Thales and the Origin of Theoretical Reasoning
Dmitri Panchenko
Published in Greek as:
Dmitri Panchenko.
ής  ές  ή ή   έ  ή
ά ή έ  ό:
ύ ώ
ή: ί 
I am most grateful to David Konstan and Richard D. McKirahan for improving my English
CONTENTS
THESIS
THE
WATER
FROM
WHICH
EVERYTHING
EMERGES
AND
INTO
WHICH
EVERYTHING RETURNS
Problem
Solution
Removing doubts
The effect of Thales’ thesis
Philosophy or science?
What motivated Thales’ approach and solution?
Supplementary Notes
The alleged anticipation of Thales in Homer’s Okeanos passages
Emergence-and-return in the Upanishads
Animated water
Thales and the circumnavigation of Africa by the Phoenicians
THALES’ EXPLANATION OF SOLAR ECLIPSES
Ancient tradition versus the modern scholarship
Evidence
An examination of suggested objections
The significance of Thales’ theory
Why did theoretical cosmology emerge in Ionia and not in Assyria or Babylonia?
THALES’ PREDICTION OF A SOLAR ECLIPSE
Evidence
Problem
Previous attempts at the reconstruction of Thales' method
2
Thales' likely method: preliminary remarks
Chronological questions
Thales' likely method: 1st version
Thales' likely method: 2nd version
HOW BIG ARE THE SUN AND MOON?
THE FOUNDER OF GREEK GEOMETRY
Evidence
The origin of geometrical proofs
Geometry as a study of correlations and its likely origin within the study of celestial bodies
Supplementary Notes
How did Thales determine the distance of a ship in the sea?
Cosmology and the proof of incommensurability of a square’s diagonal with its side
HOW DO WE KNOW ABOUT THALES?
Supplementary Notes
An explanation of doxographic misattributions to Thales
Thales as a monopolist and the father of federalism
THEORETICAL KNOWLEDGE AND INTERPESONAL INTERACTION
ACKNOWLEDGEMENTS
3
THESIS
“The achievement of Thales,” notes Guthrie, “has been represented by historians in two entirely
different lights: on the one hand, as a marvelous anticipation of the modern scientific thinking,
and on the other as nothing but a transparent rationalization of a myth.” According to Guthrie
himself, one may say that “ideas of Thales and other Milesians created a bridge between the two
worlds – the world of the myth and the world of the mind.”1
I believe, however, that the true achievement of Thales lay in the adoption of that
intellectual procedure which forms the basis of all theoretical knowledge: he inaugurated the
tradition of arguable statements about the unobservable.
1 W. K. C. Guthrie, A History of Greek Philosophy, vol. 1 (Cambridge 1962) 70.
4
THE
WATER
FROM
WHICH
EVERYTHING
EMERGES
AND
INTO
WHICH
EVERYTHING RETURNS
Problem
There is a widespread belief that philosophy starts with Thales’ assertion that water is the
origin of all things. Many assume that there is a connection between Thales’ thesis and the
beginning of science. Having read through the extensive literature on the subject, however, I
cannot find a satisfactory answer to the question of what exactly makes this assertion of Thales
so important and what made it live. Apparently, some other scholars have a similar feeling, and
therefore they tend to minimize Thales’ innovation and consider his thesis about water as merely
one of the long array of traditional cosmogonies. Today, the prevailing view is that Thales only
presented in his own words what the Egyptians or Babylonians had said previously.2
The question of the Middle Eastern origin of the Thales’ thesis is not, of course, as
important as that of its meaning: is it an assertion about what was first in the world (as it is
presented in traditional cosmogonies), or was it also an assertion about the basic element of all
things? (If the latter, then a fundamental difference from the Middle Eastern cosmogonies is
obvious).
The latter interpretation, which goes back to Aristotle and Theophrastus, was the
prevailing one until the middle of the twentieth century, shared by the majority of those scholars
who wrote about Thales, the Milesians, and the birth of philosophy and science. What, then, did
those authors say about (a) the motives that made Thales advance his proposition about water,
and (b) the historical significance of this proposition?
The most typical is the following. We are told that Thales and the other Milesian
philosophers proceeded from the assumption of a fundamental unity of all material things that is
to be found behind their apparent diversity. So the task of these philosophers was to establish
what exactly provided this unity: one said it was water; another, the Boundless; yet another, air.
