) applies:
For the radius of curvature � one obtains:
x = a (� - sin�) und y = a (cos� - 1).
� � 2 �
�� 4asin .
Since the angles � increase from the initial height h to the rest position with � = � respectively
the sine decreases from �/2 after exceeding of the rest position to the reversal point again,
the conditions for the computation of the periodic time are fulfilled.
The initial height is:
If one inserts h in (m), applies with l = 4 a:
h = 2 a + y = a (cos�0 + 1).
� �
cos � �1 �
2 2
0 0
s �l� cos l.
Since the tangential acceleration bt works always vertically to the radius of curvature �, one
obtains for it:
�0
� �
b �� cos g.
t 2
If �0 = 0 holds, then bt = g holds, if �0 = � holds, then bt = 0 holds. Therefore must hold the
multiplier alpha = 1 and apply:
With (o) arises finally for the periodic time:
�0
� �
b �� cos g.
t 2
l T �2 � . g
This was already proven before by Huygens centuries ago.
2.1.4. The Ellipse Pendulum
To the ellipse (fig. 3) the parameter equation (3) applies:

2 2
x y
� � 1.
2 2
a b
For the radius of curvature � results after differentiation (see appendix):
��
� � 3
4 2 2 2 2 2
a �ax�bx From the rest position with x = 0 to the reversal points x increases, and since a 2 x 2 > b 2 x 2
holds, the radius of curvature is continuously reduced. In the rest position � is therefore:
With
the initial height h is:
� � �
© 1983-2012 by Boris Haase page 98 of 154
4
ab
2
a
l .
b
x
y � �b 1� a
2
2
� 2 �
x
h � b � y � b�1�1 � �.
� 2
a �
� �
With (m) arises therefore for the direction way s:
2 2
� �
s � 2a a � a � x .
Thus the direction way is independent of the semi-minor axis of the ellipse. The tangential
acceleration bt is (after fig. 3):
With (o) one obtains for the periodic time:
bxg
bt � cos� g �
.
4 2 2 2 2
a �ax�bx .
� �
4 2 2 2 2 2 2
a � a x � b x 2a a � a � x
T �2 �
bxg
.
For x = 0 the periodic time is not defined, for very small x applies however:
2
a l
T � 2� � 2 � .
bg g
For x = a the proposition results: The periodic time on an ellipse with maximum amplitude is
independent of the semi-minor axis.
2.2. Experiment to the Mathematical Pendulum

For temporal reasons the experimental part was limited to the mathematical pendulum. Not
only making of evolutes would be on the other hand very complex, but during the cycloid respectively
ellipse oscillation also larger sources of error would be opened. To this the difficulty
belongs to let the pendulum swing exactly to the evolute, since already after few oscillations
the pendulum leaves the vertical plane. In addition impulse respectively friction forces
arises with the beginning of the swinging and in the support, which with large amplitudes the
respective pendulum let become the mathematical pendulum.
The latter can be regarded therefore as part for the whole.
2.2.1. Experimental Setup
Two bars of a meter are connected with a third and four sleeves and pushed symmetrically
through two ceiling hooks. In the centre additionally a protractor and the support for the pendulum
thread of 1.60 m length are fastened.
An air cushion lane is placed in such a way parallel to it on the bench that its centre is vertically
under the point of the protractor. An on the centre placed lane carriage of 0.2 kg mass
is clamped in such a way by two springs that between the clamping at the end of the bench
and the carriage a direction parameter of 2 N/m prevails.
A stop watch is set up ready to hand by the initial height of the pendulum and the carriage.
An illustration to the experiment is on the title page. In the appendix also all used devices are
specified.
2.2.2. Test Procedure and Results
First was convinced by the independence of the periodic time of the mass of the pendulum,
as once one approx. 5 kg heavy ball, another time the lane carriage weighted on 1 kg of
mass were fastened to the pendulum thread. The difference of the measured periodic time
amounted to hundredths a second on each of the ten periods.
During the simulation of the mathematical pendulum by the harmonic oscillator the time difference
per oscillation amounted to 0.6 s (back and forth) with ten oscillations and 60° of
maximum amplitude of the pendulum.
For the computation of the mass of the harmonic oscillator the formula was used:
2lD
m � .
cos g
© 1983-2012 by Boris Haase page 99 of 154
�0
� 2 �
The latter can be determined directly from the periodic times for the two systems.
Here the direction parameter D0 for the oscillator is the double of the spring constants equal
in size of the used tension springs. The periodic time of the oscillator is therefore:
m
T �2 � (4).
2D
The periodic time of the mathematical pendulum calculated above is:

l
T �2 � .
cos g
© 1983-2012 by Boris Haase page 100 of 154
�0
� 2 �
The damping of the pendulum during a amplitude of 60° amounted to 1°, those of the oscillator
0.01 m during a amplitude of 0.9 m.
The measured values for amplitudes of the mathematical pendulum from 0° to 90° are specified
in tab. 1 in the appendix.
2.3. Computations of errors
The periodic time of the mathematical pendulum became so far specified over the elliptical
integral
with
(2):
�
2
�
0
d�
2 2
1�ksin� 0 � 2 �
k sin �
�
2 2 2 2
13 � 4 13 � �5
2
� � � � � � � � � � �
T � 2� 1� k � k � k � ... .
l 1
g 2 2 4 2 4 6
In order to be able to compare directly with the new formula for the periodic time:
the function value
l
T �2 � .
cos g
f( � ) �
0
�0
� 2 �
1
0 � 2 �
cos �
is converted with the help of the series with |x| < 1:
2 3
p p(p �1)x (1� x) � 1� px �
1� 2
and the relationship:
p(p �1)(p � 2)x
�
1� 2 � 3
� ... (2)
f( 0 )
1
4
2
1 sin 0 �
� �
�
with
into the comparison series:
�0
� 2 �
� 2 �
2 2
x � �sin � � k
2 2
k 15 � k 15 � �9
k
� � � � � � � � � �
2 4 6
1 � � � � ...
2 12 � 2 12 � �3
2
From this results that the two series correspond up to the first square member. If one divides
the old by the new series and subtracts 1, then results the after the amount smaller series of
the relative error:

1 4 1 6 231 8
64 64 16384
k � k � k � ... .
If one divides in reverse with same subtraction, then the relative error is larger:
1 4 1 6 235 8
64 64 16384
k � k � k � ... .
The number of the absolute error arises as a result of subtraction of the old from the new
series:
1 4 5 6 335 8
k � k � k � ... .
64 256 16384
The values for selected angles from 0° to 90° of all series specified here are held in the appendix
in tables.
2.4. Discussion
Here is once to think about the proportionalities arising in the formula:
T �2� First it is to be noted that the direction way s is not proportional to the acceleration a of the
repelling force FR, but the function value f(�0), contained in a, must be considered.
The length of the oscillation way is adapted over the direction way: If the initial height h is
very small, becomes the distance to cover on the oscillation way in y-direction and concomitantly
the periodic time smaller.
If the oscillation way is very flat in addition, the small initial height confronts a large pendulum
length, so that one obtains a mean for the length of the direction way, as it appears extra
clearly with maximum amplitudes of the ellipse pendulum.
With highly curved oscillation ways and large initial heights as with the mathematical pendulum
the periodic time is relatively larger.
In the direct proximity of the rest position the numerical values of direction way and acceleration
cancel out, so that the direction way becomes the length l of the pendulum and the acceleration
becomes the standard acceleration due to gravity g.
In the rest position itself the periodic time is strictly taken not defined, because the initial
height h and the acceleration a become there zero.
The larger the acceleration a is, the smaller is the periodic time, otherwise reverse conditions
are present.
These realisations could be relative well confirmed in the experiment to the mathematical
pendulum.
3. Conclusion
In the review can be said that the real approach agrees not completely with in this for clarity
reasons stated.
© 1983-2012 by Boris Haase page 101 of 154
2lh
a

Thus only the problem of the mathematical pendulum was solved and then a general problem
solution was established. All periodic times were computed without knowledge of the
periodic times indicated in the corresponding literature, their insight like the experiment took
place only weeks later.
The calculation method could be indeed very simplified and regarding the accuracy to the old
procedure the margin of error of 0.01 respectively one per cent did not need to be exceeded.
Here the ellipse pendulum could not be incorporated, since about its periodic time no literature
data could be found.
Most likely the margin of error will shift however upward, since the mathematical pendulum
as special case of the ellipse pendulum, whose periodic time can be transferred with equal
long semi axes into those of the mathematical pendulum, possesses already a deviation from
scarcely one per cent with maximum amplitude in respect of its periodic time.
The uncontradictedness of the periodic time of the cycloid pendulum to the literature data is
however given.
3.1. Critical Appreciation of the Paper
Without doubt the evolutes problem is not yet completely solved. If one does not presuppose
anymore the pendulum length in rest position, one must perhaps nevertheless hark back to
procedures of the infinitesimal analysis and series expansion, in order to obtain a larger accuracy.
Thereto however is contradictory on the one hand the mathematical pendulum, on the other
hand the Cycloid pendulum.
With the first a distinct evolute is missing despite deviation, with the latter exists a deviation
despite the presence of an evolute.
Thus the new procedure must be considered as independent.
The measurements to further periodic times than that of the mathematical pendulum unfortunately
missing in this paper would afford a more exact clarifying of circumstances. Here
however very high demands are to be made on the measuring accuracy and the run of the
experiments.
Altogether the procedure developed in this paper requires a certain adjustment in the way of
thinking, yet it should be able to be applied due to the obtained good results in physics.
4. Appendix
Figures
© 1983-2012 by Boris Haase page 102 of 154

© 1983-2012 by Boris Haase page 103 of 154

All constructions took place by (9).
Auxiliary Calculations
The general formula (3) applies for the radius of curvature:
��
� � 3
2 2 2
x � y
xy � yx
The common cycloid has the parameter equation (2):
For
one can write therefore
With
x = a (� - sin�) and y = a (cos� - 1).
� � 3
2 2 2
x � y
2 2 2 2 2 2 2 2
�a � 2cos �a � cos �a � sin �a � � �2a � 2cos � a �
© 1983-2012 by Boris Haase page 104 of 154
.
3 3
2 2
2 2
xy � yx � (a � cos� a)( �cos �a) � ( �sin �a)sin �a � a � cos� a
applies thus to the radius of curvature �:
� � 2 �
� � 2a 2(1� cos �) � 4asin .
If one writes with the ellipse temporarily: x = sin φ a and
then arises:
Thereby the radius of curvature is:
2
x y � �b 1� 2 � �cos � b,
a
xy � yx � cos� a(cos � b) � sin� b( �sin � a) � ab.
��
� � 3
2 2 2 2 2
cos � a � sin � b
If one revokes the transformation, one obtains after extension of the fraction with a 3 for �:
��
ab
� � 3
4 2 2 2 2 2
a �ax�bx The evolute of the common cycloid is likewise a cycloid with same a (5). To the evolute for
the ellipse applies however (6):
2 2 3
(a � b )cos t
��
a
And
4
ab
.
.

with x = a cos t and y = b sin t.
��
2 2 3
(a � b )sin t
b
In order to be able to compute the tangential acceleration bt of the ellipse, the following initial
considerations are necessary:
From this follows directly:
For
one can write after extending with
2 2
a � x q
tan � � � .
x 2 2
a � x
2 2
a � x
q � .
x
cos�
�
y
�
y
q y
�a �
�
� x
x
�
�
�
2 2
�
2
2 2
ax
2 2
a � x
bx
cos ��
.
4 2 2 2 2
a �ax�bx © 1983-2012 by Boris Haase page 105 of 154
� y
To convert the formula for the periodic time of the ellipse pendulum:
T �2� 2
� �
4 2 2 2 2 2 2
a � a x � b x 2a a � a � x
into those of the mathematical pendulum, let x = sin(�0) a and a = b = 1. Thus applies:
Therefore finally is:
bxg
� 2
2
x �
a 2�1� 1� �
� 2
a �
l 2(1�cos �0)
� �
T � 2� � 2 �
.
xg sin� g
l
T �2 �
.
cos g
�0
� 2 �
0

Test devices
2 table clamps for the bench with two holders for the springs
2 1 m long tension springs with a spring constant of approx. 2 N/m and a diameter of
approx. 0.01 m
1 2 m long air cushion lane with air regulator
2 lane carriages with blind and external hook of each 0.2 kg of mass
1 sphere mass of approx. 5 kg of mass
1 pendulum thread of at the most 1.60 m length
1 stop watch
2 ceiling hooks
1 up to 2 m extendable support with holder
7 Sleeves
7 bars with twice 1 m, once 0.6 m, twice 0.5 m, once 0.1 m and once 0.2 m length as angle
bars
1 clamp for protractor with small piece of wood
1 protractor
1 adhesive tape
as well as various burden weights
Tables
Tab. 1
�0/° Texp/s Tthn/s Ttha/s �Tan/% �Taa/%
90 2.95 3.02 3.00 2.26 1.52
80 2.87 2.90 2.89 1.02 0.58
70 2.78 2.80 2.80 0.86 0.61
60 2.72 2.73 2.72 0.26 0.13
50 2.65 2.67 2.66 0.60 0.54
40 2.61 2.62 2.62 0.31 0.29
30 2.58 2.58 2.58 0.09 0.08
20 2.55 2.56 2.56 0.29 0.29
10 2.52 2.54 2.54 0.90 0.90
5 2.51 2.54 2.54 1.15 1.15
Texp = experimentally determined periodic time (average values)
Tthn = theoretical periodic time by the new procedure
Ttha = theoretical periodic time by the old procedure
�Tan = absolute difference of Texp and Tthn with Tthn as reference value
�Taa = absolute difference of Texp and Ttha with Ttha as reference value
Here are:
l = 1.60 m
g = 9,80665 m/s 2
© 1983-2012 by Boris Haase page 106 of 154

Tab. 2
�0/° f(T0)n f(T0)a �f(T0)rkl �f(T0)rgr �f(T0)a
90 1.18921 1.18034 0.74558 0.75118 0.88665
80 1.14254 1.13749 0.44214 0.44411 0.50517
70 1.10489 1.10214 0.24815 0.24877 0.27418
60 1.07457 1.07318 0.12916 0.12933 0.13879
50 1.05042 1.04978 0.06045 0.06049 0.06350
40 1.03159 1.03134 0.02418 0.02418 0.02494
30 1.01748 1.01741 8*10 -3 8*10 -3 8*10 -3
20 1.00768 1.00766 1*10 -3 1*10 -3 1*10 -3
10 1.00191 1.00191 1*10 -4 1*10 -4 1*10 -4
5 1.00048 1.00048 6*10 -6 6*10 -6 6*10 -6
4 1.00030 1.00030 3*10 -6 2*10 -6 2*10 -6
3 1.00017 1.00017 8*10 -7 7*10 -7 8*10 -7
2 1.00008 1.00008 3*10 -7 2*10 -7 2*10 -7
1 1.00002 1.00002 2*10 -7 1*10 -7 1*10 -7
0 1.00000 1.00000 0 0 0
f(T0)n = function value of the periodic time of the mathematical pendulum, with which the periodic
time of the Cycloid pendulums must be multiplied, by the new procedure
f(T0)a = the same by the old procedure
�f(T0)rkl = smaller relative difference of the two
�f(T0)rgr = larger relative difference of the two
�f(T0)a = absolute difference of the two
Here are all delta �f(T0)x specified in per cent.
5. Bibliography
1. Arnold, Günter
Formeln der Mathematik, Ed. by H. Netz
3 rd edition, 1977, Carl Hauser, München (9)
2. Beyer, William H. (Editor)
CRC Handbook of Mathematical Sciences
5 th edition, 1978, CRC Press Inc., 2255 Palm Beach Lakes Blvd. (8)
3. Deutsch, Harri (Editors)
Kleine Enzyklopädie Mathematik
2 nd newly arr. edition, 1980, Harri Deutsch, Thun, Frankfurt/M. (3)
4. Dorn, Friedrich / Bader, Franz
Physik in einem Band (4) und Physik-Oberstufe, Volume O (1)
Newly arr. edition, 1976, Hermann Schroedel, Hannover
5. Fichtenholz, G. M.
Differential- und Integralrechnungen 1
german orig. ed., 1964, VEB Deutscher Verlag der Wissenschaften, Berlin (6)
6. Franke, Hermann (Editor)
© 1983-2012 by Boris Haase page 107 of 154

dtv-Lexikon der Physik in 10 Bänden
3 rd newly arr. and ext. edition, 1970, Deutscher Taschenbuch Verlag, München (5)
7. Sieber, Helmut
Mathematische Begriffe und Formeln
1 st edition, 1973, Ernst Klett, Stuttgart (7)
8. Spiegel, Murray R.
Allgemeine Mechanik
German orig. ed., 1976, McGraw-Hill Inc., Düsseldorf (2)
© 1983-2012 by Boris Haase page 108 of 154

Addendum:
Today, I am certainly in a position to calculate the correct periodic times and to state the error
concerning my approximate formula.
It applies:
With x = x(t) and y = y(t) applies:
The approximate formula reads:
2
1 ds
0 � � 2 2
mgh mgh m .
dt
s0 x0 2 t0
2 2
8 1 8 1�y�8x�y T � ds dx dt.
g � � �
h � h g � y � y g � y � y
0 0 0 0 0 0
3 3
2 2 2 2 2 2 2 2
� � � � 0 � � �0��
� � 0 � 0 � 0 �
2lh 2 1 y (0) y 1 y 2 x(0) y(0) y x y
T � 2� � 2� � 2 �
.
a gy� y ��(0) gy x(0)y(0) � y(0)x(0)
With x = a sin φ, y = b - b cos φ,
0 0
© 1983-2012 by Boris Haase page 109 of 154
0 � 2 �
2 2 2 2 2 2
ds dx dy a cos b sin d , k sin �
� � � � � � � �
and
2 a � b
� � 2
a
exactly applies for the ellipse pendulum:
2 2
2 �0
2 2
8a 1� � sin �
T � d .
bg �
�
cos� � cos�
With ε 2 < 1 the calculation of the integral yields the series expansion:
0
1 2 2 2 9 4 3 2 4 3 4 4 6
� 4 64 8 4
�
2�a T � 1� k � � k � k � � k � � k � O (k ) .
bg
The series expansion of the approximate formula
reads:
T �
4 2 2
2 a 1 sin
� � � �
0 � 2 �
bgcos �
1 2 2 2 5 4 3 2 4 3 4 4 6
� 4 32 4 2
�
2�a T � 1� k � � k � k � � k � � k � O (k ) .
bg
Both formulas are identical up to the quadratic term as for the mathematical pendulum and
confirm the quality of the approximation procedure. To obtain a better approximate formula,
y(x) is to develop into a Taylor series around x = 0. For |y'| < 1, then numerator and denominator
of the integral can be developed into series and easily be integrated after multiplying
them out. Otherwise, the integral can be computed by numerical quadrature or by develop-
0
0

ment of a Taylor series of the integrand with arbitrary precision. The latter is always possible
by suitable substitution of x, and sufficient differentiability of the integrand. Interval arithmetic
secures the results.
My actual aim was less the calculation of concrete periodic times, but the mathematical reduction
of the difficult integration to a relatively easy differentiation (with simple integration).
Precisely this yields the just mentioned development of a Taylor series, which is possibly to
repeat for separate interval limits.
© 1983-2012 by Boris Haase page 110 of 154

Universe
The universe can be regarded both as infinite n-dimensional cube, as well - isomorphic defined
to it - as the n-dimensional sphere one obtains if one erects in the central point of the
cube in a further dimension a line of length 2 as the diameter of a unit sphere with shifted
central point and projects all points of the cube uniquely into the boundary of this sphere by
calculating the respective intersection points on the connecting line between cube points and
the end point of the erected line - the North Pole - with the spherical boundary. Thus, the
sphere has indeed finite extent and each point can be reached in finite time, but the spherical
boundary contains infinitely many points that lie closest to the North Pole.
The n dimensions include not only the space, but all scaled substances (see reference theory),
thus in particular the time. The beginning of the universe lies in the central point of the
cube; that is diametrically opposed to the North Pole at the South Pole. If one assumes a
beginning of time, the negative half-axis resp. its equivalent in the spherical boundary is
missing. Around the South Pole are the simplest worlds, around the North Pole the most
complex ones. With all these considerations, we should remember that L is not bound to any
model of the universe, but each model helps us to understand the universe better and has its
advantages and disadvantages. Its possible homogeneity speaks for the cube model, the
finite reachability of each substance point for the sphere model.
However, we cannot prove how big the radius of the universe at all is, but only of our one,
since we would need to know the coordinates that go beyond the three-dimensional space,
as follows from the n-dimensional sphere equation. Time and space intervals on the unit
sphere become shorter and shorter with time. This can be counteracted with the expansion
of time and space.
The length of small distances can only be measured as larger than the smallest distance, if
its total length makes up a smaller number of these distances than the number concerning
the length measured with the smallest distance as standard, which is less than or equal to
the total length. It is therefore definitely possible that a reduction towards the North Pole cannot
be measured.
With every expansion of the universe from the potential of L, the existing worlds slip towards
the South Pole. At the North Pole, the residence of L, the worlds are replenished from the
new world level. It was tacitly assumed that no dimension is distinguished from another one,
and deformations of the unit sphere or cube are implausible and unnecessary. For, an (almost)
arbitrary possibility of shaping the worlds in the universe remains unaffected. Nevertheless,
each world is strictly to investigate and to define by L, before it is released.
Mind that points in space have neither form nor extension, so one can push them together,
arbitrarily close. They are still something and may have distances with nothing in between. It
is our conception that can fill in the between, and provides extension. The faster moving universe
makes sense and is wanted by L. Skipping intervals can counteract a too-fast. Analogous
applies for all other substances. It is therefore important that L makes the laws of nature
appropriate. This applies particularly for chaotic or strongly inhomogeneous worlds, and
those with multiple time axes.
It is measurable, whether a world is homogenous or not. Every creature has deserved a
world in the universe according to its karma. A material world represents a simplification for
their (first) creatures in order to limit their possibilities because of lack of development. Each
world can become an immaterial one with extended rules, during higher development and
growing, usefully directed freedom. For the functioning, generally many rules are needed -
individually and in general, which must be transparent and efficient, as well as conceived and
supported by L.
© 1983-2012 by Boris Haase page 111 of 154

Politics
The contents of the politics of the religion of love are outsourced to www.relil.org.
© 1983-2012 by Boris Haase page 112 of 154

Religion
The contents of the religion of love are outsourced to the sites www.relil.eu, www.relil.net and
www.relil.de.
On www.relil.eu the contents are structured by topics and shall be sometime released in
book form.
By www.relil.net involves the Wiki RelilWiki and on www.relil.de one can listen to lectures.
© 1983-2012 by Boris Haase page 113 of 154

About me
Birth:
1964 in Kiel
Address:
Cranachstr. 4, D-63452 Hanau
Occupation:
Management assistant in data processing (IHK)
Studies:
Mathematics (minor subject informatics) and philosophy (minor subjects political science and
sociology) at the universities TU Clausthal, U Goettingen and FU Hagen
Work:
Clinical centre Hanau
Hobbies:
L, religion, inventing, internet and fitness
Largest existing misfortune:
Unjustness in the world
Favourite residence:
Berlin
Perfect luck:
To be with L
Most excusable defect:
Inability
Favourite person:
Albert Einstein
Unperson:
Adolf Hitler:
Male favourite characteristic:
Intellect
Female favourite characteristic:
Empathy
Favourite virtue:
Justice
Favourite activity:
Solving real problems
Favourite occupation:
Enunciator
Main characteristic:
© 1983-2012 by Boris Haase page 114 of 154

Dedication
Favourite characteristic of the friends:
Greatness
Largest own defect:
Pushing the boundary
Dream of the luck:
Finding fulfilment
Largest theoretical misfortune:
Non-existence of L
Missing characteristic:
Adeptness in dealing with others
Favourite colour:
Brown
Favourite object:
Computer
Largest defect of others:
Cruelness
Best reform:
Charter of the human rights
Most missing natural gift:
Mixing well
Wish to die:
Free at last
Present state of mind:
Exerted
Maxim:
Decide for you.
Motto:
Your mission protects you.
Visions:
Man becomes immortal. Ze is not any more in zis traditional shell but forms a unit with a supercomputer.
The diseases are vanquished. There are at the most still disturbances. The
metabolism of man is in line with each environment - also hostile ones like other planets. Ze
uses current skilfully. Ze integrates all positive substances of the reference theory. Ze communicates
telepathically and controls the telepathy.
Humans possess approximately the same intelligence since they need this for an equivalent
survival. Death is vanquished: Nobody becomes old. Tolerance is very important since wanting
A can have equivalent reasons in relation to not A. Animals and plants are integrated in
the metabolic politics and optimisation. There is a large religion into that all different can be
translated. With the language it is similar.
© 1983-2012 by Boris Haase page 115 of 154

