Stuff about Thales

7/28/2019 Stuff about Thales

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Thales

Author(s): D. R. DicksSource: The Classical Quarterly, New Series, Vol. 9, No. 2 (Nov., 1959), pp. 294-309Published by: Cambridge University Press on behalf of The Classical AssociationStable URL: http://www.jstor.org/stable/637659 .

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THALESTHE Greeks attributed to Thales a great many discoveriesand achievements.Few, if any, of these can be said to rest on thoroughlyreliabletestimony,mostof them being the ascriptionsof commentatorsand compilerswho lived any-thing from 700 to I,ooo years after his death-a period of time equivalent tothat between William the Conquerorand the present day. Inevitably therealso accumulated round the name of Thales, as round that of Pythagoras (thetwo being oftenconfused'),a number of anecdotesof varyingdegreesof plausi-bility and of no historical worth whatsoever. These and the achievementscredited to Thales have, of course, been painstakingly brought together byHermann Diels in DerFragmenteerVorsokratiker.zseful and necessary (thoughnot entirely comprehensive3)as this work undoubtedly is, it neverthelesshasprobably contributedas much as any other book to the exaggerated and falseview of Thales which we meet in so many modern histories of science orphilosophy, and which it is the purpose of this article to combat. In Diels,quotationsfrom sourcessuch as Proclus, AMtius,Eusebius, Plutarch,Josephus,lamblichus, Diogenes Laertius,Theon Smyrnaeus,Apuleius, Clemens Alexan-drinus, and Pliny, of different dates and varying reliability, are listed indis-criminately side by side with a few from Herodotus, Plato, and Aristotle, inorder to provide material for a biography of Thales; but so uncertain is thismaterial that there is no agreement among the 'authorities'even on the mostfundamental facts of his life-e.g. whether he was a Milesian or a Phoenician,whether he left any writings or not, whether he was married or single-muchlesson the actual ideas and achievementswith which he is credited.The criticalevaluation of the worth of these citations is left entirely to the reader. Futurehistorians of classicalantiquitywho (in the not improbableevent of a generalcataclysm) may have to rely entirely on secondary sources such as Diels arelikely to form an extremely erroneousidea of the validity and completenessofour knowledge of Thales.

It is worth while examining the material in Diels a little more closely. Verybroadly, the sourcesmay be classifiedin two main divisions, namely, writersbefore 320 B.C. (Thales'floruit s usually and probably correctly given as thefirst quarter of the 6th century B.C.)and those after this date-some beingnearly a millennium after it, e.g. Proclus (5th century A.D.) and Simplicius(6th century A.D.). In the first division there are only three writers in Diels'slist who mention Thales, viz. Herodotus (Diels 4, 5, and 6-the references areto the numbered quotations in Diels's section on Thales, which are discussedhere in numerical order), Plato (Diels 9; also Rep.Io. 6ooa-cf. Diels 3), andAristotle (Diels Io, 12, and 14). What do they tell us about him? Herodotus,who calls him a Milesian of Phoenician descent, mentions with approval hise.g. the well-known story of the sacrificeof an ox on the occasion of the discovery thatthe angle on a diameter of a circle is a rightangle is told about both Thales and Pytha-goras (Diog. Laert. I. 24-25); cf. Schwartzin P.W. s.v. 'Diogenes Laertios', col. 741;Pfeiffer, Callimachus,1949, i. i68.2 8th ed. 1956, edited by W. Kranz.

3 There are in classical literature at leastthree mentions of Thales not included byDiels, viz. Aristophanes, Clouds I8o; BirdsIoo9; Plautus, Captivi 274; and there areprobably more. Cf. O. Gigon, Der Ursprungdergriechischen hilosophie,1945, p. II, for aplea for a really complete collection ofnotices regarding the Pre-Socratics.

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THALES 295recommendation to the Ionians to form a federation with one paramountassemblyin Teos (i. 170 = Diels 4). Relying on this notice and the inclusionof Thales among the Seven Wise Men, Gigon' suggests that Thales' 'book'(ifhe ever wrote one--see below) containedpoliticalmaterial.Then comes themuch discussedpassage (I. 74 = Diels 5) about Thales' prediction of a solareclipse--Herodotus' actual words are: -4vU LperaAAayyvTad-rv T'ie 7pp'pr79SeaA.TgMMtLArgoSrot-aIoa I7pO)YdpevaeEacEOae, vpov7rpoO~4ervo"cLatrrovY"roi-ov, 'v 7i5 8 Ka'L 'cVETO ~tTafloAq. The eclipse s generally egardedasbeing that of 28 May 585 B.c.,2 and Thales is supposedto have predictedit bymeans of the old lunar cycle of 18years and 11 days, i.e. 223 lunarmonths, inwhich both solar and lunar eclipses may repeat themselves in roughly thesamepositions.Much has been made of this cycle,often(but quiteerroneously3)called the 'Saros',which Thales is supposedto have borrowed fromthe Baby-lonians;4modern historiansof sciencehave eagerlyseized on it as evidence forthe traditionalpictureof Thales as the intermediarybetween the wisdom of theEast and Greece, so that now it figures prominently in practically everyaccount of Thales. The Babylonians,however,did not usecyclesto predictsolareclipses, but computed them from observations of the latitude of the moonmade shortly before the expected syzygy.5 Moreover, as Neugebauer says:'There exists no cycle for solar eclipses visible at a given place; all modemcycles concern the earth as a whole. No Babylonian theory for predicting asolar eclipse existed at 6o0 B.C., as one can see from the very unsatisfactorysituation 400 years later; nor did the Babylonians ever develop any theorywhich took the influence of geographicallatitude into account.'6Yet the man.ner in which Herodotus reports the prediction, o0pov 7TpoOL'CEVOSTe'vxavTrvTooVov,7would lead one to supposethat Thales did make use of a cycle. It isperhapsjust possible that he may have heard of the I8-year cycle for lunarphenomena, and may have connected it with the solareclipseof 585 in such away as to give rise to the story that he predicted it; if so, the fulfilment of the'prediction'was a strokeof pure luck and not science,since he had no concep-tion of geographical latitude and no means of knowingwhether a solareclipsewould be visible in a particularlocality. It is difficult to see what the remark,allegedly quoted from Eudemusby Dercyllides,8 o the effect that 'Thales wasthe first to discoveran eclipse of the sun' ( ... EvperpproiT ..ALov 'KAtC4LV),

O. Gigon, Der Ursprungder griechischenPhilosophie,1945, P- 42.2 Cf. Boll in P.W. s.v. 'Finsternisse', col.2353; Heath, Aristarchus f Samos, 1913, PP-13-16; Fotheringham in J.H.S. xxxix[19I9], I8o ff., and in M.N.R.A.S. lxxxi[1920], io8.3 Cf. O. Neugebauer, The Exact SciencesnAntiquity,2nd ed. 1957, PP. 141-2.4 Ptolemy mentions it (Synt. math., ed.Heiberg, i. 269. x8 f.) and also the eAsLyo'ds,a similar cycle obtained by multiplying theformer by 3, making 669 lunar months or19,756 days, but attributes both to ol ric

rTaAaLdo'rpoLtaO7Gpar7KOl,which refers toGreek astronomers earlier than Hipparchusand not to the Babylonian astronomers,whom Ptolemy always calls oLXaA8taKoi.

s F. X. Kugler, SternkundendSterndienstnBabel, ii (x909), 58 f.; O. Neugebauer,AstronomicalCuneiformTexts, i (1956), 68-69,I15, i6o f.6 Ex. Sci., p. 142. As regards the use of thei8-year cycle he says (ibid.), 'there arecertain indications that the periodic recur-rence of lunar eclipses was utilised in thepreceding period [i.e. before 311 B.c.] bymeans of a crude I8-year cycle which wasalso used for other lunar phenomena' (myitalics).7 Diels's suggestion (Antike Technik, 3rded. 1924, p. 3, n. i) that 6eav-ro'here means'solstice' has nothing to recommend it.8 Ap. Theon. Smyrn., p. 198. 14, ed.Hiller = Diels 17.