They arrived at this presumption of unity beyond diversity partly through a certain intuition,
partly under the influence of some impressions obtained from experience. Yet interpretations of
2 U. Hölscher, "Anaximander und die Anfänge der Philosophie," Hermes 81 (1953); 257-277; 385 ff.; H. Schwabl,
"Weltschöpfung," RE, Suppl. 9 (1962) 1514; G. S. Kirk, J. E. Raven, M. Schofield, The Presocratic Philosophers
2nd ed. (Cambridge 1983) 92 ff.; M. L. West, Early Greek Philosophy and the Orient (Oxford 1971) 208; Andrei V.
Lebedev, “Demiurg in Thales?”, in Text: Semantika i Struktura (Moscow 1983) 51 f. (in Russian).
5
this kind suggest no explanation of how the idea of the unity of all material things could have
become a presumption, a reference point for investigation and discussions for the first
philosophers, whereas everyday experience unambiguously indicates that the different material
things around us are not alike – some are derived from things of one sort, and others from things
of quite other sorts.
Let us consider some concrete proposals. John Burnet suggested that the opposition of
day and night, the changes of the seasons, and so forth brought the first philosophers to an idea
about the critical importance of the interplay of opposites in the world around us. "That,
however, was not enough. The earliest cosmologists could find no satisfaction in the view of the
world as a perpetual contest between opposites. They felt that these must somehow have a
common ground, from which they had issued and to which they must return once more."3 Yet
Burnet does not explain how one can ‘feel’ that.
According to Theodor Gomperz, Thales’ thesis could have been stimulated by
observations of plants obtaining nutrition from soil, air and water to become, in turn, food for
animals, as well as by observations of the decay of living organisms – in other words, by the
processes of organic circulation.4 However, such observations, although they could probably
lead to the assumption that there are a number of interrelated transitions and circulations which
connect separate things, could not lead to the conclusion that all things are modifications of one
stuff.
Admittedly some of the facts of experience which scholars adduce (like those related to
metalwork, or the introduction of coinage) could support the idea of all things’ unity despite their
apparent diversity after this idea had already been proposed. But no observations could produce
this idea, because (to quote Michael Stokes) “the world around us has nothing obviously
suggesting a single material.”5
Thus the scholars who do believe that Thales was the first philosopher, de facto ascribe to
his thesis an arbitrary character.6
As a matter of fact, this brings their position close to the views of those scholars who
deny the philosophical character of Thales’ ideas, and makes such a position internally
inconsistent. Moreover, it leaves the fate of Thales’ initiative mysterious. It is possible to assume
that Thales advanced his thesis about the material unity of the world on the basis of somewhat
3 J. Burnet, Early Greek Philosophy, 3rd ed. (London 1920) 9.
4 T. Gomperz, Griechische Denker, Bd. 1 (Berlin; Leipzig 1922) 38 f.
5 M. C. Stokes, One and Many in Presocratic Philosophy (Washington 1971) 39.
6 H. Frankfort and H. A. Frankfort et al., Before Philosophy. The Intellectual Adventure of Ancient Man: An Essay
on Speculative Thought in the Ancient Near East (Chicago 1977) 377, while accepting the traditional interpretation
of philosophy of the Milesians are consistent when they write: “Their sayings sound rather like inspired oracles. And
no wonder, for these men proceeded, with preposterous boldness, on an entirely unproved assumption.”
6
subtle, irrational reasons. But why, then, was Thales’ initiative taken up; why were several
generations of Greek philosophers, who rejected his concrete suggestion (everything comes from
water), concerned to solve his problem, so that responses to Thales’ thesis and reactions to these
responses formed to a considerable extent the content of subsequent philosophical development?
A miracle is followed by a miracle!
Further, it is true and significant that Thales replaced a narration by an assertion7 and that
his assertion compares favorably with the Middle Eastern cosmogonies which are far from being
clear, simple and unequivocal statements;8 and that instead of mythical characters, he sets up
observable objects.9 Nevertheless, it is not necessarily the case that every unambiguous assertion
that characterizes observable objects is fruitful – in particular, such an extravagant assertion as
“everything comes from water.”
The question must be considered anew.
Solution
Theories are not created directly from observations (as implied by Gomperz’s and
Burnet’s trains of thought), nor from experience in a broad sense (as those scholars believe who
refer to the introduction of coinage or to a city-state universum). Theories are influenced both by
observation and by social experience; however, they come from specific problem situations.10
Let us try to understand exactly what problem Thales was trying to solve. First of all we
shall look at the key testimony of Aristotle (Metaph. 983 b6 ff.), who says that the first
philosophers, when discussing the problem of the principle () meant something “of which
all existing things consist, from which they first come to be, and into which they are finally
destroyed”
(              
 ). A little further on Aristotle calls Thales “the founder of this type of
philosophy” (11 A 12 DK).
