Thales Wiki

Click here to load reader

  • date post

  • Category


  • view

  • download


Embed Size (px)



Transcript of Thales Wiki

  • Thales

    For other uses, see Thales (disambiguation).

    Thales of Miletus (/eliz/; Greek: ( -), Thals; c. 624 c. 546 BC) was a pre-SocraticGreek philosopher from Miletus in Asia Minor, and oneof the Seven Sages of Greece. Many, most notablyAristotle, regard him as the rst philosopher in the Greektradition.[1] Aristotle reported Thales hypothesis aboutthe nature of matter that the originating principle ofnature was a single material substance: water.According to Bertrand Russell, Western philosophy be-gins with Thales.[2] Thales attempted to explain natu-ral phenomena without reference to mythology and wastremendously inuential in this respect. Almost all ofthe other Pre-Socratic philosophers follow him in at-tempting to provide an explanation of ultimate substance,change, and the existence of the world without referenceto mythology. Those philosophers were also inuentialand eventually Thales rejection of mythological expla-nations became an essential idea for the scientic revolu-tion. He was also the rst to dene general principles andset forth hypotheses, and as a result has been dubbed theFather of Science, though it is argued that Democritusis actually more deserving of this title.[3][4]

    In mathematics, Thales used geometry to solve problemssuch as calculating the height of pyramids and the dis-tance of ships from the shore. He is credited with therst use of deductive reasoning applied to geometry, byderiving four corollaries to Thales Theorem. As a result,he has been hailed as the rst true mathematician and isthe rst known individual to whom a mathematical dis-covery has been attributed.[5]

    1 LifeThe current historical consensus is that Thales was bornin the city of Miletus around the mid 620s BC. Miletuswas an ancient Greek Ionian city on the western coast ofAsia Minor (in what is today Aydin Province of Turkey),near the mouth of the Maeander River.

    1.1 BackgroundThe dates of Thales life are not exactly known, but areroughly established by a few dateable events mentioned inthe sources. According to Herodotus (and determinationby modern methods) Thales predicted the solar eclipse of

    May 28, 585 BC.[6] Diogenes Lartius quotes the chron-icle of Apollodorus of Athens as saying that Thales diedat the age of 78 in the 58th Olympiad (548545 BC),and attributes his death to heat stroke while watching theGames.Diogenes Lartius states that (according to Herodotusand Douris and Democritus") Thales parents were Ex-amyes and Cleobuline, then traces the family line backto Cadmus, a mythological Phoenician prince of Tyre.Diogenes then delivers conicting reports: one thatThales married and either fathered a son (Cybisthus orCybisthon) or adopted his nephew of the same name;the second that he never married, telling his mother asa young man that it was too early to marry, and as anolder man that it was too late. Plutarch had earlier toldthis version: Solon visited Thales and asked him why heremained single; Thales answered that he did not like theidea of having to worry about children. Nevertheless, sev-eral years later, anxious for family, he adopted his nephewCybisthus.[7]

    Thales involved himself in many activities, taking the roleof an innovator. Some say that he left no writings, otherssay that he wrote On the Solstice and On the Equinox. (Nowriting attributed to him has survived.) Diogenes Lar-tius quotes two letters from Thales: one to Pherecydesof Syros oering to review his book on religion, and oneto Solon, oering to keep him company on his sojournfrom Athens. Thales identies the Milesians as Atheniancolonists.[8]

    1.2 Business

    An olive mill and an olive press dating from Roman times inCapernaum, Israel.


  • 2 1 LIFE

    Several anecdotes suggest that Thales was not solely athinker but was also involved in business and politics.One story recounts that he bought all the olive presses inMiletus after predicting the weather and a good harvestfor a particular year. In another version of the same story,Aristotle explains that Thales reserved presses ahead oftime at a discount only to rent them out at a high pricewhen demand peaked, following his predictions of a par-ticularly good harvest. This rst version of the storywould constitute the rst creation and use of futures,whereas the second version would be the rst creation anduse of options. Aristotle explains that Thales objectivein doing this was not to enrich himself but to prove to hisfellowMilesians that philosophy could be useful, contraryto what they thought.[9]

    1.3 PoliticsThales political life had mainly to do with the involve-ment of the Ionians in the defense of Anatolia against thegrowing power of the Persians, who were then new to theregion. A king had come to power in neighboring Lydia,Croesus, who was somewhat too aggressive for the size ofhis army. He had conquered most of the states of coastalAnatolia, including the cities of the Ionians. The story istold in Herodotus.[10]

    The Lydians were at war with the Medes, a remnant ofthe rst wave of Iranians in the region, over the issue ofrefuge the Lydians had given to some Scythian soldiersof fortune inimical to the Medes. The war endured forve years, but in the sixth an eclipse of the Sun (men-tioned above) spontaneously halted a battle in progress(the Battle of Halys).

    Total eclipse of the Sun

    It seems that Thales had predicted this solar eclipse. TheSeven Sages were most likely already in existence, asCroesus was also heavily inuenced by Solon of Athens,

    another sage. Whether Thales was present at the battle isnot known, nor are the exact terms of the prediction, butbased on it the Lydians and Medes made peace immedi-ately, swearing a blood oath.The Medes were dependencies of the Persians underCyrus. Croesus now sided with the Medes against thePersians and marched in the direction of Iran (with farfewer men than he needed). He was stopped by the riverHalys, then unbridged. This time he had Thales with him,perhaps by invitation. Whatever his status, the king gavethe problem to him, and he got the army across by digginga diversion upstream so as to reduce the ow, making itpossible to ford the river. The channels ran around bothsides of the camp.The two armies engaged at Pteria in Cappadocia. As thebattle was indecisive but paralyzing to both sides, Croesusmarched home, dismissed his mercenaries and sent emis-saries to his dependents and allies to ask them to dispatchfresh troops to Sardis. The issue became more pressingwhen the Persian army showed up at Sardis. DiogenesLaertius[11] tells us that Thales gained fame as a coun-selor when he advised the Milesians not to engage in asymmachia, a ghting together, with the Lydians. Thishas sometimes been interpreted as an alliance, but a rulerdoes not ally with his subjects.Croesus was defeated before the city of Sardis by Cyrus,who subsequently spared Miletus because it had taken noaction. Cyrus was so impressed by Croesus wisdom andhis connection with the sages that he spared him and tookhis advice on various matters.The Ionians were now free. Herodotus says that Thalesadvised them to form an Ionian state; that is, a bouleu-terion (deliberative body) to be located at Teos in thecenter of Ionia. The Ionian cities should be demoi, ordistricts. Miletus, however, received favorable termsfrom Cyrus. The others remained in an Ionian League of12 cities (excluding Miletus now), and were subjugatedby the Persians.While Herodotus reported that most of his fellow Greeksbelieve that Thales did divert the river Halys to assistKing Croesus military endeavors, he himself nds itdoubtful.[12]

    1.4 Sagacity

    Diogenes Laertius[13] tells us that the Seven Sages werecreated in the archonship of Damasius at Athens about582 BC and that Thales was the rst sage. The same story,however, asserts that Thales emigrated to Miletus. Thereis also a report that he did not become a student of natureuntil after his political career. Much as we would like tohave a date on the seven sages, wemust reject these storiesand the tempting date if we are to believe that Thales wasa native of Miletus, predicted the eclipse, and was withCroesus in the campaign against Cyrus.