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296 D. R. DICKSactually means. It can hardlymean that he was the first to notice solareclipse;but if it means that he was the first to discover the cause of one, then it iscertainlywrong, for he could not possiblyhave possessedthisknowledgewhichneither the Egyptians nor the Babyloniansnor his immediate successorspos-sessed.' In fact the reportis an obvious amplificationof Herodotus' story witha furtherdiscoveryattributed to Thales (that he also found the cycle of the sunwith relation to the solstices) thrown in for good measure, merely because itseemed plausible to Eudemus or Dercyllides. After Herodotus,z the doxo-graphical writers and Latin authors like Cicero and Pliny (cf. Diels 5) go onrepeating the story with or without further embellishment, but it is perhapssignificantthat no other writer in the firstgroup of sources (i.e. those before320 B.C.)mentions it. Of modern commentators,Martin3 ong ago rejectedtheentire story,Dreyer4 s extremely sceptical, and Neugebauer,5the most recentauthority, also refuses to credit it.Next in Diels's collection is Herodotus' story (I. 75 = Diels 6) of Thales'reputed diversionof the river Halys to enable King Croesus to invade Cappa-docia-a story,be it noted,which Herodotusreportsas being generallybelievedamong the Greeks, but which he himself explicitly refuses to accept.6 ThenPlato (Rep.Io. 6ooa), in a discussionof the desirabilityof toleratingHomer inthe ideal state, takes Thales as an example of the clever technician, dAA' ta 86E6S1r I pya ao~ov avspo ro)a alrlvotat KaaEVlXavo"El' rExva' '-wasvaamaerpctgE&Ayov-rat, wcorrEp0 &aAEwE 7rEploV^ MLAq-covKal Avaxdpanoso-oZKVOov.7 Elsewhere (Theaet. I74a = Diels 9) he is cited as an example of theabsent-mindedstar-gazerwho is so intent on the heavens that he does not seewhat is at his feet and falls into a well.8 Aristotle (Pol. A, I259a5 = Diels Io)tells the story of Thales' foresight and business acumen in buying up all theolive-presses in Miletus and Chios during one winter, in anticipation of abumper olive crop later; when this duly materialized he was able to hire themout at great profit to himself.Finally, in this firstgroup of sources,Thales' philosophical speculationsarelimited to two main propositionsonly, each accompanied by a more or lessfanciful corollary,viz. (i) that water is the primarysubstance of the universe(Diels I2), and that the world rests on water (Diels 14), and (2) that every-thing is full of gods rarvra ~AX4p7E0EVDiels 22), and that the lodestone has asoul (ibid.). It is worth noting the manner in which Aristotle reports thesespeculations; as regards (I), which seems to be the most definite, Aristotle

' Cf. G. S. Kirk and J. E. Raven, ThePresocraticPhilosophers,1957, p. 78-Kirk'sreference to 'the undoubted fact of Thales'prediction' is a considerable overstatement.2 Gigon (op. cit., p. 52) thinks that Hero-dotus may have taken the story from a poemof Xenophanes, who perhaps expressedincredulity at the report; but it seems muchmore probable that Herodotus is relating thegenerally accepted hearsay of his time.3 RevueArchlologique,x [1864], 170-99.

4 J. L. E. Dreyer, A Historyof Astronomy(originally entitled A Historyof thePlanetarySystems), repr. 1953 (Dover Publications,New York), p. 12.s Ex. Sci., p. 142. Neugebauer complains

of the vagueness of Herodotus' report, butthis is somewhatunjust; obviously, whatimpressedHerodotuswasthe suddenchangefrom bright daylight to comparativedark-ness-hence the choice of the words~peaA-Aay' and plrafloA1.6 C%hyE A'Eyw, KaTd 7%ov'aast yVESvpa~effllaaE royv rpardoY,dCg 78 troAAhd AdOyo,r6v 'EAAmvwvy, OaA-q- oLd MA7ato ~SEflLfPaaE.Kirkand Raven (op. cit., p. 76) cite this as'convincing evidence' for Thales' reputationas an engineer-the adjective seems hardlyappropriate.7 On this and the scholion (= Diels 3),see below.8 This earliestexample of a perennially



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THALES 297says, OaArsg&C"T'7S tLav'n7)Sao qXyos ?oao(lacro cuSwp b77alvW LSL Kal7 ")vyi E' iSars 7ToIcvao EtaL),Aaflcov'cws 7 6v zr5oA-wavra V'IKK.r.A.,andin another place (decaeloB 13. 294a28)troOroydp[i~v yn-v1' "8aros- KEcTOat]apxaOdTraTovpE&A7)jalLEVrTvAdyov, v OacwvETEFYOaA-iv7~v MArjatov:asregards (2) Aristotle's words are (de anima A, 411a8), oOEv L9(ws Kalt19ag'0 'rrcvrar'rprl OE~-vELvaL,while elsewhere he is even more hesitant (dean.A, 405a19), SOLKE K e aA7)sec Jv cITO/1V7/L4OVEVOVUL&W)TLKOV&77 tbVyjVrTroAafltEv,ITTEpTv Aov l OvyX74vXELV,Or rc3v lrqpovKWVEL.nell, n anarticle which examines critically the process of transmissionof Thales' philo-sophicalopinions,'notes that the firstquotation(Metaph. . 3- 983b2 = Diels I2)gives a false impressionof definiteness on Aristotle'spart, because the passagecontinues (984aI) El ievovvapXala rSaT-r-Ka'7aAati7TETvXYKEVvaaerrpplOb1JUEsg so/8a, ca' &&V7AoVL'oq,&q,aA$- rOtAE'aL oiro bcToqvo auleaL t7rpt-rgS pdrP7Strtas, and Diels ought certainly to have continued the quotationas far as this.2In several other instancesSnell correctswhat appear in Diels asphilosophical speculations attributed by AMtius o Thales, and shows that inreality these stem directly from Aristotle's own interpretationswhich thenbecame incorporated n the doxographicaltradition as erroneousascriptions oThales3-and, one might add, are duly perpetuatedby Diels-Kranz.So much, then, for what may be termed the primary authorities for ourknowledge of Thales' life and opinions,e.g. writers before320 B.C.What is thegeneral impressionwe obtain from them? Surely, that he had a reputationchiefly as apracticalman of affairs,who was capable of giving sensiblepoliticaladvice (his recommendation to the Ionians to unite), was astute in businessmatters (the transaction with the olive-presses),and had an inquiring turn ofmind with a bent towards natural science and the ability to put to practicaluse whatever knowledge he possessed(the stories of the eclipsepredictionandthe diversion of the riverHalys). This pictureof Thales is amply substantiatedby the other references to him in classical writers not listed in Diels, e.g.Aristophanes, CloudsI80; Birds Ioo9; Plautus, Captivi274-in each of thesepassages he is cited as the typical example of the clever man (perhaps notalways scrupulous n his methods ? CloudsI8o--cf. the storyof the olive-presses)noted as much for his resourcefulnessas for his sagacity.The singlediscordantnote is Plato's storyof his falling into a well, but then this is the kind of anec-dote which might be told about anyone interested in astronomy, and is byno means an indication of habitual absent-mindednesson Thales' part. It isnot surprising hat a man endowed with the qualitiesenumerated above shouldin due coursebe numberedamong the Seven Wise Men of Greece. There waspopular genre of comic story has been sub-jected to a solemn discussion and analysisby M. Landmann and J. O. Fleckenstein,'Tagesbeobachtung von Sterner in Alter-tumrn',Vierteljahrschr. . Naturf. Gesch. inZiirich, xxxviii [I19431, 98 f., in the course ofwhich it is suggested that the story is not'echt oder unecht', but contains a germ ofhistorical truth in that Thales probablyobserved stars in daylight from the bottomof a well! The article contains an entirelyuncritical account of Thales' alleged achieve-ments and discoveries, with the usual