Humans create themselves virtual spaces. The virtual spaces can use more dimensions than
the existing in nature. For this purpose, man must be able to combine matter arbitrarily. Ze
can build as many references as ze can use matter. The construction of arbitrary references
lets zer surmount arbitrary distances. Ze creates own time axes in that the time can proceed
with other speeds.
There is a uniform, central controlled human policy. The poverty is vanquished, the differences
between poor and rich also as far as possible. Wars do not take place since there is
nothing that is worth to fight for. The problem of the overpopulation is solved. The human
reproduction can take place also on non-sexual way. The genes are so far decoded that no
unmeant manipulation can take place.
True democracy prevails. Each human is involved after its qualifications in everything. Everyone
can qualify zerself for everything - completely after his notions. There is only one economic
system and one currency.
© 1983-2012 by Boris Haase page 116 of 154

Bibliography
1) Hamp, Vinzenz; Stenzel, Meinrad; Kürzinger, Josef (Hrsg.): Die Heilige Schrift des Alten
und Neuen Testamentes; 4. Aufl.; 1988; Pattloch Verlag; München; ISBN 3629052002; Bilder
von Rembrandt.
2) W.-Winter, L. (Bearb.); Ullmann, Ludwig (Übertr.): Der Koran - Das Heilige Buch des Islam;
1. Aufl.; 1986; Wilhelm Goldmann Verlag; München; ISBN 3442086132; Taschenbuch.
3) Grimm, Georg: Die Lehre des Buddho; 20. unveränd. Aufl.; 1979; R. Löwit; Wiesbaden;
ISBN 3894272120; Hrsg. von M. Keller-Grimm und Max Hoppe.
4) Fromer, Jakob (Übertr.): Der Babylonische Talmud; 2. Aufl.; 1988; Fourier-Verlag; Wiesbaden;
ISBN 3921695880; kommentierte Auswahl.
5) Franz, Albert; Baum, Wolfgang; Kreutzer, Karsten: Lexikon philosophischer Grundbegriffe
der Theologie; 2. Aufl.; 2007; Herder; Freiburg; ISBN 9783451290954; korrigierte Fassung
der Erstauflage.
6) Sharamon, Shalila; Baginski, Bodo J.: Das Chakra-Handbuch; 50. Aufl.; 2006; Windpferd;
Aitrang; ISBN 3893850384; Taschenbuch.
7) Alston, William P.: A Realist Conception of Truth; 1st Ed.; 1996; Cornell University Press;
Ithaca and London; ISBN 0801484103; Taschenbuch.
8) Cumpsty, John S.: Religion As Belonging; 1st Ed.; 1991; University Press of America;
Lanham; ISBN 0819183598; A General Theory of Religion.
9) Alston, William P.: Perceiving God; 2nd Printing; 1995; Cornell University Press; Ithaca
and London; ISBN 0801481554; The Epistemology of Religious Experience.
10) Stiver, Dan R.: The Philosophy of Religious Language; Reprint; 1997; Blackwell; Malden;
ISBN 1557865825; Sign, Symbol, and Story.
11) Fischer, Johannes: Theologische Ethik; 1. Aufl.; 2002; Kohlhammer; Stuttgart; ISBN
3170168916; Grundwissen und Orientierung.
12) Jörns, Klaus-Peter: Die neuen Gesichter Gottes; 1. Aufl.; 1997; C. H. Beck; München;
ISBN 340642936X; Was die Menschen heute wirklich glauben.
13) Krieg, Carmen; Kucharz, Thomas; Volf, Miroslav (Hrsg.): Die Theologie auf dem Weg in
das dritte Jahrtausend; 1. Aufl.; 1996; Chr. Kaiser; Gütersloh; ISBN 3579020080; Festschrift.
14) Anzenbacher, Arno: Einführung in die Ethik; 1. Aufl.; 1992; Patmos; Düsseldorf; ISBN
3491779251; Philosophische Grundlagenprobleme.
15) Sharma, Arvind (Ed.): Fragments of Infinity; 1st Ed.; 1991; Prism Press; Dorset; ISBN
1853270660; Essays in Religion and Philosophy.
16) Ratzinger, Joseph: Einführung in das Christentum; Neuausg.; 2005; Weltbild; Augsburg;
ISBN 382894949320; Benedikt XVI..
17) Ratzinger, Joseph: Glaube - Wahrheit - Toleranz; 2. Aufl.; 2003; Herder; Freiburg; ISBN
3451281104; Das Christentum und die Weltreligionen.
18) Ratzinger, Joseph: Jesus von Nazareth; 1. Aufl.; 2007; Herder; Freiburg; ISBN
9783451298615; Erster Teil von der Taufe im Jordan bis zur Verklärung.
19) Ratzinger, Joseph: Gott und die Welt; 1. Aufl.; 2000; Deutsche Verlags-Anstalt; Stuttgart
München; ISBN 3421054282; Glauben und Leben in unserer Zeit.
20) Szczesny, Gerhard; Wilhelm, Kurt: Die Antwort der Religionen; 1. Aufl.; 1964; Szczesny;
München; ASIN B0000BFUGR; 31 Fragen.
21) Drewermann, Eugen: Kleriker; 3. Aufl.; 1992; Deutscher Taschenbuch Verlag; München;
ISBN 3423300108; Psychogramm eines Ideals.
22) Smith, Huston: Eine Wahrheit viele Wege; 2. Aufl.; 1994; Hermann Bauer; Freiburg;
ISBN 3762604657; Die großen Religionen der Welt.
23) Hirsch, Eike Christian: Vorsicht auf der Himmelsleiter; 1. Aufl.; 1987; Hoffmann und
Campe; Hamburg; ISBN 3455086284; Auskünfte in Glaubensfragen.
24) Hick, John: Religion; 1. Aufl.; 1996; Diederichs; München; ISBN 3424013110; Die
menschlichen Antworten auf die Frage nach Leben und Tod.
25) Thomas, Gordon; Morgan-Witts, Max: Der Vatikan; Lizenzausg.; 1984; Manfred Pawlak;
Herrsching; ISBN 3881993223; Mechanismen kirchlicher Macht.
26) Trillhaas, Wolfgang: Religionsphilosophie; 1. Aufl.; 1972; Walter de Gruyter; Berlin; ISBN
3110038684; Lehrbuch.
© 1983-2012 by Boris Haase page 117 of 154

27) Vries, S. Ph. de: Jüdische Riten und Symbole; 9. Aufl.; 2003; Rowohlt; Reinbek; ISBN
3499187582; Taschenbuch.
28) Borchert, Bruno: Mystik; 1. Aufl.; 1997; Herder; Freiburg; ISBN 3451045300; Das Phänomen
- Die Geschichte - Neue Wege.
29) James, William: Die Vielfalt religiöser Erfahrung; 1. Aufl.; 1997; Insel; Frankfurt und Leipzig;
ISBN 345833484X; Mit einem Vorwort von Peter Sloterdijk.
30) Lanczkowski, Günter: Geschichte der nichtchristlichen Religionen; 1. Aufl.; 1989; Fischer;
Frankfurt am Main; ISBN 3596245648; aktualisierte und erweiterte Neuausgabe.
31) Küng, Hans: Christ sein; 3. Aufl.; 2004; Piper; München; ISBN 3492217362; Taschenbuch.
32) Küng, Hans: Existiert Gott?; 3. Aufl.; 2004; Piper; München; ISBN 3492221440; Antwort
auf die Gottesfrage der Neuzeit.
33) Küng, Hans: Das Christentum; 1. Aufl. Taschenbuch; 1999; Piper; München; ISBN
3492229409; Die religiöse Situation der Zeit.
34) Küng, Hans: Das Judentum; 1. Aufl. Taschenbuch; 1999; Piper; München; ISBN
3492228275; Die religiöse Situation der Zeit.
35) Küng, Hans: Der Islam; 1. Aufl. Taschenbuch; 2006; Piper; München; ISBN 3492247091;
Geschichte, Gegenwart, Zukunft.
36) Ruh, Ulrich; Seeber, David; Walter, Rudolf (Hrsg.): Handwörterbuch religiöser Gegenwartsfragen;
2. Aufl.; 1989; Herder; Freiburg; ISBN 3451216124; Sonderausgabe.
37) Adam, Gottfried; Lachmann, Rainer (Hrsg.): Religionspädagogisches Kompendium; 5.
neubearb. Aufl.; 1997; Vandenhoeck & Ruprecht; Göttingen; ISBN 352561330X; Taschenbuch.
38) Henning, Christian; Murken, Sebastian; Nestler, Erich (Hrsg.): Einführung in die Religionspsychologie;
1. Aufl.; 2003; Ferdinand Schöningh; Paderborn; ISBN 350699011X; Taschenbuch.
39) Kühn, Ulrich: Christologie; 1. Aufl.; 2003; Vandenhoeck & Ruprecht; Göttingen; ISBN
3525032412; Taschenbuch.
40) Stolz, Fritz: Grundzüge der Religionswissenschaft; 2., überarb. Aufl.; 1997; Vandenhoeck
& Ruprecht; Göttingen; ISBN 3525032919; Taschenbuch.
41) Moeller, Bernd: Geschichte des Christentums in Grundzügen; 6., verb. Aufl.; 1996;
Vandenhoeck & Ruprecht; Göttingen; ISBN 3525032803; Taschenbuch.
42) Jäger, Christoph (Hrsg.): Analytische Religionsphilosophie; 1. Aufl.; 1998; Ferdinand
Schöningh; Paderborn; ISBN 3506994891; Taschenbuch.
43) Fraas, Hans-Jürgen: Die Religiosität des Menschen; 1. Aufl.; 1990; Vandenhoeck & Ruprecht;
Göttingen; ISBN 3525032749; Ein Grundriss der Religionspsychologie.
44) Johann-Adam-Möhler-Institut (Hrsg.): Kleine Konfessionskunde; 2., durchges. und akt.
Aufl.; 1997; Bonifatius; Paderborn; ISBN 3897100002; Taschenbuch.
45) Lanczkowski, Günter (Bearb.): Meyers Kleines Lexikon Religionen; 1. Aufl.; 1987; Bibliographisches
Institut; Mannheim; ISBN 3411026588; hrsg. von d. Red. für Religion und Theologie.
46) Beyerhaus, Peter; Padberg, Lutz E. v. (Hrsg.): Eine Welt - eine Religion?; 1. Aufl.; 1988;
Schulte & Gerth; Asslar; ISBN 3877397751; Die synkretistische Bedrohung unseres Glaubens
im Zeichen von New Age.
47) Paden, William E.: Am Anfang war Religion; Dt. Erstausg.; 1990; Gerd Mohn; Gütersloh;
ISBN 3579007874; Die Einheit in der Vielfalt.
48) Möhler, Johann Adam; Newman, John Henry; Guardini, Romano et al.: Gott in dieser
Zeit; 1. Aufl.; 1990; Matthias Grünewald; Mainz; ISBN 3786715114; Eine Herausforderung
der Theologie.
49) Schweitzer, Albert: Das Christentum und die Weltreligionen; 2., unveränd. Aufl.; 1984; C.
H. Beck; München; ISBN 3406067816; Zwei Aufsätze zur Religionsphilosophie.
50) Mynarek, Hubertus: Ökologische Religion; 1. Aufl.; 1986; Wilhelm Goldmann; München;
ISBN 3442120055; Ein neues Verständnis der Natur.
51) Pöhlmann, Horst Georg: Der Atheismus oder der Streit um Gott; 5. Aufl.; 1986; Gerd
Mohn; Gütersloh; ISBN 3579052187; Taschenbuch.
© 1983-2012 by Boris Haase page 118 of 154

52) Lehmann, Karl: Es ist Zeit, an Gott zu denken; 2. Aufl.; 2000; Herder; Freiburg; ISBN
34515054; Ein Gespräch mit Jürgen Hoeren.
53) Khoury, Adel Th.; Hünermann, Peter (Hrsg.): Wer ist Gott?; 1. Aufl.; 1983; Herder; Freiburg;
ISBN 3451080796; Die Antwort der Weltreligionen.
54) Löhr, Gebhard: Gott - Gebote - Ideale; 1. Aufl.; 1991; Vandenhoeck & Ruprecht; Göttingen;
ISBN 3525335768; Analytische Philosophie und theologische Ethik.
55) Grün, Anselm; Sartorius, Christiane: Dem Himmel zur Ehre - Der Erde zum Zeichen; 3.
Aufl.; 1997; Herder; Freiburg; ISBN 3451237946; Menschliches Reifen im Ordensleben.
56) Hawking, Stephen W.: Ist alles vorherbestimmt?; 1. Aufl.; 1996; Rowohlt; Reinbek; ISBN
3499220679; Sechs Essays.
57) Lyre, Holger: Informationstheorie; 1. Aufl.; 2002; Wilhelm Fink; München; ISBN
3825222896; Eine philosophisch-naturwissenschaftliche Einführung.
58) Reinhardt, Fritz; Soeder, Heinrich: dtv-Atlas zur Mathematik Band 1; 9. Aufl.; 1991; Deutscher
Taschenbuch Verlag; München; ISBN 3423030070; Grundlagen, Algebra und Geometrie.
59) Reinhardt, Fritz; Soeder, Heinrich: dtv-Atlas zur Mathematik Band 2; 5. Aufl.; 1984; Deutscher
Taschenbuch Verlag; München; ISBN 3423030089; Analysis und angewandte Mathematik.
60) Bronstein, Il'ja N. (Begr.); Grosche, Günter (Bearb.); Zeidler, Eberhard: Teubner-
Taschenbuch der Mathematik Teil 1; 1. Aufl.; 1996; Teubner; Leipzig; ISBN 3815420016;
Taschenbuch.
61) Grosche, Günter (Hrsg.): Teubner-Taschenbuch der Mathematik Teil 2; 7. Aufl.; 1995;
Teubner; Leipzig; ISBN 3815421004; vollst. überarb. und wesentlich erw. Neufassung.
62) Grosche, G.; Ziegler, V. (Hrsg.): Taschenbuch der Mathematik; Nachdruck der 20. Aufl.;
1983; Harri Deutsch; Thun; ISBN 3871444928; Neubearbeitung, ältere Ausgabe.
63) Bronstein, I. N.; Semendjajew, K. A.: Taschenbuch der Mathematik; 3. Aufl.; 1984; Harri
Deutsch; Thun; ISBN 3871444936; Ergänzende Kapitel.
64) Schmidt, Werner: Lehrprogramm Vektorrechnung; 1. Aufl.; 1978; Verlag Chemie; Weinheim;
ISBN 3527210741; Mit Beispielen aus der Physik.
65) Kleppner, Daniel; Ramsey, Norman: Lehrprogramm Differential- und Integralrechnung; 2.
Aufl.; 1982; Verlag Chemie; Weinheim; ISBN 3527210911; Taschenbuch.
66) Fischer, Gerd: Analytische Geometrie; 6., überarb. Aufl.; 1992; Friedrich Vieweg; Braunschweig;
ISBN 3528572353; Taschenbuch.
67) Guillen, Michael: Brücken ins Unendliche; 2. Aufl.; 1987; Deutscher Taschenbuch Verlag;
München; ISBN 3423106980; Die menschliche Seite der Mathematik.
68) Benesch, Hellmuth: dtv-Atlas zur Psychologie Band 1; 1. Aufl.; 1987; Deutscher Taschenbuch
Verlag; München; ISBN 3423032243; Tafeln und Texte.
69) Benesch, Hellmuth: dtv-Atlas zur Psychologie Band 2; 1. Aufl.; 1987; Deutscher Taschenbuch
Verlag; München; ISBN 3423032251; Tafeln und Texte.
70) Heinrich, Dieter; Hergt, Manfred: dtv-Atlas zur Ökologie; 3. Aufl.; 1994; Deutscher Taschenbuch
Verlag; München; ISBN 3423032286; Tafeln und Texte.
71) Abels, Heinz: Einführung in die Soziologie 1; 1. Aufl.; 2001; Westdeutscher Verlag;
Wiesbaden; ISBN 353113610; Der Blick auf die Gesellschaft.
72) Abels, Heinz: Einführung in die Soziologie 2; 1. Aufl.; 2001; Westdeutscher Verlag;
Wiesbaden; ISBN 3531136119; Die Individuen in ihrer Gesellschaft.
73) Jäger, Wieland: Reorganisation der Arbeit; 1. Aufl.; 1999; Westdeutscher Verlag; Wiesbaden;
ISBN 3531134736; Ein Überblick zu aktuellen Entwicklungen.
74) Soziologie, Arbeitsgruppe: Denkweisen und Grundbegriffe der Soziologie; 13. Aufl.;
1998; Campus Verlag; Frankfurt am Main; ISBN 3593347156; Eine Einführung.
75) Weber, Max: Soziologische Grundbegriffe; 6., erneut durchges. Aufl.; 1984; Mohr; Tübingen;
ISBN 3165448302; Taschenbuch-Sonderausgabe.
76) Bourdieu, Pierre: Die feinen Unterschiede; 1. Aufl.; 1987; Suhrkamp; Frankfurt am Main;
ISBN 3518282581; Kritik der gesellschaftlichen Urteilskraft.
77) Herfurtner, Rudolf: Gloria von Jaxtberg oder die Prinzessin vom Pfandhof; 1. Aufl.; 1988;
Thienemann; Stuttgart, Wien; ISBN 3522425006; Bilder von Reinhard Michl.
© 1983-2012 by Boris Haase page 119 of 154

78) Temming, Rolf L.: Illustrierte Geschichte der Eisenbahn; 1. Aufl.; 1976; Manfred Pawlak;
Herrsching; ASIN B0000BMJT1; ohne ISBN.
79) Shulman, Sandra: Geschichte der Astrologie; 1. Aufl.; 1978; Rheingauer Verlagsgesellschaft;
Eltville; ISBN 3881020187; Von der Antike bis zur Gegenwart.
80) Glück, Helmut (Hrsg.): Metzler-Lexikon Sprache; 2., überarb. und erw. Aufl.; 2000; Metzler;
Stuttgart, Weimar; ISBN 347601519X; Mit 70 Abbildungen, davon 17 Karten.
81) Prechtl, Peter; Burkard, Franz-Peter (Hrsg.): Metzler-Philosophie-Lexikon; 1. Aufl.; 1996;
Metzler; Stuttgart, Weimar; ISBN 3476012573; Begriffe und Definitionen.
82) Lutz, Bernd (Hrsg.): Metzler-Philosophen-Lexikon; 1. Aufl.; 1989; Metzler; Stuttgart; ISBN
3476006395; Dreihundert biographisch-weltgeschichtliche Porträts von den Vorsokratikern
bis zu den Neuen Philosophen.
83) Störig, Hans Joachim: Kleine Weltgeschichte der Philosophie; 17., vollst. überarb. und
erw. Aufl.; 1999; Kohlhammer; Stuttgart; ISBN 3170160702; gebunden.
84) Schmidinger, Heinrich: Metaphysik; 1. Aufl.; 2000; Kohlhammer; Stuttgart; ISBN
3170163086; Ein Grundkurs.
85) Heidegger, Martin: Sein und Zeit; 17. Aufl.; 1993; Niemeyer; Tübingen; ISBN
3484701226; gebunden.
86) Heidegger, Martin: Über den Humanismus; 9. Aufl.; 1991; Vittorio Klostermann; Frankfurt
am Main; ISBN 3465022742; broschiert.
87) Hüntelmann, Rafael: Existenzontologie; 1. Aufl.; 1997; Röll; Dettelbach; ISBN
392752283X; gebunden.
88) Siegmann, Georg: Plotins Philosophie des Guten; 1. Aufl.; 1990; Königshausen & Neumann;
Würzburg; ISBN 3884794671; Eine Interpreatation von Enneade VI 7.
89) Hartmann, Nicolai: Der Aufbau der realen Welt; 3. Aufl.; 1964; Walter de Gruyter; Berlin;
ASIN B0000BJ3UP; Grundriss der allgemeinen Kategorienlehre.
90) Weyl, Hermann: Philosophie der Mathematik und Naturwissenschaft; 7. Aufl.; 2000;
Oldenbourg; München; ISBN 3486467972; Scientia Nova.
91) Trillhaas, Wolfgang: Ethik; 3., neubearb. und erw. Aufl.; 1970; Walter de Gruyter; Berlin;
ASIN B0000BTTHQ; Sondereinband.
92) Balzer, Wolfgang: Die Wissenschaft und ihre Methoden; 1. Aufl.; 1997; Alber; München;
ISBN 3495478531; Grundsätze der Wissenschaftstheorie.
93) Körner, Stephan: Erfahrung und Theorie; 1. Aufl.; 1970; Suhrkamp; Frankfurt am Main;
ISBN 3518570633; Ein wissenschaftstheoretischer Versuch.
94) Weizsäcker, Carl Friedrich von: Zeit und Wissen; 1. Aufl.; 1992; Carl Hanser; München,
Wien; ISBN 3446163670; gebunden.
95) Weizsäcker, Carl Friedrich von: Bewusstseinswandel; 1. Aufl.; 1988; Carl Hanser; München,
Wien; ISBN 3446146490; gebunden.
96) Swinburne, Richard: Gibt es einen Gott?; 1. deutsche Aufl.; 2006; Ontos; Heusenstamm;
ISBN 3937202919; Englisch: Is there a God?, 1996.
97) Russ, Jaqueline: Les méthodes en philosophie; Cinquième tirage; 1992; Armand Colin;
Paris; ISBN 220033088X; Taschenbuch.
98) Jonas, Hans: Wissenschaft als persönliches Erlebnis; 1. Aufl.; 1987; Vandenhoeck &
Ruprecht; Göttingen; ISBN 3525013426; Sammlung Vandenhoeck.
99) Brüntrup, Godehard: Das Leib-Seele-Problem; 1. Aufl.; 1996; Kohlhammer; Stuttgart;
ISBN 3170140051; Eine Einführung.
100) Ulke, Karl-Dieter: Vorbilder im Denken; 1. Aufl.; 1988; Kösel; München; ISBN
3466400627; 32 Porträts großer Philosophen.
101) Kühn, Manfred: Kant; 1. Aufl.; 2003; C. H. Beck; München; ISBN 3406509185; Eine
Biographie.
102) Sollbach, Armin: Erhabene Kunst der Vernunft; 1. Aufl.; 1996; Hahner Verlagsgesellschaft;
Aachen-Hahn; ISBN 3892940703; gebunden.
103) Gaarder, Jostein: Sofies Welt; 1. Aufl.; 1993; Carl Hanser; München, Wien; ISBN
3446173471; Roman über die Geschichte der Philosophie.
104) Berner, Knut: Theorie des Bösen; 1. Aufl.; 2004; Neukirchener Verlag; Neukirchen-
Vluyn; ISBN 3788720476; Zur Hermeneutik destruktiver Verknüpfungen.
© 1983-2012 by Boris Haase page 120 of 154

105) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band I/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047211; Vorgeschichte - Frühe
Hochkulturen.
106) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band I/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047211; Vorgeschichte - Frühe
Hochkulturen.
107) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band II/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047238; Hochkulturen des mittleren
und östlichen Asiens.
108) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band II/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047246; Hochkulturen des mittleren
und östlichen Asiens.
109) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band III/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047254; Griechenland - Die hellenistische
Welt.
110) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band III/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047262; Griechenland - Die hellenistische
Welt.
111) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band IV/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047270; Rom - Die römische
Welt.
112) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band IV/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047289; Rom - Die römische
Welt.
113) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band V/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047297; Islam - Die Entstehung Europas.
114) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band V/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 35480472997; Islam - Die Entstehung
Europas.
115) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VI/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047319; Weltkulturen - Renaissance
in Europa.
116) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VI/II; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047327; Weltkulturen - Renaissance
in Europa.
117) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VII/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047335; Von der Reformation
zur Revolution.
118) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VII/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047343; Von der Reformation
zur Revolution.
119) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VIII/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047351; Das neunzehnte Jahrhundert.
120) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band VIII/2;
Taswchenbuchausgabe; 1976; Ullstein; Frankfurt am Main; ISBN 3548147364; Das neunzehnte
Jahrhundert.
121) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band IX/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047378; Das zwanzigste Jahrhundert.
122) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band IX/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047384; Das zwanzigste Jahrhundert.
123) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band X/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047394; Die Welt von heute.
© 1983-2012 by Boris Haase page 121 of 154

124) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band X/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047408; Die Welt von heute.
125) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band XI/1; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047416; Summa Historica.
126) Mann, Golo; Heuss, Alfred (Hrsg.): Propyläen Weltgeschichte Band XI/2; Taschenbuchausgabe;
1976; Ullstein; Frankfurt am Main; ISBN 3548047424; Summa Historica.
127) Reiners, Ludwig: Stilkunst; Ungekürzte Sonderausgabe; 1980; C. H. Beck; München;
ISBN 3406025250; Ein Lehrbuch deutscher Prosa.
128) Gregor-Dellin, Martin (Hrsg.): Deutsche Schulzeit; 1. Aufl.; 1979; Nymphenburger Verlagshandlung;
München; ISBN 3485003530; Erinnerungen und Erzählungen aus drei Jahrhunderten.
129) Ende, Michael: Die unendliche Geschichte; 1. Aufl.; 1979; Thienemann; Stuttgart; ISBN
3522128001; gebunden.
130) Ende, Michael: Momo; 7. Aufl.; 1977; Thienemann; Stuttgart; ISBN 3522119401; Märchen-Roman.
131) Sager, Peter: Realismus; 4. Aufl.; 1982; DuMont; Köln; ISBN 3770106563; Kunst zwischen
Illusion und Wirklichkeit.
132) Biermann, Kurt-R.: Carl Friedrich Gauß; 1. Aufl.; 1990; C. H. Beck; München; ISBN
340634240X; Der "Fürst der Mathematiker" in Briefen und Gesprächen.
133) Reich-Ranicki, Marcel (Hrsg.): Anbruch der Gegenwart; 1. Aufl.; 1987; Piper; München;
ISBN 3492018920; Deutsche Geschichten 1900-1918.
134) Scharnagl, Hermann: Geheimnisse aus dem Kloster; 1. Aufl.; 2005; Gondrom; Bindlach;
ISBN 3811224905; Gesundheit und Lebenskunst aus der Stille.
135) Fessler, Beate: Der neue Medikamentenführer; 2. Aufl.; 1999; Südwest; München;
ISBN 3517076805; Das Arzneimittel-Standardwerk zum Nachschlagen: Über 1900 Wirkstoffe
und Medikamente.
136) Ameln, Falko von: Konstruktivismus; 1. Aufl.; 2004; A. Francke; Tübingen, Basel; ISBN
3772033644; Die Grundlagen systematischer Therapie, Beratung und Bildungsarbeit.
137) Müller, Horst M. (Hrsg.): Arbeitsbuch Linguistik; 1. Aufl.; 2002; Ferdinand Schöningh;
Paderborn; ISBN 3506970070; UTB 2169.
138) Greene, Brian: Der Stoff, aus dem der Kosmos ist; 1. Aufl.; 2006; Pantheon; München;
ISBN 3570550028; Raum, Zeit und die Beschaffenheit der Wirklichkeit.
139) Kinder, Hermann; Hilgemann, Werner: dtv-Atlas zur Weltgeschichte Band II; 14. Aufl.;
1979; Deutscher Taschenbuch Verlag; München; ISBN 342303002X; Von der Französischen
Revolution bis zur Gegenwart.
140) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 1; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 3423030410; A - B.
141) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 2; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 3423030429; C - El.
142) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 3; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 3423030437; Em - Glo.
143) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 4; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 3423030445; Glu - Kel.
144) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 5; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 342303045?; Ken - Lic.
145) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 6; Lizenzausgabe; 1970; Deutscher
Taschenbuch Verlag; München; ISBN 3423030461; Lie - Oz.
146) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 7; Lizenzausgabe; 1971; Deutscher
Taschenbuch Verlag; München; ISBN 342303047X; P - Re.
147) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 8; Lizenzausgabe; 1971; Deutscher
Taschenbuch Verlag; München; ISBN 3423030488; Rh - Stra.
148) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 9; Lizenzausgabe; 1971; Deutscher
Taschenbuch Verlag; München; ISBN 3423030496; Stre - Vir.
149) Franke, Hermann (Hrsg.): dtv-Lexikon der Physik Band 10; Lizenzausgabe; 1971;
Deutscher Taschenbuch Verlag; München; ISBN 342303050X; Vis - Z.
© 1983-2012 by Boris Haase page 122 of 154

150) Asimov, Isaac: Die exakten Geheimnisse unserer Welt Band 1; 1. Aufl.; 1988; Knaur;
München; ISBN 3426039214; Kosmos, Erde, Materie, Technik.
151) Asimov, Isaac: Die exakten Geheimnisse unserer Welt Band 2; 1. Aufl.; 1988; Knaur;
München; ISBN 3426039222; Bausteine des Lebens.
152) Marsch, Friederike; Marsch, Detlef: Physik für Krankenpflegeberufe; 4., durchgesehene
Aufl.; 1992; Thieme; Stuttgart; ISBN 3135833046; 74 Abbildungen.
153) Sexl, Roman; Sexl, Hannelore: Weiße Zwerge - Schwarze Löcher; 2., erw. Aufl.; 1984;
Vieweg; Braunschweig; ISBN 3528172142; Einführung in die relativistische Astrophysik.
154) Berninger, Ernst H.: Otto Hahn; 1. Aufl.; 1979; Rowohlt; Reinbek; ISBN 3499502046;
Monographie.
155) Einstein, Albert: Über die spezielle und allgemeine Relativitätstheorie; 21. Aufl.; 1982;
Vieweg; Braunschweig; ISBN 352806059X; Band 59.
156) Fölsing, Albrecht: Albert Einstein; 1. Aufl.; 1995; Suhrkamp; Frankfurt am Main; ISBN
3518389904; Eine Biographie.
157) Cramer, Friedrich: Der Zeitbaum; 1. Aufl.; 1996; Insel; Frankfurt am Main; ISBN
3458335498; Grundlegung einer allgemeinen Zeittheorie.
158) Davies, Paul: Prinzip Chaos; 1. Aufl.; 1990; Goldmann; München; ISBN 3442114691;
Die neue Ordnung des Kosmos.
159) Davies, Paul: Gott und die moderne Physik; 1. Aufl.; 1989; Goldmann; München; ISBN
3442114764; Taschenbuch.
160) Pitsch, Werner Josef: Chemie für Krankenpflegeberufe; 3., überarb. Aufl.; 1992; Thieme;
Stuttgart; ISBN 313663103X; 66 Abbildungen, 10 Tabellen.
161) Hermann, Peter: Allgemeine und Anorganische Chemie; 5. Aufl.; 1993; Gustav Fischer;
Jena; ISBN 3334002373; Einführung für Biologen, Mediziner und Pharmazeuten.
162) Weizsäcker, Carl Friedrich von: Aufbau der Physik; 1. Aufl.; 1988; Deutscher Taschenbuch
Verlag; München; ISBN 3423108991; Taschenbuch.
163) Weizsäcker, Carl Friedrich von: Die Einheit der Natur; 3. Aufl.; 1983; Deutscher Taschenbuch
Verlag; München; ISBN 346611386X; Studien.
164) Görnitz, Thomas: Carl Friedrich von Weizsäcker; 1. Aufl.; 1992; Herder; Freiburg; ISBN
3451041251; Ein Denker an der Schwelle zum neuen Jahrtausend.
165) Ditfurth, Hoimar von: Wir sind nicht nur von dieser Welt; 7. Aufl.; 1990; Deutscher Taschenbuch
Verlag; München; ISBN 342310290X; Naturwissenschaft, Religion und die Zukunft
des Menschen.
166) Vester, Frederic: Phänomen Stress; 5. Aufl.; 1983; Deutscher Taschenbuch Verlag;
München; ISBN 3421026831; Wo liegt sein Ursprung, warum ist er lebenswichtig, wodurch
ist er entartet?.
167) Vester, Frederic: Neuland des Denkens; 1. Aufl.; 1984; Deutscher Taschenbuch Verlag;
München; ISBN 342102703X; Vom technokratischen zum kybernetischen Zeitalter.
168) Kleinschmidt, Nina; Eimler, Wolf-Michael: Wer hat das Schwein zur Sau gemacht?; 3.
Aufl.; 1984; Knaur; München; ISBN 3426037238; Mafia-Methoden in der deutschen Landwirtschaft.
169) Arieti, Silvano: Schizophrenie; 5. Aufl.; 1993; Piper; München; ISBN 3492107133; Ursachen,
Verlauf, Therapie - Hilfen für Betroffene.
170) Wemmer, Ulrich; Korczak, Dieter: Gesundheit in Gefahr; 1. Aufl.; 1993; Fischer; Frankfurt
am Main; ISBN 3596105110; Daten-Report 1993/94.
171) Holtmeier, Hans-Jürgen: Gesundheit aus dem Meer; 1. Aufl.; 1983; Molden; München;
ISBN 3889190227; Ratgeber.
172) Flechtner, Hans-Joachim: Grundbegriffe der Kybernetik; 5. Aufl.; 1984; Deutscher Taschenbuch
Verlag; München; ISBN 3423044225; Eine Einführung.
173) Burnett, Frances: Der kleine Lord; 1. Aufl.; 1972; Knaur; München; ISBN 3426011042;
Mit 29 Bildern von Martin und Ruth Koser-Michaels.
174) Dannenberg, Hans-Dieter: Schwein haben; 1. Aufl.; 1990; Gustav Fischer; Jena; ISBN
3334002985; Historisches und Histörchen vom Schwein.
175) Musil, Robert: Gesammelte Werke 3; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300036; Der Mann ohne Eigenschaften.
© 1983-2012 by Boris Haase page 123 of 154

176) Musil, Robert: Gesammelte Werke 4; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300044; Der Mann ohne Eigenschaften.
177) Musil, Robert: Gesammelte Werke 5; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300052; Der Mann ohne Eigenschaften.
178) Musil, Robert: Gesammelte Werke 6; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300060; Prosa und Stücke.
179) Musil, Robert: Gesammelte Werke 7; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300079; Kleine Prosa - Aphorismen - Autobiographisches.
180) Musil, Robert: Gesammelte Werke 8; 1. Aufl.; 1978; Rowohlt; Reinbek; ISBN
3499300087; Essays und Reden.
181) Bundesministerium des Innern (Hrsg.): Was Sie schon immer über Umweltschutz wissen
wollten; 2. Aufl.; 1981; Kohlhammer; Stuttgart; ISBN 3170072595; Aufklärung der Öffentlichkeit
in Umweltfragen.
182) Falke, Jutta; Kaspar, Ulrich (Hrsg.): Politiker beschimpfen Politiker; 2., durchges. Aufl.;
1998; Reclam; Leipzig; ISBN 3379016179; Mit einem Nachwort von Heiner Geißler.
183) Lucas, Manfred: Arbeitszeugnisse richtig deuten; 17., aktualisierte Aufl.; 1997; Econ;
Düsseldorf; ISBN 3612213105; Taschenbuch.
184) Heinser, Bernhard (Hrsg.): Weihnachten; 7. Aufl.; 1995; Deutscher Taschenbuch Verlag;
München; ISBN 3423240008; Prosa aus der Weltliteratur.
185) ohne Angaben: Marco Polo Reiseführer; 1. Aufl.; 1997; Mairs Geographischer Verlag;
Ostfildern; ISBN 3895254401; Die wichtigsten Sprachen.
186) Kammer, Hilde; Bartsch, Elisabet: Jugendlexikon Politik; 2., akt. und. erw. Aufl.; 1977;
Rowohlt; Reinbek; ISBN 3499161834; 800 einfache Antworten auf schwierige Fragen.
187) Chen, Chao-Hsiu: Feng Shui; 3. Aufl.; 1996; Wilhelm Heyne; München; ISBN
345310997X; Gesund und glücklich wohnen in Buddhas Haus und Garten.
188) James, Paul: Prince Edward; 1. Aufl.; 1995; Lübbe; Bergisch Gladbach; ISBN
340461321X; Der jüngste Sohn der Queen.
189) Ferguson, Sarah: Meine Geschichte; 3. Aufl.; 1996; Lübbe; Bergisch Gladbach; ISBN
3404126505; Aufgeschrieben von Jeff Coplon.
190) Lexikonredaktion des Franz Schneider Verlages (Hrsg.): Reiten A - Z; 1. Aufl.; 1977;
Franz Schneider; München; ISBN 3505077828; Das Lexikon für Pferdefreunde.
191) Schäfer, Michael: Die Sprache des Pferdes; 1. Aufl.; 1980; Rowohlt; Reinbek; ISBN
3499173824; Lebensweise und Ausdrucksformen.
192) Smythe, R. H.: Pferdeverhalten - verständlich gemacht; 2. Aufl.; 1976; Franckh'sche
Verlagshandlung; Stuttgart; ISBN 3440042391; Franckhs Reiterbibliothek.
193) Zeeb, Klaus: Pferde dressiert von Fredy Knie; 1. Aufl.; 1975; Rowohlt; Reinbek; ISBN
3499169290; Eine Verhaltensstudie.
194) Stern, Horst: Bemerkungen über Pferde; Unkekürzte Ausgabe; 1977; Rowohlt; Reinbek;
ISBN 3499168413; Taschenbuch.
195) Podhajsky, Alois: Die klassische Reitkunst; 1. Aufl.; 1980; Rowohlt; Reinbek; ISBN
349917037X; Eine Reitlehre von den Anfängen bis zur Vollendung.
196) Berg, Dagmar von (Hrsg.): Reiterbrevier; 1. Aufl.; 1979; Wilhelm Heyne; München;
ISBN 3453420618; Taschenbuch.
197) Einstein, Albert: Mein Weltbild; Unveränd. Ausg.; 1989; Ullstein; Frankfurt am Main;
ISBN 3548346839; Hrsg. von Carl Seelig.
198) Einstein, Albert; Born, Hedwig; Born, Max: Briefwechsel 1916-1955; Ungekürzte Ausg.;
1986; Ullstein; Frankfurt am Main; ISBN 3548343457; Geleitwort von Bertrand Russell, Vorwort
von Werner Heisenberg.
199) Wenzel-Bürger, Eva: Gottlieb Engel; 1. Aufl.; 1989; Carlsen; Hamburg; ISBN
3551035954; Pixi-Buch.
200) Drösser, Christoph: Fuzzy Logic; 1. Aufl.; 1995; Rowohlt; Reinbek; ISBN 3499196190;
Methodische Einführung in krauses Denken.
201) Krishnamurti, Jiddu: Fragen und Antworten; 3. Aufl.; 1986; Goldmann; München; ISBN
3442117534; und sein Gespräch mit Prof. David Bohm über das Erwachen der Intelligenz.
© 1983-2012 by Boris Haase page 124 of 154

202) Bibliographisches Institut Mannheim: Taschenbuch der Vornamen; 1. Aufl.; 1973; Humboldt;
München; ISBN 3581662109; gekürzt aus der Originalausgabe des Duden-
Taschenbuches Bd. 4: Lexikon der Vornamen.
203) Whitaker, James: Charles gegen Diana; 1. Aufl.; 1993; Wilhelm Heyne; München; ISBN
3453075285; Szenen einer Ehe.
204) Stendhal: Le Rose et le Vert - Rosa und Grün; Originalausgabe; 1977; Deutscher Taschenbuchverlag;
München; ISBN 3423091266; zweisprachig.
205) Maurier, Daphne du: Meine Cousine Rachel; Ungekürzte Ausgabe; 1979; Ullstein;
Frankfurt am Main; ISBN 3548032192; Roman.
206) Hill, Paul: Gestohlene Jahre; 2. Aufl.; 1991; Lübbe; Bergisch Gladbach; ISBN
340461206X; Erfahrungen.
207) Burkowski, Ursula: Weinen in der Dunkelheit; 8. Aufl.; 1993; Lübbe; Bergisch Gladbach;
ISBN 3404612442; Erfahrungen.
208) Benoit, Michel: Gefangener Gottes; 1. Aufl.; 1993; Lübbe; Bergisch Gladbach; ISBN
3404612728; Erfahrungen.
209) Schneider, Wolf: Der vierstöckige Hausbesitzer; Ungekürzte Ausg.; 1996; Deutscher
Taschenbuch Verlag; München; ISBN 3423305479; Plauderstunde Deutsch mit 33 Fragezeichen.
210) Krämer, Walter; Trenkler, Götz: Lexikon der populären Irrtümer; 8. Aufl.; 1999; Piper;
München; ISBN 3492224466; 500 kapitale Missverständnisse, Vorurteile und Denkfehler von
Abendrot bis Zeppelin.
211) Padrutt, Hanspeter: Der epochale Winter; Vom Autor durchges. Neuaufl.; 1997; Diogenes;
Zürich; ISBN 3257218451; Zeitgemäße Betrachtungen.
212) Thüsen, Heidi Bohnet-von der (Hrsg.): Denkanstöße '90; Originalausgabe; 1989; Piper;
München; ISBN 3492110584; Ein Lesebuch aus Philosophie, Natur- und Humanwissenschaften.
213) Lorenz, Konrad: Die acht Todsünden der zivilisierten Menschheit; 21. Aufl.; 1989; Piper;
München; ISBN 3492100503; Taschenbuch.
214) Nasemann, Andrea: Guter Rat bei der Wohnungssuche; 1. Aufl.; 1997; C. H. Beck;
München; ISBN 3423506180; Rechtsfragen zu Wohnungsvermittlung, Abschluss und Inhalt
des Mietvertrages, Wohngeld und Umzug.
215) Eysenck, Hans Jürgen: Intelligenz-Test; 185.-194. Tausend; 1988; Rowohlt; Reinbek;
ISBN 3499168782; Taschenbuch.
216) Zeller, Alfred P. (Red.): 1000 Fragen - 1000 Antworten; Neuaufl.; 1987; Delphin; München;
ISBN 3773531141; Taschenbuch.
217) Rühmann, Heinz: Das war's; Ungekürzte Ausgabe; 1985; Ullstein; Frankfurt am Main;
ISBN 3548205216; Erinnerungen.
218) Browne, Dik: Hägar der Schreckliche; 5. Aufl.; 1992; Goldmann; München; ISBN
3442119731; Harte Zeiten, Ein Mann - ein Wort, Ohne Furcht und Tadel.
219) Lust, Thea: Gehe ins Rathaus und ärgere dich täglich; Originalausg.; 1987; Rowohlt;
Reinbek; ISBN 3499159864; Ein Behörden-Abenteuer-Buchspiel.
220) Marcks, Marie: Schöne Aussichten; 2. Aufl.; 1984; Deutscher Taschenbuch Verlag;
München; ISBN 3423101954; Karikaturen.
221) Bruno, Rainer: MS Duz; Originalausg.; 1991; Rowohlt; Reinbek; ISBN 3499129124;
Computisch für Hochstapler.
222) Stein, Uli: O Mann!; Originalausg.; 1984; Knaur; München; ISBN 3426021293; 99 Zacken
aus der Krone der Schöpfung.
223) Stein, Uli: Leicht behämmert; 2. Aufl.; 1989; Lappan; Oldenburg; ISBN 345302401X;
Erfindungen, die uns gerade noch gefehlt haben.
224) Traxler, Hans: Gmbh & Kohl KG; 1. Aufl.; 1984; Schirmer-Mosel; München; ISBN
3888141559; Diesem...,unserem Lande!.
225) Wandrey, Uwe (Hrsg.): Heilig Abend zusammen!; 50.-59. Tsd.; 1985; Rowohlt; Reinbek;
ISBN 3499150476; Ein garstiges Allerlei.
226) Bosc: Love and Order; Deutsche Ausgabe; 1973; Diogenes; Zürich; ISBN 3257200668;
Cartoons.
© 1983-2012 by Boris Haase page 125 of 154

227) Tennant, Rich: Computer sind auch nur Menschen; 1. Aufl.; 1993; Goldmann; München;
ISBN 3442079926; Cartoons.
228) Haffner, Sebastian: Geschichte eines Deutschen; 1. Aufl.; 2002; Deutscher Taschenbuch
Verlag; München; ISBN 3423308486; Die Erinnerungen 1914-1933.
229) Walsch, Neale Donald: Gespräche mit Gott Band 1; 1. Aufl.; 2006; Goldmann; München;
ISBN 3442217865; Ein ungewöhnlicher Dialog.
230) Walsch, Neale Donald: Gespräche mit Gott Band 2; 13. Aufl.; 1998; Goldmann; München;
ISBN 3442336120; Gesellschaft und Bewusstseinswandel.
231) Walsch, Neale Donald: Gespräche mit Gott Band 3; 10. Aufl.; 1999; Goldmann; München;
ISBN 3442336279; Kosmische Weisheit.
232) Walsch, Neale Donald: Zuhause in Gott; 1. Aufl.; 2006; Goldmann; München; ISBN
3442337623; Über das Leben nach dem Tode.
233) Hofstadter, Douglas R.: Gödel, Escher, Bach; 8. Aufl.; 1986; Klett-Cotta; Stuttgart; ISBN
360893037X; ein endloses geflochtenes Band.
234) Hofstadter, Douglas R.: Metamagicum; 1. Aufl.; 1988; Klett-Cotta; Stuttgart; ISBN
3608930892; Fragen nach der Essenz von Geist und Struktur.
235) Pelletier, Robert: Das Buch der Aspekte; 1. Aufl.; 1985; Hugendubel; München; ISBN
3880342776; Astrologie.
236) Fankhauser, Alfred: Horoskopie; 4. Aufl.; 1985; Orell Füssli; Zürich; ISBN 3280015693;
Mit 40 Figuren.
237) Hand, Robert: Das Buch der Transite; 1. Aufl.; 1984; Hugendubel; München; ISBN
3880342415; Lebenzyklen erkennen und nutzen.
238) Fellowship, Rosicrucian: Ephemerides 1900-2000; 3rd ed.; 1984; Maison Rosicrucienne;
Aubenas; ISBN 2902450206; Astrologie.
239) Prónay, Alexander von: Die große Partnerschafts-Analyse; 2. Aufl.; 1990; Rohm; Bietigheim;
ISBN 3876831237; Die Beziehungen zwischen den Menschen im
Horoskopvergleich.
240) Sachs, Gunter: Die Akte Astrologie; 3. Aufl.; 1997; Goldmann; München; ISBN
3442307465; Wissenschaftlicher Nachweis eines Zusammenhangs zwischen den Sternzeichen
und dem menschlichen Verhalten.
241) Banzhaf, Hajo; Haebler, Anna: Schlüsselworte zur Astrologie; 1. Aufl.; 1994; Hugendubel;
München; ISBN 3880347638; gebunden.
242) Kühn, Volker; Walter, Günter: "Ich bejahe die Frage rundherum mit Ja"; 1. Aufl.; 1985;
Rasch & Röhring; Hamburg; ISBN 3891360398; Einführung in die Kanzlersprache - Mit Kohl-
Kode.
243) Strunz, Ulrich: Forever Young; 5. Aufl.; 2004; Gräfe & Unzer; München; ISBN
3774240019; Das Ernährungsprogramm.
244) Sheldrake, Rupert: Das Gedächtnis der Natur; 4. Aufl.; 1991; Scherz; Bern, München,
Wien; ISBN 3502136505; Das Geheimnis der Entstehung der Formen in der Natur.
245) Blavatsky, Helena Petrowna: Die Geheimlehre; 3. Aufl.; 1992; Adyar; Satteldorf; ISBN
3927837113; Gekürzte Ausgabe.
246) Chown, Marcus: Das Universum nebenan; 1. Aufl.; 2003; Deutscher Taschenbuch Verlag;
München; ISBN 3423243651; Revolutionäre Ideen in der Astrophysik.
247) Brothers, Joyce; Eagan, Edward P. F.: In 10 Tagen zum vollkommenen Gedächtnis;
Genehmigte Lizenzausg.; 2001; Weltbild; Augsburg; ISBN 3893509631; gebunden.
248) Werner, Günther T.; Nelles, Michaele: Rückenschule; 5. Aufl.; 2003; Gräfe & Unzer;
München; ISBN 3774218005; Endlich schmerzfrei und entspannt.
249) Schonert-Hirz, Sabine: Alles wollen, alles können, alles schaffen energy; 4. Aufl.; 2005;
Gräfe & Unzer; München; ISBN 3774232296; Stress in Energie umwandeln - Innere Kraftquellen
entdecken - Ziele sicher erreichen.
250) Medawar, Peter B.: Ratschläge für einen jungen Wissenschaftler; 1. Aufl.; 1984; Piper;
München; ISBN 3492028675; gebunden.
251) Jelínek, J.: Das große Bilderlexikon des Menschen in der Vorzeit; 1. Aufl.; 1975; Bertelsmann;
Gütersloh; ISBN 3570031500; gebunden.
252) Öztürk, Yasar Nuri: 400 Fragen zum Islam 400 Antworten; 3. Aufl.; 2003; Grupello;
Düsseldorf; ISBN 3933749174; Ein Handbuch.
© 1983-2012 by Boris Haase page 126 of 154

