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Albert EinsteinMeetkunde en ervaring Geometry and exprience

Oorsponklike titel:Original title:

GEOMETRIE UND ERFAHRUNG

Vertaal in Afrikaans deur Ponti Venter, voorsien van -kantlynkommentaar, - 'n inleidende agtergrond oor Einstein se wysgerige denke, - terminologiese verduidelikings, - met 'n hersiene vertaling in Engels deur 'n onbe kende vertaler - en geïndekseer

Translated into Afrikaans by Ponti Venter, - provided with marginal comments, - an introductory background to Einstein's philosophical thinking - explanations of terminlogy- together with a revised translation into English by an unknown translator, - and indexed

Outeursreg op buitebladontwerp/Author's rights on cover design: Z C Venter en Ponti VenterKopiereg: Vraagteken UitgewersCopyright: Question Mark PublishersOuteursreg op vertaling in Afrikaans, inleiding oor Einstein se denke, kantlyn-kommentare en terminologiese endnotas: Ponti VenterAuthor's rights on translation into Afrikaans, introduction on Einstein's thought, comments in the margin and terminological endnotes: Ponti Venter

Druk en bind/ Printing and binding: Easyart printers: H v/ C o Wolmrans & Sol plaatje. 018 293 2756; design1@easyartprinters.co.za

ISBN: 978-1-86822-576-7

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VOORWOORDHierdie vertaling het 90 persent voltooid in my laai gelê vir se ker twee dekades soos verskeie ander stukke. Fi-nan siële en ander steun was afwesig. My uitgangspunt is nog altyd dat ‘n kleiner taal soos Afri kaans homself nie kan handhaaf deur eksklusiwisme nie. Dis altyd ‘n vreugde as kollegas wat ander moedertale praat hulle in Afrikaans aan my voorstel. Inklusief denkend bied ek sover moontlik my vertalings aan saam met verta-lings in Engels. Dit bevoordeel beide die Afrikaansta-lige stu den te asook studente wat En gels gebruik maar aan Afri kaanse universiteite stu deer. Ek hoop dat dit ook die breë leserspubliek kan help om iets meer erf-lating van fundamentele geleerdheidstradisies te sien. Ons lees te min en kyk te veel. Ons absorbeer te veel ‘informasie’ te vinnig, en verteer te min. Lees stel ‘n mens se volle kenfunksie in werking; den-kend dekodeer: self prentjies maak want die kode vertel sonder om te teken; jy moet abstraherend dink; jy word gedwing om in te sien en deur te sien in ‘n ge dag tewêreld wat jy nie direk ont halwe duidelikheid kan ondervra nie; jouself in ‘n historiese per spektief van millenia tot eergis-ter plaas; jou te laat meevoer in ‘n ander le we. In lees het jy tyd vir krities-kyk na wat die grotes gedink het; jy het refleksietyd. Goed en baie lees is deel van ons sosia lise ring; deel van opgroei, omdat jy rustig en op ‘n afstand ‘n kykie kry in die mensheid se dwaashede en die verstandighede. Lees is ‘n essensiële deel van die oor brugging van ons vervreemding; afstand-skat tussen waar ons is en waar ons van daan kom; van volwas se-wor ding. Belese mense word nie maklik aan die neus ge lei nie.Diktatoriale regimes hou van sensuur; hulle word mak-

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PREFACEThe Afrikaans translation below has been lying, 90 per cent com plete, in my desk drawer for about two de cades, like some other pieces. Financial and other sup port have been absent. My point of departure has always been that a minority language, like Afrikaans, cannot sustain itself through outward exclusivism. It is always a joy for me when colleagues speaking other mother tongues present them selves to me in Afrikaans. My thinking is inclusive, therefore, as far possible, I offer my translations to gether with translations into English. There are advantages in this, both for Afrikaans lan guage students and for those stu dents who use English but study at Afrikaans medi-um universities. I do also hope that it can help the wider rea ding public to un derstand some thing more of the fundamental traditions in scholarship. Reading engages one’s total act of knowing. One has to de code thinkingly: image the undrawn pictures re lat ed by the code; think abstractly, being forced to see in and see through a world of thought which one can not direct-ly cross-question for the sake of clarity; si tuate yourself in a historical perspective of mille nia up to the day before yesterday; be taken along in another person’s life. In reading one has time to critically assess the great thin kers‘ thoughts; one has time for reflection. Rea ding well and rea ding much is part of our socialisation, part of gro wing up, since in quiet and from a distance one gains a peek into the foolishness and prudence of hu-mankind. Reading is an essential part of the bridging of our alienati on; of estimating the distance between where we are and where we come from; of our coming to age. Literate people are not easily led by the nose.Dictatorial regimes love censorship; they are more easily