imaginary picture of him as the transmitterof Egyptian and Babylonian wisdom.I B. Snell, 'Die Nachrichten uiber dieLehren des Thales und die Anfainge dergriechischen Philosophie- und Literatur-geschichte', Philologusxcvi (1944), 170-82.2 Id., op. cit., p. 172.3 Op. cit. pp. I70 and I71 with footnote(i). Thales, of course, was not the onlyearly thinker to be thus treated by Aristotle;Anaxagoras was another-cf. F. M. Corn-ford, 'Anaxagoras' Theory of Matter-II',C.Q. xxiv [1930], 83-95.



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298 D. R. DICKSnever complete agreement among the ancient writers on the names of theSeven or even on the number itself,' but four names occur regularly in thevarious lists given--Thales, Solon, Bias, and Pittacus; and these, be it noted,were all essentiallypracticalmen who played leading roles in the affairs of theirrespectivestates, and were far better known to the earlier Greeksas lawgiversand statesmen than as profound thinkersand philosophers. As we shall see,it is only from the second group of sources,i.e. writers after 320 B.C., that weobtain the picture of Thales as the pioneer in Greek scientific thinking, par-ticularly in regard to mathematics and astronomy which he is supposed tohave learnt about in Babylonia and Egypt. In the earlier tradition he is afavouriteexample of the intelligent man who possessessome technical 'know-how'.3One very importantpoint that can be established from considerationof thisfirstgroup of sources is that no written work by Thales was available for con-sultation to either Herodotus, Plato, or Aristotle--the tradition about him,even as early as the fifthcenturyB.C.,was evidently based entirelyon hearsay.This seems quite certain; for all mentions of him are introduced by wordssuch as Obaa', A'yi-a, c~O%, oKE, and the like, and never4 is a citation giventhat reads as though taken directly from a work by Thales himself. This facthas obvious implications for our judgement of the trustworthinessof the in-formation that later writersgive us about him. It is even doubtfulwhether heeverproduced anywrittenworkat all ;5certainlythere was a persistent raditionin later antiquity that he left none.6It would seem that alreadyby Aristotle'stime the early Ionians were largely names only7 to which popular traditionattached various ideas or achievements with greater or less plausibility;

x See Diog. Laert., 1. 40 f.2 Werner Jaeger, Aristotle,2nd ed. 1948(translated into English by R. Robinson),Appendix II, 'On the Origin and Cycle ofthe Philosophic Life', p. 454, is surely wrongin saying that the reports emphasizing thepractical and political activities of the SevenWise Men were first introduced into thetradition by Dicaearchus in the latter half ofthe fourth century. In the case of Thales, atany rate, it is the earlytradition as exempli-fied by Herodotus that makes him a practicalstatesman, while the later doxographers foiston to him any number of discoveries andachievements, in order to build him up asa figure of superhuman wisdom. Jaeger isalso wrong in asserting that Plato had madeThales 'a pure representative of the theoreti-cal life' (op. cit., p. 453)-he apparentlyoverlooks Rep. Io. 6ooa, where this is farfrom being the case, and he takes the wellstory too seriously. On the other hand, he isundoubtedly right to emphasize the com-paratively late origin of the traditionalpicture of Pre-Socratic philosophy, 'thewhole picture that has come down to us ofthe history of early philosophy was fashionedduring the two or threegenerationsfromPlatoto the immediate pupils of Aristotle' (429).

3 See especially Plato, Rep. Io. 6ooa (andBurnet, Early GreekPhilosophy,p. 47 n. I)where Thales is coupled with Anacharsis,who is said to have invented the potter'swheel and the anchor.4 The single apparent exception (Met. I.3. 983"21 = Diels I2), where Aristotleseems to be more definite, has already beenshown to be illusory, in that if the quotationwere carried to its proper end we should findthe familiar OaA -AyTera again. Kirk andRaven (op. cit., p. 85) also remark on thecautious manner in which Aristotle cites

Thales; cf. Snell, op. cit., pp. 172 and 177-but Snell's insistence that Aristotle is notrelying merely on oral tradition but mustbe using a pre-Platonic written source(which Snell identifies as Hippias) is hardlyconvincing on the evidence available.s What Diels (pp. 8o-8I) prints as'Angebliche Fragmente' of Thales' worksare, of course, completely spurious, as Dielshimself points out.6 Diog. Laert. I. 23, Kal Ka7adtvas tliavyypapL.a KaT7ALrEV ;SV: Cf. Joseph. c.Ap.I. 2; Simplicius, Phys. 23. 29.7 Cf. Kirk and Raven, p. 218-Aristotle,Plato, and Pythagoras.