  • 2.1 Water as a rst principle 3

    The Ionic Stoa on the Sacred Way in Miletus

    Thales received instruction from an Egyptian priest. Itwas fairly certain that he came from awealthy, establishedfamily, in a class which customarily provided higher edu-cation for their children. Moreover, the ordinary citizen,unless he was a seafaring man or a merchant, could notaord the grand tour in Egypt, and did not consort withnoble lawmakers such as Solon.Thales participated in some games, most likelyPanhellenic, in which he won a bowl twice. Hededicated it to Apollo at Delphi. As he was not known tohave been athletic, his event was probably declamation,and it may have been victory in some specic phase ofthis event that led to his sagacious designation.

    2 TheoriesThe Greeks often invoked idiosyncratic explanationsof natural phenomena with reference to the will ofanthropomorphic gods and heroes. Instead, Thales aimedto explain natural phenomena via rational hypotheses thatreferenced natural processes themselves. For example,rather than assuming that earthquakes were the result ofsupernatural whims Thales explained them by hypothe-sizing that the Earth oats on water and that earthquakesoccur when the Earth is rocked by waves.Thales was a hylozoist (one who thinks that matter isalive).[14] That interpretation by later commentatorsthat Thales treated matter as being alivemay have beensubstituted for his thinking that the properties of na-ture arise directly from material processes. The lat-ter thesis is more consistent with modern ideas of howproperties arise as emergent characteristics of thosecomplex systems involved in the processes of evolutionand developmental change.Thales, according to Aristotle, asked what was the na-ture (Greek Arche) of the object so that it would be-have in its characteristic way. Physis () comes fromphyein (), to grow, related to our word be.[15](G)natura is the way a thing is born,[16] again with the

    stamp of what it is in itself.Aristotle[17] characterizes most of the philosophers atrst () as thinking that the principles in theform of matter were the only principles of all things,where principle is arche, matter is hyle (wood ormatter, material) and form is eidos.Arche is translated as principle, but the two words donot have precisely the same meaning. A principle ofsomething is merely prior (related to pro-) to it eitherchronologically or logically. An arche (from , torule) dominates an object in some way. If the arche istaken to be an origin, then specic causality is implied;that is, B is supposed to be characteristically B just be-cause it comes from A, which dominates it.The archai that Aristotle had in mind in his well-knownpassage on the rst Greek scientists are not necessarilychronologically prior to their objects, but are constituentsof it. For example, in pluralism objects are composedof earth, air, re and water, but those elements do notdisappear with the production of the object. They remainas archai within it, as do the atoms of the atomists.What Aristotle is really saying is that the rst philoso-phers were trying to dene the substance(s) of which allmaterial objects are composed. As a matter of fact, that isexactly what modern scientists are attempting to accom-plish in nuclear physics, which is a second reason whyThales is described as the rst western scientist.

    2.1 Water as a rst principle

    Thales most famous philosophical position was hiscosmological thesis, which comes down to us througha passage from Aristotle's Metaphysics.[18] In the workAristotle unequivocally reported Thales hypothesis aboutthe nature of matter that the originating principle of na-ture was a single material substance: water. Aristotle thenproceeded to proer a number of conjectures based onhis own observations to lend some credence to why Thalesmay have advanced this idea (though Aristotle didnt holdit himself). Aristotle considered Thales position to beroughly the equivalent to the later ideas of Anaximenes,who held that everything was composed of air.Aristotle laid out his own thinking about matter and formwhich may shed some light on the ideas of Thales, inMetaphysics 983 b6 811, 1721. (The passage containswords that were later adopted by science with quite dif-ferent meanings.)

    That from which is everything that exists andfrom which it rst becomes and into which itis rendered at last, its substance remaining un-der it, but transforming in qualities, that theysay is the element and principle of things thatare. For it is necessary that there be somenature (), either one or more than one,

  • 4 2 THEORIES

    from which become the other things of the ob-ject being saved... Thales the founder of thistype of philosophy says that it is water.

    In this quote we see Aristotles depiction of the problemof change and the denition of substance. He asked if anobject changes, is it the same or dierent? In either casehow can there be a change from one to the other? The an-swer is that the substance is saved, but acquires or losesdierent qualities (, the things you experience).Aristotle conjectured that Thales reached his conclusionby contemplating that the nourishment of all things ismoist and that even the hot is created from the wet andlives by it. While Aristotles conjecture on why Thalesheld water was the originating principle of water is hisown thinking, his statement that Thales held it was wateris generally accepted as genuinely originating with Thalesand he is seen as an incipient matter-and-formist.Heraclitus Homericus[19] states that Thales drew his con-clusion from seeing moist substance turn into air, slimeand earth. It seems likely that Thales viewed the Earthas solidifying from the water on which it oated and theoceans that surround it.Writing centuries later Diogenes Laertius also states thatThales taught Water constituted (, 'stoodunder') the principle of all things.[20]

    2.1.1 Inuences

    Later scholastic thinkers would maintain that in hischoice of water Thales was inuenced by Babylonian orChaldean religion, that held that a god had begun creationby acting upon the pre-existing water. HistorianAbrahamFeldman holds this does not stand up under closer exam-ination. In Babylonian religion the water is lifeless andsterile until a god acts upon it, but for Thales water itselfwas divine and creative. He maintained that All thingsare full of gods, and to understand the nature of thingswas to discover the secrets of the deities, and through thisknowledge open the possibility that one could be greaterthan the grandest Olympian.[21]

    Feldman points out that while other thinkers recognizedthe wetness of the world none of them was inspired toconclude that everything was ultimately aquatic.[21] Hefurther points out that Thales was a wealthy citizen ofthe fabulously rich Oriental port of Miletus...a dealer inthe staples of antiquity, wine and oil...He certainly han-dled the shell-sh of the Phoenicians that secreted thedye of imperial purple.[21] Feldman recalls the stories ofThales measuring the distance of boats in the harbor, cre-ating mechanical improvements for ship navigation, giv-ing an explanation for the ooding of the Nile (vital toEgyptian agriculture and Greek trade), and changing thecourse of the river Halys so an army could ford it. Ratherthan seeing water as a barrier Thales contemplated theIonian yearly religious gathering for athletic ritual (held

    on the promontory of Mycale and believed to be ordainedby the ancestral kindred of Poseidon, the god of the sea).He called for the Ionian mercantile states participating inthis ritual to convert it into a democratic federation underthe protection of Poseidon that would hold o the forcesof pastoral Persia. Feldman concludes that Thales sawthat water was a revolutionary leveler and the elemen-tal factor determining the subsistence and business of theworld[21] and the common channel of states.[21]

    Feldman considers Thales environment and holds thatThales would have seen tears, sweat, and blood as grant-ing value to a persons work and the means how life giv-ing commodities travelled (whether on bodies of water orthrough the sweat of slaves and pack-animals). He wouldhave seen that minerals could be processed from watersuch as life-sustaining salt and gold taken from rivers. Hewouldve seen sh and other food stus gathered from it.Feldman points out that Thales held that the lodestonewas alive as it drew metals to itself. He holds that Thalesliving ever in sight of his beloved sea would see waterseem to draw all trac in wine and oil, milk and honey,juices and dyes to itself, leading him to a vision of theuniverse melting into a single substance that was value-less in itself and still the source of wealth.[21] Feldmanconcludes that for Thales "...water united all things. Thesocial signicance of water in the time of Thales inducedhim to discern through hardware and dry-goods, throughsoil and sperm, blood, sweat and tears, one fundamentaluid stu...water, the most commonplace and powerfulmaterial known to him.[21] This combined with his con-temporarys idea of "spontaneous generation" allow us tosee how Thales could hold that water could be divine andcreative.Feldman points to the lasting association of the theorythat all whatness is wetness with Thales himself, point-ing out that Diogenes Laertius speaks of a poem, prob-ably a satire, where Thales is snatched to heaven by thesun, Perhaps it was an elaborate paronomasia based onthe fact that thal was the Phoenician word for dew.[21]