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liker getref deur skrywers as deur sluipmoor de naars. Mon digwording ver on derstel dat jy uit verskeie bronne put. Vandagse bronne is spoedbronne, son der ruimte vir oor denking en deur denking.Selfs filosowe het min tyd om te dink; ook van hulle word snelle ‘na vorsinguitsette’ verwag. Tempo en hoe-veel heid het gelyk geword aan kwaliteit. Volwasse en ryp geleerdheid word nie met spoed verwerf nie. Mo no teo-re tiese teg niese navorsing kan met spoed gedoen word. Ge leerdheidsgegronde, krities-deurdagte na vor sings in-sigte neem dekades. In ons liberaal-ekonomisties e tyd is bestuurders soms oorbemagtig; die optredes van talle is onryp-dikterend en ook eksploiterend - dit be moei lik aka-de mici se rypwor ding t o v moeilike kwessies as ook die optimering van talentverskeidenheid. Belangrik, hoewel die vertalings in die eerste plek die uni-versi teite op oog het, sien ek myself nie as ‘n handboek-skrywer nie. Eer der ‘n ontsluiter; iemand wat pro beer om die stof van ‘n ver steekte skat af te blaas. My breër doel is om ‘n wysgerige lesers kring te bou, wyer as net studente. En ek hoop hierdie publikasie maak ‘n bydrae daartoe. Dit staan die leser dus vry om eers die vertaalde teks te lees, voor dat my kommentaar aan die orde kom. En ja, ek het nie die pretensie dat ek Einstein deurskou het nie. Nog lank nie.Wat die vertaling betref: vir die Afrikaans het ek die oor-spronlike Duits gebruik. Die vertaling in Engels kom van ‘n internet-geskandeerde teks met tipiese skande rings-foute. Vertaler en datum onvermeld. Vergeleke by die Duits is dit nie oral goed nie. Aanpassing by die Afri-kaans het ook bygedra om dit te verander.

Potchefstroom September 2011

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hit by writers than by assassins. Becoming mature im-plies drawing on many sources. Contemporary sour ces are high-speed ones; no space for consideration or think-ing through. Even philosophers have little time to think: they also have to produce speedy ‘research outputs’. Rate and quan tity have become equal to quality. Mature and ripen ed learning is not acquired speedily. Mono-theo retical technical research can be done with speed. Critically thought-through, insightful research rooted in lear ning takes de cades. In our liberal-economistic era managers may be over-empowered; die behaviour of many is immaturely dictating; also exploitative - this over-complicates academics' maturation regarding difficult issues, and the optimising of a variety of talents. Important: these translations are primarily aim ed at uni-versities but I do not see myself as an author of textbooks. Ra ther as a discloser – somebo dy who tries to blow away the dust from hidden trea sures. My wider aim is to build philo so phi cal rea dership, wider than on ly students. I hope that this pu blication will con tri bu te to this.The reader is therefore free to read the translated text first, be fore reading my com ments. And no, I do not pretend to have seen all through Einstein. Not for a long time to come!As far as the translation itself is concerned: for the Afri-kaans I have used the original German. The English origin ates form a scan ned internet text, with typical scan-ning errors; translator and date not given. Compared to the German it is deficient in places. Alignment with Af-rikaans also contributed to changes.

Potchefstroom September 2011

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TEGNIESE GEBRUIKE * Verwysings na die termverduidelikings in die Endnotas is in die teks aan gedui met boskrifnommers soos voet-note, maar in hakies, byvoorbeeld:

"... metafisika(1) ... "

* Die enkele voetnoot in die Einsteinteks is normaal ge-nommer, d w s sonder die hakies.