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THALES 299naturally this process gave rise to numerous permutationsand combinationsof the names and the attributesamong the later writersof our second group ofsources. Even the works of men like Anaximanderand Xenophanes, the exis-tence of whose writingsin the sixth centuryB.C.anyway is unquestioned,by thefourthcenturyB.C.either had disappearedcompletelyor were extant in one ortwo scatteredcopies distinguished by their rarity;I and if this was the situationin the time of Aristotle, it can confidently be said that the chances that theoriginal works of the earlier Pre-Socraticswere still readily available to hispupils, such as Theophrastusand Eudemus,much less to their excerptorsandimitators in succeeding centuries,are extremely small. Nearly always when alater commentator attributes some idea to Thales or any other early Ionianthe ascription is based not on the original work, nor even on some otherwriter's citation of the original, but on some 'authority'two, three, four, five,or more stages removed from the original (see below).It is when we come to the second main group of sources, i.e. writers after320 B.C., that Thales' stature begins to take on heroic proportions and heappearsas the figureso dear to modern historians of science and philosophy-the founder of Greek mathematics and astronomy,the transmitterof ancientEgyptian and Babylonianwisdom, the first man to subjectthe empiricalknow-ledge of the orient to the rigorouslyanalytic Greekmethod of reasoning; and,of course, the later the 'authority' the more freely does he ascribe all sorts ofknowledge to Thales.2It is again to Hermann Diels that we are indebted for adetailed examination of these later sources. His large volume, DoxographiGraeci,which first appeared in 1879 and achieved a second edition in I929,remains the standard work on the subject. Diels's results are by now wellknown.3 In 263 pages of Prolegomena he gives a detailed, critical discussionof the doxographical writers from Theophrastus (4th-3rd centuries B.c.) toTzetzes (12th century A.D.), analyses the probable sources of each writer'sinformation,and traceswith patient ingenuity the interconnexionsand ramifi-cations of these sourcesamong the host of epitomators,excerptors,and com-pilers who flourished in later antiquity. Briefly, one of the main results ofDiels's work is the re-emergence of Aetius, an eclectic of the first or secondcenturies A.D.,4 whose lost Zvvaywy-q -r&v pOrdK'rTYovs shown to be largelypreservedin the pseudo-PlutarcheanPlacitaPhilosophorumnd in the 'EKAoyaTof Stobaeus.sAll such collections of &dpxaKovrar placita are derivedultimatelyfrom the OQvacUtyv&tac of Theophrastus who, following the example initiatedby Aristotle (e.g. at the beginning of the Metaphysics),et out to record theopinions of the early thinkers on various problems of philosophy and naturalscience; but Diels shows that our extant sources,far fromtakingtheirmaterialdirectly fromTheophrastus'work,preferredto useone or more intermediaries,so that what we actually read in them comes to us not even at second, but atthird or fourth or fifth hand. Thus Aetius did not use Theophrastusdirectly,but (with additions from other sources) an epitome of him which Diels callsI Cf. Diels, Dox. p. 219; P. 112.2 Oddly enough, this tendency can also beseen in modern times. Earlier writers, likeTannery, are far less prone to exaggerateThales' achievements than more recent ones,such as van der Waerden-on whom seefurther below.

3 There are summaries in Zeller, Outlines

of the History of GreekPhilosophy,I3th ed.repr. 1948, pp. 4-8; Burnet, Early GreekPhilosophy,4th ed. repr. 1952, PP. 33-38;Kirk and Raven, op. cit., pp. I-7; cf. P.-H.Michel, De Pythagore Euclide,1950, PP. 72-x67-a useful reference section for all thesources relevant to Greek mathematics.4 Dox., p. xo1. 5 Dox., pp. 45 f.



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300 D. R. DICKSthe Vetusta lacita'and which seems to have appeared towards the end of thesecond century B.c., possibly in the school of Posidonius. Obviously this useof intermediate sources, copied and recopied from century to century, witheach writer adding additional pieces of information of greater or less plausi-bility from his own knowledge, provided a fertile field for errors in transmis-sion, wrong ascriptions,and fictitious attributions-as can be seen, forexample,in the scrap-bookof Diogenes Laertius.zAMtius imselfis by no means alwaysa reliable source; Snell3has shown how two passages,which in Diels-Kranzare accepted as genuine opinions of Thales, are in fact merely AMtius'nter-pretations of remarks by Aristotle which have nothing to do with Thales.Similarly,A6tius'couplingof Thales and Pythagoras(!) in connexionwith thedivision of the celestialsphereinto five zones is entirelyerroneous,as the theoryof zones (i.e. the bands of the globe bounded by the 'arctic', 'antarctic',equator, and tropics) can hardly have been formulated before the time ofEudoxus.4Now if Theophrastus himself was in error on any point either throughmisinterpretation or lack of reliable information (which we have not theslightestreason to doubt was frequentlythe case as regardsthe Pre-Socratics5),it is perfectlyobvious that there is no chance at all that his later copyistsandexcerptorswould either recognize or be in a position to correct the error.Wehave seen alreadythat even if Thales did write a book it was no longer extantin Aristotle's time. This being the case, it can be taken forgrantedthat no copywas available to Theophrastus either. Hence all that he knew about Thaleswas what he could gather from Aristotle'sprevious mentions of him, supple-mented perhaps by a few more scraps of informationgained from hearsay.6We have seen the type of information that Aristotle possessed, and this, itshould be remembered, was the direct, authentic line of the tradition. Yetmodern commentatorspersistin ascribingas much, if not more, weight to theexaggerated stories of Thales' achievements given by post-Theophrasteanwriters who had to rely on their own imaginations to bolster the meagreaccount that was all that Aristotleor Theophrastuscould give. It needs to beborne in mind that the preservationof old texts and the carefulreferringbackto the ipsissima erbaof the author are comparativelymodern innovations ofscholarship,which, though seeming to us of fundamentalimportance,were byno means so regarded by the ancients. Cicero makes a revealingremark n thisconnexion: talking about Aristotle'swork on the early handbooks of rhetoric,he says 'ac tantum inventoribusipsis suavitate et brevitate dicendi praestititut nemo illorum praecepta ex ipsorum [i.e. veterum scriptorum] libris co-gnoscat,sed omnes qui quod illi praecipiantvelint intellegeread hunc quasiadquendam multo commodioremexplicatorem revertantur'.7Exactly the sameholds true for the early philosophers; if one wanted to know their opinions,one consulted Theophrastus or Eudemus (on whom see more below) or

' Dox., pp. 179 f.2 Cf. Schwartz in P. W. s.v. 'DiogenesLaertios'; Dox., pp. I6 f.3 Op. cit., pp. 170-I, 176.4 Cf. J. O. Thomson, History of AncientGeography,948, pp. I12 and 116.s Cf. G. S. Kirk, Heraclitus: the CosmicFragments,1954, pp. 20-25.

6 What Gigon (op. cit., pp. 43-44) callsthe 'anekdotische und apophthegmatischetOberlieferung'.7 De invent.2. 2. 6. Further on he mentionsIsocrates whose book Cicero knows to existbut which he has not himself found, althoughhe has come across numerous writings byIsocrates' pupils.



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THALES 3o0Menon'-one would not bother to go back to the original works even in theunlikelyevent of their being still available.2There is, therefore,nojustificationwhatsoever for supposing that very late commentators,such as Proclus (5thcentury A.D.) and Simplicius (6th century A.D.), can possibly possess moreauthentic informationabout the Pre-Socratics han the earlierepitomatorsandexcerptorswho took their accounts from the above disciplesof the PeripateticSchool, who in turn depended mainly on Aristotle himself and perhaps to asmall extent on an oral traditionsuchas obviouslyforms the basisofHerodotus'stories about Thales.