253) Wolf, Notker: Worauf warten wir?; 1. Aufl.; 2006; Rowohlt; Reinbek; ISBN 3499620944;
Ketzerische Gedanken zu Deutschland.
254) Frankl, Viktor E.: Der unbewusste Gott; 8. Aufl.; 2006; Deutscher Taschenbuch Verlag;
München; ISBN 342335058X; Psychotherapie und Religion.
255) Schellenbaum, Peter: Gottesbilder; 3. Aufl.; 2004; Deutscher Taschenbuch Verlag;
München; ISBN 3423340797; Religion, Psychoanalyse, Tiefenpsychologie.
256) Wetzig-Würth, Herta; Müller, Peter: Das psychotherapeutische Gespräch; 1. Aufl.;
2000; Springer; Berlin; ISBN 3540672516; Therapeutisch wirksame Dialoge in der Arztpraxis.
257) Dieterich, Michael: Seelsorge kompakt; 1. Aufl.; 2006; Brockhaus; Wuppertal; ISBN
3417249465; Zehn Grundlagen für eine ganzheitlich orientierte Beratung und Therapie.
258) Becker, Volker J.: Gottes geheime Gedanken; 1. Aufl.; 2006; Books on Demand; Norderstedt;
ISBN 3833448059; Was uns westliche Physik und östliche Mystik über Gott und
Geist, Urknall und Universum, Sinn und Sein sagen können.
259) Otto, Rudolf: Das Heilige; 41.-44. Tsd.; 1979; C. H. Beck; München; ISBN 3406025234;
Über das Irrationale in der Idee des Göttlichen und sein Verhältnis zum Rationalen.
260) Augustinus, Aurelius: Aufstieg zu Gott; 1. Aufl.; 2001; Patmos; Düsseldorf; ISBN
3491703328; Hrsg., eing. und übers. von Ladislaus Boros.
261) Henry, Gray; Marriott, Susannah: Perlen des Glaubens; 1. Aufl.; 2003; Hugendubel;
München; ISBN 3720523810; Wege zu Meditation und Spiritualität: Rosenkränze, Gebetsketten
und heilige Worte.
262) Lauxmann, Frieder: Wonach sollen wir uns richten?; 1. Aufl.; 2002; Kreuz; Stuttgart;
ISBN 3783121140; Ethische Grundmodelle von den Zehn Geboten bis zum Projekt Weltethos.
263) Lauxmann, Frieder: Die Philosophie der Weisheit; 1. Aufl.; 2002; Nymphenburger; München;
ISBN 3485009229; Die andere Art zu denken.
264) Eastman, Dick: Wunder sind mir kein Problem; 1. Aufl.; 1998; Hänssler; Neuhausen-
Stuttgart; ISBN 3775128794; Wie Gott jedes Haus erreicht.
265) Mertz, Bernd A.: Das Grundwissen der Astrologie; 1. Aufl.; 1999; Seehamer; Weyarn;
ISBN 3934058043; Persönlichkeit, Lebensplan, Partnerschaft, Zukunft.
266) Taeger, Hans Hinrich: Astroenergetik; 1. Aufl.; 1983; Papyrus; Hamburg; ISBN
3922731112; Die zwölf kosmischen Energien.
267) Ebertin, Reinhold: Kombination der Gestirneinflüsse; 12. Aufl.; 1983; Ebertin; Freiburg;
ISBN 3871860506; Astrologie.
268) Ring, Thomas: Astrologische Menschenkunde III; 6. Aufl.; 1984; Bauer; Freiburg; ISBN
3762604231; Kombinationslehre.
269) Andrieu, Irène: Karma im Horoskop; 1. Aufl.; 1989; Hugendubel; München; ISBN
3880344388; Die Deutung von Mondknoten, rückläufigen Planeten und Karmaregenten.
270) Huber, Bruno: Intelligenz im Horoskop; 1. Aufl.; 1981; Astrologisch-Psychologisches
Institut; Adliswil; ISBN 3855231070; Autodidacta No. 107.
271) Muckenschnabel, W. R.: Was die Handschrift verrät; Sonderausg.; 1986; Gondrom;
Bindlach; ISBN 3811204572; Graphologie.
272) Klages, Ludwig: Handschrift und Charakter; 28. Aufl.; 1982; Bouvier; Bonn; ISBN
3416003128; Gemeinverständlicher Abriss der graphologischen Technik.
273) Bonert, Klaus W.; Bielkine, Helga; Hand, Robert: Ephemeride 1850-2050; 2., neu
berechn. Aufl.; 1988; Astron; Hamburg; ISBN 3925822003; Der Asteroiden Ceres, Pallas,
Juno, Vesta und von Cheiron, Isis.
274) Ebertin, Reinhold: Direktionen - Mitgestalter des Schicksals; 12. Aufl.; 1988; Ebertin;
Freiburg; ISBN 3871860700; Astrologie.
275) Stein, Zane B.: Chiron; 2., erw. Aufl.; 1988; Chiron; Dusslingen; ISBN 3925100067; Astrologie.
276) Rudhyar, Dane: Das astrologische Häusersystem; 3. Aufl.; 1984; Hugendubel; München;
ISBN 3880340994; Das Spektrum der individuellen Erfahrung.
277) Rohr, Richard; Ebert, Andreas: Das Enneagramm; 28. Aufl.; 1996; Claudius; München;
ISBN 353262088X; Die 9 Gesichter der Seele.
© 1983-2012 by Boris Haase page 127 of 154

278) Wheeler, Mortimer: Römische Kunst und Architektur; 1. Aufl.; 1969; Droemer/Knaur;
München; ASIN B0000BU5R7; Mit 215 Abbildungen, davon 60 in Farben.
279) Sempé: Wie das Leben so spielt; 1. Aufl.; 1988; Diogenes; Zürich; ISBN 3257020244;
Der gesellschaftliche Aufstieg des Monsieur Lambert.
280) Boynton, Sandra: Schokolade; 1. Aufl.; 1984; DuMont; Köln; ISBN 377011522; Eine
verzehrende Leidenschaft.
281) Iding, Doris: Für mehr Lebensenergie - Bewusstes Atmen; 2. Aufl.; 2000; Südwest;
München; ISBN 351706162X; Gesundheit und Vitalität mit der Atemtherapie.
282) Denk, Roland: Neue Segelschule; 9., überarb. Aufl.; 1985; BLV Verlagsgesellschaft;
München; ISBN 3405129915; Vom Anfänger zum Führerschein A/R.
283) Organ, Maren (Übers.): Fit, elastisch und gesund; 17. Aufl.; 1989; Hoffmann & Campe;
Hamburg; ISBN 3455020305; Das tägliche Training für jedermann.
284) Pollay, Heinz: Das Reiterabzeichen leicht gemacht; 3., durchges. Aufl.; 1978; BLV Verlagsgesellschaft;
München; ISBN 3405119316; und alles zum Thema Reiter-Pass (FN).
285) Blake, Henry: Versteh dein Pferd; 3. Aufl.; 1976; Albert Müller; Rüschlikon-Zürich; ISBN
327500607X; Neue Wege der Verständigung.
286) Fehringer, Otto: Unser Pferd; 2. Aufl.; 1960; Reimer; Berlin; ASIN B0000BHYJO; Das
neue Pferdebuch für alle.
287) Müseler, Wilhelm: Reitlehre; 43. Aufl.; 1977; Parey; Berlin; ASIN B0000BSRGN; Mit 95
Abbildungen.
288) Blendinger, Wilhelm: Psychologie und Verhaltensweisen des Pferdes; 3. Aufl.; 1977;
Hoffmann; Heidenheim; ISBN 3873433613; mit Vergleichen aus der Psychologie anderer
Tiere und des Menschen.
289) Linneweh, Klaus: Kreatives Denken; 6. Aufl.; 1994; Dieter Gitzel; Rheinzabern; ISBN
3921184223; Techniken und Organisation produktiver Kreativität.
290) Golluch, Norbert; Kochan, Stano: Das fröhliche Frauenhasserbuch; 1. Aufl.; 1986;
Eichborn; Frankfurt am Main; ISBN 3821818220; Humor.
291) Mayer, Jeffrey J.: Zeitmanagement für Dummies; 2. Nachdruck; 1999; MITP; Bonn;
ISBN 3826627601; mit CD-ROM.
292) Metzig, Werner; Schuster, Martin: Lernen zu lernen; 4. Aufl.; 1998; Springer; Berlin;
ISBN 3540646582; Lernstrategien wirkungsvoll einsetzen.
293) Dobson, John H.: Learn New Testament Greek; 2nd Ed.; 1997; Bible Society; Swindon;
ISBN 0564082252; with tape.
294) Stock, Leo: Langenscheidts Kurzgrammatik Altgriechisch; 12. Aufl.; 2000; Langenscheidt;
Berlin; ISBN 3468350309; Das Wichtigste aus der Grammatik mit praktischen Beispielen.
295) Kaiser, Birgit (Bearb.): Langenscheidts Grammatiktafel Französisch; 5. Aufl.; 2000;
Langenscheidt; Berlin; ISBN 3468361513; Eine konzentrierte und übersichtliche Darstellung
der Grammatik.
296) Buzan, Tony: Speed Reading; 6. Aufl.; 1999; MVG; Landsberg; ISBN 3478719607;
Schneller lesen, mehr verstehen, besser behalten.
297) Neges, Gertrud; Neges, Richard: Kompaktwissen Management; 2., überarb. und erw.
Aufl.; 1999; Wirtschaftsverlag Ueberreuter; Wien; ISBN 3706405172; Alles, was Führungskräfte
wissen müssen, mit vielen Fallbeispielen und Checklisten.
298) ohne Angaben: Die Geschichte der Familie; 1. Aufl.; 1975; ECM; Freiburg/Schweiz;
ohne ISBN; Moderne Familie.
299) Emde-Naegelsbach, Barbara; Zeller, Alfred P. (Bearb.): Sammeln macht Spaß; 1. Aufl.;
1975; ECM; Freiburg/Schweiz; ohne ISBN; Moderne Familie.
300) Weiß, Max: Schach; genehmigte Ausgabe; 1976; Buch und Zeit Verlagsgesellschaft;
Köln; ohne ISBN; Einführung, Taktik, Musterspiele.
301) Remarque, Erich Maria: Im Westen nichts Neues; 1. Aufl.; 1974; Ullstein; Berlin; ohne
ISBN; Einführung von Hans Habe, Originalillustrationen von Gilbert Koull.
302) Rochester, Jack B.; Gantz, John: Der nackte Computer; 1. Aufl.; 1984; DuMont; Köln;
ISBN 3770116623; Für Laien und Fachleute, Kritiker und Enthusiasten - Erfinder, Rekorde,
Geschichte, Fehler, Anekdoten, Fakten.
© 1983-2012 by Boris Haase page 128 of 154

303) Eiden, Christoph; Fiebelmann, Heinz; Kramer, Mike: PC Hardware; 1. Aufl.; 1997; BHV;
Kaarst-Büttgen; ISBN 3893602682; Verstehen, Aufrüsten, Optimieren.
304) Hansen, Hans Robert: Wirtschaftsinformatik I; 5., neubearb. und erw. Aufl.; 1986; Fischer;
Stuttgart; ISBN 3437401726; Einführung in die betriebliche Datenverarbeitung.
305) Göpfrich, Hans Rudolf: Wirtschaftsinformatik II; 3., völlig neubearb. und erw. Aufl.;
1988; Fischer; Stuttgart; ISBN 3437401971; Strukturierte Programmierung in COBOL.
306) Hansen, Hans Robert: Wirtschaftsinformatik I; 6., neubearb. und stark erw. Aufl.; 1992;
Fischer; Stuttgart; ISBN 3437402862; Einführung in die betriebliche Datenverarbeitung.
307) Vester, Frederic: Denken, Lernen, Vergessen; 11. Aufl.; 1984; Deutscher Taschenbuch
Verlag; München; ISBN 3421026726; Was geht in unserem Kopf vor, wie lernt das Gehirn,
und wann lässt es uns im Stich?.
308) Bender, Hans: Parapsychologie; 28.-32. Tsd.; 1980; Fischer; Frankfurt am Main; ISBN
3596263166; Ihre Ergebnisse und Probleme.
309) Döbereiner, Wolfgang: Schütze; 7. Aufl.; 1981; Wilhelm Heyne; München; ISBN
3453460162; 23. November - 21. Dezember.
310) Eysenck, Hans Jürgen; Nias, David: Astrologie; 1. Aufl.; 1984; Deutscher Taschenbuch
Verlag; München; ISBN 3423103507; Wissenschaft oder Aberglaube?.
311) Prónay, Alexander von: Die Sterne haben doch recht; 1. Aufl.; 1982; Moewig; Hamburg;
ISBN 381183164X; Astrologie.
312) Weltenburger, Martin (Hrsg.): Das persönliche Horoskop für alle, die am 25. August
geboren sind; 1. Aufl.; 1987; Das persönliche Geburtstagsbuch; München; ISBN
3818411581; Astrologie.
313) Bear, Sun; Wabun: Indianische Astrologie der Erde; 1. Aufl.; 1986; Goldmann; München;
ISBN 3442109779; 21. Mai - 20. Juni, Hirsch, Geboren unter dem Mond der Maisaussaat,
Das Medizinrad.
314) Weiss, C. Joachim: Der Astrokalender 1987; 1. Aufl.; 1986; Wilhelm Heyne; München;
ISBN 3453417259; Ein Jahreshoroskop für alle Sternzeichen von Januar bis Dezember.
315) Heath, Ian: Das Jungfrau-Buch; 1. Aufl.; 1985; Droemer/Knaur; München; ISBN
3426261715; Taschenbuch.
316) Sakoian, Frances; Acker, Louis S.: Das große Lehrbuch der Astrologie; 4. Aufl.; 1982;
Droemer/Knaur; München; ISBN 3426076071; Wie man Horoskope stellt und nach neuesten
wissenschaftlichen Erkenntnissen Charakter und Schicksal deutet.
317) ohne Angaben: Die Deutsche Ephemeride V 1961-1970; 6. Aufl.; 1982; Barth; München;
ISBN 3502688052; Astrologie.
318) Sargent, Lois Haines: Partnerschaftsastrologie; 1. Aufl.; 1988; Droemer/Knaur; München;
ISBN 3426041847; Was Horoskope über Beziehungen zu Mitmenschen aussagen.
319) Meyer, Hermann: Partnerschaft, Gesundheit und Glück in der psychologischen Astrologie;
Genehmigte Taschenbuchausgabe; 1988; Wilhelm Heyne; München; ISBN 3453009371;
Vorschläge zur eigenen Schicksalsgestaltung.
320) Roscher, Michael: Das Buch der Horoskope; 1. Aufl.; 1990; Droemer/Knaur; München;
ISBN 3426042347; 240 Horoskope bekannter Persönlichkeiten.
321) Lundsted, Betty: Astrologische Aspekte; 1. Aufl.; 1988; Droemer/Knaur; München; ISBN
3426041825; Ihre weibliche und männliche Seite.
322) Gauquelin, Michel: Kosmische Einflüsse auf menschliches Verhalten; 1. Aufl.; 1983;
Hermann Bauer; Freiburg; ISBN 3762606064; esotera Taschenbücherei.
323) ohne Angaben: Alles über den Jungfrau-Menschen 24. August - 23. September; 5.
Aufl.; 1979; Moewig; Rastatt; ISBN 3811869922; Wesen und Verhalten in allen Lebenslagen.
324) Dietrich, Eva: Astro-Graphologie; 1. Aufl.; 1981; Goldmann; München; ISBN
3442108586; Der neue Schlüssel zur Charakterdeutung und Selbsterkenntnis.
325) Cobbaert, Anne-Marie: Graphologie; 1. Aufl.; 1982; Droemer/Knaur; München; ISBN
3426041022; Schriften erkennen und deuten, mit 273 Schriftproben im laufenden Text.
326) Ehwald, Ursula; Lauster, Peter: Handschriften deuten; 1. Aufl.; 1976; Humboldt; München;
ISBN 3581662744; So beurteilt die Graphologie den Charakter, mit Testfolgen und
Tips.
© 1983-2012 by Boris Haase page 129 of 154

327) Schmid, Horst: Biorhythmik; Genehmigte Sonderausgabe; 1980; Buch und Zeit; Köln;
ohne ISBN; Die neue Lebenshilfe, Höhen und Tiefen der persönlichen Lebenskurven vorausberechnen
und danach handeln.
328) Thurber, James: Zehn goldene Regeln für das Zusammenleben/Der Hund, der die Leute
biss; 1. Aufl.; 1991; Rowohlt; Reinbek; ISBN 3499130505; Taschenbuch.
329) Kratz, Hans-Jürgen: Das Vorstellungsgespräch; 1. Aufl.; 1996; Walhalla; Regensburg;
ISBN 3802938402; Optimal vorbereitet auf Ihren Live-Auftritt.
330) Oberbeil, Klaus: Gesundheit aus der Natur - Biostoffe; 1. Aufl.; 1998; Südwest; München;
ISBN 3517080217; Mit Vitaminen, Mineralien, Spurenelementen, Enzymen und
Bioflavonoiden viele Krankheiten heilen.
331) Hargreaves, Gloria; Wilson, Peggy: Die Schrift als Ausdruck der Persönlichkeit; 1. Aufl.;
1985; Rowohlt; Reinbek; ISBN 3499179156; Ein graphologisches Handbuch von A-Z.
332) Salny, Abbie; Grosswirth, Marvin: Das endgültige Mensa-Quiz-Buch; 1. Aufl.; 1987;
DuMont; Köln; ISBN 3770117344; Für Genies und solche, die es werden wollen - mit Witz,
Tempo und Wissen gegen den intelligentesten Club der Welt.
333) Salberg-Steinhardt, Barbara: Die Schrift: Geschichte - Gestaltung - Anwendung; 1.
Aufl.; 1983; DuMont; Köln; ISBN 377011454X; Ein Lern- und Lehrbuch für die Praxis.
334) Butschkow, Peter: Viel Spaß im Büro!; 2. Aufl.; 1992; Lappan; Oldenburg; ISBN
3890824102; Cartoons.
335) Gaymann, Peter: Hühner auf Reisen; 1. Aufl.; 1990; Wilhelm Heyne; München; ISBN
3453037022; Cartoons.
336) Serebriakoff, Victor: Mensa Quadrat; 1. Aufl.; 1989; Wilhelm Heyne; München; ISBN
3453031105; Denksportaufgaben für Hochbegabte.
337) Knieß, Michael: Kreativitätstechniken; 1. Aufl.; 2006; Deutscher Taschenbuch Verlag;
München; ISBN 3423509066; Methoden und Übungen.
338) Weisbach, Christian-Rainer: Professionelle Gesprächsführung; 4., überarb. und erw.
Aufl.; 1999; Deutscher Taschenbuch Verlag; München; ISBN 3432058455; Ein praxisnahes
Lese- und Übungsbuch.
339) Statistisches Bundesamt (Hrsg.): Zahlenkompass; 4. Aufl.; 1996; Metzler-Poeschel;
Stuttgart; ISBN 3824604485; Statistisches Taschenbuch für Deutschland.
340) Oheim, Gertrud: Einmaleins des guten Tons; 6. Aufl.; 1955; Bertelsmann; Gütersloh;
ohne ISBN; Praktische Ratgeber.
341) Schneider, Wolf: Deutsch für Kenner; 5. Aufl.; 2000; Piper; München; ISBN
3492222161; Die neue Stilkunde.
342) Buchholz, Kai (Hrsg.): Liebe; 1. Aufl.; 2007; Goldmann; München; ISBN 3442077567;
Ein philosophisches Lesebuch.
343) Schmitt, Anton: Führer durch Fulda; 14. Aufl.; 1995; Parzeller; Fulda; ISBN
3790002585; Mit Planskizze und zahlreichen Abbildungen.
344) Reincke, Madeleine (Bearb.): Großbritannien und Nordirland; 7. Aufl.; 1998; Baedeker;
Ostfildern; ISBN 3875045068; Reiseführer mit großer Reisekarte.
345) Abend, Bernhard; Schliebitz, Anja: Schweiz; 11. Aufl.; 2004; Baedeker; Ostfildern; ISBN
3875045211; Reiseführer mit großer Reisekarte.
346) Beck, Vera; Bernhard, Marianne; Eisenschmid, Rainer; Reincke, Madelein: Berlin; 13.
Aufl.; 2000; Baedeker; Ostfildern; ISBN 3875041267; Reiseführer mit großem Stadtplan.
347) Bauer, E.-G.; Eisenschmid, Rainer; Grünewald, Margit et al.: Dresden; 10. Aufl.; 2006;
Baedeker; Ostfildern; ISBN 3829710275; Reiseführer mit großem Cityplan.
348) Beck, Vera; Branscheid, Barbara; Galenschovski, Carmen et al.: Frankfurt am Main; 6.
Aufl.; 1998; Baedeker; Ostfildern; ISBN 3895251437; Reiseführer mit großem Stadtplan.
349) Kelch, Johannes; Linde, Helmut et al.: München; 9. Aufl.; 2000; Baedeker; Ostfildern;
ISBN 3875041275; Reiseführer mit großem Stadtplan.
350) Bourmer, Achim; Eisenschmid, Rainer; Schliebitz, Anja et al.: New York; 8. Aufl.; 1998;
Baedeker; Ostfildern; ISBN 3895258105; Reiseführer mit großem Stadtplan.
351) Reincke, Madeleine (Bearb.): Paris; 10. Aufl.; 1999; Baedeker; Ostfildern; ISBN
3875040597; Reiseführer mit großer Reisekarte.
352) Reincke, Madeleine (Bearb.): Rom; 10. Aufl.; 1998; Baedeker; Ostfildern; ISBN
3875041259; Reiseführer mit großem Stadtplan.
© 1983-2012 by Boris Haase page 130 of 154

