MOTION MOUNTAIN

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276 8 thought and language F I G U R E 168 Fibonacci numbers and spirals from washers (© Donald Simanek). Ref. 247 Challenge 282 s Challenge 283 e of beauty in nature. This is not the case, as Figure 168 shows. Mark a spot on a surface, and put washers around it in by hand in a spiral manner; you will find the same spiralsthatyoufindinmanyflowers,andthus,attheirborder,thesameFibonaccinumbers. ThisargumentbyDonaldSimanekshowsthatthereisnothingdeep,complicatedoreven mysterious in the appearance of Fibonacci numbers in plants. For an opposite point of view, see reference Ref. 247. ∗∗ Prime numbers are a favourite playground for mathematicians. A famous result on all prime numbersp i states ∞ ∏ i=1(1− 1 pi 2 )= 6 π 2 (106) Can you imagine how this result is proven? ∗∗ Digits owe their name to the latin word ‘digitum’ or finger. In times when writing onpaperwasexpensive, it was already possible to count up to 9999 using the two hands, with a system developed by Beda Venerabilis and popularized, for example, by Luca Pacioli. Can you develop a similar system? Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
Chapter 9 CONCEPTS, LIES AND PATTERNS OF NATURE Ref. 256 “DieGrenzenmeinerSprachebedeuten die Grenzenmeiner Welt.* LudwigWittgenstein, Tractatus, 5.6” “DerSatzisteinBildderWirklichkeit. DerSatz isteinModellderWirklichkeit, sowiewir sie unsdenken.** LudwigWittgenstein, Tractatus, 4.01” In contrast to mathematics, physics does aim at being a language. But t is ambitious: it aims to express everything, with complete precision, and, n particular, all examples and possibilities of change.*** Like any language, physics consists of concepts and sentences. In order to be able to express everything, it must aim to use few words for a lot of facts.**** Physicists are essentially lazy people: they try to minimize the effort in everything they do. The concepts in use today have been optimized by the combined effort of many people to be as practical, i.e., as powerful as possible. A concept is called powerful when it allows one to express in a compact way a large amount of information, meaning that it can rapidly convey a large number of details about observations. General statements about many examples of motion are calledrules orpatterns. In the past, it was often said that ‘laws govern nature’, using an old and inappropriate ideology. A physical ‘law’ is only a way of saying as much as possible with as few words as pos- * ‘Thelimits ofmylanguage arethelimits ofmyworld.’ ** ‘Aproposition isapictureofreality. Aproposition isamodelofreality aswe imagine it.’ ***Allobservationsareaboutchange.Thevarioustypesofchangearestudiedbythevarioussciences;they are usuallygrouped in the three categories ofhuman sciences,formal sciencesandnatural sciences.Among the latter, the oldest are astronomy and metallurgy. Then, with the increase of curiosity in early antiquity, came the natural science concerned with the topic of motion: physics. In the course of our walk it will become clear that the unusual definition of physics as the study of change indeed covers the whole set of topics studied in physics. In particular it includes the more common definition of physics as the study of matter,itsproperties, its componentsandtheirinteractions. **** A particular, specificobservation, i.e., a specific example of input shared by others, is called a fact, or in other contexts, an event. A striking and regularly observed fact is called a phenomenon, and a general observationmadein many differentsituations iscalled a(physical) principle.(Often,whenaconceptisintroducedthatisusedwithothermeaninginotherfields,inthiswalkitisprecededbythequalifier‘physical’ or ‘mathematical’ inparentheses.)Actionsperformedtowardstheaimofcollectingobservationsarecalled experiments. The concept of experiment became established in the sixteenth century; in the evolution of a child,it canbestbecompared tothat activitythat hasthesame aimofcollecting experiences:play. Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
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ChristophSchiller MOTION MOUNTAIN t
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Editiovicesima octava. Proprietassc
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DieMenschenstärken,die Sachenklär
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8 preface PHYSICS: Describing motio
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10 preface Your donation to the cha
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12 contents Do we see what exists?
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Light, Charges and Brains Inourques
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16 1 electricity and fields F I G U
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18 1 electricityandfields F I G U R
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42 1 electricity and fields Oersted
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44 1 electricity and fields Vol. IV
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48 1 electricity and fields Ref. 24
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Vol. IV, page 231 Chapter 2 THE DES
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Chapter 3 WHAT IS LIGHT? Ref. 57 Pa
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104 3 what is light? Page 84 gases
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106 3 what is light? Fre - Waveleng
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108 3 what is light? Challenge 110
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110 3 what is light? incoming light
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112 3 what is light? Ref. 70 Challe
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114 3 what is light? F I G U R E 69
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116 3 what is light? light Ref. 72
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Chapter 4 IMAGES AND THE EYE - OPTI
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142 4 images and the eye - optics 2
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Chapter 5 ELECTROMAGNETIC EFFECTS R
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362 bibliography 10 Thiseffect hasf
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CREDITS Acknowledgements Many peopl
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NAME INDEX A Abbott A Abbott,T.A.37
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404 name index Z Zybin Motion Mount
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406 subject index A units 328 Aplys
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408 subject index C classical class
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412 subject index F finite finite 2
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426 subject index W Wien’s Wien
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