Diels,3 in a comparative examination of four later works which dependultimatelyon Theophrastus,viz. Hippolytus'Philosophoumena,seudo-Plutarch'sStromata,Diogenes Laertius, and Adtius (the 'biographical doxographers'asBurnet calls them4),shows that in each case two primarysourcescan be traced,(a) a 'futtilissimumVitarum compendium', a very inferiorcompilationbasedon biographical material of dubious authenticity gleaned from the samesources as were presumably used by Aristoxenus and the later writers of'Successions' (A asoxat) such as Sotion-this must represent the pre-literaryoral tradition of popular hearsay; and (b) a good epitome of Theophrastusby some unknownwriter. It is particularly noteworthythat the noticesregard-ing Thales, Pythagoras,Heraclitus,and Empedoclesare entirelyderivedfromthe first inferior source-yet another indication of the paucity of genuineknowledge about these early figures.One result of this lack of informationwasthat very soon certain doctrinesthat later commentatorsinvented for Thales,and that became fixed in the doxographicaltradition,were then accepted intothe biographical tradition, and thus, because they may be repeated by dif-ferent authorsrelyingon differentsources,may producean illusoryimpressionof genuineness.This can be shown to have happened in the case of the dogma0 KOUato0EJ0bvxo,which in reality stemmed from Aristotle and not from Thales,but which reappears in the biographical tradition that underlies both thescholion on Plato, Rep. Io. 6ooa and Diogenes Laertius I. 27.5I must now discuss the source on which modern scholars6rely most of all tosubstantiatetheir exaggeratedviews of Thales' knowledgeand achievements-namely, Eudemus, who to some extent bridgesthe gap between what I havecalled the primary and secondarysources for our knowledge of Thales. It isgenerally considered that it is from Eudemus' FEWtETtLK-? UT-rop'a,ApLtOtp-LK71KZcrropta,and AarpoAoyuK LaUTopa'7hat all later writers derive their information

' Cf. Jaeger, Aristotle,p. 335; in the workof compiling a comprehensive history ofhuman knowledge Menon was allotted thefield of medicine, Eudemus that of mathe-matics and astronomy and perhaps theology,and Theophrastus that of physics and meta-physics.2 Cf. Diels, Dox., p. 128.3 Dox., pp. I45 f.4 Early GreekPhilos., p. 36.5 Snell, op. cit., pp. 175-6.6 Such as, F. Cajori, A Historyof Mathe-matics, 1919, pp. I5 f.; D. E. Smith, Historyof Mathematics, (1923), 64f.; G. Sarton,Introductiono theHistoryof Science, epr. 1950,i. 72; W. Capelle, Die Vorsokratiker,th ed.

1953, pp. 67 f.; B. L. van der Waerden,ScienceAwakening, 954, pp. 86 f.; G. Hauser,Geometrieder Griechenvon Thales bis Euklid,1955, PP- 43-49; Gomperz, GreekThinkers,repr. 1955, i. 46-48; 0. Becker, Das mathe-matischeDenkenderAntike,1957, PP- 37 f.-toname but a few. Even T. L. Heath, who wasaware of the flimsiness of the evidence onwhich our knowledge of Thales is based, isinclined to over-estimate his achievements-cf. Historyof GreekMathematics, 921, i. 128 f.;Manualof GreekMathematics,1931, pp. 81 f.7 All three now only extant in meagrefragments, recently edited with a commen-tary by F. Wehrli, EudemosvonRhodos(DieSchule des Aristoteles, Heft viii), 1955.



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302 D. R. DICKSabout GreeksciencebeforeEuclid,' and theremay well be a good deal of truthin this view. Unfortunately it does not help us at all in assessingthe trust-worthiness of Eudemus' statements about such an early figure as Thales, fortwo reasons. In the firstplace, if, as has already been shown, neither Aristotlenor Theophrastuspossessedany written work by Thales, what reason is thereto supposethat Eudemushad access to such? If he did not, then he knew nomore about Thales than the other two did since he had to rely on the sameinadequate sources; and thereforeany achievement which later writers creditto Thales on the authority of Eudemus alone is likely to be a mere inventionof his own or (as we shall see below) a rationalizationof a presumedstate ofaffairs n Thales' time. Secondly,thereis somereasonto supposethat Eudemus'works were lost quite soon afterthe fourthcenturyB.c.2 and that the same fatebefell them as overtookTheophrastus'OVluLK{V 8d&aL, .e. they were excerptedand rearrangedby the epitomators,and then laterwriters took theirquotationsfrom these intermediate sources rather than from the original works. Proclus,from whose Commentary n the First Book of Euclid come most of the extantfragments of Eudemus' PewtlerptK7 laoTopta,3 although he usually quotes asthough directlyfromthe original (Jg[fatv EiE7StzoS),wice gives the impressionthat in fact he may be using intermediaries,when he mentions old dsar-opas-avaypdavrwe4 and ol rrTEplrv Eqpov.5 Even Simplicius, who purports toquoteverbatim fromEudemus,6may have takenhisquotationfrom asecondarysource, for he says on one occasion, cosE3871 '.s -Ev i~, ) EVrpp 7-9 dO'ErpoAoyuLKIau'optasaTE4rltV7LOVEVaEcL~WorLyEVqrrapa Ev89kov oih afafiv.7The authority of Eudemus is especially invoked to support the view ofThales as the founder of Greek geometry. The following propositions arecommonly attributed to him:8

(I) that a circle is bisected by its diameter;(2) that the angles at the base of an isoscelestriangle are equal (the wordactually used is 'ooost 'similar', instead of toaos);(3) that when two straightlinesintersect, the vertically opposite angles areequal;(4) that if two triangles have two angles and one side equal, the trianglesare equal in all respects.For the first two of these, Eudemus is not specificallycited by Proclus as hisauthority, but it is generallyassumedthat they are derivedfrom Eudemus--how far this assumptionis justified may be inferred from the following con-

I Cf. Martini in P. W. s.v. 'Eudemos';Wehrli, op. cit., p. 14.2 Cf. Michel, op. cit., pp. 82-83, quotingTannery.3 Wehrli, op. cit., pp. 54-67.4 Id. frag. I33 ad fin.s Id., frag. 137.6 Id., frag. 140, p. 59, I. 24, K8O'aopwtLTa rd 70roE38-4potvKa-rd "ew AEyo'puEVa.7 Id., frag. 148. Heath, however, sees noreason to doubt that these late commentatorsof the fifth and sixth centuries A.D., such asProclus, Simplicius, and Eutocius, consultedEudemus at first hand (Hist. of Gk. Maths.ii. 530 f.; cf. The ThirteenBooks of Euclid's

Elements,2nd ed. repr. 1956 (Dover Publica-tions, New York), i. 29-38. Heath contra-dicts Tannery's view (cf. also Martini inP.W. s.v. 'Eudemos'; Heiberg, Philol. xliii.330 f.), but offers no explanation of thepassages I have cited above; he does agreethat in the case of Oenopodes, for example,Proclus gives a quotation which cannot havebeen at first hand.8 Heath, H.G.M. i. 130 (cf. Man., p. 83),v. d. Waerden, p. 87, Hauser, p. 45, andBecker, p. 38, give less well-authenticatedlists.9 Cf. Heath, Euclid,p. 36.