353) Branscheid, Barbara; Bourmer, Achim; Luippold, Dieter et al.: Rügen - Hiddensee; 5.
Aufl.; 2003; Baedeker; Ostfildern; ISBN 3895254363; Reiseführer mit großer Inselkarte.
354) Galenschovski, Carmen; Reincke, Madeleine et al.: Wien; 11. Aufl.; 2002; Baedeker;
Ostfildern; ISBN 3875041321; Reiseführer mit großem Cityplan.
355) Höh, Peter: Insel Usedom; 1. Aufl.; 2001; Reise Know-How; Bielefeld; ISBN
3894166916; Urlaubshandbuch.
356) Nicholson, Robert; Barber, Romek (Des.): Colour London Streetfinder; 1st Ed.; 1991;
Nicholson; London; ISBN 0702816884; Spiral Bound.
357) Leech, Michael: New York; Überarb. Ausg.; 1997; Könemann; Köln; ISBN 389508879X;
Reiseführer.
358) Geiss, Heide Marie Karin: München; 5., akt. Aufl.; 2000; DuMont; Köln; ISBN
377012670X; Reise-Taschenbuch.
359) Sorges, Jürgen: Rom; Kompl. akt. Aufl.; 2000; Polyglott; München; ISBN 3493597088;
Reiseführer.
360) Redell, August (Hrsg.): Norderney erzählt; 2. Aufl.; 1995; Hansen & Hansen; Münsterdorf;
ISBN 3879803056; Geschichten, Anekdoten, Erinnerungen.
361) Stiemert, Elisabeth; Schmidt, Waltraut: Kater Timtetater; 1. Aufl.; 1986; Gerstenberg;
Hildesheim; ISBN 3806740577; Taschenbuch.
362) Clark, Elisabeth: Das Eselchen und der Weihnachtsmann; 1. Aufl.; 1998; Coppenrath;
Münster; ISBN 3815717086; Illustriert von Jan Ormerod.
363) Weis, Erich (Bearb.): Grund- und Aufbauwortschatz Englisch; 1. Aufl.; 1989; Klett;
Stuttgart; ISBN 3125195101; Taschenbuch.
364) Schäfer, Karl-Heinz; Zimmermann, Bernhard (Bearb.): Langenscheidts Taschenwörterbuch
Altgriechisch; 7. Aufl.; 1998; Langenscheidt; Berlin; ISBN 3468100310; Altgriechisch -
Deutsch, Deutsch - Altgriechisch.
365) Pertsch, Erich (Bearb.): Langenscheidts Taschenwörterbuch Lateinisch; 29. Aufl.; 1980;
Langenscheidt; Berlin; ISBN 3469102003; Lateinisch - Deutsch, Deutsch - Lateinisch.
366) Lange-Kowal, Ernst Erwin (Bearb.): Langenscheidts Schulwörterbuch Französisch; 12.
Aufl.; 1981; Langenscheidt; Berlin; ISBN 346813150X; Französisch - Deutsch, Deutsch -
Französisch.
367) Fuchs, Sebastian; Wenzel, Veronika (Bearb.): Langenscheidts Universal-Sprachführer
Niederländisch; 1. Aufl.; 1998; Langenscheidt; Berlin; ISBN 3468232306; Praktische Redewendungen
und Wörter für die Reise.
368) Dierkes, Hans (Hrsg.): Philosophische Anthropologie; 1. Aufl.; 1995; Reclam; Stuttgart;
ISBN 3150150124; Arbeitstexte für den Unterricht.
369) Leibniz, Gottfried Wilhelm: Monadologie; 1. Aufl.; 1998; Reclam; Stuttgart; ISBN
3150078539; Französisch/Deutsch.
370) Aristoteles: Nikomachische Ethik; 1. Aufl.; 1999; Reclam; Stuttgart; ISBN 3150085861;
Übersetzung und Nachwort von Franz Dirlmeier.
371) Sainsbury, R. M.: Paradoxien; 1. Aufl.; 1994; Reclam; Stuttgart; ISBN 315008881X; Aus
dem Englischen übersetzt von Vincent C. Müller.
372) Kant, Immanuel: Die Religion innerhalb der Grenzen der bloßen Vernunft; 1. Aufl.;
2004; Reclam; Stuttgart; ISBN 3150012317; Hrsg. von Rudolf Malter.
373) Heidegger, Martin: Der Ursprung des Kunstwerkes; 1. Aufl.; 1997; Reclam; Stuttgart;
ISBN 3150084466; Mit einer Einführung von Hans-Georg Gadamer.
374) Aristoteles: Metaphysik; Bibliograph. erg. Ausg.; 1997; Reclam; Stuttgart; ISBN
3150079136; Übersetzt und herausgegeben von Franz F. Schwarz.
375) Martens, Ekkehard: Zwischen Gut und Böse; 1. Aufl.; 1997; Reclam; Stuttgart; ISBN
3150096359; Elementare Fragen angewandter Philosophie.
376) Peirce, Ch. S.; James, W.; Schiller, F. C. S.; Dewey, J.: Pragmatismus; 1. Aufl.; 1997;
Reclam; Stuttgart; ISBN 3150097991; Mit einer Einleitung herausgegeben von Ekkehard
Martens.
377) Strawson, Peter Frederick: Einzelding und logisches Subjekt (Individuals); 1. Aufl.;
1995; Reclam; Stuttgart; ISBN 3150094100; Ein Beitrag zur deskriptiven Metaphysik.
378) Konfuzius: Gespräche; 1. Aufl.; 2002; Reclam; Stuttgart; ISBN 3150096561; Aus dem
Chinesischen übersetzt und herausgegeben von Ralf Moritz.
© 1983-2012 by Boris Haase page 131 of 154

379) Mittelstraß, Jürgen (Hrsg.): Enzyklopädie Philosophie und Wissenschaftstheorie Band
1: A-G; Unveränd. Sonderausg.; 2004; Metzler; Stuttgart; ISBN 3476020126; Lexikon.
380) Mittelstraß, Jürgen (Hrsg.): Enzyklopädie Philosophie und Wissenschaftstheorie Band
2: H-O; Unveränd. Sonderausg.; 2004; Metzler; Stuttgart; ISBN 3476020126; Lexikon.
381) Mittelstraß, Jürgen (Hrsg.): Enzyklopädie Philosophie und Wissenschaftstheorie Band
3: P-So; Unveränd. Sonderausg.; 2004; Metzler; Stuttgart; ISBN 3476020126; Lexikon.
382) Mittelstraß, Jürgen (Hrsg.): Enzyklopädie Philosophie und Wissenschaftstheorie Band
4: Sp-Z; Unveränd. Sonderausg.; 2004; Metzler; Stuttgart; ISBN 3476020126; Lexikon.
383) Inwood, Michael: Heidegger; 1. Aufl.; 2004; Herder; Freiburg; ISBN 3926642467; Spektrum
Meisterdenker.
384) Nishitani, Keiji: Was ist Religion?; 1. Aufl.; 2001; Insel; Frankfurt am Main; ISBN
3458344292; Taschenbuch.
385) Möbuß, Susanne: Plotin; 1. Aufl.; 2005; Panorama; Wiesbaden; ISBN 3926642637;
Große Denker.
386) Martin, Gottfried: Platon; 46.-50. Tsd.; 1980; Rowohlt; Reinbek; ISBN 3499501503; in
Selbstzeugnissen und Bilddokumenten.
387) Bloch, Ernst; Herzfelde, Wieland: Briefwechsel 1938-1949; 1. Aufl.; 2001; Suhrkamp;
Frankfurt am Main; ISBN 3518582593; Wir haben das Leben wieder vor uns.
388) Mainzer, Klaus: Computerphilosophie zur Einführung; 1. Aufl.; 2003; Junius; Hamburg;
ISBN 3885063832; Taschenbuch.
389) Machiavelli, Niccolò: Der Fürst; 1. Aufl.; 1990; Insel; Frankfurt am Main; ISBN
3458329072; Taschenbuch.
390) Pauen, Michael; Roth, Gerhard (Hrsg.): Neurowissenschaften und Philosophie; 1. Aufl.;
2001; Fink; München; ISBN 3770535480; Eine Einführung.
391) Buhr, Manfred; Kosing, Alfred: Kleines Wörterbuch der marxistisch-leninistischen Philosophie;
2., überarb. und erw. Aufl.; 1974; Dietz; Berlin; ohne ISBN; gebunden.
392) Jaspers, Karl: Die großen Philosophen; 6. Aufl.; 1997; Piper; München; ISBN
3492210023; Erster Band.
393) Alquié, Ferdinand: Plans de philosophie générale; 1. Aufl.; 2000; La Table Ronde; Paris;
ISBN 2710309955; Taschenbuch.
394) Wittgenstein, Ludwig: Tractatus logico-philosophicus/Philosophische Untersuchungen;
1. Aufl.; 1990; Reclam; Leipzig; ISBN 3379006483; Taschenbuch.
395) Kranz, Walther: Die griechische Philosophie; Lizenzausg.; 1997; Dieterich; Leipzig;
ISBN 388059922X; Zugleich eine Einführung in die Philosophie überhaupt.
396) Peirce, Charles Sanders: Vorlesungen über Pragmatismus; 1. Aufl.; 1991; Meiner;
Hamburg; ISBN 3787309845; Mit Einleitung und Anmerkungen neu herausgegeben von Elisabeth
Walther.
397) Brentano, Franz: Philosophische Untersuchungen zu Raum, Zeit und Kontinuum; 1.
Aufl.; 1976; Meiner; Hamburg; ISBN 3787303561; Aus dem Nachlass mit Anmerkungen von
Alfred Kastil herausgegeben und eingeleitet von Stephan Körner und Roderick M. Chrisholm.
398) Luckner, Andreas: Martin Heidegger: "Sein und Zeit"; 1. Aufl.; 1997; Schöningh; Paderborn;
ISBN 350699476X; Ein einführender Kommentar.
399) Birnbacher, Dieter; Hoerster, Norbert (Hrsg.): Texte zur Ethik; 5. Aufl.; 1984; Deutscher
Taschenbuch Verlag; München; ISBN 3423060425; dtv Bibliothek.
400) Hofmeister, Heimo: Philosophisch denken; 2., durchges. Aufl.; 1997; Vandenhoeck &
Ruprecht; Göttingen; ISBN 3525032757; Taschenbuch.
401) Heidegger, Martin; Jaspers, Karl: Briefwechsel 1920-1963; 1. Aufl.; 1992; Piper; München;
ISBN 3492112609; Mit 4 Abbildungen auf Tafeln.
402) Kunzmann, Peter; Burkard, Franz-Peter; Wiedmann, Franz: dtv-Atlas zur Philosophie;
2. Aufl.; 1992; Deutscher Taschenbuch Verlag; München; ISBN 3423032294; Tafeln und
Texte, mit 111 farbigen Abbildungsseiten.
403) Platon: Menon/Kratylos/Euthydemos/Hippias maior; 1. Aufl.; 1991; Insel; Frankfurt am
Main; ISBN 3458331034; Griechisch und Deutsch.
404) Warning, Rainer: Rezeptionsästhetik; 4., unveränd. Aufl.; 1993; Fink; München; ISBN
3770510534; Theorie und Praxis.
© 1983-2012 by Boris Haase page 132 of 154

405) Hügli, Anton; Lübcke, Poul (Hrsg.): Philosophielexikon; 2. Aufl.; 1998; Rowohlt; Reinbek;
ISBN 3499554534; Personen und Begriffe der abendländischen Philosophie von der
Antike bis zur Gegenwart.
406) Hegenbart, Rainer: Wörterbuch der Philosophie; 1. Aufl.; 1984; Humboldt; München;
ISBN 3581664852; Das unentbehrliche Nachschlagewerk über Begriffe und Persönlichkeiten
der Philosophie, über 1500 Stichwörter.
407) Lutz, Bernd (Hrsg.): Die großen Philosophen des 20. Jahrhunderts; 1. Aufl.; 1999;
Deutscher Taschenbuch Verlag; München; ISBN 3423325178; Biographisches Lexikon.
408) Höffe, Otfried: Aristoteles; 2., überarb. Aufl.; 1999; C. H. Beck; München; ISBN
3406419607; Mit 7 Abbildungen.
409) Kant, Immanuel: Kritik der reinen Vernunft; 1. Aufl.; 1998; Meiner; Hamburg; ISBN
3787313192; Nach der 1. und 2. Orig.-Ausg. hrsg. von Jens Timmermann. Mit einer Bibliographie
von Heiner Klemme.
410) Kant, Immanuel: Grundlegung zur Metaphysik der Sitten; 1. Aufl.; 1999; Meiner; Hamburg;
ISBN 3787314431; Mit einer Einleitung hrsg. von Bernd Kraft und Dieter Schönecker.
411) Hegel, Georg Wilhelm Friedrich: Phänomenologie des Geistes; 1. Aufl.; 1988; Meiner;
Hamburg; ISBN 3787307699; Mit einer Einleitung von Wolfgang Bonsiepen.
412) Fetscher, Iring: Marx; 1. Aufl.; 2004; Panorama; Wiesbaden; ISBN 3926642483; Spektrum
Meisterdenker.
413) Gardiner, Patrick: Kierkegaard; 1. Aufl.; 2004; Panorama; Wiesbaden; ISBN
3926642319; Spektrum Meisterdenker.
414) Tanner, Michael: Nietzsche; 1. Aufl.; 2004; Panorama; Wiesbaden; ISBN 3926642459;
Spektrum Meisterdenker.
415) Möbuß, Susanne: Sartre; 1. Aufl.; 2004; Panorama; Wiesbaden; ISBN 3926642300;
Spektrum Meisterdenker.
416) Roth, Gerhard: Fühlen, Denken, Handeln; 1. Aufl.; 2003; Suhrkamp; Frankfurt am Main;
ISBN 3518292781; Wie das Gehirn unser Verhalten steuert.
417) Andersen, Svend: Einführung in die Ethik; 1. Aufl.; 2000; Walter de Gruyter; Berlin;
ISBN 3110150735; Studienbuch.
418) Eliade, Mircea: Die Religionen und das Heilige; 1. Aufl.; 1998; Insel; Frankfurt am Main;
ISBN 345833887X; Elemente der Religionsgeschichte.
419) Dalai Lama: Einführung in den Buddhismus; 16. Aufl.; 2001; Herder; Freiburg; ISBN
3451049465; Die Harvard-Vorlesungen.
420) Hillebrandt, Alfred (Übers.): Upanishaden; 47.-49. Tsd.; 1990; Diederichs; München;
ISBN 3424005754; Die Geheimlehre der Inder.
421) Kennedy, Alex: Was ist Buddhismus?; 1. Aufl.; 1985; Goldmann; München; ISBN
3442123968; Lehre und Weltsicht einer großen geistigen Tradition, die heute auch das westliche
Denken beeinflusst.
422) Rinpoche, Sogyal: Funken der Erleuchtung; 1. Aufl.; 1995; Bertelsmann; Rheda-
Wiedenbrück; ohne ISBN; Buddhistische Weisheit für jeden Tag des Jahres.
423) Esposito, John L.: Von Kopftuch bis Scharia; 3. Aufl.; 2004; Reclam; Leipzig; ISBN
3379201057; Was man über den Islam wissen sollte.
424) Engemann, Wilfried: Einführung in die Homiletik; 1. Aufl.; 2002; Francke; Tübingen;
ISBN 3772022774; Taschenbuch.
425) England, Roger; Bancroft, Anne (Hrsg.): Spirituelle Kostbarkeiten; 1. Aufl.; 2002; Hermann
Bauer; Freiburg; ISBN 3762608652; Zen.
426) Lechner, Odilo: Engel; 1. Aufl.; 2004; Wilhelm Heyne; München; ISBN 3453879449;
Begegnungen mit Gottes Boten.
427) Wachtturm Bibel- und Traktat-Gesellschaft (Hrsg.): Die Suche der Menschheit nach
Gott; 1. Aufl.; 1990; Wachtturm-Gesellschaft; Selters; ohne ISBN; Religion.
428) Wehr, Gerhard: Europäische Mystik; Genehmigte Lizenzausg.; 2005; Panorama; Wiesbaden;
ISBN 3926642548; Eine Einführung.
429) Schweer, Thomas; Rink, Steffen: Benedikt XVI.; 1. Aufl.; 2005; Ullstein; Berlin; ISBN
354836828X; Der deutsche Papst.
430) Dalai Lama: Der Wille zum Frieden; 1. Aufl.; 2005; Fischer; Frankfurt am Main; ISBN
3596167221; Taschenbuch.
© 1983-2012 by Boris Haase page 133 of 154

431) Knoblauch, Hubert: Religionssoziologie; 1. Aufl.; 1999; Walter de Gruyter; Berlin; ISBN
3110163470; Sammlung Göschen 2094.
432) Largier, Niklaus (Übers.): Das Buch von der geistigen Armut; 1. Aufl.; 1989; Artemis;
Zürich; ISBN 3760807461; Eine mittelalterliche Unterweisung zum vollkommenen Leben.
433) Schumann, Hans Wolfgang: Die großen Götter Indiens; 1. Aufl.; 2004; Hugendubel;
Kreuzlingen; ISBN 3896314297; Grundzüge von Hinduismus und Buddhismus.
434) Gunturu, Vanamali: Hinduismus; 1. Aufl.; 2002; Hugendubel; Kreuzlingen; ISBN
3720523446; Taschenbuch.
435) Ess, Hans van: Der Konfuzianismus; 1. Aufl.; 2003; C. H. Beck; München; ISBN
3406480063; Mit 4 Abbildungen und 1 Karte.
436) Hasenfratz, Hans-Peter: Religion - was ist das?; 1. Aufl.; 2002; Herder; Freiburg; ISBN
3451053225; Lebensorientierung und Andere Wirklichkeit.
437) Vinzent, Markus (Hrsg.): Theologen; 1. Aufl.; 2004; Metzler; Stuttgart; ISBN
3476020258; 185 Porträts von der Antike bis zur Gegenwart.
438) Steinseifer, Wolfgang (Hrsg.): Die Bibel auf einen Blick; 1. Aufl.; 2004; Brockhaus;
Wuppertal; ISBN 3417206472; Taschenbuch.
439) Härle, Wilfried: Dogmatik; 2., überarb. Aufl.; 2000; Walter de Gruyter; Berlin; ISBN
3110165899; Lehrbuch.
440) Drosdowski, Günther (Hrsg.): Duden, Die deutsche Rechtschreibung Band 1; 21., völlig
neu bearb. und erw. Aufl.; 1996; Dudenverlag; Mannheim; ISBN 3411040114; Auf der
Grundlage der neuen amtlichen Rechtschreibregeln.
441) Auberle, Anette; Klosa, Annette (Bearb.): Duden, Herkunftswörterbuch Band 7; 3., völlig
neu bearb. und erw. Aufl.; 2001; Dudenverlag; Mannheim; ISBN 3411040734; Etymologie
der deutschen Sprache.
442) Eickhoff, Birgit; Haller-Wolf, Angelika; Klosa, Annette et al. (Bearb.): Duden, Das Bedeutungswörterbuch
Band 10; 3., neu bearb. und erw. Aufl.; 2002; Dudenverlag; Mannheim;
ISBN 341104103X; Wortbildung und Wortschatz.
443) Baumgärtner, Klaus; Steger, Hugo et al.: Funk-Kolleg Sprache 1; 128.-130. Tsd.; 1985;
Fischer; Frankfurt am Main; ISBN 3596261112; Eine Einführung in die moderne Linguistik.
444) Baumgärtner, Klaus; Steger, Hugo et al.: Funk-Kolleg Sprache 2; 106.-107. Tsd.; 1986;
Fischer; Frankfurt am Main; ISBN 3596261120; Eine Einführung in die moderne Linguistik.
445) Gerhardt, Rudolf; Leyendecker, Hans: Lesebuch für Schreiber; 1. Aufl.; 2005; Fischer;
Frankfurt am Main; ISBN 3596164117; Vom richtigen Umgang mit der Sprache und von der
Kunst des Zeitunglesens.
446) Franck, Norbert: Schreiben wie ein Profi; 4., überarb. und erw. Aufl.; 2005; Bund-
Verlag; Frankfurt am Main; ISBN 3766335952; Leitfaden für Texte mit Pfiff und Struktur.
447) Berkenbusch, Eckhard: Praktisches Chinesisch I; 1. Aufl.; 1994; Kommerzieller Verlag;
Peking; ISBN 7100016754; Lehrbuch.
448) Berkenbusch, Eckhard: Praktisches Chinesisch II; 1. Aufl.; 1994; Kommerzieller Verlag;
Peking; ISBN 7100016827; Lehrbuch.
449) Wingen, Hans: Wörterbuch Deutsch - Esperanto; 2. Nachdruck; 1984; Olms; Hildesheim;
ISBN 3487070804; Taschenbuch.
450) Grosjean-Maupin, E.: Plena Vortaro de Esperanto kun Suplemento; 9. Aufl.; 1980; Sennacieca
Asocio Tutmonda; Paris; ohne ISBN; Suplemento kompilita de Prof. G. Waringhien.
451) Sieber, Helmut: Mathematische Begriffe und Formeln; 1. Aufl.; 1973; Klett; Stuttgart;
ISBN 3127124007; Formelsammlung.
452) Laugwitz, Detlef: Zahlen und Kontinuum; Unveränd. Nachdruck; 1994; Bibliographisches
Institut; Mannheim; ISBN 341103128X; Lehrbücher und Monographien zur Didaktik
der Mathematik Band 5.
453) Lorenzen, Paul: Lehrbuch der konstruktiven Wissenschaftstheorie; 1. Aufl.; 1987; Bibliographisches
Institut; Mannheim; ISBN 3411031549; gebunden.
454) Ebbinghaus, Heinz-Dieter; Flum, Jörg; Thomas, Wolfgang: Einführung in die mathematische
Logik; 3., vollst. überarb. und erw. Aufl.; 1992; Bibliographisches Institut; Mannheim;
ISBN 3411156031; Mathematik.
455) Scheid, Harald: Zahlentheorie; 1. Aufl.; 1991; Bibliographisches Institut; Mannheim;
ISBN 3411148411; Mathematik.
© 1983-2012 by Boris Haase page 134 of 154

456) Scheid, Harald: Wahrscheinlichkeitsrechnung; 1. Aufl.; 1992; Bibliographisches Institut;
Mannheim; ISBN 3411158417; Mathematische Texte Band 6.
457) Lüneburg, Heinz: Vorlesungen über Lineare Algebra; 1. Aufl.; 1993; Bibliographisches
Institut; Mannheim; ISBN 3411161515; Versehen mit der zu ihrem Verständnis nötigen Algebra
sowie einigen Bemerkungen zu ihrer Didaktik.
458) Ebbinghaus, Heinz-Dieter: Einführung in die Mengenlehre; 4. Aufl.; 2003; Spektrum
Akademischer Verlag; Heidelberg; ISBN 3827414113; Mathematik.
459) Wirth, Niklaus: Algorithmen und Datenstrukturen mit Modula-2; 4., neubearb. und erw.
Aufl.; 1986; Teubner; Stuttgart; ISBN 3519022605; Mit zahlreichen Figuren, Tabellen, Übungen
und Programmen.
460) Brandstädt, Andreas: Graphen und Algorithmen; 1. Aufl.; 1994; Teubner; Stuttgart;
ISBN 3519021315; Mit zahlreichen Abbildungen.
461) Schwarz, Hans Rudolf: Methode der finiten Elemente; 2., überarb. und erw. Aufl.; 1984;
Teubner; Stuttgart; ISBN 3519123495; Eine Einführung unter besonderer Berücksichtigung
der Rechenpraxis.
462) Collatz, Lothar: Differentialgleichungen; 6., überarb. und erw. Aufl.; 1981; Teubner;
Stuttgart; ISBN 3519220334; Eine Einführung unter besonderer Berücksichtigung der Anwendungen.
463) Beisel, Ernst-Peter; Mendel, Manfred: Optimierungsmethoden des Operations Research
Band 1; 1. Aufl.; 1987; Vieweg; Braunschweig; ISBN 3528089768; Lineare und ganzzahlige
Optimierung.
464) Beisel, Ernst-Peter; Mendel, Manfred: Optimierungsmethoden des Operations Research
Band 2; 1. Aufl.; 1991; Vieweg; Braunschweig; ISBN 3528063076; Optimierung in
Graphen.
465) Heuser, Harro: Funktionalanalysis; 2., neubearb. und erw. Aufl.; 1986; Teubner; Stuttgart;
ISBN 3519122065; Theorie und Anwendung.
466) Lavine, Shaughan: Unerstanding the Infinite; 2nd printing; 1998; Harvard University
Press; Cambridge; ISBN 0674921178; Includes bibliographical references and index.
467) Eisenreich, Günther; Sube, Ralf: Dictionary of Mathematics - Wörterbuch Mathematik;
1. Aufl.; 1987; Harri Deutsch; Thun; ISBN 3871449393; mit etwa 35000 Wortstellen, zweisprachige
Studentenausgabe.
468) Kosmol, Peter: Optimierung und Approximation; 1. Aufl.; 1991; Walter de Gruyter; Berlin;
ISBN 3110123630; Lehrbuch.
469) Kowalsky, Hans-Joachim: Lineare Algebra; 9., überarb. und erw. Aufl.; 1979; Walter de
Gruyter; Berlin; ISBN 3110081644; Mathematik.
470) Beyer, Otfried; Gottwald, Siegfried; Schlosser, Hartmut et al.: Kleine Enzyklopädie Mathematik;
Nachdruck der 2., völlig überarb. Aufl.; 1980; Harri Deutsch; Thun; ISBN
3871443239; gebunden.
471) Bosch, Siegfried: Algebra; 1. Aufl.; 1993; Springer; Berlin; ISBN 3540568336; Mathematik.
472) Walter, Wolfgang: Analysis 1; 3., verb. Aufl.; 1992; Springer; Berlin; ISBN 3540552340;
Mit 145 Abbildungen.
473) Remmert, Reinhold: Funktionentheorie 1; 3., verb. Aufl.; 1992; Springer; Berlin; ISBN
3540552332; Mit 70 Abbildungen.
474) Remmert, Reinhold: Funktionentheorie 2; 1. unveränd. Nachdruck der 1. Aufl.; 1992;
Springer; Berlin; ISBN 3540553843; Mit 19 Abbildungen.
475) Rollnik, Horst: Quantentheorie 1; 2. Aufl.; 2003; Springer; Berlin; ISBN 3540437886;
Grundlagen, Wellenmechanik, Axiomatik.
476) Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar: Bausteine des Chaos; Dt.
Erstausg.; 1998; Rowohlt; Reinbek; ISBN 3499602504; Fraktale.
477) Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar: Chaos; Dt. Erstausg.; 1998;
Rowohlt; Reinbek; ISBN 3499605511; Bausteine der Ordnung.
478) Kröber, Karl Günter: Ein Esel lese nie; 1. Aufl.; 2003; Rowohlt; Reinbek; ISBN
3499615762; Mathematik der Palindrome.
479) Granados, Gilberto; Gurgsdies, Erik: Lern- und Arbeitsbuch Ökonomie; 1. Aufl.; 1999;
Dietz; Bonn; ISBN 3801202704; Wirtschaft.
© 1983-2012 by Boris Haase page 135 of 154