Thus we have a triad. We can hardly hope that someday we will be able to learn the exact
words of Thales. However, we have enough information to make judgments as to the structure of
his statement. A comparison with genuine fragments by the philosophers who were Thales’
younger contemporaries shows that his assertion should be not three-fold, but two-fold.
The combination of coming-into-being and destruction appears in Anaximander, the
closest follower of Thales: “out of those things whence is generation for existing things, into
these
again
does
their
destruction
take
place”
(       
7 W. Windelband, Geschichte der abendländischen Philosophie im Altertum (München 1923) 20.
8 G. E. R. Lloyd, Methods and Problems in Greek Science (New York; Cambridge 1991) 287.
9 C. J. Classen, "Thales," RE, Suppl., 10 (1965) 941.
10 In this issue I follow the philosophy of knowledge by Karl R. Popper.
7
       – 12 B 1 DK). The same combination is found in
Xenophanes:
"Everything
comes
from
earth
and
into
earth
everything
dies"
(         – 21 B 27 DK).
That Thales’ thesis was of two parts – in one form or another of the idea that all comes
out of water and is resolved into water – is confirmed regularly by doxographic tradition (Dox.
276; 579; 589, etc.).
Xenophanes’ phrase and the doxographers’ formulations are somewhat ambiguous as to
the first part of the pair: they may be understood as saying that everything originated from earth
(or water), or that everything consists of earth (or water), or that everything originated and
consists of earth (or water).11 The considerations of symmetry speak clearly in favour of the first
possibility. Moreover, it is very strange to say that things dissolve, destroy, or die into earth (or
water) if they are earth (or water). The wording of Anaximander’s fragment is less ambiguous
and, on analogy, it certainly suggests that Thales said that all things originated from, were born
out of water.12 In such a case the first part of the Aristotelian triad (“of which all existing things
consist”) should be understood as a natural retrospection and generalization. Aristotle is not
talking about the initial problem of the Milesians, but about what became a common practice of
philosophical investigation along the lines established by the Milesians. He has in mind first of
all the post-Parmenidean situation; it is for Anaxagoras, Empedocles, and the Atomists, rather
than for the Milesians, that things consist of the same indestructible elements “from which they
first come to be, and into which they are finally destroyed”. In this sense, those who have
insisted that Thales was talking about the origin of things were absolutely correct.13 But this is
only one part of the truth.
The second part of the truth is that Thales talked about water as something into which all
things are finally resolved. This makes the Thales’ assertion critically different from the Middle
Eastern (as well as traditional Greek) cosmogonies, where there is nothing comparable.14 This
also demonstrates clearly one-sided character of the view according to which Thales chose water
because it could be regarded as the source of life:15 it is absolutely unnecessary in such a case to
11 Cf. remarks by Gregory Vlastos in M. C. Stokes, One and Many, 40.
12 Cf. G. E. R. Lloyd's remarks in M. Grant and R. Kitzinger, Civilization of the Ancient Mediterranean: Greece
and Rome, vol. 3 (New York 1988) 1588.
13 Keimpe Algra (in The Cambridge Companion to Early Greek Philosophy, ed. by A. A. Long [Cambridge 1999]
51) notes that a related idea of Thales (attested by Aristotle and the doxographers) that the earth rests on water is
rather strange “if the assumption is that the earth still is water.”
14 This was properly noted in Wolfgang Detel, "Das Prinzip des Wassers bei Thales", in Kulturgeschichte des
Wassers, ed. H. Boekme (Frankfurt am Main 1988) 43-64, esp. 53.
15 If this opinion goes back to Aristotle, then it should be noticed that Aristotle obviously was not concerned why
Thales made water a principle, but rather why he had chosen water rather than air or something else. It is true, of
course, that “Aristotle does not provide examples proving that things return to water” (Jaap Mansfeld, “Aristotle and
Others on Thales, or The Beginnings of Natural Philosophy, in his Studies in the Historiography of Greek
8
bring up the question of into what everything is destroyed; and the same question would be
equally superfluous for the riddle, “What is the oldest?”16
Everything points to the conclusion that Thales’ thesis contained an assertion about the
origin out of which everything emerged and into which everything returns. It is not surprising for
Thales to be reasoning about the origin of things – this was a traditional subject familiar from
ancient cosmogonies. But why did he need to search for an origin into which everything returns?