    2.2 Beliefs in divinity

    Thales applied his method to objects that changed to be-come other objects, such as water into earth (or so hethought). But what about the changing itself? Thales didaddress the topic, approaching it through lodestone andamber, which, when electried by rubbing together, alsoattracts. It is noteworthy that the rst particle known tocarry electric charge, the electron, is named for the Greekword for amber, (lektron).How was the power to move other things without themovers changing to be explained? Thales saw a common-ality with the powers of living things to act. The lodestoneand the amber must be alive, and if that were so, therecould be no dierence between the living and the dead.When asked why he didnt die if there was no dierence,

  • 2.2 Beliefs in divinity 5

    he replied because there is no dierence.Aristotle dened the soul as the principle of life, thatwhich imbues the matter and makes it live, giving it theanimation, or power to act. The idea did not originatewith him, as the Greeks in general believed in the dis-tinction between mind and matter, which was ultimatelyto lead to a distinction not only between body and soulbut also between matter and energy.If things were alive, they must have souls. This beliefwas no innovation, as the ordinary ancient populations ofthe Mediterranean did believe that natural actions werecaused by divinities. Accordingly, the sources say thatThales believed that all things were full of gods.[22] Intheir zeal to make him the rst in everything some saidhe was the rst to hold the belief, which must have beenwidely known to be false.However, Thales was looking for something more gen-eral, a universal substance of mind. That also was inthe polytheism of the times. Zeus was the very person-ication of supreme mind, dominating all the subordi-nate manifestations. From Thales on, however, philoso-phers had a tendency to depersonify or objectify mind, asthough it were the substance of animation per se and notactually a god like the other gods. The end result was atotal removal of mind from substance, opening the doorto a non-divine principle of action.Classical thought, however, had proceeded only a littleway along that path. Instead of referring to the person,Zeus, they talked about the great mind:

    Thales, says Cicero,[23] assures that water isthe principle of all things; and that God is thatMind which shaped and created all things fromwater.

    The universal mind appears as a Roman belief in Virgilas well:

    In the beginning, SPIRIT within (spiritus intus)strengthens Heaven and Earth,

    The watery elds, and the lucid globe of Luna,and then --

    Titan stars; and mind (mens) infused throughthe limbsAgitates the whole mass, and mixes itself withGREAT MATTER (magno corpore)" [24]

    2.2.1 Reputation

    Thales (who died around 30 years before the time ofPythagoras and 300 years before Euclid, Eudoxus ofCnidus, and Eudemus of Rhodes) is often hailed as therst Greek mathematician.[25] While some historians,

    such as Colin R. Fletcher, point out that there couldhave been a predecessor to Thales who would've beennamed in Eudemus lost book History of Geometry it isadmitted that without the work the question becomesmere speculation.[25] Fletcher holds that as there is noviable predecessor to the title of rst Greek mathemati-cian, the only question is whether Thales qualies as apractitioner in that eld; he holds that Thales had at hiscommand the techniques of observation, experimenta-tion, superposition and deductionhe has proved him-self mathematician.[25]

    The evidence for the primacy of Thales comes to usfrom a book by Proclus who wrote a thousand years afterThales but is believed to have had a copy of Eudemusbook. Proclus wrote Thales was the rst to go to Egyptand bring back to Greece this study.[25] He goes on to tellus that in addition to applying the knowledge he gainedin Egypt He himself discovered many propositions anddisclosed the underlying principles of many others to hissuccessors, in some case his method being more general,in others more empirical.[25]

    Other quotes from Proclus list more of Thales mathemat-ical achievements:They say that Thales was the rst to demonstrate thatthe circle is bisected by the diameter, the cause of thebisection being the unimpeded passage of the straight linethrough the centre.[25]

    "[Thales] is said to have been the rst to have known andto have enunciated [the theorem] that the angles at thebase of any isosceles triangle are equal, though in themore archaic manner he described the equal angles assimilar.[25]

    This theorem, that when two straight lines cut one an-other, the vertical and opposite angles are equal, was rstdiscovered, as Eudemus says, by Thales, though the sci-entic demonstration was improved by the writer of Ele-ments.[25]

    Eudemus in his History of Geometry attributes this the-orem [the equality of triangles having two angles and oneside equal] to Thales. For he says that the method bywhich Thales showed how to nd the distance of ships atsea necessarily involves this method.[25]

    "Pamphila says that, having learnt geometry from theEgyptians, he [Thales] was the rst to inscribe in a circle aright-angled triangle, whereupon he sacriced an ox.[25]

    In addition to Proclus, Hieronymus of Rhodes also citesThales as the rst Greek mathematician. Hieronymusheld that Thales was able to measure the height of thepyramids by a successful application of geometry (aftergathering data by using his sta and comparing its shadowto those cast by the pyramids). We receive variations ofHieronymus story through Diogenes Laertius, Pliny theElder, and Plutarch.[25] Due to the variations among tes-timonies, such as the story of the sacrice of an ox onthe occasion of the discovery that the angle on a diam-

  • 6 2 THEORIES

    eter of a circle is a right angle in the version told byDiogenes Laertius being accredited to Pythagoras ratherthan Thales, some historians (such as D. R. Dicks) ques-tion whether such anecdotes have any historical worthwhatsoever.[12]

    2.2.2 Practice and theory

    Thales was known for his innovative use of geometry. Hisunderstanding was theoretical as well as practical. Forexample, he said:

    Megiston topos: hapanta gar chorei ( )Space is the greatest thing, as it contains allthings

    Topos is in Newtonian-style space, since the verb, chorei,has the connotation of yielding before things, or spreadingout to make room for them, which is extension. Withinthis extension, things have a position. Points, lines, planesand solids related by distances and angles follow from thispresumption.Thales understood similar triangles and right triangles,and what is more, used that knowledge in practical ways.The story is told in DL (loc. cit.) that he measured theheight of the pyramids by their shadows at the momentwhen his own shadow was equal to his height. A right tri-angle with two equal legs is a 45-degree right triangle, allof which are similar. The length of the pyramids shadowmeasured from the center of the pyramid at that momentmust have been equal to its height.This story indicates that he was familiar with the Egyptianseked, or seqed - the ratio of the run to the rise of a slope(cotangent). The seked is at the base of problems 56, 57,58, 59 and 60 of the Rhind papyrus - an ancient Egyptianmathematics document.In present day trigonometry, cotangents require the sameunits for run and rise (base and perpendicular), but thepapyrus uses cubits for rise and palms for run, resultingin dierent (but still characteristic) numbers. Since therewere 7 palms in a cubit, the seked was 7 times the cotan-gent.To use an example often quoted in modern referenceworks, suppose the base of a pyramid is 140 cubits andthe angle of rise 5.25 seked. The Egyptians expressedtheir fractions as the sum of fractions, but the decimalsare sucient for the example. What is the rise in cubits?The run is 70 cubits, 490 palms. X, the rise, is 490 di-vided by 5.25 or 9313 cubits. These gures suced forthe Egyptians and Thales. We would go on to calculatethe cotangent as 70 divided by 9313 to get 3/4 or .75 andlooking that up in a table of cotangents nd that the angleof rise is a few minutes over 53 degrees.Whether the ability to use the seked, which precededThales by about 1000 years, means that he was the rst

