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Thales

Author(s): D. R. DicksReviewed work(s):Source: The Classical Quarterly, New Series, Vol. 9, No. 2 (Nov., 1959), pp. 294-309Published by: Cambridge University Press on behalf of The Classical Association

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THALES

THE 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 neverthelesshas

probably contributedas much as any other book to the exaggerated and falseview of Thales which we meet in so many modern histories of science or

philosophy, 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

providematerial for a

biographyof

Thales;but so uncertain is this

material 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 are

likely 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 sacrifice

of 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; Birds

Ioo9; Plautus, Captivi 274; and there are

probably more. Cf. O. Gigon, Der Ursprungdergriechischen hilosophie,1945, p. II, for a

plea for a really complete collection ofnotices regarding the Pre-Socratics.







THALES 295

recommendation 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 solar

eclipse--Herodotus' actual words are:-4v

U LperaAAayyvTad-rv T'ie 7pp'pr79S

eaA.TgMMtLArgoSrot-aIoa I7pO)YdpevaeEacEOae, vpov7rpoO~4ervo"cLatrrovY

"roi-ov,'v 7i5 8 Ka'L 'cVETO ~tTafloAq. The eclipse s generally egardedas

being 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 predictsolar

eclipses, 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 modem

cycles 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 is

perhapsjust possible that he may have heard of the I8-year cycle for lunar

phenomena, and may have connected it with the solareclipseof 585 in such a

way 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 Sciencesn

Antiquity,2nd ed. 1957, PP. 141-2.4 Ptolemy mentions it (Synt. math., ed.

Heiberg, i. 269. x8 f.) and also theeAsL•y•o'ds,a similar cycle obtained by multiplying the

former by 3, making 669 lunar months or

19,756 days, but attributes both to ol ricrTaAaLdo'rpoLtaO7Gpar7KOl,which refers toGreek astronomers earlier than Hipparchusand not to the Babylonian astronomers,whom Ptolemy always calls oLXaA8taKoi.

s F. X. Kugler, SternkundendSterndienstn

Babel, ii (x909), 58 f.; O. Neugebauer,AstronomicalCuneiformTexts, i (1956), 68-69,I15, i6o f.

6 Ex. Sci., p. 142. As regards the use of the

i8-year cycle he says (ibid.), 'there arecertain indications that the periodic recur-rence of lunar eclipses was utilised in the

preceding 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.







296 D. R. DICKS

actually 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 is

certainlywrong, for he could not possiblyhave possessedthisknowledgewhich

neither 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 on

repeating the story with or without further embellishment, but it is perhapssignificantthat no other writer in the firstgroup of sources (i.e. those before

320 B.C.)mentions it. Of modern commentators,Martin3 ong ago rejectedtheentire story,Dreyer4 s extremely sceptical, and Neugebauer,5the most recent

authority, 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 generallybelieved

among 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

Ipya ao~ov avspo •ro)a •alrlvotat

KaaE••Vl•Xavo"

El' rExva' '-wasvaama

erpctgE&Ayov-rat, wcorrEp0 &aAEwE 7rEploV^ MLAq-covKal Avaxdpanoso-o

ZKVOov.7

Elsewhere(Theaet. I74a

= Diels9)

he is cited as anexample

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 the

olive-presses in Miletus and Chios during one winter, in anticipation of a

bumper 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

~AX4p•7E0EVDiels 22), and that the lodestone has a

soul (ibid.). It is worth noting the manner in which Aristotle reports these

speculations; 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 the

generally 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- oLdMA7ato•

~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







THALES 297

says, OaArsg&C"T'7S

tLav'n7)Sao• qXyos• ?•oao(lacro

cu•Swp b77alvW LSL Kal7• ")vyi E' iSars 7ToIcvao EtaL),Aaflcov'cws 7 6v zr5oA-wavra V'IKK.r.A.,and

in another place (decaeloB 13. 294a28)troOroydp[i~v yn-v1'"8aros- KEcTOat]

apxaOdTraTovpE&A7)jalLEVrTvAdyov, v OacwvE••TEFYOaA-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 tbVyjV

rTroAafltEv,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 as

philosophical speculations attributed by AMtius o Thales, and shows that in

reality these stem directly from Aristotle's own interpretationswhich thenbecame incorporated n the doxographicaltradition as erroneousascriptions o

Thales3-and, one might add, are duly perpetuatedby Diels-Kranz.So much, then, for what may be termed the primary authorities for our

knowledge of Thales' life and opinions,e.g. writers before320 B.C.What is the

general impressionwe obtain from them? Surely, that he had a reputationchiefly as apracticalman of affairs,who was

capableof

givingsensible

politicaladvice (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 substantiated

by the other references to him in classical writers not listed in Diels, e.g.Aristophanes, CloudsI80; Birds Ioo9; Plautus, Captivi274-in each of these

passages he is cited as the typical example of the clever man (perhaps not

always 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 was

popular 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. in

Ziirich, 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 der

griechischen 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.