This very characteristic of the origin suggests a clue: that which is capable of reabsorbing all
things is apparently indestructible and therefore always present, eternal. But why need it to be
such? I can offer only one answer, though it is an answer in two interrelated parts: Thales wished
to find an origin that would not need another one – the true origin; only an assertion about such
an origin might claim to be convincing. That was his problem situation.
Traditional cosmogonies were in a way suggestive. They depicted a chain of births of
specific creatures (generally, these are gods), some of which gave birth to or created other things
of the world. And the question would remain forever: what is the origin of the one who is at the
beginning of the genealogical series? Thus, Thales could see that any genealogical series recedes
to infinity – on the condition, of course, that nothing would ever come out of nothing. I assume
that Thales accepted this principle. In that case, the only way to avoid the regressus ad infinitum
was to postulate the existence of something eternal.
This eternal must have, however, a connection with the real world full of diverse things;
it must be capable of generating things. In the traditional cosmogonies the question of the origin
of the primeval material remained obscure; and nothing in human experience made it easy to
understand how from a number of beings the world full of material things could emerge.
Therefore the true origin must be material, it must be stuff. This stuff, further, must be conducive
to transformations, for a single stuff can produce diverse things only through transformations.
Now, things do not come to be out of nothing. Are they annihilated completely? Are they
destroyed into nothing? The answer to such questions does not come to one’s mind as
automatically as the acceptance of the principle “nothing comes out of nothing”. I suppose that a
typical answer among people unaffected by science, philosophy or related educational systems
would be, “I don’t know”. I assume, however, that for anyone who was prepared to address such
Philosophy [Assen; Maastricht 1990] 126-146, esp. 136), but this is by no means surprising for a context in which
Aristotle conjectures about Thales’ reasons for choosing a particular origin of things. In general, Aristotle never
shows much interest in the philosophy of the Milesians. The number and character of his references to Anaximander
and Anaximenes do not even guarantee that he ever read their books (compare his references to Anaxagoras,
Empedocles, or Democritus). Milesian philosophy was no longer influential in his age. One may also suppose that
Milesian philosophy was not easy for Aristotle to argue with. It is probably characteristic that “Aristotle had no
patience with the idea that water, air, or the boundless can of its own accord change into a cosmos” (Keimpe Algra
in The Cambridge Companion, 54).
16 As was suggested by A. V. Lebedev, “An Original Formulation of Thales’ Thesis   Y ,”
in Balcanica (Moscow 1985) 167-175 (in Russian).
9
questions, it was very difficult to imagine things turning into nothing. Both logic and experience,
under close examination, would rather support a negative answer. If one assumes that all things,
as we know them, derive directly or indirectly from a certain original stuff, one has to see that
this source is in danger of exhaustion. And since this source of things was never born, but existed
always, there was enough time for it to become exhausted. Hence the acceptance of the
possibility that things perish into nothing leads to very strange consequences. Now, melting
snow is not destroyed into nothing, but turns into water. Wood is destroyed by fire, but ash is
always to be found in its place. Observations of the decay of living organisms (cited by
Gomperz) would also point to a similar conclusion, though in a less unambiguous way. One
obvious counter-example would be drying of water: where there was a puddle in the morning
there is nothing in the afternoon; where there was a river in the spring, there is just dry bed in the
height of the summer. Yet everybody knew that the effect was somehow connected with heating.
Everybody also knew what happens to water under particularly strong heating: boiling water
produces visible vapor. Under certain conditions, vapor rising from earth could be also observed.
An extrapolation suggested itself: when exposed to heat, water is not annihilated, but invariably
turns into vapor. One would thus arrive at the conclusion that things undergo transformations
rather than being destroyed into nothing. And in order to meet the danger of the exhaustion of
the generating source of things, one would assume backwards transformations, so to speak, or a
cyclical transformation: things not only emerge from a certain source, but also return into it.
And since not a single part of the world could come out of nothing or be destroyed into
nothing, the principle of transformation must be applied to the whole complex of things. In other
words, one has to assume a common origin for all things.
One can see that the unity of all things in Thales’ reasoning was not the premise (as
considered until now), but a consequence, a conclusion he had to arrive at. It was the way of
avoiding an infinite regress by introducing a cycle of transformations of matter, so that nothing
comes out of nothing and is destroyed into nothing.