    Thales Theorem: DEBC

    = AEAC

    = ADAB

    to dene trigonometry is a matter of opinion. Morepractically Thales used the same method to measure thedistances of ships at sea, said Eudemus as reported byProclus (in Euclidem). According to Kirk & Raven(reference cited below), all you need for this feat is threestraight sticks pinned at one end and knowledge of youraltitude. One stick goes vertically into the ground. A sec-ond is made level. With the third you sight the ship andcalculate the seked from the height of the stick and itsdistance from the point of insertion to the line of sight.The seked is a measure of the angle. Knowledge of twoangles (the seked and a right angle) and an enclosed leg(the altitude) allows you to determine by similar trianglesthe second leg, which is the distance. Thales probably hadhis own equipment rigged and recorded his own sekeds,but that is only a guess.Thales Theorem is stated in another article. (Actuallythere are two theorems called Theorem of Thales, onehaving to do with a triangle inscribed in a circle andhaving the circles diameter as one leg, the other theo-rem being also called the intercept theorem.) In additionEudemus attributed to him the discovery that a circle isbisected by its diameter, that the base angles of an isosce-les triangle are equal and that vertical angles are equal.According to a historical Note,[26] when Thales visitedEgypt, he observed that whenever the Egyptians drew twointersecting lines, they would measure the vertical anglesto make sure that they were equal. Thales concluded thatone could prove that all vertical angles are equal if oneaccepted some general notions such as: all straight anglesare equal, equals added to equals are equal, and equalssubtracted from equals are equal. It would be hard toimagine civilization without these theorems.

    Inuences Due to the scarcity of sources concerningThales and the diversity among the ones we possess, there

  • 2.2 Beliefs in divinity 7

    is a scholarly debate over possible inuences on Thalesand the Greek mathematicians that came after him.Historian Roger L. Cooke points out that Proclus does notmake any mention of Mesopotamian inuence on Thalesor Greek geometry, but is shown clearly in Greek as-tronomy, in the use of sexagesimal system of measur-ing angles and in Ptolemys explicit use of Mesopotamianastronomical observations.[27] Cooke notes that it maypossibly also appear in the second book of Euclids El-ements, which contains geometric constructions equiva-lent to certain algebraic relations that are frequently en-countered in the cuneiform tablets. Cooke notes Thisrelation however, is controversial.[27]

    Historian B.L. Van der Waerden is among those advo-cating the idea of Mesopotamian inuence, writing Itfollows that we have to abandon the traditional beliefthat the oldest Greek mathematicians discovered geome-try entirely by themselvesa belief that was tenable onlyas long as nothing was known about Babylonian mathe-matics. This in no way diminishes the stature of Thales;on the contrary, his genius receives only now the honourthat is due to it, the honour of having developed a logicalstructure for geometry, of having introduced proof intogeometry.[25]

    Some historians, such as D. R. Dicks takes issue with theidea that we can determine from the questionable sourceswe have, just how inuenced Thales was by Babyloniansources. He points out that while Thales is held to havebeen able to calculate an eclipse using a cycle called theSaros held to have been borrowed from the Babylo-nians, The Babylonians, however, did not use cyclesto predict solar eclipses, but computed them from ob-servations of the latitude of the moon made shortly be-fore the expected syzygy.[12] Dicks cites historian O.Neugebauer who relates that No Babylonian theory forpredicting solar eclipse existed at 600 B.C., as one cansee from the very unsatisfactory situation 400 year later;nor did the Babylonians ever develop any theory whichtook the inuence of geographical latitude into account.Dicks examines the cycle referred to as 'Saros - whichThales is held to have used and which is believed to stemfrom the Babylonians. He points out that Ptolemy makesuse of this and another cycle in his book Mathemati-cal Syntaxis but attributes it to Greek astronomers earlierthan Hipparchus and not to Babylonians.[12] Dicks notesHerodotus does relate that Thales made use of a cycleto predict the eclipse, but maintains that if so, the ful-llment of the 'prediction' was a stroke of pure luck notscience.[12] He goes further joining with other historians(F. Martini, J.L. E. Dreyer, O. Neugebauer) in rejectingthe historicity of the eclipse story altogether.[12] Dickslinks the story of Thales discovering the cause for a solareclipse with Herodotus claim that Thales discovered thecycle of the sun with relation to the solstices, and con-cludes he could not possibly have possessed this knowl-edge which neither the Egyptians nor the Babylonians norhis immediate successors possessed.[12] Josephus is the

    only ancient historian that claims Thales visited Babylo-nia.Herodotus wrote that the Greeks learnt the practice ofdividing the day into 12 parts, about the polos, and thegnomon from the Babylonians. (The exact meaning ofhis use of the word polos is unknown, current theories in-clude: the heavenly dome, the tip of the axis of thecelestial sphere, or a spherical concave sundial.) Yeteven Herodotus claims on Babylonian inuence are con-tested by somemodern historians, such as L. Zhmud, whopoints out that the division of the day into twelve parts(and by analogy the year) was known to the Egyptians al-ready in the second millennium, the gnomon was knownto both Egyptians and Babylonians, and the idea of theheavenly sphere was not used outside of Greece at thistime.[28]

    Less controversial than the position that Thales learntBabylonian mathematics is the claim he was inuencedby Egyptians. Pointedly historian S. N. Bychkov holdsthat the idea that the base angles of an isosceles trian-gle are equal likely came from Egypt. This is because,when building a roof for a home - having a cross sec-tion be exactly an isosceles triangle isn't crucial (as itsthe ridge of the roof that must t precisely), in contrast asymmetric square pyramid cannot have errors in the baseangles of the faces or they will not t together tightly.[27]Historian D.R. Dicks agrees that compared to the Greeksin the era of Thales, there was a more advanced state ofmathematics among the Babylonians and especially theEgyptians - both cultures knew the correct formulae fordetermining the areas and volumes of simple geometri-cal gures such as triangles, rectangles, trapezoids, etc.;the Egyptians could also calculate correctly the volume ofthe frustum of a pyramid with a square base (the Baby-lonians used an incorrect formula for this), and used aformula for the area of a circle...which gives a value for of 3.1605--a good approximation.[12] Dicks also agreesthat this would have had an eect on Thales (whom themost ancient sources agree was interested in math and as-tronomy) but he holds that tales of Thales travels in theselands are pure myth.The ancient civilization andmassive monuments of Egypthad a profound and ineradicable impression on theGreeks. They attributed to Egyptians an immemorialknowledge of certain subjects (including geometry) andwould claim Egyptian origin for some of their own ideasto try and lend them a respectable antiquity (such as theHermetic literature of the Alexandrian period).[12]

    Dicks holds that since Thales was a prominent gure inGreek history by the time of Eudemus but nothing cer-tain was known except that he lived in Miletus.[12] Atradition developed that as Milesians were in a positionto be able to travel widely Thales must have gone toEgypt.[12] As Herodotus says Egypt was the birthplace ofgeometry he must have learnt that while there. Since hehad to have been there, surely one of the theories on Nile


    Flooding laid out by Herodotus must have come fromThales. Likewise as he must have been in Egypt he hadto have done something with the Pyramids - thus the taleof measuring them. Similar apocryphal stories exist ofPythagoras and Plato traveling to Egypt with no corrob-orating evidence.As the Egyptian and Babylonian geometry at the time wasessentially arithmetical, they used actual numbers andthe procedure is then described with explicit instruc-tions as to what to do with these numbers there wasno mention of how the rules of procedure were made,and nothing toward a logically arranged corpus of gen-eralized geometrical knowledge with analytical 'proofssuch as we nd in the words of Euclid, Archimedes,and Apollonius.[12] So even had Thales traveled there hecould not have learnt anything about the theorems he isheld to have picked up there (especially because there isno evidence that any Greeks of this age could use Egyp-tian hieroglyphics).[12]

    Likewise until around the second century BC and the timeof Hipparchus (c. 194-120 BC) the Babylonian generaldivision of the circle into 360 degrees and their sexa-gesimal system was unknown.[12] Herodotus says almostnothing about Babylonian literature and science, and verylittle about their history. Some historians, like P. Schn-abel, hold that the Greeks only learned more about Baby-lonian culture from Berossus, a Babylonian priest who issaid to have set up a school in Cos around 270 BC (but towhat extent this had in the eld of geometry is contested).Dicks points out that the primitive state of Greek math-ematics and astronomical ideas exhibited by the pecu-liar notions of Thales successors (such as Anaximander,Anaximenes, Xenophanes, and Heraclitus), which histo-rian J. L. Heiberg calls a mixture of brilliant intuitionand childlike analogies,[29] argues against the assertionsfrom writers in late antiquity that Thales discovered andtaught advanced concepts in these elds.