298 D. R. DICKS

never 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'.3

One very importantpoint that can be established from considerationof this

firstgroup 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%,

•o•KE,and the like, and never4 is a citation given

that 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

antiquitythat he left none.6It would seem that

alreadybyAristotle's

time 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 the

practical and political activities of the SevenWise Men were first introduced into the

tradition by Dicaearchus in the latter half ofthe fourth century. In the case of Thales, at

any 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 and

achievements, 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 far

from being the case, and he takes the wellstory too seriously. On the other hand, he is

undoubtedly right to emphasize the com-

paratively late origin of the traditional

picture of Pre-Socratic philosophy, 'thewhole picture that has come down to us ofthe history of early philosophy was fashioned

during 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 been

shown to be illusory, in that if the quotationwere carried to its proper end we should findthe familiar

OaA•-AyTera again. Kirk and

Raven (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 not

relying 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 KaT•7ALrEV ;SV: Cf. Joseph. c.Ap.I. 2; Simplicius, Phys. 23. 29.

7 Cf. Kirk and Raven, p. 218-Aristotle,Plato, and Pythagoras.







THALES 299

naturally 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 the

original 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 after

320 B.C., that Thales' stature begins to take on heroic proportions and he

appearsas the figureso dear to modern historians of science and philosophy-the founder of Greek mathematics and astronomy,the transmitterof ancient

Egyptian 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 of

knowledge 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 second

centuries 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 initiated

by 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 be

seen in modern times. Earlier writers, like

Tannery, 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 Greek

Philosophy,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.







300 D. R. DICKS

the 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, with

each 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.4

Now if Theophrastus himself was in error on any point either throughmisinterpretation or lack of reliable information (which we have not the

slightestreason to doubt was frequentlythe case as regardsthe Pre-Socratics5),it is perfectlyobvious that there is no chance at all that his later copyistsand

excerptorswould 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

Theophrastuseither. Hence all that he knew about Thales

was 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 the

exaggerated 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 carefulreferringback

to 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 quasiad

quendam 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. 'Diogenes

Laertios'; Dox., pp. I6 f.

3 Op. cit., pp. 170-I, 176.4 Cf. J. O. Thomson, History of Ancient

Geography,948, pp. I12 and 116.

s Cf. G. S. Kirk, Heraclitus: the Cosmic

Fragments,1954, pp. 20-25.

6 What Gigon (op. cit., pp. 43-44) callsthe 'anekdotische und apophthegmatische

tOberlieferung'.7 De invent.2. 2. 6. Further on he mentions

Isocrates whose book Cicero knows to existbut which he has not himself found, althoughhe has come across numerous writings byIsocrates' pupils.







THALES 3o0

Menon'-one would not bother to go back to the original works even in the

unlikelyevent of their being still available.2There is, therefore,nojustificationwhatsoever for supposing that very late commentators,such as Proclus (5th

century A.D.) and Simplicius (6th century A.D.), can possibly possess moreauthentic informationabout the Pre-Socratics han the earlierepitomatorsand

excerptorswho 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. 27.5

I 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 is

generally considered that it is from Eudemus'FEWtET•tLK-? UT-rop'a,ApLtOtp-LK71K

Zcrropta,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 was

aware 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.







302 D. R. DICKS

about 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, for

two 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 same

inadequate 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 excerpted

and 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 extant

fragments of Eudemus' PewtlerptK7laoTopta,3

although he usually quotes as

though directlyfromthe original (Jg[fatv EiE7StzoS),wice gives the impressionthat in fact he may be using intermediaries,when he mentions old ds

ar-opas-avaypdavrwe4 and ol rrTEplrv Eqpov.5 Even Simplicius, who purports to

quoteverbatim fromEudemus,6may have takenhisquotationfrom asecondarysource, for he says on one occasion, cosE•3871 '.s -Ev i~,

•) EVr•pp7-9 dO'ErpoAoyuLK

Iau'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 are

commonly 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 word

actually used is'ooost

'similar', instead of toaos);

(3) that when two straightlinesintersect, the vertically opposite angles are

equal;(4) that if two triangles have two angles and one side equal, the triangles

are equal in all respects.

For the first two of these, Eudemus is not specificallycited by Proclus as his

authority, 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'aopwtL

Ta 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 as

Proclus, 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 the

passages 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, and

Becker, p. 38, give less well-authenticatedlists.

9 Cf. Heath, Euclid,p. 36.







THALES 303

siderations. As regards (i) it should be observed that Thales is said to have

'proved' (d'roSetaL) this, a statement which itself arouses suspicion since even

Euclid 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 scientifically

proving (3).z Most revealing,however, is the mannerin which (4) is reported;here Proclus' actual words are,3

EiYrloos.TSev rais YEWtLETrptKa u'rTopatS Edl

OaA7lvrov-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' geometrical

knowledge. 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 processof

step-by-stepdeduction from certain fixed definitionsand postulateswas not

developed 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.