* Die bronverwysings is gedoen soos in sommige natuur-wetenskapstydskrife, in die teks genommer soos wat die behoefte aan 'n verwysings homself getoon het. In die ver wysingslys is hulle in numeriese volgorde geplaas. In die teks is hulle aangedui met die betrokke nommer in ha kies, maar met 'n asterisk vooraan, byvoorbeeld:

"... metafisika (*20), soos ..."

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TECHNICAL USAGE* References to the terminological explanations in the Endnotes have been indicated in the text with superscript numbering like foornotes , but in brackets, for example:

"... metaphysics(1) ..."

* The single footnote in the Einstein text has been indi-cated normally, i e wwithout the brrackets.

* Source references have done liike in some natural scien-ce journals, numbered in the text according to the need for references. In the list of refereences they have been placed in numerical order. In the text they have been in-dicated by the relevant number in brackets, but with an asterisk up front, for example:

"... metaphysics (*20), such as ..."

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INHOUD/CONTENTSVOORWOORD PREFACE

EINSTEIN'S THOUGHT 2EINSTEIN SE DENKE 3Ultrapositivism and ideal-type metaphysics 2Ultrapositiwisme en ideaaltipiese metafisika 3Rationalism goes downhill 6Nedergang van die Rasionalisme 7Irrationalism takes the lead 10Irrasionalisme neem die leisels 11Einstein’s irrationalist context 18Einstein se irrasionalistiese konteks 19Einstein: Pragmatism and Operationalism 22Einstein: Pragmatisme en Operasionalisme 23Universals 26Universalia 27 Realism 28 Realisme 29 Subjectivism 28 Subjektiwisme 29Einstein a nominalist? 32Einstein ‘n nominalis? 33The metaphysician Einstein - his worldview 40Die metafiskus Einstein- sy wêreldbeskouing 41A ‘dead’ reality? 56‘n ‘Dooie’ werklikheid 57‘Faith’ and ‘science’ 64‘Geloof ’ en ‘wetenskap’ 65EINSTEIN: MEETKUNDE EN ERVARING 70EINSTEIN: GEOMETRY AND EXPERIENCE 71WISKUNDE EN WERKLIKHEID 70MATHEMATICS AND REALITY 71Certainty of mathematics 70Wiskundige sekerheid 71Certainty of natural science 70Natuurwetenskaplike sekerheid 71

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Irrationalist a priori 72Irrasionalistiese a priori 73Logicistic and formalistic 72Logisisties en formalisties 73'Form versus 'content' 72'Vorm' versus 'inhoud' 73A PRIORI VERSUS CONVENTION 72A PRIORI VERSUS KONVENSIE 73Self-evident & a priori 74Self-evident & a priori 75Nominalism or conceptualism 74Nominalisme of konsepsualisme 75Mathematics and reality 74Wiskunde en realiteit 75Schematic normative definitions 74Skematiese normatiewe definisies 75ORIGIN OF GEOMETRY 76OORSPRONG VAN MEETKUNDE 77Mathematics from techno-praxis 76Wiskunde uit tegnopraktyk 77Form versus content 76Vorm versus inhoud 77AXIOMATIC VS PRACTICAL GEOMETRY 76AKSIOMATIESE VS PRAKTIESE MEETKUNDE 77‘Experience’ 76‘Ervaring’ 77Physics as practical geometry 78Fisika as praktiese geometrie 79Physics as science of position 78Fisika as posisiewetenskap 79Relativity needs different geometry 78Relatiwiteit vereis ander geometrie 79Vorm en inhoud 78Form and content 79NATURAL BODIES VS GEOMETRICAL BODIES 80NATUURLIKE VS GEOMETRIESE LIGGAME 81Poincaré insists on Euclid 80Poincaré hou by Euklides 81

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Ideal type abstraction 80Ideaaltipe abstraksie 81Beauty & simplicity 80Skoonheid en eenvoud 81Positionality 80Posisionaliteit 81LAWS 82WETTE 83Conventionalism 82Konvensionalisme 83'Natural laws' unobservable - conventional status 82'Natuurwette' nie-observeerbaar - konvenssionele status 83Logical Positivism - atomic propositions 82Logiese Postivisme - atomêre proposisies 83TRANSFORMATIVE ABSTRACTION 84TRANSFORMATIEWE ABSTRAKSIE 85Operationalism 84Operasionalisme 85Abstraction - methodological fixation 84Abstraksie - metodologiese fiksasie 85From dynamics to statics 84Van dinamika tot statika 85POSITIONAL RELATIVITY OF DISTANCE 84POSISIONELE A84-5FSTANDSRELATIWITEIT 85Static vs dynamic = form vs object 84Staties vs dinamies = vorm vs objek 85TIME 86TYD 87Time = operation 86Tyd = operasie 87Tyd = measured distance 86Tyd = gemete afstand 87Transformative proposition 88Transformasiestelling 89Applicability of conventions ` 88Toepaslikheid van konvensies 89Verification: pragmatic success 88Verifikasie: pragmatiese sukses 89