    3 InterpretationsIn the long sojourn of philosophy there has existed hardlya philosopher or historian of philosophywho did notmen-tion Thales and try to characterize him in someway. He isgenerally recognized as having brought something new tohuman thought. Mathematics, astronomy and medicinealready existed. Thales added something to these dier-ent collections of knowledge to produce a universality,which, as far as writing tells us, was not in tradition be-fore, but resulted in a new eld.Ever since, interested persons have been asking what thatnew something is. Answers fall into (at least) two cate-gories, the theory and the method. Once an answer hasbeen arrived at, the next logical step is to ask how Thalescompares to other philosophers, which leads to his clas-sication (rightly or wrongly).

    3.1 TheoryThe most natural epithets of Thales are "materialist" and"naturalist", which are based on ousia and physis. TheCatholic Encyclopedia notes that Aristotle called him aphysiologist, with the meaning student of nature.[30]On the other hand, he would have qualied as an earlyphysicist, as did Aristotle. They studied corpora, bod-ies, the medieval descendants of substances.Most agree that Thales stamp on thought is the unity ofsubstance, hence Bertrand Russell:[31]

    The view that all matter is one is quite a rep-utable scientic hypothesis."...But it is still a handsome feat to have dis-covered that a substance remains the same indierent states of aggregation.

    Russell was only reecting an established tradition; forexample: Nietzsche, in his Philosophy in the Tragic Ageof the Greeks, wrote:[32]

    Greek philosophy seems to begin with an ab-surd notion, with the proposition that water isthe primal origin and the womb of all things. Isit really necessary for us to take serious noticeof this proposition? It is, and for three reasons.First, because it tells us something about theprimal origin of all things; second, because itdoes so in language devoid of image or fable,and nally, because contained in it, if only em-bryonically, is the thought, 'all things are one.'"

    This sort of materialism, however, should not be confusedwith deterministic materialism. Thales was only trying toexplain the unity observed in the free play of the qualities.The arrival of uncertainty in the modern world made pos-sible a return to Thales; for example, John Elof Boodinwrites (God and Creation):

    We cannot read the universe from the past...

    Boodin denes an emergent materialism, in which theobjects of sense emerge uncertainly from the substrate.Thales is the innovator of this sort of materialism.

    3.2 Rise of theoretical inquiryIn the West, Thales represents a new kind of inquiringcommunity as well. Edmund Husserl[33] attempts to cap-ture the newmovement as follows. Philosophical man is anew cultural conguration based in stepping back frompregiven tradition and taking up a rational inquiry intowhat is true in itself;" that is, an ideal of truth. It beginswith isolated individuals such as Thales, but they are sup-ported and cooperated with as time goes on. Finally theideal transforms the norms of society, leaping across na-tional borders.

  • 93.3 Classication

    The term "Pre-Socratic" derives ultimately from thephilosopher Aristotle, who distinguished the earlyphilosophers as concerning themselves with substance.Diogenes Laertius on the other hand took a strictly ge-ographic and ethnic approach. Philosophers were eitherIonian or Italian. He used Ionian in a broader sense, in-cluding also the Athenian academics, who were not Pre-Socratics. From a philosophic point of view, any group-ing at all would have been just as eective. There isno basis for an Ionian or Italian unity. Some scholars,however, concede to Diogenes scheme as far as referringto an Ionian school. There was no such school in anysense.The most popular approach refers to a Milesian school,which is more justiable socially and philosophically.They sought for the substance of phenomena and mayhave studied with each other. Some ancient writers qual-ify them as Milesioi, of Miletus.

    4 Inuence on others

    Thales (Electricity), sculpture from The Progress of Railroad-ing (1908), main facade of Union Station (Washington, DC)

    Thales had a profound inuence on other Greek thinkersand therefore on Western history. Some believeAnaximander was a pupil of Thales. Early sources re-port that one of Anaximanders more famous pupils,Pythagoras, visited Thales as a young man, and that

    Thales advised him to travel to Egypt to further his philo-sophical and mathematical studies.Many philosophers followed Thales lead in searching forexplanations in nature rather than in the supernatural; oth-ers returned to supernatural explanations, but couchedthem in the language of philosophy rather than of mythor of religion.Looking specically at Thales inuence during the pre-Socratic era, it is clear that he stood out as one of therst thinkers who thought more in the way of logos thanmythos. The dierence between these twomore profoundways of seeing the world is that mythos is concentratedaround the stories of holy origin, while logos is concen-trated around the argumentation. When themythical manwants to explain the world the way he sees it, he explainsit based on gods and powers. Mythical thought does notdierentiate between things and persons and furthermoreit does not dierentiate between nature and culture. Theway a logos thinker would present a world view is radicallydierent from the way of the mythical thinker. In its con-crete form, logos is a way of thinking not only about indi-vidualism, but also the abstract. Furthermore, it focuseson sensible and continuous argumentation. This lays thefoundation of philosophy and its way of explaining theworld in terms of abstract argumentation, and not in theway of gods and mythical stories.

    5 Reliability of sources

    Thales, Nuremberg Chronicle.

    Because of Thales elevated status in Greek culture an


    intense interest and admiration followed his reputation.Due to this following, the oral stories about his life wereopen to amplication and historical fabrication, even be-fore they were written down generations later. Most mod-ern dissension comes from trying to interpret what weknow, in particular, distinguishing legend from fact.Historian D.R. Dicks and other historians divide the an-cient sources about Thales into those before 320 BCand those after that year (some such as Proclus writ-ing in the 5th century C.E. and Simplicius of Ciliciain the 6th century C.E. writing nearly a millennium af-ter his era).[12] The rst category includes Herodotus,Plato, Aristotle, Aristophanes, and Theophrastus amongothers. The second category includes Plautus, Aetius,Eusebius, Plutarch, Josephus, Iamblichus, DiogenesLartius, Theon of Smyrna, Apuleius, Clement ofAlexandria, Pliny the Elder, and John Tzetzes among oth-ers.The earliest sources on Thales (living before 320 BC)are often the same for the other Milesian philosophers(Anaximander, and Anaximenes). These sources wereeither roughly contemporaneous (such as Herodotus) orlived within a few hundred years of his passing. More-over, they were writing from an oral tradition that waswidespread and well known in the Greece of their day.The latter sources on Thales are several ascriptions ofcommentators and compilers who lived anything from700 to 1,000 years after his death[12] which includeanecdotes of varying degrees of plausibility[12] and inthe opinion of some historians (such as D. R. Dicks) ofno historical worth whatsoever.[12] Dicks points out thatthere is no agreement among the 'authorities even onthe most fundamental facts of his life--e.g. whether hewas a Milesian or a Phoenician, whether he left any writ-ings or not, whether he was married or single-much lesson the actual ideas and achievements with which he iscredited.[12]