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THALES 303siderations. As regards (i) it should be observed that Thales is said to have'proved' (d'roSetaL) this, a statement which itself arouses suspicion since evenEuclid did not claim to do this, but was content to state it as a 'definition'(gpos);' on the other hand, we are told that Thales only 'noted and stated'(d)ern LKariEtv) (2) and 'discovered' (e"ppEv) without scientificallyproving (3).z Most revealing,however, is the mannerin which (4) is reported;here Proclus' actual words are,3 EiYrloos.TSev rais YEWtLETrptKa u'rTopatS EdlOaA7lvrov-To vayELr O%wp7'(ta. r v yap -rcv ev OaAr'rT7-irAo'ov&Tr6o'rauavt'o Tpd7Trovaaiv 8EtKV'VLa, ov'-rCTrpOapaxpOau' a 7w dvayKatov, 'Eudemus in his"History of Geometry" attributes this theorem to Thales; for he says thatThales must have made use of it for the method by which, they ay,he showedthe distance of ships at sea' (my italics). This, as Burnet remarks,4 s a clearindication of the real basis for all the statements about Thales' geometricalknowledge. Because his was the most notable name in early Greek historyabout whom various traditional storieswere told (as in Herodotus),because healso had a reputation for putting his technical knowledge to practical use(hence the report-which was nothing more than hearsay, as qaal proves-of his measuring the distance of ships from the shore), and because it soonbecame firmly fixed in the tradition that he had learnt geometry in Egypt(on this see further below), then it seemed obvious to later generationsbrought up on Euclid and the logical, analytical method of expressing geo-metricalproofs,that Thales mustcertainlyhave knownthe simplertheoremsinthe Elements, hich it was supposedhe formulatedin the terms familiarto post-Euclidean mathematicians. From this it was only a short and inevitable stepto ascribingthe actual discoveriesof thesegeometricalpropositions o the greatman.5 In fact, however, the formal, rigorousmethod of proof by a processofstep-by-stepdeduction from certain fixed definitionsand postulateswas notdeveloped until the time of Eudoxusin the first half of the fourthcenturyB.c.,and there is not the slightestlikelihood that it was known to Thales.6He mayhave possessedsomemathematicalknowledgeof the empiricaltype of Egyptianor Babylonian mathematics, but that this took the form which Proclus-Eudemuswould have us supposeis quite out of the question.Also regardedas stemmingfromEudemus,althoughadmittedlynot his in its

I Euclid, Elements, Def. 17.2 Cf. Heath, H.G.M. i. 131.3 Wehrli, frag. 134.4 E.G.P., p. 45; cf. Gigon, op. cit., p. 55.s There is an excellent modern example ofthis type of rationalization in the oft-re-peated statement that the Egyptians of thesecond millennium B.c. knew that a trianglewith sides of 3, 4, and 5 units was right-angled, and used this fact in marking outwith ropes the base angles of their monu-ments; hence, it issaid, they knew empiricallythis special case of the general 'theorem ofPythagoras'. In actual fact, there is no truthin this at all, and the whole story originatedin a piece of typical guesswork by M. Cantor(whose VorlesungeniberGeschichte er Mathe-matik, 4 vols., 188o-I908, is probably re-sponsible for more erroneous beliefs in this

field than any other book--cf. 0. Neuge-bauer, Isis, xlvii [1956], 58, for a just ap-praisal of it). Because Cantor thought thatropes representing a triangle with sides of3, 4, and 5 were the simplest means for con-structing a right-angle, he assumed that thiswas the method used by the Egyptians. Un-fortunately, there is no evidence that theyknew that such a triangle was right-angled;cf. Heath, Man., p. 96; v. d. Waerden, p. 6.6 Cf. Neugebauer, Ex. Sci., pp. 147-8. Itsbeginnings may be dated back to Hippo-crates in the last half of the fifth centuryB.c., if he was really the first to compose abook of 'Elements' (aroLXedCa)s Proclus says(in the 'Eudemian Summary'-see below-Wehrli, frag. 133, p. 55, 1. 7): cf. v. d.Waerden, pp. I35-6.



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304 D. R. DICKSpresent form,' is the so-called Eudemian ummary, brief, 'potted' history ofgeometry which Proclus prefixes to his Commentaryn theFirstBookof Euclid.2It is here that we find for the first time the explicit statementthat Thales wentto Egypt and thence introduced geometry into Greece: &aA77 s6rpaov dAi'yv7r'rovA cowJEvp77yayEv tSTrqv'EAAc'Sa7+vGEOpQavratyr-v [yeWLErpiaV]Ka2roAAaMva o'o' eipev, TroAAZv~rag pxas 'roZ~/LzEc'i'c r v t3cnyaaTro (Wehrli,p. 54, 11.18-20). Nowhere in the primarygroup of sources do we find Thales'name linked directly with either the beginningsof geometry or Egypt (or, forthat matter, Babylonia); it is only in the secondary sources,and apparentlyfirst in Eudemus (if we assume that he is the authority for Proclus'account),that these connexionsare made. This is worth emphasizingand is in itselfverysuggestive. It seems highly probable that the whole picture painted for us bylater writersof Thales as the founder of Greekgeometryon the basisof know-ledge he had acquired in Egypt is nothing more than the amplificationandlinking together of separatenotices in Herodotus. The processseems to havebeen as follows: Thales was a prominent figure in early Greek history aboutwhom practicallynothing certain was known except that he lived in Miletus;Milesianswere in a positionto be able to travelwidely; the two most interesting'barbarian' civilizations known to the Greeks were the Egyptian and theMesopotamian; therefore Thales (it was assumed) must have visited Egyptand Babylonia; but Herodotus4says that geometry originated in Egypt andthence came into Greece; therefore (it was assumed)Thales must have learntit there and introducedit to the Greeks. It was left to modern commentators oadd yet anotherstage to the myth by envisagingThales (becauseof his allegedprediction of an eclipse) as the transmitterof Babylonian astronomicallore.5Once granted that Thales visited Egypt, then, of course, a number of otherstories followed automatically. For example, it would naturally be assumedthat he saw the most strikingphenomenonof life in Egypt, the annualfloodingof the Nile; Herodotus6reports three theories about this and in each caseomits to name the originator; what more natural, therefore, than to ap-propriatethe firstof these for Thales?7Similarlyit would be assumedthat hesaw the pyramids; therefore,the storyfollowed that he measured theirheights(Diels 21). The only surprising thing about these stories (apart from theseriousnesswith which modernscholars treat them8)is that there are not moreof them.

I Cf. Heath, H.G.M. i. I18f.; Euclid,PP. 37-38-2 Proclus Diadochus, In primumEuclidisElementorum ibrum comment.,Prologus II,pp. 64 f. ed. Friedlein; Wehrli, frag. 133,PP- 54-56-3Wehrli (op. cit., 11I5) points out thatEudemus follows Herodotus' view even inthe face of a different opinion expressed byAristotle.

4 2. 0og; cf. Diod. Sic. i. 8I. 2; Strabo757 and 787.s In fact, a visit of Thales to Babylonia iseven less well authenticated than a visit toEgypt-Josephus (c.Ap. I. 2) seems to be theonly writer to mention the former; but sinceEgyptian astronomy never evolved beyond a

very elementary level and did not concernitself with eclipses (cf. Neug., Ex. Sci.,pp. 8o-9I; 95 ad fin.), some connexionbetween Thales and Babylonia had to bemanufactured. This was made the moreplausible by reference to Herodotus' state-ment (2. 109) that the Greeks learnt aboutthe 'polos', the gnomon, and the division ofthe day into 12 parts (but on this see below)from the Babylonians. 6 2. 20 f.7 Aetius 4.1. I = Diels 16; cf. Diod.Sic. I. 38.8 e.g. Gomperz, Gigon, H61scher, andHauser accept them all apparently without aqualm; Gigon (op. cit., p. 87) even acceptsCicero's story (de div. I. 50. I 2) aboutAnaximander's foretelling an earthquake.