Water fitted the task well. The transformations of water were universally observable –
how it turns into vapor or ice, condenses from the mist on one’s clothes, appears as dew and
even can be seen as a melted metal.17 There was plenty of water – below, from above, around.
Sailors reported on its immense expanse in the west, east and south, and nobody could indicate
its boundaries. And no organism capable of moving or growing was seen to have existed without
water.
17 It is a part of ancient tradition (Hippol. Ref. 1.1; not in DK) that the choice of water was connected with such
properties. Cf. J. Burnet, Early Greek Philosophy, 49.
10
Removing doubts
The suggested interpretation is strictly based on the evidence. However, I will adduce
additional arguments to the effect that all the motifs involved in my interpretation of Thales’
water thesis were known in the sixth century.
Pherecydes of Syros, a younger contemporary of Thales, who composed a kind of
theocosmogony, seems to have recognized the problem of the infinite regress, for he says: “Zas,
Chronus and Chtonia existed always” (7 B 1 DK).
The principle ‘nothing out of nothing’ is directly expressed in Alcaeus' fr. 320 Campbell:
“And nothing would come out of nothing.” We are told, by the way, that Alcaeus praised Thales
in one of his poems (11 A 11a DK).18
I previously cited the fragments of Anaximander and Xenophanes in which the
emergence-and-return formula is clearly present. Additional comments on Anaximander’s
wording seem appropriate. Simplicius quotes him as saying: “out of those things whence is the
generation for existing things, into these again does their destruction take place (   
         ”. Despite the plural  many
scholars would like to take it as somehow pointing to the Apeiron, but it has been shown that
such an interpretation is not to be recommended.19 Simplicius understood it as a reference to
elements, which is clearly anachronistic. Charles Kahn seeks to rectify Simplicius’ interpretation
by substituting the opposites for elements: “Hot arises out of cold, dry out of damp, and each
must perish into its source…” (195 f.). But it is difficult to see how hot could arise out of cold,
and it is characteristic that the cosmogonic process begins in Anaximander with the separation of
hot and cold. I propose to take Anaximander’s wording as a formulation of a general principle
that is supposed to be clear to the readers from a previous discussion (and also, perhaps, from the
familiarity with Thales’ water thesis).
To be sure, Anaximander must also have had in mind some specific processes. Charles
Kahn (184 f.) makes some plausible suggestions. “He must have recognized essentially the same
process at work in the production of the fiery thunderbolt out of wind and cloud, themselves in
turn produced from evaporating moisture. The downward return of quenched fire and condensing
rain cloud will counteract the upward surge of dryness and heat, and thus preserve the balance of
the whole”. What Kahn refers to may be described as the generation of things out of water and
their return into water. A similar comment can be made on his other suggestion: “Like
18 See further:
   “          ”,  16 (1987)
139-167. A. P. D. Mourelatos, “Pre-Socratic Origins of the Principle That There Are No Origins from Nothing,” The
Journal of Philosophy, 78 (1981) 649-665 provides strong arguments against the idea that the principle ‘nothing out
of nothing’ entered philosophy only with Parmenides.
19 C. H. Kahn, Anaximander and the Origins of Greek Cosmology (New York 1960) 172 f.
11
Xenophanes, Anaximander may have taught that the progressive drying-up of the sea would
eventually be reversed, so that the earth will sink back into the element from which it has
arisen”.
Speaking more generally: which of the basic things could have been naturally
associated with the idea of the emergence-and-return? Certainly not fire, hardly air or wind.
Earth is an obvious option while considering the plants and trees, but not for a large variety of
things. It is characteristic that even Xenophanes, who assigns to earth an important role, resorts
to the sea as a source of generation (B 30 DK) and cites water as generating principle along with
earth (B 29; 33 DK). In short, the idea of an entity from which things emerge and into which
they return most naturally comes with water, more precisely with observing the large scale
circulation of water, its evaporating from the sea and returning with rains and emptying rivers.20
One arrives at the same conclusion (that it was Thales rather than Anaximander who
introduced the emergence-and-return principle) from more abstract considerations. Since things
not only were generated once by water but also continue to emerge from water, they are likely to
return into water, for otherwise there would be a danger, as we already saw, that the amount of
water would continually decrease. But Anaximander with his emphasis on a boundless source of
generation was not in need of such a concern with backwards transformations. If his boundless
source of existing things was indeed inexhaustible (as some testimonies suggest), he could in
principle postulate an endless series of ever new modifications of an original stuff. It is possible
that Thales too was prepared to admit that the water on which the earth rests was of indefinite
extension.21 But this is not the same as to assert positively that it is boundless, in the sense of
inexhaustible. Psychologically, it was easier to think of a hidden entity, conceived in a
speculative way (as the Apeiron), that it is inexhaustible than of water the evaporation of which
one could frequently see. Besides, backwards transformations of clouds and ice into water were
just a matter of fact.