    Contrasting the work of the more ancient writers withthose of the later, Dicks points out that in the works ofthe early writers Thales and the other men who wouldbe hailed as the Seven Sages of Greece had a dierentreputation than that which would be assigned to them bylater authors. Closer to their own era, Thales, Solon, Biasof Priene, Pittacus of Mytilene and others were hailedas essentially practical men who played leading roles inthe aairs of their respective states, and were far betterknown to the earlier Greeks as lawgivers and statesmenthan as profound thinkers and philosophers.[12] For ex-ample, Plato praises him (coupled with Anacharsis) forbeing the originator of the potters wheel and the anchor.Only in the writings of the second group of writers (work-ing after 320 BC) do we obtain the picture of Thales asthe pioneer in Greek scientic thinking, particularly in re-gard to mathematics and astronomy which he is supposedto have learnt about in Babylonia and Egypt.[12] Ratherthan the earlier tradition [where] he is a favourite exam-

    ple of the intelligent man who possesses some technical'know how'...the later doxographers [such as Dicaearchusin the latter half of the fourth century BC] foist on to himany number of discoveries and achievements, in order tobuild him up as a gure of superhuman wisdom.[12]

    Dicks points out a further problem arises in the surviv-ing information on Thales, for rather than using ancientsources closer to the era of Thales, the authors in laterantiquity (epitomators, excerptors, and compilers[12])actually preferred to use one or more intermediaries,so that what we actually read in them comes to us noteven at second, but at third or fourth or fth hand. ...Ob-viously this use of intermediate sources, copied and re-copied from century to century, with each writer addingadditional pieces of information of greater or less plausi-bility from his own knowledge, provided a fertile eld forerrors in transmission, wrong ascriptions, and ctitiousattributions.[12] Dicks points out that certain doctrinesthat later commentators invented for Thales...were thenaccepted into the biographical tradition being copied bysubsequent writers who were then cited by those comingafter them and thus, because they may be repeated bydierent authors relying on dierent sources, may pro-duce an illusory impression of genuineness.[12]

    Doubts even exist when considering the philosophical po-sitions held to originate in Thales in reality these stemdirectly from Aristotles own interpretations which thenbecame incorporated in the doxographical tradition as er-roneous ascriptions to Thales.[12] (The same treatmentwas given by Aristotle to Anaxagoras.)Most philosophic analyses of the philosophy of Thalescome from Aristotle, a professional philosopher, tutor ofAlexander the Great, who wrote 200 years after Thalesdeath. Aristotle, judging from his surviving books, doesnot seem to have access to any works by Thales, althoughhe probably had access to works of other authors aboutThales, such as Herodotus, Hecataeus, Plato etc., as wellas others whose work is now extinct. It was Aristotlesexpress goal to present Thales work not because it wassignicant in itself, but as a prelude to his own workin natural philosophy.[34] Georey Kirk and John Raven,English compilers of the fragments of the Pre-Socratics,assert that Aristotles judgments are often distorted byhis view of earlier philosophy as a stumbling progress to-ward the truth that Aristotle himself revealed in his phys-ical doctrines.[35] There was also an extensive oral tradi-tion. Both the oral and the written were commonly reador known by all educated men in the region.Aristotles philosophy had a distinct stamp: it professedthe theory of matter and form, which modern scholas-tics have dubbed hylomorphism. Though once verywidespread, it was not generally adopted by rationalistand modern science, as it mainly is useful in metaphysicalanalyses, but does not lend itself to the detail that is of in-terest to modern science. It is not clear that the theory ofmatter and form existed as early as Thales, and if it did,

  • 11

    whether Thales espoused it.While some historians, like B. Snell, maintain that Aristo-tle was relying on a pre-Platonic written record byHippiasrather than oral tradition, this is a controversial position.Representing the scholarly consensus Dicks states thatthe tradition about him even as early as the fth cen-tury B.C., was evidently based entirely on hearsay....Itwould seem that already by Aristotles time the early Io-nians were largely names only to which popular traditionattached various ideas or achievements with greater orless plausibility.[12] He points out that works conrmedto have existed in the sixth century BC by Anaximanderand Xenophanes had already disappeared by the fourthcentury BC, so the chances of Pre-Socratic material sur-viving to the age of Aristotle is almost nil (even less likelyfor Aristotles pupils Theophrastus and Eudemus and lesslikely still for those following after them).The main secondary source concerning the details ofThales life and career is Diogenes Laertius, "Lives ofEminent Philosophers".[36] This is primarily a biograph-ical work, as the name indicates. Compared to Aristotle,Diogenes is not much of a philosopher. He is the onewho, in the Prologue to that work, is responsible for thedivision of the early philosophers into Ionian and Ital-ian, but he places the Academics in the Ionian school andotherwise evidences considerable disarray and contradic-tion, especially in the long section on forerunners of theIonian School. Diogenes quotes two letters attributedto Thales, but Diogenes wrote some eight centuries afterThales death and that his sources often contained unre-liable or even fabricated information,[37] hence the con-cern for separating fact from legend in accounts of Thales.It is due to this use of hearsay and a lack of citing originalsources that leads some historians, like Dicks andWernerJaeger, to look at the late origin of the traditional pictureof Pre-Socratic philosophy and view the whole idea asa construct from a later age, the whole picture that hascome down to us of the history of early philosophy wasfashioned during the two or three generations from Platoto the immediate pupils of Aristotle.[38]

    6 See also Know thyself Material monism The Astrologer who Fell into a Well

    7 Notes[1] Aristotle, Metaphysics Alpha, 983b18.

    [2] Russell, Bertrand (1945). The History of Western Philos-ophy. New York: Simon and Schuster.

    [3] Singer, C. (2008). A Short History of Science to the 19thcentury. Streeter Press. p. 35.

    [4] Needham, C. W. (1978). Cerebral Logic: Solving theProblem of Mind and Brain. Loose Leaf. p. 75. ISBN0-398-03754-X.

    [5] (Boyer 1991, Ionia and the Pythagoreans p. 43)

    [6] Herodotus, 1.74.2, and A. D. Godleys footnote 1; Pliny,2.9 (12) and Bostocks footnote 2.

    [7] Plutarch (1952). Solon. In Robert Maynard Hutchins.Lives. Great Books of the Western World 14. Chicago:William Benton. p. 66.

    [8] Diogenes Lartius, 1.43, 44.

    [9] Aristotle, Politics 1259a

    [10] Book 1

    [11] 1.25

    [12] D. R. Dicks (November 1959). Thales.The Classical Quarterly 9 (2): 294309.doi:10.1017/S0009838800041586.

    [13] 1.22

    [14] Farrington, B., 1944 Greek Science. Pelican

    [15] English physics comes from it, but the latter is a Greekloan. In addition the quite ancient native English word becomes from the same Indo-European root.

    [16] The initial g of the archaic Latin gives the root away as*gen-, beget.

    [17] Metaphysics 983b6

    [18] 983 b6 8-11

    [19] Quaes. Hom. 22, not the same as Heraclitus of Ephesus

    [20] Work cited, paragraph 27.

    [21] Abraham Feldman (Oct 1945). Thoughts on Thales.The Classical Journal 41 (1): 46.

    [22] Aristotle,De Anima, 411a7. For other ancient sources seethe discussion in Kirk and Raven, The Presocratic Philoso-phers, 93-7.