480) ohne Angaben: BGB - Das Bürgerliche Gesetzbuch; 1. Aufl.; 1991; Goldmann; München;
ISBN 3442136326; Der vollständige Text mit Kommentaren und Beispielen.
481) Anzenbacher, Arno: Einführung in die Philosophie; Nachdr. der 3., verb. Aufl.; 1989;
Herder; Wien; ISBN 3210246270; Lizenzausgabe des gleichnamigen Schulbuchs.
482) Völkel, Michael: Das Lexikon der TV-Moderatoren; 1. Aufl.; 2003; Schwarzkopf &
Schwarzkopf; Berlin; ISBN 3896025244; Anekdoten, Fakten und Sprüche aus 50 Jahren TV-
Geschichte.
483) Störig, Hans Joachim: Abenteuer Sprache; 2. Aufl.; 2003; Deutscher Taschenbuch Verlag;
München; ISBN 342330863X; Ein Streifzug durch die Sprachen der Erde.
484) Hermann, Ursula; Rüme, Klaus; Raum, Norbert (Bearb.): Wahrig Fremdwörterlexikon;
Sonderausg.; 1987; Orbis; München; ISBN 3570026817; Vorwort von Gerhard Wahrig.
485) Möller, Christian: Einführung in die Praktische Theologie; 1. Aufl.; 2004; Francke; Tübingen;
ISBN 3772030122; Taschenbuch.
486) Schnelle, Udo: Einleitung in das Neue Testament; 5., durchges. Aufl.; 2005;
Vandenhoeck & Ruprecht; Göttingen; ISBN 3525032382; Taschenbuch.
487) Kreiner, Armin: Gott im Leid; Erw. Neuausg.; 2005; Herder; Freiburg; ISBN
3451286246; Zur Stichhaltigkeit der Theodizee-Argumente.
488) Eliade, Mircea: Geschichte der religiösen Ideen Band 1; 1. Aufl.; 2002; Herder; Freiburg;
ISBN 3451052741; Von der Steinzeit bis zu den Mysterien von Eleusis.
489) Eliade, Mircea: Geschichte der religiösen Ideen Band 2; 1. Aufl.; 2002; Herder; Freiburg;
ISBN 3451052741; Von Gautama Buddha bis zu den Anfängen des Christentums.
490) Eliade, Mircea: Geschichte der religiösen Ideen Band 3; 1. Aufl.; 2002; Herder; Freiburg;
ISBN 3451052741; Von Mohammed bis zum Beginn der Neuzeit.
491) Eliade, Mircea: Geschichte der religiösen Ideen Band 4; 1. Aufl.; 2002; Herder; Freiburg;
ISBN 3451052741; Vom Zeitalter der Entdeckungen bis zur Gegenwart.
492) Volpi, Franco (Hrsg.): Großes Werklexikon der Philosophie Band 1: A bis K;
Jubiläumsausg.; 2004; Kröner; Stuttgart; ISBN 3520839016; gebunden.
493) Volpi, Franco (Hrsg.): Großes Werklexikon der Philosophie Band 2: L bis Z;
Jubiläumsausg.; 2004; Kröner; Stuttgart; ISBN 3520839016; gebunden.
494) Fontana, David: Kursbuch Meditation; 1. Aufl.; 1994; Barth; München; ISBN
350262187X; Alles über die verschiedenen Meditationstechniken und ihre Anwendung, Anleitungen
zur Wahl der geeigneten Methode.
495) Ortberg, John: Jeder ist normal, bis du ihn kennen lernst; 4. Aufl.; 2005; Gerth Medien;
Asslar; ISBN 3865910432; Wie zwischenmenschliche Beziehungen gelingen.
496) ohne Angaben: Katechismus der Katholischen Kirche; 1. Aufl.; 2005; Pattloch; München;
ISBN 3629021409; Kompendium.
497) Grom, Bernhard: Religionspsychologie; 1. Aufl.; 1992; Kösel; München; ISBN
3466203589; auch Vandenhoeck & Ruprecht.
498) Lanoo (Christian Anders): Der Sinn des Lebens - Nirvana Band 1; 1. Aufl.; 2000; Books
on Demand; Norderstedt; ISBN 3898114295; Buddhismus wie er sein sollte und esoterische
Wissenschaften.
499) Lanoo (Christian Anders): Der Sinn des Lebens - Nirvana Band 2; 1. Aufl.; 2000; Books
on Demand; Norderstedt; ISBN 3898114309; Buddhismus wie er sein sollte und esoterische
Wissenschaften.
500) Wilber, Ken: Integrale Spiritualität; 1. Aufl.; 2007; Kösel; München; ISBN
9783466345090; Spirituelle Intelligenz rettet die Welt.
501) Hawkins, David R.: Die Ebenen des Bewusstseins; 5. Aufl.; 2006; VAK; Kirchzarten;
ISBN 3932098021; Von der Kraft, die wir ausstrahlen.
502) Hofmeister, Klaus; Bauerochse, Lothar (Hrsg.): Viele Stimmen - eine Sprache; 1. Aufl.;
2001; Echter; Würzburg; ISBN 3429023823; Beten in den Weltreligionen.
503) Scherhag, Richard; Blüthgen, Joachim; Lauer, Wilhelm: Klimatologie; 9., verb. Aufl.;
1977; Westermann; Braunschweig; ISBN 3141602840; Geographie.
504) Grix, Rolf; Knöll, Wilhelm: Lernfeld Gesellschaft; 3. Aufl.; 1975; Diesterweg; Frankfurt
am Main; ISBN 3425016679; Lehr- und Arbeitsbuch für den politischen Unterricht.
505) Görgens, Alfred: Kulinarisches Solo; 1. Aufl.; 1991; Falken; Niedernhausen; ISBN
3806811547; Gerichte für eine Person.
© 1983-2012 by Boris Haase page 136 of 154

506) Hinz, Thomas: Aquarellmalerei; Nachaufl.; 1983; Falken; Niedernhausen; ISBN
3806850992; Materialien, Techniken, Motive.
507) Dawkins, Richard: Der Gotteswahn; 1. Aufl.; 2007; Ullstein; Berlin; ISBN
9783550086885; gebunden.
508) Hawkins, David R.: Das All-sehende Auge; 3. Aufl.; 2006; Sheema-Medien; Wasserburg;
ISBN 3931560198; gebunden.
509) Hawkins, David R.: Licht des Alls; 1. Aufl.; 2006; Sheema-Medien; Wasserburg; ISBN
3931560201; Die Wirklichkeit des Göttlichen.
510) Renftel, Lars-Oliver; Schaffer-Hartmann, Richard (Hrsg.): Hanau; 1. Aufl.; 2002; CoCon;
Hanau; ISBN 3928100920; Geschichte, Kultur, Gegenwart.
511) Sach, Jacky; Faust, Jessica: Zen; 1. Aufl.; 2004; Lotos; München; ISBN 3778781669;
Entspannung für Körper und Geist, Kraft und Frieden für die Seele.
512) Beck, Charlotte Joko: Zen im Alltag; 1. Aufl.; 2005; Droemer/Knaur; München; ISBN
3426665611; Aus dem Amerikanischen von Bettine Braun.
513) Carstensen, Kai-Uwe; Ebert, Christian; Endriss, Cornelia et al. (Hrsg.: Computerlinguistik
und Sprachtechnologie; 2., überarb. und erw. Aufl.; 2004; Elsevier; München; ISBN
3827414075; gebunden.
514) Lubkowitz, Mark: Webseiten programmieren und gestalten; 2., erw. Aufl.; 2005; Galileo
Press; Bonn; ISBN 3898425576; Mit CD-ROM.
515) Michel, Reiner M.: Know-how der Unternehmensplanung; 2., völlig neubearb. und erw.
Aufl.; 1991; Sauer; Heidelberg; ISBN 3793870243; Budgetierung, Controlling, Taktische Planung,
Langfristplanung und Strategie.
516) Manekeller, Wolfgang; Reinert-Schneider, Gabriele: Gutes Deutsch schreiben und
sprechen; 1. Aufl.; 1989; Falken; Niedernhausen; ISBN 3806844321; gebunden.
517) Auffarth, Christoph; Bernard, Jutta; Mohr, Hubert (Hrsg.): Metzler Lexikon Religion
Band 1; 1. Aufl.; 1999; Metzler; Stuttgart; ISBN 3476015513; Gegenwart - Alltag - Medien.
518) Auffarth, Christoph; Bernard, Jutta; Mohr, Hubert (Hrsg.): Metzler Lexikon Religion
Band 2; 1. Aufl.; 1999; Metzler; Stuttgart; ISBN 3476015521; Gegenwart - Alltag - Medien.
519) Auffarth, Christoph; Bernard, Jutta; Mohr, Hubert (Hrsg.): Metzler Lexikon Religion
Band 3; 1. Aufl.; 2000; Metzler; Stuttgart; ISBN 347601553X; Gegenwart - Alltag - Medien.
520) Auffarth, Christoph; Bernard, Jutta; Mohr, Hubert (Hrsg.): Metzler Lexikon Religion
Band 4; 1. Aufl.; 2002; Metzler; Stuttgart; ISBN 3476015548; Gegenwart - Alltag - Medien.
521) ohne Angaben: Lexikon der östlichen Weisheitslehren; Lizenzausg.; 2005; Albatros;
Düsseldorf; ISBN 349196136X; Buddhismus, Hinduismus, Taoismus, Zen.
522) Kreiner, Armin: Das wahre Antlitz Gottes - oder was wir meinen, wenn wir Gott sagen;
1. Aufl.; 2006; Herder; Freiburg; ISBN 3451287765; gebunden.
523) Monroe, Robert A.: Der zweite Körper; Taschenbuchausg.; 2007; Wilhelm Heyne; München;
ISBN 9783453700611; Astral- und Seelenreisen in ferne Sphären der geistigen Welt.
524) ohne Angaben: Brockhaus-Enzyklopädie Band 1; 19., völlig neubearb. Aufl.; 1986;
Brockhaus; Mannheim; ISBN 3765311014; A - Apt.
525) ohne Angaben: Brockhaus-Enzyklopädie Band 2; 19., völlig neubearb. Aufl.; 1987;
Brockhaus; Mannheim; ISBN 3765311022; Apu - Bec.
526) ohne Angaben: Brockhaus-Enzyklopädie Band 3; 19., völlig neubearb. Aufl.; 1987;
Brockhaus; Mannheim; ISBN 3765311030; Bed - Brn.
527) ohne Angaben: Brockhaus-Enzyklopädie Band 4; 19., völlig neubearb. Aufl.; 1987;
Brockhaus; Mannheim; ISBN 3765311049; Bro - Cos.
528) ohne Angaben: Brockhaus-Enzyklopädie Band 5; 19., völlig neubearb. Aufl.; 1988;
Brockhaus; Mannheim; ISBN 3765311057; Cot - Dr.
529) ohne Angaben: Brockhaus-Enzyklopädie Band 6; 19., völlig neubearb. Aufl.; 1988;
Brockhaus; Mannheim; ISBN 3765311065; Ds - Ew und erster Nachtrag.
530) ohne Angaben: Brockhaus-Enzyklopädie Band 7; 19., völlig neubearb. Aufl.; 1988;
Brockhaus; Mannheim; ISBN 3765311073; Ex - Frt.
531) ohne Angaben: Brockhaus-Enzyklopädie Band 8; 19., völlig neubearb. Aufl.; 1989;
Brockhaus; Mannheim; ISBN 3765311081; Fru - Gos.
532) ohne Angaben: Brockhaus-Enzyklopädie Band 9; 19., völlig neubearb. Aufl.; 1989;
Brockhaus; Mannheim; ISBN 376531109X; Got - Herp.
© 1983-2012 by Boris Haase page 137 of 154

533) ohne Angaben: Brockhaus-Enzyklopädie Band 10; 19., völlig neubearb. Aufl.; 1989;
Brockhaus; Mannheim; ISBN 3765311103; Herr - Is.
534) ohne Angaben: Brockhaus-Enzyklopädie Band 11; 19., völlig neubearb. Aufl.; 1990;
Brockhaus; Mannheim; ISBN 3765311111; It - Kip.
535) ohne Angaben: Brockhaus-Enzyklopädie Band 12; 19., völlig neubearb. Aufl.; 1990;
Brockhaus; Mannheim; ISBN 376531112X; Kir - Lag und zweiter Nachtrag.
536) ohne Angaben: Brockhaus-Enzyklopädie Band 13; 19., völlig neubearb. Aufl.; 1990;
Brockhaus; Mannheim; ISBN 3765311138; Lah - Maf.
537) ohne Angaben: Brockhaus-Enzyklopädie Band 14; 19., völlig neubearb. Aufl.; 1991;
Brockhaus; Mannheim; ISBN 3765311146; Mag - Mod.
538) ohne Angaben: Brockhaus-Enzyklopädie Band 15; 19., völlig neubearb. Aufl.; 1991;
Brockhaus; Mannheim; ISBN 3765311154; Moe - Nor.
539) ohne Angaben: Brockhaus-Enzyklopädie Band 16; 19., völlig neubearb. Aufl.; 1991;
Brockhaus; Mannheim; ISBN 3765311162; Nos - Per.
540) ohne Angaben: Brockhaus-Enzyklopädie Band 17; 19., völlig neubearb. Aufl.; 1992;
Brockhaus; Mannheim; ISBN 3765311170; Pes - Rac.
541) ohne Angaben: Brockhaus-Enzyklopädie Band 18; 19., völlig neubearb. Aufl.; 1992;
Brockhaus; Mannheim; ISBN 3765311189; Rad - Rüs und dritter Nachtrag.
542) ohne Angaben: Brockhaus-Enzyklopädie Band 19; 19., völlig neubearb. Aufl.; 1992;
Brockhaus; Mannheim; ISBN 3765311197; Rut - Sch.
543) ohne Angaben: Brockhaus-Enzyklopädie Band 20; 19., völlig neubearb. Aufl.; 1993;
Brockhaus; Mannheim; ISBN 3765311200; Sci - Sq.
544) ohne Angaben: Brockhaus-Enzyklopädie Band 21; 19., völlig neubearb. Aufl.; 1993;
Brockhaus; Mannheim; ISBN 3765311219; Sr - Teo.
545) ohne Angaben: Brockhaus-Enzyklopädie Band 22; 19., völlig neubearb. Aufl.; 1993;
Brockhaus; Mannheim; ISBN 3765311227; Tep - Ur.
546) ohne Angaben: Brockhaus-Enzyklopädie Band 23; 19., völlig neubearb. Aufl.; 1994;
Brockhaus; Mannheim; ISBN 3765311235; Us - Wej.
547) ohne Angaben: Brockhaus-Enzyklopädie Band 24; 19., völlig neubearb. Aufl.; 1994;
Brockhaus; Mannheim; ISBN 3765311243; Wek - Zz und vierter Nachtrag.
548) Scholze-Stubenrecht, Werner; Sykes, John (Red.): Brockhaus-Enzyklopädie Band 29;
19., völlig neubearb. Aufl.; 1996; Brockhaus; Mannheim; ISBN 3765311294; Wörterbuch
Englisch: Englisch - Deutsch, Deutsch - Englisch.
549) ohne Angaben: Brockhaus-Enzyklopädie Band 30; 19., völlig neubearb. Aufl.; 1996;
Brockhaus; Mannheim; ISBN 3765311316; Ergänzungen A - Z.
550) Hornby, A. S.; Cowie, A. P.; Gimson, A. C.: Oxford Advanced Learner's Dictionary of
Current English; 12. Druck; 1981; Cornelsen & Oxford University Press; Berlin; ISBN
3810900486; Revised and updated.
551) Baer, Dieter; Wermke, Matthias (Bearb.): Duden, Das große Fremdwörterbuch; 2., neu
bearb. und erw. Aufl.; 2000; Dudenverlag; Mannheim; ISBN 3411041625; Herkunft und Bedeutung
der Fremdwörter.
552) Müller, Kristiane; Urban, Eberhard (Hrsg.): Die Weibsbilder im Spiegel der Karikatur; 1.
Aufl.; 1987; Edition Aktuell; Menden; ISBN 3924456518; Eine Kultur- und Sittengeschichte
des 19. Jahrhunderts.
553) Bayer, Karl: Nota bene!; 1. Aufl.; 1993; Artemis & Winkler; Zürich; ISBN 3760810926;
Das lateinische Zitatenlexikon.
554) Waechter, Friedrich-Karl: Opa Hucke's Mitmach-Kabinett; 2. Aufl.; 1977; Beltz &
Gelberg; Weinheim; ISBN 3407805152; Jugendbuch.
555) Wulff, David M.: Psychology of Religion; 2nd Ed.; 1997; John Wiley & Sons; New York;
ISBN 0471037060; Classic and Contemporary.
556) Bieri, Peter (Hrsg.): Analytische Philosophie des Geistes; 3., unveränd. Aufl.; 1997;
Beltz Athenäum; Weinheim; ISBN 3895471178; Neue wissenschaftliche Bibliothek.
557) Meixner, Uwe: Einführung in die Ontologie; 1. Aufl.; 2004; Wissenschaftliche Buchgesellschaft;
Darmstadt; ISBN 3534154584; Philosophie.
558) Tiedemann, Paul: Internet für Philosophen; 2., überarb. Aufl.; 1999; Primus; Darmstadt;
ISBN 3896781081; Eine praxisorientierte Einführung.
© 1983-2012 by Boris Haase page 138 of 154

559) Brüning, Walther: Grundlagen der Strengen Logik; 1. Aufl.; 1996; Königshausen &
Neumann; Würzburg; ISBN 3826012046; Philosophie.
560) Schnell, Rainer; Hill, Paul B.; Esser, Elke: Methoden der empirischen Sozialforschung;
6., völlig überarb. und erw. Aufl.; 1999; Oldenbourg; München; ISBN 3486250434; gebunden.
561) Sikin, Evgenij: Lineare Räume und Abbildungen; 1. Aufl.; 1994; Spektrum, Akademischer
Verlag; Heidelberg; ISBN 3860253050; Mathematik.
562) Sachs, Lothar: Angewandte Statistik; 8., völlig neu bearb. und erw. Aufl.; 1997; Springer;
Berlin; ISBN 3540604948; Anwendung statistischer Methoden.
563) Jänich, Klaus: Lineare Algebra; 2. Aufl.; 1981; Springer; Berlin; ISBN 3540104704; Ein
Skriptum für das erste Semester.
564) Hämmerlin, Günther; Hoffmann, Karl-Heinz: Numerische Mathematik; 2. Aufl.; 1991;
Springer; Berlin; ISBN 354053539X; Mit 72 Abbildungen.
565) Zimbardo, Philip G.: Psychologie; 4., neubearb. Aufl.; 1983; Springer; Berlin; ISBN
3540121234; Mit 322 zum Teil farbigen Abbildungen.
566) Dambmann, Gerhard; Lange, Helmut; Rohde, Manfred: Mit Edmund Hillary durch den
Himalaya; 2. Aufl.; 1987; Herder; Freiburg; ISBN 3451210754; Mit zahlreichen Abbildungen.
567) Molcho, Samy: Körpersprache; 1. Aufl.; 1984; Mosaik; München; ISBN 3570049736; Mit
Fotografien von Thomas Klinger und Hans Albrecht Lusznat.
568) Roetzel, Bernhard: Der Gentleman; 1. Aufl.; 1999; Könemann; Köln; ISBN 3895086371;
Handbuch der klassischen Herrenmode.
569) Vass, László; Molnár, Magda: Herrenschuhe handgearbeitet; 1. Aufl.; 1999; Könemann;
Köln; ISBN 3895081116; Fotografie Georg Valerius.
570) Savant, Marilyn vos; Fleischer, Leonore: BrainBuilding; 1. Aufl.; 1992; Falken;
Niedernhausen; ISBN 3806847045; Das 12-Wochen-Trainingsprogramm für Gedächtnis,
Logik, Kreativität.
571) Hürlimann, Gertrud I.: Astrologie; 3. Aufl.; 1984; Novalis; Schaffhausen; ISBN
3721430026; Ein methodisch aufgebautes Lehrbuch.
572) Jöckle, Clemens: Das große Heiligenlexikon; 1. Aufl.; 2003; Parkland; Köln; ISBN
3893400451; Mit zahlreichen Abbildungen.
573) Halbfas, Hubertus: Die Bibel; 3. Aufl.; 2002; Patmos; Düsseldorf; ISBN 3491703344; Mit
zahlreichen Abbildungen.
574) Halbfas, Hubertus: Das Christentum; 1. Aufl.; 2004; Patmos; Düsseldorf; ISBN
3491703778; Mit zahlreichen Abbildungen.
575) Quinn, Philipp L.; Taliaferro, Charles (Ed.): A Companion to Philosophy of Religion; 1st
Ed. paperback; 1999; Blackwell; Oxford; ISBN 0631213287; Blackwell Companions to Philosophy
9.
576) Cooper, David (Ed.): A Companion to Aesthetics; Reprint; 1997; Blackwell; Oxford;
ISBN 0631196595; Blackwell Companions to Philosophy 3.
577) Kim, Jaegwon; Sosa, Ernest (Ed.): A Companion to Metaphysics; Reprint; 1998; Blackwell;
Oxford; ISBN 0631199993; Blackwell Companions to Philosophy 7.
578) Inwagen, Peter van; Zimmerman, Dean W. (Ed.): Metaphysics: The Big Questions; 1st
Ed.; 1998; Blackwell; Oxford; ISBN 0631205888; Philosophy.
579) Bunnin, Nicholas; Tsui-James, E. P. (Ed.): The Blackwell Companion to Philosophy;
Reprint; 1998; Blackwell; Oxford; ISBN 0631187898; Blackwell Companions to Philosophy 1.
580) Kugler, Gernot; Böhmer, Ernst; Kümmel, Gerd et al.: Kaufmännische Betriebslehre
Hauptausgabe; 20. Aufl.; 1990; Europa-Lehrmittel; Haan-Gruiten; ISBN 3808590203; Verfasst
von Lehrern an Kaufmännischen Schulen.
581) Deitermann, Manfred; Schmolke, Siegfried: Industriebuchführung mit Kosten- und Leistungsrechnung
IKR; 14., durchges. Aufl.; 1990; Winklers; Darmstadt; ISBN 3804566219;
Einführung und Praxis.
582) Bodden, Horst; Kaußen, Herbert; Renné, Rudi: Past and Future; 2. Aufl.; 1980; Langenscheidt-Longman;
München; ISBN 3526503117; Elective Courses in English for Level II.
583) Bates, Martin; Dudley-Evans, Tony: General Science; New Ed.; 1982; Longman; Essex;
ISBN 0582748607; English for Science and Technology.
© 1983-2012 by Boris Haase page 139 of 154