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Macro-application of Riemann 88Makrotoepassing van Riemann 89SPATIALLY INFINITE VS SPATIALLY FINITE 90RUIMTELIK EINDIG VS RUIMTELIK ONEINDIG 91Theory: inertia, gravity, & finite universe 90Teorie: traagheid, swaartekrag & eindige heelal 91Mach's Ultra-Positivism 92Mach se Ultra-Positivisme 93Philosophical requirement determines physics 92Wys gerige vereiste bepaal fisika 93REPRESENTATION: PICTURING = EXPERIENCE 92REPRESENTASIE: VOORSTELLING = ERVARING 93Micro-macro extrapolation 92Mikro-makro-ekstrapolasie 93Gravitational deviation from Newton 92Swaartekrag-afwykings van Newton 93Stabilising & gravity 94Stabilisering en swaartekrag 95MULTI-DIMENSIONAL VISUALISING: PROJECTION 96MULTI-DIMENSIONELE VISUALISERING: PROJEKSIE 97Formalistic logical atomism 96Formalistiese logisese atomisme 97Pragmatic geometrical abstraction 96Pragmatiese geometriese abstraksie 97Visualisation 96Visualisering 97PRAGMATIC DEFINING 96PRAGMATIESE DEFINIËRING 97Pragmatic action definitions 96Pragmatiese doendefinisies 97Spheres, planes and action definitions 96Sfere, vlakke en doendefinisies 97Definition via operations 98Definisie via operasies 99FROM RIEMANN TO EUCLID 98VAN RIEMANN NA EUKLIDES 99Greek worldpicture 100Griekse wêreldbeeld 101

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SPACE = SPACE MEASURING = GEOMETRY 100 RUIMTE = RUIMTEMETING = MEETKUNDE 101Spheric space = spheric geometry 102Sferiese ruimte = sferiese meetkunde 103Object = science 102Objek = wetenskap 103Instrument = object 102Instrument = objek 103Operationalism = technicism 104Operasionalisme = tegnisisme 105Retro-polation 104Retropolasie 105Operationalistic play 106Operasionalistiese spel 107Operational imagination 106Operasionele verbeelding 107Instrument behaves like object 106Instrument gedra hom soos objek 107Picturing versus calculation 106Veraanskouliking vs berekening 107Picturing transforms abstractions 106Veraanskouliking omvorm abstraksies 107‘Representation’ problematised 106‘Representasie’ geproblematiseer 107ENDNOTAS: TERMINOLOGIE 108ENDNOTES: TERMINOLOGY 1091. Positiwisme 1081. Postivism 1092. Metafisika 1082. Metaphysics 1093. Hermetisties 1103. Hermetistic 1114. Ideaaltipe 1144. Ideal type 1155. Rasionalisme 1185. Rationalism 1196. Irrasionalisme 1206. Irrationalism 121

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7. Naturalisme 1207. Naturalism 1218 Verbeelding 1228. Imagination 1239. Konstruktiwisme 1229. Constructivism 12310. Pragmatisme 12610. Pragmatism 12711. Operasionalisme 13011. Operationalism 13112. Kriterium van waarheid 13012. Criterion of truth 13113. Intramentale sekerheid 13213. Intra-mental certainty 13314. Konvensionalisme 13414. Conventionalism 13515. Wêreldbeskouing 13615. Worldview 13716. Sciëntisme en determinisme 13616. Scientism and determinism 13717 Veraanskouliking ` 13817 Picturing 139VERWYSINGS 144REFERENCES 144FIGURE 1/ FIGUUR 1 148FIGURE 2/ FIGUUR 2 149

INDEX/ INDEKS 150