    [23] De natura Deorum, i.,10

    [24] Virgil:"Aeneid, vi., 724-727.

    [25] Colin R. Fletcher (December 1982). The MathematicalGazette (The Mathematical Association) 66 (438): 267.

    [26] William G. Shute, William W. Shirk, George F. Porter,Plane and Solid Geometry, American Book Company(1960) pp. 25-27

    [27] Roger L. Cooke (2005). The History of Mathematics: ABrief Course. John Wiley & Sons, Inc.

    [28] Leonid Zhmud (2006). The Origin of the History of Sci-ence in Classical Antiquity. Die Deutsche Bibliothek.


    [29] J. L. Gesch (1925). D.Math. UndNaturwiss. imAltertum.Munich. p. 50.

    [30] Turner, Catholic Encyclopedia.

    [31] Wisdom of the West

    [32] 3

    [33] The Vienna Lecture

    [34] See Aristotle, Metaphysics Alpha, 983b 1-27.

    [35] Kirk and Raven, The Presocratic Philosophers, SecondEdition (Cambridge University Press, 1983) 3.

    [36] Translation of his biography on Thales: Thales, clas-sicpersuasion site; original Greek text, under , theLibrary of Ancient Texts Online site.

    [37] See McKirahan, Richard D., Jr. (1994). Philosophy Be-fore Socrates. Indianapolis: Hackett. p. 5. ISBN 0-87220-176-7.

    [38] Werner Jaeger (1948). Aristotle (2nd ed.). p. 454.

    8 References Burnet, John (1957) [1892]. Early Greek Philoso-

    phy. The Meridian Library. Third Edition

    Diogenes Lartius, Life of Thales, translated byRobert Drew Hicks (1925).

    Herodotus; Histories, A. D. Godley (translator),Cambridge: Harvard University Press, 1920; ISBN0-674-99133-8. Online version at Perseus

    Hans Joachim Strig: Kleine Weltgeschichte derPhilosophie. Fischer, Frankfurt/M. 2004, ISBN 3-596-50832-0.

    Kirk, G.S.; Raven, J.E. (1957). The PresocraticPhilosophers. Cambridge: University Press.

    G. E. R. Lloyd. Early Greek Science: Thales to Aris-totle.

    Nahm, Milton C. (1962) [1934]. Selections fromEarly Greek Philosophy. Appleton-Century-Crofts.

    Pliny the Elder; The Natural History (eds. John Bo-stock, M.D., F.R.S. H.T. Riley, Esq., B.A.) London.Taylor and Francis. (1855). Online version at thePerseus Digital Library.

    Turner, William (1910). The Catholic Encyclope-dia Volume 8. Ionian School of Philosophy. NewYork: Robert Appleton.

    9 Further reading Couprie, Dirk L. (2011). Heaven and Earth in An-

    cient Greek Cosmology: from Thales to HeraclidesPonticus. Springer. ISBN 9781441981158.

    Luchte, James (2011). Early Greek Thought: Beforethe Dawn. London: Bloomsbury Publishing. ISBN978-0567353313.

    O'Grady, Patricia F. (2002). Thales of Miletus:The Beginnings of Western Science and Philosophy.Western Philosophy Series 58. Ashgate. ISBN9780754605331.

    Mazzeo, Pietro (2010). Talete, il primo losofo.Bari: Editrice Tipograca.

    10 External links Media related to Thales at Wikimedia Commons Quotations related to Thales at Wikiquote Works written by or about Thales at Wikisource Thales of Miletus from The Internet Encyclopediaof Philosophy

    Thales of Miletus from the MacTutor History ofMathematics archive

    Livius, Thales of Miletus by Jona Lendering Thales Thales Theorem - Math Open Reference (with in-teractive animation)

    Thales biography by Charlene Douglass (with exten-sive bibliography)