584) Holtermann, Horst: Ianua Linguae Graecae; 3. Aufl.; 1979; Vandenhoeck & Ruprecht;
Göttingen; ISBN 3525720793; Lese- und Übungsbuch für den griechischen Anfangsunterricht
am Gymnasium.
585) Erdle-Hähner, Rita; Freitag, Günter; Matthes, Dietmar et al. (Hrsg.): Etudes Francaises
Cours Intensif 1; 1. Aufl.; 1980; Klett; Stuttgart; ISBN 3125206006; Schulbuch Französisch.
586) Erdle-Hähner, Rita; Freitag, Günter; Matthes, Dietmar et al. (Hrsg.): Etudes Francaises
Cours Intensif 1; 1. Aufl.; 1981; Klett; Stuttgart; ISBN 3125206200; Grammatisches Beiheft.
587) Erdle-Hähner, Rita; Freitag, Günter; Rolinger, Hermann et al. (Hrsg.): Etudes
Francaises Cours de base Deuxième degré; 1. Aufl.; 1979; Klett; Stuttgart; ISBN
3125202205; Grammatisches Beiheft.
588) Erdle-Hähner, Rita; Freitag, Günter; Rolinger, Hermann et al. (Hrsg.): Etudes
Francaises Cours de base Troisième degré; 1. Aufl.; 1981; Klett; Stuttgart; ISBN
3125203201; Grammatisches Beiheft.
589) Willers, Hermann (Bearb.): Langenscheidts Grammatiktafel Italienisch; 1. Aufl.; 1982;
Langenscheidt; Berlin; ISBN 3468361807; Regeln und zahlreiche praktische Beispiele.
590) Willers, Hermann (Bearb.): Langenscheidts Verb-Tabellen Italienisch; 7. Aufl.; 1982;
Langenscheidt; Berlin; ISBN 3468341814; Unregelmäßige und regelmäßige Verben richtig
konjugiert.
591) Bunke, Horst: Modellgesteuerte Bildanalyse; 1. Aufl.; 1985; Teubner; Stuttgart; ISBN
3519024810; Dargestellt anhand eines Systems zur automatischen Auswertung von Sequenzszintigrammen
des menschlichen Herzens.
592) Baumann, Rüdeger: Informatik mit Pascal; 1. Aufl.; 1981; Klett; Stuttgart; ISBN
3127177402; Schulbuch.
593) Börger, Egon: Berechenbarkeit, Komplexität, Logik; 3., verb. und erw. Aufl.; 1992; Vieweg;
Braunschweig; ISBN 3528289287; Algorithmen, Sprachen und Kalküle unter besonderer
Berücksichtigung ihrer Komplexität.
594) Aho, Alfred V.; Hopcroft, John E.; Ullman, Jeffrey D.: The Design and Analysis of Computer
Algorithms; 1st Ed.; 1974; Addison Wesley; London; ISBN 0201000296; Informatics.
595) Grams, Timm: Denkfallen und Programmierfehler; 1. Aufl.; 1990; Springer; Berlin; ISBN
3540520392; Mit 17 Abbildungen.
596) Lehnert, Uwe: Der EDV-Dozent; Akt. und erw. Aufl.; 1992; Markt und Technik; Haar;
ISBN 387791201X; Planung und Durchführung von EDV-Lehrveranstaltungen.
597) Woll, Artur: Allgemeine Volkswirtschaftslehre; 10., überarb. und erg. Aufl.; 1990;
Vahlen; München; ISBN 3800614758; Vahlens Handbücher für Wirtschafts- und Sozialwissenschaften.
598) Bruce, Betsy: Jetzt lerne ich Dreamweaver 4; 1. Aufl.; 2001; Markt und Technik; München;
ISBN 3827260957; Deutsche Übersetzung: Judith Muhr.
599) Steyer, Ralph: Opera 5; 1. Aufl.; 2001; Markt und Technik; München; ISBN
3827261147; So surfen Sie bequem und schnell durchs Netz!.
600) Sturm, Eberhard: Programmieren in PL/I; 1. Aufl.; 1990; Vieweg; Braunschweig; ISBN
3528047925; Eine moderne Einführung.
601) Todino, Grace; Strang, John; Peek, Jerry: UNIX - ein praktischer Einstieg; 1. Aufl.;
1996; O'Reilly; Bonn; ISBN 3930673290; Erste Schritte mit Unix.
602) Knuth, Donald Ervin: The Art of Computer Programming Volume 3; 2nd Ed.; 1998; Addison
Wesley; Reading; ISBN 0201896850; Sorting and Searching.
603) Doberenz, Walter; Kowalski, Thomas: Datenbankprogrammierung mit Visual Basic 6; 1.
Aufl.; 1999; Microsoft Press; Unterschleißheim; ISBN 3860634852; Grundlagen, Rezepte
und Anwendungsbeispiele zur Datenbankprogrammierung mit Visual Basic 6, DAO und
ADO.
604) Barnert, Silvia; Boeckh, Martin; Delbrück, Matthias et al.: Der Brockhaus - Computer
und Informationstechnologie; 1. Aufl.; 2002; Brockhaus; Mannheim; ISBN 3765302511;
Hardware, Software, Multimedia, Internet, Telekommunikation.
605) Andrews, Mark: Visual C++ jetzt!; 1. Aufl.; 1996; Microsoft Press; Unterschleißheim;
ISBN 3860630202; Das komplette Lernpaket: mit voll funktionsfähiger Version von Microsoft
Visual C++.
© 1983-2012 by Boris Haase page 140 of 154

606) Steyer, Ralph: Java 2; 1. Aufl.; 2002; Markt und Technik; München; ISBN 3827262429;
Kompakt, komplett, kompetent.
607) Franke, Matthias: Visual Basic 6; 1. Aufl.; 1998; Data Becker; Düsseldorf; ISBN
3815811449; Mit den Supersteps zum Erfolg.
608) Graf, Ludwig (Hrsg.): Telekolleg 2 Datenverarbeitung; 1. Aufl.; 1990; TR-Verlagsunion;
München; ISBN 3805821476; Informatik.
609) Maubach, Claudia; Dörr, Cornelia: 3D WohnDesigner; 3. Aufl.; 1996; Data Becker; Düsseldorf;
ISBN 3815869617; Der Profi-Designer in einer neuen Generation.
610) Harten, Hans-Ulrich: Physik für Mediziner; 3., neubearb. und erg. Aufl.; 1977; Springer;
Berlin; ISBN 3540081828; Eine Einführung.
611) Jahrreiß, Heribert: Einführung in die Physik für Studenten der Medizin und der Naturwissenschaften;
1. Aufl.; 1977; Deutscher Ärzte-Verlag; Köln-Lövenich; ISBN 3769100352;
Mit vollständiger Berücksichtigung des Gegenstandskatalogs für die Ärztliche Vorprüfung
und entsprechenden Texthinweisen.
612) Rebhan, Eckhard: Theoretische Physik I; 1. Nachdruck; 2001; Spektrum Akademischer
Verlag; Heidelberg; ISBN 3827402468; Mechanik, Elektrodynamik, Relativitätstheorie, Kosmologie.
613) Krueger, Franz R.: Physik und Evolution; 1. Aufl.; 1984; Paul Parey; Berlin; ISBN
348961934X; Physikalische Ansätze zu einer Einheit der Naturwissenschaften auf evolutiver
Grundlage.
614) Haken, Hermann: Synergetik; 1. Aufl.; 1982; Springer; Berlin; ISBN 354011050X; Eine
Einführung.
615) Dorn, Friedrich; Bader, Franz: Physik in einem Band; 1. Aufl.; 1976; Schroedel; Hannover;
ISBN 3507861704; Schulbuch.
616) Hawking, Stephen W.: Eine kurze Geschichte der Zeit; 176.-215. Tsd.; 1988; Rowohlt;
Reinbek; ISBN 3498028847; Die Suche nach der Urkraft des Universums.
617) Kaufmann, H.; Jecklin, L.: Grundlagen der anorganischen Chemie; 8. Aufl.; 1977;
Birkhäuser; Basel; ISBN 3764309377; Chemie.
618) Cuny, Karl-Heinz; Weber, Walter: Chemie - Welt der Stoffe; 1. Aufl.; 1975; Schroedel;
Hannover; ISBN 3507861801; Experiment - Struktur - Modell.
619) Mortimer, Charles E.: Chemie; 3., neubearb. Aufl.; 1980; Thieme; Stuttgart; ISBN
313484303X; Das Basiswissen der Chemie in Schwerpunkten.
620) Lipschutz, Seymour: Wahrscheinlichkeitsrechnung; Nachdruck; 1980; McGraw-Hill;
Düsseldorf; ISBN 0070843619; Theorie und Anwendung.
621) J. Kelly Beatty, Brian O'Leary, Andrew Chaikin (Hrsg.): Die Sonne und ihre Planeten; 1.
Aufl.; 1983; Physik-Verlag; Weinheim; ISBN 3876640563; Weltraumforschung in einer neuen
Dimension.
622) Pugnetti, Gino: Beethoven und seine Zeit; 1. Aufl.; 1965; Vollmer; Wiesbaden; ohne
ISBN; Musiker.
623) Arndt, Claudia Maria; Bernsen, Thomas; Breuer, Klaus et al.: Jahrbuch des Rhein-Sieg-
Kreises 2007; 1. Aufl.; 2006; Edition Blattwelt; Niederhofen; ISBN 3936256241; Landschaft
und Natur, Geschichte und Geschichten, Leben und Kultur, Wirtschaft und Technik, Chronik
2005 / 2006.
624) Mayer, Ferdinand (Bearb.): Diercke Weltatlas; 5. Aufl. der Neubearb.; 1975; Westermann;
Braunschweig; ISBN 3141005001; 200 Kartenseiten.
625) The American Astro Analysis Institute (Hrsg.): Jungfrau; 1. Aufl.; 1979; Goldmann;
München; ISBN 3442100283; Astrologie.
626) Orban, Peter; Zinnel, Ingrid; Weller, Thea: Symbolon; 1. Aufl.; 1993; Hugendubel; München;
ISBN 3880347069; Das Spiel der Erinnerungen - Zur Symbolik astrologischer Aspekte.
627) Seifert, Traudl: Heilige in Kunst und Legende; Unveränd. Aufl.; 1973; Schuler; München;
ASIN B0000BNU4O; Mit zahlreichen Abbildungen.
628) Traeger, Jörg: Renaissance und Religion; 1. Aufl.; 1997; C. H. Beck; München; ISBN
3406428010; Die Kunst des Glaubens im Zeitalter Raphaels.
629) Kühn, Helga-Maria; Brinkmann, Jens-Uwe: Göttingen; 1. Aufl.; 1985; Vandenhoeck &
Ruprecht; Göttingen; ISBN 3525391587; Fotos von Helmut Scheiter und Hans Wilder.
© 1983-2012 by Boris Haase page 141 of 154

630) Lipschutz, Seymour; Poe, Arthur: Programmieren mit FORTRAN einschließlich strukturiertes
FORTRAN; 1. Aufl.; 1981; McGraw-Hill; Hamburg; ISBN 0070920303; Theorie und
Anwendung.
631) Spiegel, Murray R.: Allgemeine Mechanik; Nachdruck; 1979; McGraw-Hill; Düsseldorf;
ISBN 0070843767; Theorie und Anwendung - Mit einer Einführung in die Lagrangeschen
und Hamiltonschen Bewegungsgleichungen.
632) Büchner, Rudolf: Bücher und Menschen; 1. Aufl.; 1976; Mohn; Gütersloh; ISBN
3570025012; Vom Buch und seinen Wirkungen in Geschichte und Gegenwart.
633) Connolly, Peter; Dodge, Hazel: Die antike Stadt; 1. Aufl.; 1998; Könemann; Köln; ISBN
3829011040; Das Leben in Athen & Rom.
634) Crosher, Judith: Die Griechen; 1. Aufl.; 1976; Falken; Wiesbaden; ISBN 380688019;
Große Völker der Vergangenheit.
635) Goscinny, Rene; Uderzo, Albert: Obelix GmbH & Co.KG; Nachdruck; 1984; Delta;
Stuttgart; ISBN 3770400232; Großer Asterix-Band XXIII.
636) Bretecher, Claire: Doktor med. Bobo; 1. Aufl.; 1986; Rowohlt; Reinbek; ISBN
3498005014; Sprechstunden nach Vereinbarung.
637) Bretecher, Claire: Agrippina; 16.-23. Tsd.; 1989; Rowohlt; Reinbek; ISBN 3498005324;
Mozart ist Asche bis auf die Musik zum Film.
638) Moers, Walter: Kleines Arschloch; 5. Aufl.; 1991; Eichborn; Frankfurt am Main; ISBN
382183000X; Prrrffzzz!!!.
639) Müller, Siegfried; Rolinger, Hermann; Wüst, Arthur (Hrsg.): Etudes Francaises Cours de
base Premier degré; 1. Aufl.; 1977; Klett; Stuttgart; ISBN 3125201500; Cahier d'exercices.
640) Erdle-Hähner, Rita; Rolinger, Hermann; Wüst, Arthur (Hrsg.): Etudes Francaises Cours
de base Deuxième degré; 1. Aufl.; 1979; Klett; Stuttgart; ISBN 3125202507; Cahier
d'exercices.
641) Erdle-Hähner, Rita; Rolinger, Hermann; Wüst, Arthur (Hrsg.): Etudes Francaises Cours
de base Troisième degré; 1. Aufl.; 1981; Klett; Stuttgart; ISBN 3125203503; Cahier
d'exercices.
642) Keller, Will (Hrsg.): Merian Berlin; 1. Aufl.; 1989; Hoffmann & Campe; Hamburg; ISBN
345528907X; Monatsheft der Städte und Landschaften.
643) Keller, Will (Hrsg.): Merian Deutsche Ostseeküste; 1. Aufl.; 1994; Hoffmann & Campe;
Hamburg; ISBN 3455294057; Monatsheft der Städte und Landschaften.
644) Heine, Helme: Uhren haben keine Bremse; Orig.ausg.; 1985; Diogenes; Zürich; ISBN
3257020139; Cartoons.
645) Goscinny, Rene; Uderzo, Albert: Asterix und Cleopatra; 2. Aufl.; 2004; Delta; Stuttgart;
ISBN 3770400569; Großer Asterix-Band II.
646) Goscinny, Rene; Uderzo, Albert: Streit um Asterix; 9. Aufl.; 2004; Delta; Stuttgart; ISBN
3770400151; Großer Asterix-Band XV.
647) Goscinny, Rene; Uderzo, Albert: Die Lorbeeren des Cäsar; 6. Aufl.; 2007; Delta; Stuttgart;
ISBN 3770400186; Großer Asterix-Band XVIII.
648) Holl, Adolf: Religionssoziologie; 1. Aufl.; 1995; ÖBV Pädagogischer Verlag; Wien; ISBN
3215073374; Materialien und Texte zur Politischen Bildung Band 8.
649) Abel, Dietrich von; Fink, Cornelia; Gillhofer, Peter et al.: Wie? Warum? Weshalb?; 1.
Aufl.; 1991; Das Beste; Stuttgart; ISBN 387070375X; Verblüffende Ideen, geniale Lösungen,
faszinierende Fakten aus Natur und Technik.
650) Shelly, Gary B.; Cashman, Thomas J.; Goodwin, Hal: RPG II, RPG III, and RPG/400;
1st Ed.; 1990; Boyd & Fraser; Boston; ISBN 0878352465; Informatics.
651) Bühl, Achim; Zöfel, Peter: SPSS für Windows Version 6.1; 3., überarb. und erg. Aufl.;
1996; Addison Wesley; Bonn; ISBN 3827311349; Praxisorientierte Einführung in die moderne
Datenanalyse.
652) Bühler, Walter K.: Gauss; 1. Aufl.; 1986; Springer; Berlin; ISBN 3540168834; Eine biographische
Studie.
653) Trökes, Anna: Yoga; 1. Aufl.; 2003; Klett; Stuttgart; ISBN 3129398732; Ankommen in
Körper, Geist und Atem.
654) Engelhardt, Friedrich Rudolf: Das Wissen von der Hand; 1. Aufl.; 1987; Hugendubel;
München; ISBN 3880343276; Handlesekunst als Wissenschaft.
© 1983-2012 by Boris Haase page 142 of 154

655) Goldmann, Gereon: Tödliche Schatten - Tröstendes Licht; 10., erw. dt. Aufl.; 2005;
EOS-Verlag; St. Ottilien; ISBN 3830671385; Erinnerungen von Pater Gereon Goldmann.
656) Virtue, Doreen: Dein Leben im Licht; 4. Aufl.; 2007; Ullstein; Berlin; ISBN
9783548742328; Heilung durch Selbsterkenntnis.
657) Fischer, Peter: Philosophie der Religion; 1. Aufl.; 2007; Vandenhoeck & Ruprecht; Göttingen;
ISBN 9783525036167; Taschenbuch.
658) Gerwin, Hanno: Was Deutschlands Prominente glauben; 1. Aufl.; 2006; Goldmann;
München; ISBN 3442154200; Taschenbuch.
659) Praagh, James van: Jenseitswelten; 4. Aufl.; 2006; Goldmann; München; ISBN
3442216249; Erkenntnisse über das Leben nach dem Tode.
660) Browne, Sylvia: Jenseits-Leben; 4. Aufl.; 2006; Goldmann; München; ISBN
3442216036; Berichte eines Mediums aus der geistigen Welt.
661) Easwaran, Eknath (Übers.): Dhammapada; 1. Aufl.; 2006; Goldmann; München; ISBN
3442217644; Buddhas zentrale Lehren.
662) Libet, Benjamin: Mind Time; 1. Aufl.; 2007; Suhrkamp; Frankfurt am Main; ISBN
9783518294345; Wie das Gehirn Bewusstsein produziert.
663) Schwanitz, Dietrich: Bildung; 21. Aufl.; 2002; Goldmann; München; ISBN
9783442151479; Alles, was man wissen muss.
664) Englisch, Andreas: Johannes Paul II.; 5. Aufl.; 2003; Ullstein; München; ISBN
3550075766; Das Geheimnis des Karol Wojtyla.
665) Hartlieb, Gabriele; Quarch, Christoph; Schellenberger, Bernardin (Hrsg: Spirituell leben;
1. Aufl.; 2006; Herder; Freiburg; ISBN 9783451056994; Haltungen - Übungen - Inspirationen.
666) Luhmann, Niklas: Liebe als Passion; 1. Aufl.; 1994; Suhrkamp; Frankfurt; ISBN
3518287249; Zur Codierung von Intimität.
667) Mello, Anthony de: Wo das Glück zu finden ist; 9., durchges. Aufl.; 2004; Herder; Freiburg;
ISBN 3451284014; Weisheitsgeschichten für jeden Tag.
668) Drewermann, Eugen: Wozu Religion?; 4. Aufl.; 2006; Herder; Freiburg; ISBN
9783451053801; Sinnfindung in Zeiten der Gier nach Macht und Geld.
669) Küng, Hans: Wozu Weltethos?; 1. Aufl.; 2006; Herder; Freiburg; ISBN 9783451057977;
Religion und Ethik in Zeiten der Globalisierung.
670) Aurobindo, Sri: Savitri; 3., unveränd. Aufl.; 2006; Hinder & Deelmann; Gladenbach;
ISBN 3873481510; Legende und Sinnbild.
671) Aurobindo, Sri: Das göttliche Leben - Erstes Buch; 3., unveränd. Aufl.; 2002; Hinder &
Deelmann; Gladenbach; ISBN 3873481723; The Life Divine.
672) Aurobindo, Sri: Das göttliche Leben - Zweites Buch Teil 1; 3., unveränd. Aufl.; 2004;
Hinder & Deelmann; Gladenbach; ISBN 3873481456; The Life Divine.
673) Aurobindo, Sri: Das göttliche Leben - Zweites Buch Teil 2; 3., unveränd. Aufl.; 2004;
Hinder & Deelmann; Gladenbach; ISBN 3873481464; The Life Divine.
674) Fox, Matthew; Sheldrake, Rupert: Engel; 1. Aufl.; 2001; Bechtermünz; Augsburg; ISBN
3828934129; Die kosmische Intelligenz.
675) Müller, Werner A.; Hassel, Monika: Entwicklungsbiologie und Reproduktionsbiologie
von Mensch und Tieren; 4., vollst. überarb. Aufl.; 2006; Springer; Berlin; ISBN 3540240578;
Ein einführendes Lehrbuch.
676) Görnitz, Thomas; Görnitz, Brigitte: Die Evolution des Geistigen; 1. Aufl.; 2008;
Vandenhoeck & Ruprecht; Göttingen; ISBN 9783525567173; Quantenphysik - Bewusstsein -
Religion.
677) Thompson, Richard F.: Das Gehirn; 3. Aufl.; 2001; Spektrum Akademischer Verlag;
Heidelberg; ISBN 3827410800; Von der Nervenzelle zur Verhaltenssteuerung.
678) Hitchens, Christopher: God is Not Great; 1st Ed.; 2008; Atlantic Books; London; ISBN
9781843545743; How Religion Poisons Everything.
679) Morandini, Simone: Teologia e fisica; 1. ed.; 2007; Morcelliana; Brescia; ISBN
9788837221157; Novecento teologico.
680) Hahn, Christoph; Hohl, Siegmar (Hrsg.): Der große Museumsführer; Akt. Sonderausg.;
2002; Bassermann; München; ISBN 3809450138; Sammlungen zu Kunst, Kultur, Natur und
Technik in Deutschland.
© 1983-2012 by Boris Haase page 143 of 154

681) Düwell, Marcus; Hübenthal, Christoph; Werner, Micha H. (Hrsg.): Handbuch Ethik; 2.,
akt. u. erw. Aufl.; 2006; Metzler; Stuttgart; ISBN 3476021246; Ansätze, Formen und zentrale
Begriffe.
682) Höffe, Otfried (Hrsg.): Lexikon der Ethik; 7., neubearb. u. erw. Aufl.; 2008; Beck; München;
ISBN 9783406568107; in Zusammenarbeit mit Maximilian Forschner, Christoph Horn
und Wilhelm Vossenkuhl.
683) Remus, Joscha: Infonautik; 1. Aufl.; 2005; Gabal; Offenbach; ISBN 3897495643; Wege
durch den Wissensdschungel.
684) Birkenbihl, Vera F.: Das innere Archiv; 4. erw. Aufl.; 2007; MVG; München; ISBN
9783636072061; Fortsetzung von "Stroh im Kopf?".
685) Williams, Thomas D.: Greater Than You Think; 1st Ed.; 2008; Faithwords; New York;
ISBN 0446514934; A Theologian Answers the Atheists About God.
686) Stilman, Anne: Grammatically Correct; Rev. Ed.; 2004; Writers Digest; Cincinnati; ISBN
1582973318; The writer's essential guide to punctuation, spellling, style, usage and grammar.
687) Schweitzer, Friedrich: Religionspädagogik; 1. Aufl.; 2006; Gütersloher Verlagshaus;
Gütersloh; ISBN 9783579054025; Lehrbuch Praktische Theologie Band 1.
688) Stiftung, Bertelsmann: Relgionsmonitor 2008; 1. Aufl.; 2007; Gütersloher Verlagshaus;
Gütersloh; ISBN 9783579064659; Kommentierte Statistik.
689) Schockenhoff, Eberhard: Grundlegung der Ethik; 1. Aufl.; 2007; Herder; Freiburg; ISBN
9783451289385; Ein theologischer Entwurf.
690) Brück, Michael von (Hrsg.): Religion - Segen oder Fluch der Menschheit?; 1. Aufl.;
2008; Verlag der Weltreligionen; Frankfurt; ISBN 9783458710165; Gefördert durch die Udo
Keller Stiftung Forum Humanum.
691) Frielingsdorf, Karl: Mein Leben mit Gott versöhnen; 1. Aufl.; 2008; Echter; Würzburg;
ISBN 9783429029777; Ein Kursbuch für geistliches Wachsen und Begleiten.
692) Rias-Bucher, Barbara: Vitamin-Küche; 1. Aufl.; 1997; Das Beste; Stuttgart; ISBN
3870706694; Die köstlichsten Rezepte für Gemüse, Salat, Getreide und Früchte.
693) Osho: Der Gott, den es nicht gibt; 1. Aufl.; 2008; Ullstein; Berlin; ISBN 9783548741604;
Westliche Religion und die Lüge von Gott.
694) Goleman, Daniel: Soziale Intelligenz; 1. Aufl.; 2008; Knaur; München; ISBN
9783426780886; Wer auf andere zugehen kann, hat mehr vom Leben.
695) Hegi, Christoph; Attinger, Gabrielle: Marco Polo Reiseführer Zürich; 8., akt. Aufl.; 2008;
Mairdumont; Ostfildern; ISBN 9783829705950; Reisen mit Insider-Tipps.
696) Stiglitz, Joseph: Die Chancen der Globalisierung; 1. Aufl.; 2008; Pantheon; München;
ISBN 9783570550489; Aus dem amerikanischen Englisch von Thorsten Schmidt.
697) Wessels, Wolfgang: Das politische System der Europäischen Union; 1. Aufl.; 2008; Verlag
für Sozialwissenschaften; Wiesbaden; ISBN 9783810040657; Politikwissenschaft.
698) Leif, Thomas; Speth, Rudolf (Hrsg.): Die fünfte Gewalt; 1. Aufl.; 2006; Verlag für Sozialwissenschaften;
Wiesbaden; ISBN 3531150332; Lobbyismus in Deutschland.
699) Marschall, Stefan: Parlamentarismus; 1. Aufl.; 2005; Nomos; Baden-Baden; ISBN
383291062X; Eine Einführung.
700) Aristoteles: Über die Seele; 1. Aufl.; 2007; Voltmedia; Paderborn; ISBN
9783867636056; Worte, die die Welt veränderten.
701) Samuelson, Paul A.; Nordhaus, William D.: Volkswirtschaftslehre; 3., akt. Aufl.; 2007;
mi-Fachverlag; Landsberg; ISBN 9783636031129; Das internationale Standardwerk der
Makro- und Mikroökonomie.
702) Osho: Autobiographie; 2. Aufl.; 2007; Ullstein; Berlin; ISBN 9783548742526; Begegnung
mit dem rebellischen Meister.
703) Ziegler, Jean: Das Imperium der Schande; 3. Aufl.; 2008; Goldmann; München; ISBN
9783442155132; Der Kampf gegen Armut und Unterdrückung.
704) Nuscheler, Franz: Lern- und Arbeitsbuch Entwicklungspolitik; 6. Aufl.; 2005; Dietz;
Bonn; ISBN 3801203506; Eine grundlegende Einführung in die zentralen entwicklungspolitischen
Themenfelder Globalisierung, Staatsversagen, Hunger, Bevölkerung, Wirtschaft und
Umwelt.
© 1983-2012 by Boris Haase page 144 of 154