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THALES 305Thus the Proclus-Eudemusinvention of a visit to Egypt by Thales had anenormouseffect on the later view of him and his achievements. The Egyptiancivilization,whether because of the massive nature of its monuments or simply

because of its antiquity, seems to have made a profound and ineradicableimpressionon the Greeks.This manifesteditself in severalways; sometimesbya readiness to attribute to the Egyptiansan immemorialknowledge of certainsubjects, e.g. geometry; sometimesby a desire to give a respectableantiquityto a body of doctrineby inventingforit an Egyptian origin, e.g. the 'Hermetic'literature of the Alexandrianperiod;' and sometimesby a tendency to supposethat no life of a great man was complete without a visit to Egypt, e.g. Thales,and compare also the apocryphal stories about Pythagoras' and Plato'stravels.2Once the travelsbecame an integralpart of the Thales tradition,thenit was easy to draw a pictureof him as the first Greekphilosopherand scientistand the first to become acquainted with the knowledge of the Egyptian andBabylonian priests-a picture which suited well the preconceived ideas thatlater generations had of what must have happened in those early centuries,but which, it must be emphasized,is entirelyhypotheticaland unsubstantiatedby any really trustworthyevidence. Modern commentators, by using everyscrap of information gleaned from late sources, regardlessof its genuinenessbut mindful of its plausibility,have enlargedthe picture and even added to itscolours so as to harmonize it with our greater knowledge of pre-Greekmathe-matics and astronomy. It still, however, remains a hypothetical picture,because it is not based on reliableevidence but on imaginary suppositions.3The evidence we have points clearly to the fact that it was Eudemus,about250 years afterThales, when already the famous names of early Greekhistorywere dim figuresof a remote antiquity about whom little definite was known,who was primarilyresponsiblefor using Thales as a convenient peg on whichto hang an accountof the beginningsofGreek mathematics. Thales' name waswell known, there were already stories about his clevernessin Herodotus andAristotle,and no written workof his remained to contradict whatever doctrinemight be assignedto him; he was, in fact, an ideal choice. Once the connexionhad been made between him and Egypt, then everythingelse fitted nicely intoplace. There is nothingsurprising n such a process.The distortion of historicalfact in later tradition and the ease with which purely imaginary accounts,

This was represented as part of thedivine teaching of the ancient Egyptian godThoth (Greek, Hermes) and his interpreters,Nechepso and Petosiris; cf. A.-J. Festugiere,La Rdvilationd'Hermes TrismIgiste,4 tom.(1944-54)-especially tom. i, pp. 70 f.2 Cf. Burnet, EarlyGreekPhilosophy, . 88;G. C. Field, Plato and His Contemporaries,2nd ed. 1948, p. 13.3 There is a curious dualism evident inmost of the modern accounts of Thales.Even those scholars who profess to recognizethe unsatisfactory nature of the evidence onwhich our knowledge of him depends con-tinue to discuss his alleged achievements asthough they are undoubtedly real. Despitethe occasional qualifying phrase (e.g. 'Thalesis said to . . .', 'tradition has it that Thales

. . .', and so on), the desire to believe is sostrong that his travels, for example, are nowtreated as an established fact. One result ofthis is that the notices about Thales inclassical dictionaries and encyclopedias arefor the most part uniformly bad; especiallymisleading are those in P. W., O.C.D., andthe EncyclopaediaBritannica-Chambers's isslightly better, while Tannery's in La GrandeEncyclopidie, om. 30 is eminently sensible.It is noteworthy that some Americanscholars in recent years are at last realizinghow little is really known about Thales: cf.D. Fleming in Isis, xlvii [1956], reviewingEssays on the Social History of Science (Cen-taurus 1953); M. Clagett, Greek Science inAntiquity, 1957, P. 56.

4509.3/4 x



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306 D. R. DICKSbuttressed by one or two circumstantial details, can be rendered entirelyplausible could be demonstrated by numerous examples; one thinks of themighty epic of Roland and its slender basis of fact in an unimportant borderskirmish,I and the famous story of the First World War about the Russiansmarching through England with 'snow on their boots'. The legend of Thalesbuilt up by the later commentators is simply another more prosaic example of asimilar type. Admittedly the lateness of a source does not in itself entirelydestroy its worth as a trustworthy authority, but it should at least make us lookmore closely into the antecedents and origin of the information provided.When, as Diels has clearly shown, this information is based on intermediariescopying and recopying from each other at third, fourth, and fifth hand, thenthe value of the late source is, I submit, negligible, and the data it provideslikely to be unauthentic and misleading. This is especially true of the earlyIonian thinkers who, as we have already seen, even to Aristotle's generationtended to be mere names attached to various traditional stories. Anything new,however plausible, that Proclus tells us about Thales must be taken with morethan the proverbial grain of salt.What view, then, based on reliable evidence, are we to take of Thales,having rejected the testimony of the secondary group of sources? We mayaccept it as a fact that he was a man of outstanding intelligence, for this isimplicit in all the references to him in the primary sources; we may also take itthat he speculated on the origin and composition of the universe and came tothe conclusion that the primary substance was water-this is well attested, butthe original statement was soon embellished by later writers and these embel-lishments were likewise attributed to Thales. Finally, we may, on the evidenceof Herodotus' story of the prediction of the eclipse and (but much moredubiously) the alleged diversion of the river Halys, regard it as highly probablethat Thales interested himself in mathematics and astronomy and possessedfor his time a more than average knowledge of both. If we wish to know whatthis knowledge consisted in, there is (owing to the lack of an original sourceand the scarcity of reliable evidence) only one legitimate means by which wecan find out, namely, by a comparative examination of the mathematics andastronomy of Thales' time, and this means in effect Egyptian and Babylonianmathematics and astronomy, for these were the only highly developed civiliza-tions with which the early Greeks came into close contact. This is most definitelynot to assert that Thales visited either Egypt or Babylonia; the evidence thathe did is, as we have seen, late and unreliable, and we are not entitled on thestrength of it to build up elaborate theories about his travels and the knowledgehe is supposed to have acquired on them. He mayhave made a tour of the wholeAegean coastline, he mayhave been conducted up and down the Nile and theEuphrates to the accompaniment of a continuous stream of information sup-plied by priestly guides, and he mayhave crossed the Mediterranean from eastto west and north to south sailing entirely at night; there is just as much orjustas little evidence for all this as there is for the traditional picture of him as thetransmitter of Egyptian and Babylonian wisdom. If, however, we are preparedto believe that he was conversant with the mathematical knowledge of his time,then this must have been of the type of Egyptian and Babylonian mathematics-regardless of whether he actually visited the countries-because there' Rhys Carpenter, Folk Tale, Fiction andSaga in the HomericEpics, repr. 1956, pp. 39-40.2 See the article by Snell, already quoted.