    Thales eclipse of sun Thales Fragments

  • 13

    11 Text and image sources, contributors, and licenses11.1 Text

    Thales Source: Contributors: MichaelTinkler, Brion VIBBER, Mav, Bryan Derk-sen, Koyaanis Qatsi, Andre Engels, XJaM, Matusz, Olivier, Lir, Michael Hardy, Llywrch, Isomorphic, Nixdorf, Ixfd64, Dcljr, Big iron,Jeandr du Toit, Adam Conover, Koxinga, Charles Matthews, Adam Bishop, Radgeek, Tpbradbury, Thue, Secretlondon, Shafei, Lumos3,Mrdice, Naturyl, Dedoleo, Chuunen Baka, Robbot, 1984, Jaredwf, PBS, Lowellian, Rursus, Diderot, Andrew Levine, Mark Krueger,Wikibot, Gat, Dave6, Giftlite, DocWatson42, Inter, Fleminra, Mrjake, Noname, Joseph Dwayne, ChicXulub, Chowbok, Clockwork-Lunch, MistToys, Joseph Myers, Jossi, JimWae, Icairns, Gscshoyru, HunterX, Robin Hood, Ukexpat, Cwoyte, Lucidish, Simonides,DanielCD, An Siarach, Noisy, Rich Farmbrough, FranksValli, Florian Blaschke, Mani1, Paul August, Bender235, ESkog, Silentlight,CanisRufus, Chairboy, Shanes, 96T, Bobo192, Smalljim, Cje, BrokenSegue, Nicke Lilltroll, Nk, Knucmo2, Jumbuck, Danski14, Alan-sohn, JYolkowski, SnowFire, Eric Kvaalen, Seans Potato Business, Velella, Leoadec, Gpvos, Sciurin, Kazvorpal, Dennis Bratland, OlegAlexandrov, FeanorStar7, Starwiz, Miaow Miaow, WadeSimMiser, Chochopk, Kristaga, Bkwillwm, Wikiklrsc, Hotshot977, Bluemoose,Fryd1e, Pfalstad, Marudubshinki, Dysepsion, Magister Mathematicae, BD2412, Melesse, Mendaliv, Rjwilmsi, Trlovejoy, Infosocialist,Kalogeropoulos, Bubba73, Reinis, Sango123, Yamamoto Ichiro, FlaBot, RexNL, Gurch, Choess, GreyCat, Piniricc65, Reediewes, Scimi-tar, Chobot, Jaraalbe, Mhking, Korg, VolatileChemical, Gwernol, YurikBot, Wavelength, RobotE, Sceptre, Jimp, Epolk, Stephenb, GaiusCornelius, Wimt, Bullzeye, Ugur Basak, Odysses, Anomie, Aftermath, Grafen, Nick, Aldux, Misza13, Yiuchung, Elizabeyth, Roy Brum-back, .marc., Botteville, Wknight94, Igin, Deville, Sshadow, Dspradau, Tevildo, JoanneB, Hyst, Whobot, Allens, Kungfuadam, GrinBot,Rykotsusei, Luk, CHITRANI, IslandHopper973, Jsnx, SmackBot, Selfworm, Moeron, Lestrade, Incnis Mrsi, Levi allemany, Zerida, Ki-mon, KocjoBot, Jagged 85, Thunderboltz, RobotJcb, Gilliam, Chris the speller, Bluebot, Master of Puppets, Martinmuse, MalafayaBot,DHN-bot, Hongooi, John Reaves, Can't sleep, clown will eat me, Sumahoy, Writtenright, OrphanBot, Addshore, Essent, Stevenmitchell,Fuhghettaboutit, EPM, Valenciano, Limexx35, Shadow1, Dreadstar, KRBN, LoveMonkey, Jaellee, DMacks, Gatoatigrado, Rickmorcom,Thejerm, Tdw1203, Nareek, Khazar, Hemmingsen, Peterlewis, IronGargoyle, The Man in Question, Munita Prasad, Noah Salzman, Op-takeover, Mets501, Nwwaew, Funnybunny, Novangelis, MTSbot, Peyre, Hu12, Mig77, Iridescent, Lottamiata, Igoldste, Happy-melon,Az1568, Dkastner, Tawkerbot2, Chetvorno, CmdrObot, JohnCD, Pfhenshaw, Moreschi, Hemlock Martinis, Shanoman, Cydebot, Ntsimp,Hebrides, Dougweller, Codetiger, DumbBOT, Chrislk02,, Thijs!bot, Epbr123, Barticus88, Headbomb, AgentPep-permint, Michael A. White, Johnwrw, Escarbot, Eleuther, AntiVandalBot, Insulanus,, Prolog, D. Webb, Wahabijaz, JAnD-bot, Deective, MER-C, BlindEagle, Acroterion, Pianodwarf, Magioladitis, VoABot II, Italus, Professor marginalia, Waacstats, Animum,EagleFan, DerHexer, Baristarim, Cedricbear, RichMac, MartinBot, Wowaconia, Jim.henderson, Rettetast, R'n'B, CommonsDelinker,Pbroks13, VirtualDelight, Tgeairn, J.delanoy, Mariehuynh, Terrek, Maurice Carbonaro, Nigholith, WFinch, Filippo Argenti, Galanskov,Joannachan, Bot-Schafter, AntiSpamBot, Chiswick Chap, Belovedfreak, NewEnglandYankee, Aervanath, Biglovinb, Cometstyles, Inwind,S, Measure for Measure, VolkovBot, ABF, Historybu90, Macedonian, Philip Trueman, TXiKiBoT, Omarraii, Dommccas, GcSwRhIc,Qxz, Someguy1221, Anna Lincoln, Ontoraul, Jackfork, LeaveSleaves, BotKung, MDfoo, JesterCountess, Gchambonthales, Why Not ADuck, Alcmaeonid, Logan, Struway, Gaelen S., SieBot, Scarian, Kevmanetti, Beavis5000, Dawn Bard, Caltas, Triwbe, Peter cohen, Peter-bruce01, Flyer22, Momo san, Oxymoron83, Harry, Gja34, Alex.muller, Dkderick, Angielaj, Trumpetcase, 3rdAlcove, Xiscobernal, Athe-nean, Atif.t2, ClueBot, The Thing That Should Not Be, XPTO, CounterVandalismBot, Singinglemon, Puchiko, Sustainablefutures2015,No such user, Excirial, Alexbot, Eeekster, Rhododendrites, Patricius Augustus, NuclearWarfare, Davitenio, Jotterbot, Basketball110, Ra-zorame, Thehelpfulone, Catalographer, Aitias, Versus22, DBodor, Cow Taurog, NorthernDrifter, Semitransgenic, Chronicler, Rror, LittleMountain 5, PL290, Jbeans, HarlandQPitt, Kbdankbot, HexaChord, Addbot, Hockeyrockcars, The Sage of Stamford, Some jerk on theInternet, Atethnekos, 15lsoucy, CanadianLinuxUser, Fluernutter, Tedmund, LaaknorBot, AndersBot, Jsf8204, Greenmangowango, Fall-enAngel7789, Mtpuls1092, Tide rolls, Alcove, First Light, Xenobot, JEN9841, Fushigi-kun, Legobot, Luckas-bot, Yobot, Les boys, THENWHOWAS PHONE?, Markcob, Johnelwayrules, AnomieBOT, Killiondude, JackieBot, Piano non troppo, Kingpin13, Zxabot, Materialsci-entist, ImperatorExercitus, Citation bot, NATALEE--xD, ArthurBot, Teddyw73, Xqbot, Gilo1969, GrouchoBot, Omnipaedista, Paulasiri2,Nedim Ardoa, GhalyBot, N419BH, Shadowjams, AlexanderVanLoon, Gummieworm, FreeKnowledgeCreator, GT5162, FrescoBot, Tan-gent747, Paine Ellsworth, Recognizance, Pergamino, Tavernsenses, Machine Elf 1735, A little insignicant, Noqoilpi, Stockback, Winterst,Pinethicket, Edderso, At-par, Calmer Waters, RedBot, Pike84, Pezanos, Tim1357, Greco22, TobeBot, Pollinosisss, Oracleofottawa, Vre-nator, Ashot Gabrielyan, Mccartjt, DARTH SIDIOUS 2, ChanDMan2010, RjwilmsiBot, Jkyriazoglou, EmausBot, ImprovingWiki, Hera-cles31, RA0808, Rarevogel, Mitartep, Princess Lirin, Wikipelli, K6ka, Andrewkim99, Finemann, Tolly4bolly, AleksandrGertsen, DASH-BotAV, Nickbyrd, Gwen-chan, ClueBot NG, Smtchahal, Michaelmas1957, Manubot, Chester Markel, Neoglyph, Jazgirl13, YOPbottle,Widr, Helpful Pixie Bot, Joevandy, Lrocky223, DBigXray, BG19bot, 23x2, Laureos, Martinosacchi, Gabloo, Davidiad, Mark Arsten,Waliddamouny, Glacialfox, Klilidiplomus, This Is M4dn355 300, TheNuszAbides, BattyBot, Liam987, Khazar2, Welshwatch, Vanisheduser sdij4rtltkjasdk3, Dexbot, Lugia2453, RideLightning, Juc123, Hillbillyholiday, Tentinator, Alphadog3200, RaphaelQS, Sapiente2222,Fredmond4, Kleobulos Jeerson, Abc 123 xyz 456, Ro2am, Monkbot, Sparklesrule, Straight Busta and Anonymous: 656

    11.2 Images File:Capernaum_roman_olive_press_by_David_Shankbone.jpg Source:

    Capernaum_roman_olive_press_by_David_Shankbone.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: DavidShankbone (attribution required)

    File:Folder_Hexagonal_Icon.svg Source: License: ? Con-tributors: ? Original artist: ?

    File:Louisstgaudens1.jpg Source: License: CC-BY-3.0Contributors: Photograph by Dan Vera Original artist: Original uploader was Danvera at en.wikipedia

    File:MiletusIonicStoa.jpg Source: License: Public domainContributors: Originally from en.wikipedia; description page is/was here. Original artist: Original uploader was Monsieurdl at en.wikipedia

    File:Nuremberg_chronicles_f_59r_2.png Source: License: Public domain Contributors: Scan from original book Original artist: Michel Wolgemut, Wilhelm Pleydenwur

    File:People_icon.svg Source: License: CC0 Contributors: Open-Clipart Original artist: OpenClipart


    File:Portal-puzzle.svg Source: License: ? Contributors: ? Original artist:?

    File:Question_book-new.svg Source: License: ? Contributors:Created from scratch in Adobe Illustrator. Based on Image:Question book.png created by User:Equazcion Original artist:Tkgd2007

    File:Solar_eclipse_1999_4_NR.jpg Source: Li-cense: CC-BY-SA-3.0 Contributors: Own work Original artist: Luc Viatour

    File:Thales_theorem_1.png Source: License: CC-BY-SA-3.0 Contributors: ? Original artist: ?

    11.3 Content license Creative Commons Attribution-Share Alike 3.0


    TheoriesWater as a first principleInfluences

    Beliefs in divinityReputationPractice and theory

    InterpretationsTheoryRise of theoretical inquiryClassification

    Influence on othersReliability of sourcesSee alsoNotesReferencesFurther readingExternal linksText and image sources, contributors, and licensesTextImagesContent license