MOTION MOUNTAIN

294 9 concepts, lies and patterns of nature
Are all physical observables known?
“Scientistshaveodiousmanners,exceptwhen
you propuptheir theory; thenyou canborrow
moneyfromthem.
The most practical way to communicate observations was developed a long
MarkTwain”
time ago:
by measurements. A measurement allows effective communication of an observation to
other times and places.This is not always as trivial as it sounds; for example, in the Middle
Ages people were unable to compare precisely the ‘coldness’ of the winters of two differentyears!Theinvention
of the thermometer provided a reliable solution to this requirement.
A measurement is thus the classification of an observation into a standard set of
observations. To put it simply:
⊳ A measurement is acomparisonwith a standard.
This definition of a measurement is precise and practical, and has therefore been universally
adopted. For example, when the length of a house is measured, this aspect of the
houseisclassifiedintoacertainsetofstandardlengths,namelythesetoflengthsdefined
by multiples of a unit. A unit is the abstract name of the standard for a certain observable.
Numbers and units allow the most precise and most effective communication of
measurement results.
For all measurable quantities, practical standard units and measurement methods
have been defined; the main ones are listed and defined in Appendix A. All units are
derived from a few fundamental ones; this is ultimately due to our limited number of
senses: length, time and mass are related to sight, hearing and touch. Our limited numberofsensesis,in
turn,duetothesmallnumberofobservables of nature. Animals and
machines share the same fundamental senses.
We call observables the different measurable aspects of a system. Most observables,
such as size, speed, position, etc. can be described by numbers, and in this case they are
quantities, i.e., multiples of some standard unit. Observables are usually abbreviated by
(mathematical) symbols, usually letters from some alphabet. For example, the symbolc
commonly specifies the velocity of light. For most observables, standard symbols have
been defined by international bodies.*The symbols for the observables that describe the
state of an object are also called variables. Variables on which other observables depend
are often calledparameters. (Remember: a parameter is a variable constant.) For example,
the speed of light is a constant, the position a variable, and the temperature is often a
parameter, on which the length of an object, for example, can depend. Note that not all
observables are quantities; in particular, parities are not multiples of any unit.
*Allmathematicalsymbolsusedinthiswalk,togetherwiththealphabetsfromwhichtheyaretaken,arelistedinAppendixAonnotation.
Theyfollowinternational standardswhenevertheyaredefined.Thestandard
symbols of the physical quantities, as defined by the International Standards Organization (ISO), the
InternationalUnionofPureandAppliedPhysics(IUPAP)andtheInternationalUnionofPureandApplied
Chemistry(IUPAC),canbefoundforexampleinthebible,i.e.,theCRCHandbookofChemistryandPhysics,
CRCPress,1992.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net