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THALES 307existed no other to which he had access.It is, therefore,only by examining thecontents of pre-Greek'mathematics that we can estimate what Thales couldhave known as distinguishedfromwhat later commentatorssupposedhe knew.It is uselessto try to reason backwardsand reconstruct,as Eudemusapparentlydid, what Thales 'must' have known from the standpoint of Eudemus' ownperiod,forby that time the formal,Euclideantype of mathematics(whichis thecharacteristicallyGreek contributionin this field) had been firmlyestablished,and if there is one thing that is quite certain it is that this type of treatmentwascompletely foreign to Egyptian and Babylonianmathematics.This is not the place for a detailed descriptionof them,2 but a few salientpoints may be noted. Both the Egyptian and the Babylonianmathematiciansknew the correct formulae for determining the areas and volumes of simplegeometricalfiguressuch as triangles,rectangles, trapezoids,etc.; the Egyptianscould also calculate correctly the volume of the frustumof a pyramid with asquare base (the Babylonians used an incorrect formula for this), and useda formula for the area of a circle, A(area) = (5d)2where d is the diameter,which gives a value forrrof 3-I605-a good approximation.3These determina-tions of area and volume were closely connected with practicalproblemssuchas the storageof grain in barns of variousshapes, the amount of earth neededin the constructionof ramps, and so forth. It is especiallynoteworthythat inboth Egyptian and Babylonian geometry the treatment is essentially arith-metical; in the texts the problem is stated with actual numbersand the pro-cedure is then describedwith explicit instructionsas to what to do with thesenumbers.4There is little indication of how the rules of procedure were dis-covered in the first place and no trace at all of the existence of a logicallyarrangedcorpusof generalized geometricalknowledgewith analytical 'proofs'such as we find in the works of Euclid, Archimedes, and Apollonius. Henceeven if we wish to assume that Thales visited Egypt (for which-let it be re-peated-there is no reliableevidence) all he could have learnt there (and evenin this he would probably have had considerable difficulty, for there is noevidence that any Greek of Thales' time could read Egyptian hieroglyphics)5was some empiricaldata about the simplergeometricalfigures,not theoremsofthe type that Eudemus attributes to him. Egyptian mathematics is essentiallyadditivein character(multiplicationand divisionarereducedto a cumbersomeprocess of successiveduplication, the sums of the factorsbeing then added togive the required answer),6and also operates entirely with fractions havingI as the denominator,with the single exception of 2; it is obviouslyunsuitedtoextensive calculations such as are necessaryin astronomicalproblems,and has

I Both Egyptian and Babylonian mathe-matics were already highly developed by thebeginning of the second millennium B.C.,andboth remained largely static until Hellenistictimes.2 Excellent accounts are given by O.Neugebauer, The Exact Sciences n Antiquity,2nd ed. 1957 (with full references to therelevant literature), and by B. L. van derWaerden, ScienceAwakening,1954 (despite anexaggerated and misleading treatment ofThales).

3 The Babylonians commonly used the

rough figure 7 = 3, but one text impliesthe more accurate value r = 3j; cf. Neuge-bauer, op. cit., p. 47.4 Cf. v. d. Waerden, pp. 63 f.s Cf. Burnet, Early GreekPhilosophy, . 17.The passage in Herodotus (2. 154) about'interpreters' significantly mentions onlyEgyptians sent to the Greek settlements inEgypt to learn the language, and saysnothing of Greeks learning Egyptian; nor isthere any mention of writing.6 Cf. Neug. p. 73.

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308 D. R. DICKSbeen described as having 'a retarding force upon numerical procedures"-very unlike the extremely flexible Babylonian system of numeration.There isnot the slightestevidence or likelihood that the Greeks of Thales' time, or forseveral centuries afterwards,understoodthe Egyptianmethods.2Only in thelate Hellenistic period do we begin to find traces in Greekwriters of the exis-tence of a type of mathematicswhich is very different fromthe classicalGreekmathematics of Euclid and Archimedes, and which has its origins in theEgyptian and Babylonian proceduresand forms 'part of this oriental traditionwhich can be followed into the Middle Ages both in the Arabic and in thewestern world'.3Similarly, there is not the slightestjustificationfor supposingthat Thales was conversantwith the sexagesimal system with its place-valuenotation which was the invaluable contribution of the Babylonians to laterGreek mathematical astronomy. There is evidence to show that neither thesexagesimal system nor the general division of the circle into 3600 (also aBabylonian invention) was known to the Greeks before the second centuryB.c., and that probably Hipparchus (c. 194-120 B.c.) was responsiblefor atleast the introductionof the latter into Greekmathematics.4Detailed knowledge of things Babylonian seems only to have reached theGreeks at a comparativelylate period; Herodotus tells us practicallynothingabout their literatureor their science and displaysonly a limitedknowledgeoftheir history.5It is generallyconsideredthat the sourcefromwhich the Greeksobtained most of their knowledge about Babylonian culture was Berossus,aBabylonian priest who is supposed to have set up a school in Cos about 270B.c. and to have produced works on Babylonian history 6 certainly, in thesecond century B.C.Hipparchus was familiar with the results of Babylonianastronomy. There is, however, no evidence that the Greeksbefore the thirdcentury B.c. knew much more about the Babylonian civilization than Hero-dotus did. Thus the modern myth-makers'determinedefforts to manufacturea connexion between Thales and Babyloniaare as fruitlessas they are withoutfoundation; even had he visited that country there is again no evidence andno likelihoodthat he could read the cuneiformscript.To sum up-there is no reliable evidence at all for the extensivetravelsthatThales is supposed to have undertaken; his mathematical knowledge couldhardly have comprisedmore than some empirical rules for the determinationof elementaryareas and volumes; his astronomicalknowledgemust have been

I Id., p. 80.2 Van der Waerden (p. 36) is very mis-leading here. The difference between theclassical Greek and the Egyptian methods ofmultiplication and division is clearly shownby Heath, Manual, pp. 29 f.3 Neug., p. 80.4The arguments and the evidence cannotconveniently be presented here, but I hopeto discuss them in a further article. Mean-while it should be noted that A. Wasser-stein's curious paper 'Thales' Determinationof the Diameters of the Sun and Moon' (asremarkable for its disregard of recent modernwork in this field as for its inconclusiveness)in J.H.S. lxxv (955), 114-16, contains littlebut unwarrantable assumptions based on

unreliable vidence.s Cf. W. W. How andJ. Wells, A Com-mentarynHerodotus,epr. 1950, i. 379-80.The only Greekborrowingsrom the Baby-lonians that Herodotusmentionsare of the'polos'(a portable,hemi-sphericalun-dial),thegnomon,andthedivisionof thedayinto12parts(inthishe isonlypartlycorrect,asitwas the day-and-night period that wasdivided nto 12 parts).6 Cf. P. Schnabel,Berossos nd die baby-lonische-hellenistischeiteratur,923. It must,however,be said thatSchnabel's onclusionsregardingBabylonianastronomyare nowuntenable,and his argumentsn supportofthe greatinfluenceof Berossus'writingsareveryspeculativeand far fromconclusive.



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THALES 309similarly elementary (probably comprising nothing more scientific than therecognition of some constellations),' since there is not the slightest likelihoodthat he was familiar with the complicated linear methods of Babylonianastronomy,and Egyptian astronomywas of a very primitivecharacter; on theother hand, he might possibly have heard of the I8-year cycle for lunarphenomena and might somehow have connected this with a solareclipseso asto give rise to the story that he predicted it; there is no reason to disbelievethe early stories of his political and commercial sagacity, or the fact that heconsidered the primary matter of the universe to be water; everything elsethat is attributed to him by later writers in the secondary group of sources(including Eudemus) can be disregarded.UniversityCollegeof the WestIndies D. R. DICKS

Kirk and Raven's description (op. cit.,pp. 81-82) of Thales' astronomical activitiesis far too optimistic. Some idea of the primi-tiveness of the astronomical ideas then cur-rent may be gained from the peculiar notionsof his successors such as Anaximander,

Anaximenes, Xenophanes, and Heraclitus,which Heiberg (Gesch.d. Math. undNaturwiss.im Altert., 1925, p. 50o)rightly characterizesas 'diese Mischung von genialer Intuitionund kindlichen Analogien'.

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