Alsoregarded

asstemming

fromEudemus,althoughadmittedlynot his in its

IEuclid, 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 of

this 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 out

with ropes the base angles of their monu-ments; hence, it issaid, they knew empiricallythis special case of the general 'theorem of

Pythagoras'. 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 that

ropes representing a triangle with sides of

3, 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.







304 D. R. DICKS

present form,' is the so-called Eudemian ummary, brief, 'potted' history of

geometry which Proclus prefixes to his Commentaryn theFirstBookof Euclid.2It is here that we find for the first time the explicit statementthat Thales went

to Egypt and thence introduced geometry into Greece: &aA77 s6rpaov dAi'yv7r'rovA cowJEvp77yayEv tSTrqv'EAAc'Sa7+vGEOpQavratyr-v [yeWLErpiaV]Ka2

roAAaMvao'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 the

Mesopotamian; 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 case

omits 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 primumEuclidis

Elementorum ibrum comment.,Prologus II,

pp. 64 f. ed. Friedlein; Wehrli, frag. 133,

PP- 54-56-3Wehrli (op. cit., 11I5) points out that

Eudemus follows Herodotus' view even inthe face of a different opinion expressed byAristotle.

4 2. 0og; cf. Diod. Sic. i. 8I. 2; Strabo

757 and 787.s In fact, a visit of Thales to Babylonia is

even less well authenticated than a visit to

Egypt-Josephus (c.Ap. I. 2) seems to be the

only writer to mention the former; but since

Egyptian 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 more

plausible by reference to Herodotus' state-ment (2. 109) that the Greeks learnt aboutthe

'polos',the

gnomon,and the division of

the 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.

8e.g. Gomperz, Gigon, H61scher, and

Hauser accept them all apparently without a

qualm; Gigon (op. cit., p. 87) even acceptsCicero's story (de div. I. 50. I 2) aboutAnaximander's foretelling an earthquake.







THALES 305

Thus 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 certain

subjects, 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 scientist

and 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 unsubstantiated

by 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.3

The 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 and

Aristotle,and no written workof his remained to contradict whatever doctrine

might be assignedto him; he was, in fact, an ideal choice. Once the connexionhad been made between him and Egypt, then everythingelse fitted nicely into

place. There is nothingsurprising

n such aprocess.

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 as

though 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 so

strong 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 is

slightly better, while Tannery's in La Grande

Encyclopidie, 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 in

Antiquity, 1957, P. 56.

4509.3/4 x







THALES 307

existed no other to which he had access.It is, therefore,only by examining the

contents of pre-Greek'mathematics that we can estimate what Thales couldhave known as distinguishedfromwhat later commentatorssupposedhe knew.

It is uselessto

tryto reason backwardsand

reconstruct,as Eudemus

apparentlydid, what Thales 'must' have known from the standpoint of Eudemus' own

period,forby that time the formal,Euclideantype of mathematics(whichis the

characteristicallyGreek contributionin this field) had been firmlyestablished,and if there is one thing that is quite certain it is that this type of treatmentwas

completely foreign to Egyptian and Babylonianmathematics.This is not the place for a detailed descriptionof them,2 but a few salient

points may be noted. Both the Egyptian and the Babylonianmathematicians

knew the correct formulae for determining the areas and volumes of simplegeometricalfiguressuch as triangles,rectangles, trapezoids,etc.; the Egyptians

could 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 these

numbers.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 to

give 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 the

beginning of the second millennium B.C.,andboth remained largely static until Hellenistic

times.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 der

Waerden, ScienceAwakening,1954 (despite an

exaggerated 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 in

Egypt to learn the language, and saysnothing of Greeks learning Egyptian; nor isthere any mention of writing.

6 Cf. Neug. p. 73.

4509.3/4 X2







308 D. R. DICKS

been 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 for

several 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 the

Egyptian 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 the

sexagesimal system nor the general division of the circle into 3600 (also aBabylonian invention) was known to the Greeks before the second century

B.c.,and that probably Hipparchus (c. 194-120 B.c.) was responsiblefor at

least the introductionof the latter into Greekmathematics.4Detailed knowledge of things Babylonian seems only to have reached the

Greeks 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,a

Babylonian priestwho is

supposedto have set

upa 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 third

century 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 without

foundation; 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 extensivetravelsthat

Thales 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

IId., p. 80.

2 Van der Waerden (p. 36) is very mis-

leading here. The difference between theclassical Greek and the Egyptian methods of

multiplication and division is clearly shown

by Heath, Manual, pp. 29 f.

3 Neug., p. 80.4The arguments and the evidence cannot

conveniently 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 little

but 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 thedayinto12

parts(inthishe is

onlypartlycorrect,asit

was 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.







THALES 309

similarly elementary (probably comprising nothing more scientific than the

recognition of some constellations),' since there is not the slightest likelihoodthat he was familiar with the complicated linear methods of Babylonian

astronomy,and Egyptian astronomywas of a very primitivecharacter; on theother hand, he might possibly have heard of the I8-year cycle for lunar

phenomena 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'.

Dicks, D. R._thales_1959_CQ, 9, 2, Pp. 294-309

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