705) Rekacewicz, Philippe (Ill.): Atlas der Globalisierung; 2., durchges. Aufl.; 2006; Taz; Berlin;
ISBN 9783937683072; Die neuen Daten und Fakten zur Lage der Welt.
706) Nohlen, Dieter; Schultze, Rainer-Olaf (Hrsg.): Lexikon der Politikwissenschaft Band 1 A-
M; 3., akt. und erw. Aufl.; 2005; Beck; München; ISBN 340654116X; Theorien, Methoden,
Begriffe.
707) Nohlen, Dieter; Schultze, Rainer-Olaf (Hrsg.): Lexikon der Politikwissenschaft Band 2
N-Z; 3., akt. und erw. Aufl.; 2005; Beck; München; ISBN 3406541178; Theorien, Methoden,
Begriffe.
708) Hilger, Georg; Ritter, Werner H.: Religionsdidaktik Grundschule; 2. Aufl.; 2008; Kösel;
München; ISBN 9783466367078; Handbuch für die Praxis des evangelischen und katholischen
Religionsunterrichts.
709) Wilber, Ken: Eros, Kosmos, Logos; 4. Aufl.; 2006; Fischer; Frankfurt; ISBN
9783596149742; Eine Jahrtausend-Vision.
710) Mutius, Bernhard von: Die Verwandlung der Welt; 1. Aufl.; 2000; Klett-Cotta; Stuttgart;
ISBN 3608942718; Ein Dialog mit der Zukunft.
711) Holtfrerich, Carl-Ludwig: Wo sind die Jobs?; 1. Aufl.; 2007; Deutsche Verlags-Anstalt;
München; ISBN 9783421042774; Eine Streitschrift für mehr Arbeit.
712) Osho: Intelligenz; 2. Aufl.; 2008; Ullstein; Berlin; ISBN 9783548741611; Die kreative
Antwort zum Jetzt.
713) Ulich, Eberhard: Arbeitspsychologie; 6., überarb. u. erw. Aufl.; 2005; vdf Hochschulverlag;
Zürich; ISBN 3728129984; Text- und Lehrbuch, Informations- und Nachschlagewerk.
714) Dreikurs, Rudolf; Soltz, Vicki: Kinder fordern uns heraus; 16. Aufl.; 2008; Klett-Cotta;
Stuttgart; ISBN 9783608944006; Wie erziehen wir sie zeitgemäß?.
715) Fischer, Marcus: Ubuntu GNU/Linux; 4., akt. und erw. Aufl.; 2009; Galileo Press; Bonn;
ISBN 9783836214391; Das umfassende Handbuch.
716) Chopra, Deepak: Die göttliche Kraft; 4. Aufl.; 2006; Deutscher Taschenbuch Verlag;
München; ISBN 9783423362726; Die sieben Stufen der spirituellen Erkenntnis.
717) Birkenbihl, Vera F.: Rhetorik; 10. Aufl.; 2002; Ariston; München; ISBN 3720522997;
Redetraining für jeden Anlass.
718) Sandel, Michael J.: Plädoyer gegen die Perfektion; 1. Aufl.; 2008; Berlin University
Press; Berlin; ISBN 9783940432032; Ethik im Zeitalter der genetischen Technik.
719) Kuan, Yu-Chien; Häring-Kuan, Petra: Der China-Knigge; 6. Aufl.; 2008; Fischer; Frankfurt;
ISBN 9783596166848; Eine Gebrauchsanweisung für das Reich der Mitte.
720) Ess, Hans van: Die 101 wichtigsten Fragen; 1. Aufl.; 2008; Beck; München; ISBN
9783406568084; China.
721) Vitzthum, Wolfgang Graf (Hrsg.): Völkerrecht; 4., neu bearb. Aufl.; 2007; De Gruyter;
Berlin; ISBN 9783899494259; Lehrbuch.
722) Grill, Bartholomäus: Ach, Afrika; 6. Aufl.; 2005; Goldmann; München; ISBN
9783442153374; Berichte aus dem Inneren eines Kontinents.
723) Stang, Friedrich: Indien; 1. Aufl.; 2002; Wissenschaftliche Buchgesellschaft; Darmstadt;
ISBN 3534062108; Mit 98 Abbildungen, 82 Bildern.
724) Johnen, Kurt: Allgemeine Musiklehre; 21. Aufl.; 2008; Reclam; Stuttgart; ISBN
9783150073520; Mit zahlreichen Notenbeispielen.
725) Michels, Ulrich: dtv-Atlas Musik; 1. Aufl.; 2008; Deutscher Taschenbuch Verlag; München;
ISBN 3423085991; Mit 250 Abbildungsseiten in Farbe.
726) Oberhoffer, Heinrich: Harmonie- und Kompositionslehre; 1. Aufl.; 2006; Elibron; New
York; ISBN 0543838323; Mit besonderer Rücksicht auf das Orgelspiel in katholischen Kirchen.
727) Kuhn, Clemens: Formenlehre der Musik; 8. Aufl.; 2007; Bärenreiter; Kassel; ISBN
9783761813928; Mit Notenbeispielen.
728) Krämer, Thomas: Harmonielehre im Selbststudium; Neuausg.; 2006; Breitkopf & Härtel;
Wiesbaden; ISBN 376510261X; Mit Notenbeispielen.
729) Kellert, Peter; Fritsch, Markus: Arrangieren und Produzieren; 4., überarb. Aufl.; 2005;
Leu; Bergisch-Gladbach; ISBN 3928825224; Musikarbeitsbuch mit CD.
730) Martinus: Das Dritte Testament - Livets Bog 2; 1. Aufl.; 2001; Martinus Verlag; Ockenfels;
ISBN 3938189312; Martinus-Institut Kopenhagen.
© 1983-2012 by Boris Haase page 145 of 154

731) Martinus: Das Dritte Testament - Das ewige Weltbild 1; 1. Aufl.; 1988; Martinus Verlag;
Ockenfels; ISBN 3938189371; Martinus-Institut Kopenhagen.
732) Baker, Jill (Hrsg.): Weltatlas & Länderlexikon; Gen. Sonderausg.; 2010; Tandem; Königswinter;
ohne ISBN; Alle Staaten der Erde mit ausführlichen Artikeln.
733) Gogh, Vincent van: Van Gogh; 1. Aufl.; 2002; Belser; Stuttgart; ISBN 3763024042;
Vorwort von Robert Hughes.
734) Oerter, Rolf; Montada, Leo (Hrsg.): Entwicklungspsychologie; 6., vollst. überarb. Aufl.;
2008; Beltz; Weinheim; ISBN 9783621276078; Lehrbuch.
735) Louis, Dirk: Visual C++ 2008; 1. Aufl.; 2008; Markt + Technik; München; ISBN
9783827243232; Das umfassende Handbuch für Programmierer.
736) Klüver, Henning; Eder, Florian: Marco Polo Reiseführer Mailand/Lombardei; 4., akt.
Aufl.; 2010; Mairdumont; Ostfildern; ISBN 9783829704847; Mit Reise-Atlas.
737) Galenschovski, Carmen: Florenz; 9. Aufl.; 2007; Baedeker; Ostfildern; ISBN
9783829711517; Reiseführer mit großem Cityplan.
738) Korte, Karl-Rudolf; Fröhlich, Manuel: Politik und Regieren in Deutschland; 3., akt. u.
überarb. Aufl.; 2009; Schöningh; Paderborn; ISBN 978382522436; Strukturen, Prozesse,
Entscheidungen.
739) Walter, Wolfgang: Analysis 2; 5., erw. Aufl.; 2002; Springer; Berlin; ISBN 3540429530;
Mit über 160 Aufgaben und Lösungen.
740) Henkel, Hans-Olaf: Der Kampf um die Mitte; 1. Aufl.; 2007; Droemer; München; ISBN
9783426274231; Mein Bekenntnis zum Bürgertum.
741) Landers, Dieter; Rogge, Lothar: Nichtstandard Analysis; 1. Aufl.; 1994; Springer; Berlin;
ISBN 3540571159; Mit 204 Übungsaufgaben.
742) Schwarz, Hans Rudolf; Köckler, Norbert: Numerische Mathematik; 7., überarb. Aufl.;
2009; Vieweg + Teubner; Wiesbaden; ISBN 9783834806833; Mit Online-Service.
743) Musch, Hans (Hrsg.): Musik im Gottesdienst - Band 2; 4., erw. u. verb. Aufl.; 1994;
ConBrio; Regensburg; ISBN 3930079224; Musiklehre, Gemeindeliedführung, Neue Geistliche
Lieder, Orgelkunde, Stimmbildung, Chorleitung, Kinderchor, Lexikon.
744) Smyth, Bill: Computing Patterns in Strings; 1st Ed.; 2003; Pearson Education; Essex;
ISBN 0201398397; Monograph.
745) Willberg, Brigitte und Hans Peter (Bearb.): Evangelisches Gesangbuch; 4., überarb.
Aufl.; 2007; Lutherische Verlagsgesellschaft; Kiel; ISBN 9783875031126; Sonderausgabe.
746) Kinder, Hermann; Hilgemann, Werner: dtv-Atlas zur Weltgeschichte Band I; 28. Aufl.;
1994; Deutscher Taschenbuch Verlag; München; ISBN 3423030011; Von den Anfängen bis
zur Französischen Revolution.
747) Dörner, Dietrich: Bauplan für eine Seele; 1. Aufl.; 2001; Rowohlt Taschenbuch Verlag;
Reinbek; ISBN 3499611937; Science Sachbuch.
748) Kleis, Constanze: Gebrauchsanweisung für Frankfurt am Main; 2. Aufl.; 2010; Piper;
München; ISBN 9783492275798; Stadtbeschreibung.
749) Asendorpf, Jens B.: Psychologie der Persönlichkeit; 4., überarb. u. erw. Aufl.; 2007;
Springer; Heidelberg; ISBN 9783540716846; Lehrbuch.
750) Friedman, Thomas L.: Die Welt ist flach; 1. Aufl.; 2008; Suhrkamp; Frankfurt; ISBN
9783518459645; Akt. u. erw. Taschenbuchausgabe.
751) Grune, Dick; Jacobs, Ceriel J. H.: Parsing Techniques; 2nd Ed.; 2009; Springer; New
York; ISBN 9781441919014; A Practical Guide.
752) Needham, Tristan: Visual Complex Analysis; Reprint; 1998; Oxford University Press;
New York; ISBN 9780198534464; Including non-Euclidean geometry.
753) Rohr, Richard: Pure Präsenz; 2. Aufl.; 2010; Claudius; München; ISBN
9783532624135; Sehen lernen wie die Mystiker.
754) Terwitte, Paulus: Das Leben findet heute statt!; 1. Aufl.; 2010; Rowohlt Taschenbuch
Verlag; Reinbek; ISBN 9783499624445; Ein Anschlag auf die Vertröstungsgesellschaft.
755) Schmidt, Robin: Rudolf Steiner; 1. Aufl.; 2011; Verlag am Goetheanum; Dornach; ISBN
9783723514238; Skizze seines Lebens.
756) Asserate, Asfa-Wossen: Afrika; 1. Aufl.; 2010; C. H. Beck; München; ISBN
9783406600968; Die 101 wichtigsten Fragen und Antworten.
© 1983-2012 by Boris Haase page 146 of 154

757) Ai, Weiwei: Macht euch keine Illusionen über mich; 1. Aufl.; 2011; Galiani; Berlin; ISBN
9783869710495; Der verbotene Blog.
758) Kristof, Nicholas D.; WuDunn, Sheryl: Die Hälfte des Himmels; 1. Aufl.; 2011; C. H.
Beck; München; ISBN 9783406621802; Wie Frauen weltweit für eine bessere Zukunft kämpfen.
759) Haase, Boris: Relil; 1. Aufl.; 2011; Epubli; Berlin; ISBN 9783844208726; Religion und
Lebensweg.
760) Bartels, Henning: Die Piratenpartei; 1. Aufl.; 2009; Contumax; Berlin; ISBN
9783861990017; Entstehung, Forderungen und Perspektiven der Bewegung.
761) Jehde, Manfred; Schippen, Michael; Wunsch, Alfred S.: Faszination Mittelalter; ohne
Angabe; 2011; Lingen; Köln; ohne ISBN; Rätsel und Geheimnisse einer Epoche.
762) Grund, Stefan; Iken, Matthias; Lauterbach, Jörn et al.: Hamburger Momente; 1. Aufl.;
2010; Hamburger Abendblatt; Hamburg; ISBN 9783939716365; 100 Kolumnen mit ganz besonderen
Einblicken in den Alltag der Hansestadt.
763) Gelbaum, Bernard R.; Olmsted, John M. H.: Counterexamples in Analysis; Republ.,
unabr., slightly corr.; 2003; Dover Publications; Mineola, New York; ISBN 9780486428758;
Mathematics.
764) Köhler, Günter: Analysis; 1. Aufl.; 2006; Heldermann; Lemgo; ISBN 3885381141; Mit
Aufgaben von Jürgen Grahl.
765) Rudin, Walter: Reelle und Komplexe Analysis; 2., verb. Aufl.; 2009; Oldenbourg; München;
ISBN 9783486591866; Mathematik.
766) Gawin, Izabella; Schulze, Dieter: CityTrip Bremen; 2., neu bearb. u. kompl. akt. Aufl.;
2010; Reise Know-How Verlag; Bielefeld; ISBN 9783831718641; Reiseführer mit großem
CityAtlas.
767) Höhne, Wieland; Missler, Eva et al.: Hamburg; 14. Aufl.; 2009; Baedeker; Ostfildern;
ISBN 9783829710336; Reiseführer mit großem Cityplan.
768) Fröba, Stephanie; Wassermann, Alfred: Die bedeutendsten Mathematiker; 1. Aufl.;
2007; Marixverlag; Wiesbaden; ISBN 9783865399168; Biografisch-werkgeschichtliche Porträts.
769) Woyke, Wichard (Hrsg.): Handwörterbuch Internationale Politik; 10., durchges. Aufl.;
2006; Budrich; Opladen; ISBN 9783825207021; Politikwissenschaft.
770) Werth, Reinhard: Die Natur des Bewusstseins; 1. Aufl.; 2010; Beck; München; ISBN
9783406605949; Wie Wahrnehmung und freier Wille im Gehirn entstehen.
771) Hörmander, Lars: An Introduction to Complex Analysis in Several Variables; 2nd Ed.;
1973; North-Holland; Amsterdam; ohne ISBN; Mathematics.
772) Fritzsche, Klaus; Grauert, Hans: From Holomorphic Functions to Complex Manifolds;
1st Ed.; 2002; Springer; New York; ISBN 0387953957; Graduate Texts in Mathematics.
773) Wells, Raymond O. Jr.: Differential Analysis on Complex Manifolds; 3rd Ed.; 2008;
Springer; New York; ISBN 9781441925350; Graduate Texts in Mathematics.
774) Müller-Burzler, Henning: Auf den Spuren der Methusalem-Ernährung; 7. Aufl.; 2011;
Windpferd; Oberstdorf; ISBN 9783893854370; Die Wiederentdeckung der Heil- und Aufbaukräfte
der Nahrung.
775) Vanderbei, Robert J.: Linear Programming; 3rd Ed.; 2008; Springer; New York; ISBN
9780387743875; Foundations and Extensions.
776) Bazaraa, Mokhtar S.; Sherali, Hanif D.; Shetty, C. M.: Nonlinear Programming; 3rd Ed.;
2006; Wiley; Hoboken; ISBN 9780471486008; Theory and Algorithms.
777) Dantzig, George B.: Lineare Programmierung und Erweiterungen; 1. Aufl.; 1966;
Springer; Berlin; ASIN B0000BQFZ8; Ökonomie und Unternehmungsforschung II.
© 1983-2012 by Boris Haase page 147 of 154

Subject Catalogue
A • B • C • D • E • F • G • H • I • J • K • L • M • N • O • P • Q • R • S • T • U • V • W • X • Y • Z
A
Achievement Interview
Activities Current
Advantages Reference Theory
Ambisexuality Ambisexuality, Linguistics
Amplitude Oscillations
B
Bit Binary font
Bitsort Sorting and Searching
Books Bibliography
C
Calculation of lengths Calculation of Times
Calculation of times Mathematics, Calculation of Times
Calculations of errors Oscillations
Calendar Calculation of Times
Clare Informatics, Programming with Stair
Classification Equitable Distributing
Clothes Internet and Co
Consciousness Consciousness
Contents Internet and Co
Continuum Reference Theory
Cube Universe
Cycloid pendulum Oscillations
D
Determinism Knowledge Representation
Dihairesis Reference Theory
Direction way Oscillations
Discussion Oscillations
E
Earthday Calculation of Times
Ellipse pendulum Oscillations
Email Internet and Co
Equitable distributing Mathematics, Equitable Distributing
Evolute Oscillations
Exams Internet and Co
Exchanges Reference Theory
Experiment Oscillations
F
Fascination Interview
Font Binary font, Linguistics
Fonto Font Fonto, Linguistics
© 1983-2012 by Boris Haase page 148 of 154

G
Geometry Mathematics, Geometry
H
Haase, Boris About me
I
Infinity Set Theory
Internet Internet and Co, Informatics
Interview Interview, Philosophy
K
Keyboard Binary font
Kinetic energy Physics
Knowledge representation Knowledge Representation, Philosophy
L
Lango Planned language Lango
Language of science Language of Science
Lept Calculation of Times
Letters Font Fonto
M
Machines Internet and Co
Mathematical pendulum Oscillations
Matter Knowledge Representation
Modal verb Reference Theory
Month Calculation of Times
N
Nonstandardanalysis Nonstandardanalysis
Number Set Theory
O
Oct Calculation of Times
Octal system Calculation of Times
Optimisation Mathematics, Optimisation
Oscillation Oscillations
Overview Introduction
P
Periodic time Oscillations
Plane Oscillations
Planned language Planned language Lango, Linguistics
Potential energy Oscillations
Probability Knowledge Representation
© 1983-2012 by Boris Haase page 149 of 154

Problem Problem Solutions
Problem solutions Problem Solutions
Programming Programming with Stair
Q
Questionnaire About me
R
Radius of curvature Oscillations
Radio computing Radio Computing
Radix sort Sorting and Searching
Reading Current
Reference Reference Theory, Knowledge Representation
Reference theory Reference Theory, Philosophy
Relation Knowledge Representation, Reference Theory
Religion of love Religion
RelilWiki Religion
Rest position Oscillations
Representations Representations
Revisional history Main Page
S
Scaling Reference Theory, Knowledge Representation
Searching Informatics, Sorting and Searching
Series Oscillations
Set Set Theory
Set theory Set Theory, Mathematics
Solution Problem Solutions
Sorting Informatics, Sorting and Searching
Space Reference Theory
Spring Oscillations
Stair Informatics, Programming with Stair
Strap Internet and Co
Subjects Subject Catalogue
Substance Reference Theory, Knowledge Representation
T
Tension energy Oscillations
Themes Main Page
Time Reference Theory
Transcendent numbers Set Theory, Transcendent numbers
Transport Internet and Co
U
Unity sphere Universe
Universal Reference Theory
Universe Universe
V
Virtual reality Internet and Co
© 1983-2012 by Boris Haase page 150 of 154

Visions About me
Vocabulary Planned language Lango
W
Week Calculation of Times
Work-results Equitable Distributing
Y
Youth researches Oscillations
© 1983-2012 by Boris Haase page 151 of 154

Definitions and Glossary
A • B • C • D • E • F • G • H • I • J • K • L • M • N • O • P • Q • R • S • T • U • V • W • X • Y • Z
A
Amfon: third substance, to which thoughts and matter are tied for exchange purposes.
B
Body of a living entity: the entirety of the material substances, referred to each other, of that
living entity.
C
Circle, deterministic: change between deterministic determination according to the divine
order and indeterministic phases, in which the creature can determine itself.
Clare: programming language (coding language after rule environment), capable
of learning (by adding rules and meta-rules), which has activatable (self-)
optimisation algorithms.
Consciousness: 1. the part of the mind that a living entity can directly access at a particular
point in time by reference,
2. the (passive) state in which we become aware of the entirety of that what
is actual for us, the content of consciousness, by presenting itself to us, so
is coming in us into being.
Continuum, finite: gapless finite total of entities which are linked by references.
Cuboid scheme: assignment of numbers to the set of natural numbers per dimension.
D
Dihairesis: progressing fragmentation of a term in its components of meaning, until
only still substance terms remain.
Don: ambisexual nominative and accusative form of the article for der/den resp.
die.
Dor: ambisexual genitive and dative form of the article for des/dem resp. der.
Doren: ambisexual genitive form of the relative pronoun for dessen/deren.
E
Earthday: working day inserted between Sunday and Monday.
F
Fonto: font developed by me for the International Phonetic Alphabet.
I
ID: identification number assigned uniquely to every person.
L
Label: referred to of a distinguished.
Lango: planned language developed by me whose vocabulary is determined democratically.
Lept: eighth part of an oct, 64th part of a day.
© 1983-2012 by Boris Haase page 152 of 154

M
Mind: generally the process, initiated by an entity, of linking immaterial substances
and references. In particular, it comprises only the more complex
links.
N
Number: selecting marking of the many and construction from it.
O
Oct: eighth part of a day.
On: 1. ambisexual nominative and accusative suffix for adjectives, substantives,
pronouns and the indefinite article and for -mann resp. -frau,
2. ambisexual indefinite pronoun for man.
Onen: ambisexual plural suffix for substantives.
Or: ambisexual genitive and dative suffix for adjectives, substantives, pronouns
and the indefinite article.
Orbital: meaning environment of a term.
R
Reference: special substance, which interlinks the substances.
Reference theory: philosophical doctrine, which is based on substances and references.
S
Signature: electronic equivalent to the manual signature.
Soul: the mind and the results of the mental processes of an entity.
Stair: programming concept for development environments that stands for standardised
transformation after individual rules.
Strap: multifunction device with diverse functions of the new media.
Subconsciousness: the sub-processes of the mind that are beyond the direct access of the
living entity.
Substance: entity which cannot be divided analytically anymore (examples, to which
substances are assigned: space, time, the one, the must).
U
URL, generic: URL which contains wildcards.
W
World: closed total which is accessible for a subject during a period.
Z
Ze: ambisexual subjective form of the personal pronoun for he/she.
Zer: ambisexual objective form of the personal pronoun for him/her.
Zerself: ambisexual reflexive form of the personal pronoun for himself/herself.
Zie: ambisexual nominative form of the personal pronoun for er/sie.
Zihn: ambisexual accusative form of the personal pronoun for ihn/sie.
Zihr: ambisexual dative form of the personal pronoun for ihm/ihr and beginning
of the corresponding possessive pronoun for sein/ihr.
© 1983-2012 by Boris Haase page 153 of 154

Zihrer: ambisexual genitive form of the personal pronoun for seiner/ihrer.
Zis: ambisexual possessive form of the personal pronoun for his/her(s).
© 1983-2012 by Boris Haase page 154 of 154