Again, Diogenes Laertius (1. 3) cites an opinion according to which Musaeus maintained
that “all things come to be from one and are resolved again into it”. What made possible such a
fictitious attribution? It was, perhaps, the fact that no author of a book On Nature claimed to be
the first to introduce this principle. But Thales left no book.
The principle of all-embracing transformations is well attested for Anaximenes’ air. In
Simplicius’ exposition, “rarefied, it becomes fire; condensed, it becomes first wind, then cloud,
and when condensed still further water, then earth and stone” (13 A 5; similarly Hippolytus, A
20 Note that the problem of how and why the sea becomes no larger even though innumerable rivers of immense
size are flowing into it every day is cited by Aristotle as “an old puzzle” (Mete. 355 b 22).
21 The ancients seem to have possessed no information on this point. Simplicius says once that Thales’ water was
limited yet another time that it was boundless (in Phys. 23. 21; 458. 23; 11 A 13 DK). No information has been
preserved on what the cosmic structure was like according to Thales.
12
7). Now, the transformations of water are observable. We can see boiling water evaporating or
snow melting. But we do not see how air condenses into water or rarefies into fire – all the more
so since Anaximenes’ air is said to be invisible (A 7). Further, Anaximenes could hardly imagine
that air can turn into stone unless he were already familiar with the idea that water does so – and
this idea is referred to as widely accepted by Melissus (B 8 DK), and is indeed accepted in
Anaxagoras (B 16) and the Pseudo-Aristotelian Problems (937 a 11). I conclude that the idea of
all-embracing transformations was originally formulated in connection with water rather than air
and, accordingly, by Thales rather than Anaximenes.
Attention to the processes of transformations that involve water and air is attested already
in Hesiod’s Works and Days (548 ff.): “And at dawn a fruitful mist is spread upon the fields of
blessed men: it is drawn from the ever-flowing rivers and is raised high above the earth by windstorm, and sometimes it turns to rain towards evening, and sometimes to wind when Thracian
Boreas huddles the thick clouds.”
The subject of Xenophanes’ utterance in the above cited fragment (B 27 DK) is
everything (cf. 21 B 29 DK: “All is earth and water that is grown and sprouts”). Again,
Anaximander’s Apeiron and Anaximenes’ air are both described in the testimonies as the origin
of all things, and I see no reason to assume that the approach originated with Anaximander and
not with Thales.22 The idea of taking all things into consideration brings us back to the motif of
transformations. If the issue were only what is the oldest, first thing, such an oldest or first need
not have been the origin of all things. But if we have a common origin of all things, and don’t
believe that things come out of nothing, it follows logically that we have a process of
transformations.
The effect of Thales’ thesis
The result obtained by Thales has also been interpreted up to now in a doubtful way: such
characterizations as ‘a guess’, ‘a philosophical’ as well as ‘scientific belief’ make us perplexed
as to the effectiveness of Thales’ initiative. To say that he abandoned mythic formulations is of
course true but also not very helpful: one would infer from many scholarly accounts of Thales’
achievement that any nonsense said about nature without reference to the gods constitutes
philosophy or science, or both. But now Thales’ water thesis can be seen differently – not as just
another version of either Egyptian or Babylonian cosmogony, not even as an assertion based on
an arbitrary and extravagant assumption of unity behind such obvious diversity, but as the
reasoning that takes into account that principle which, being a generalization of human
22 Classen underlines similar universalism in another thesis that is ascribed to Thales, "everything is full of gods."
See C. J. Classen, "Thales", 941.
13
experience, is the foundation of common sense and of causal explanations, namely: something
cannot appear out of nothing. Further, it was reasoning about the origins of things that managed
to meet the problem of an infinite regress.
Thales discovered a way, and perhaps the only fruitful way, of discussing both the origin
of things and nature as a whole. The particular ‘origin’, such as water, can certainly be identified
as something different. But if we refuse to accept the homogeneity and unity of the material
world derived from the ‘origin’ through transformations, we must postulate the existence of a
part of the world that appeared out of nothing. On the other hand, without transformation (in that
broad sense of the word which may include the compositions and decompositions of atoms) we
will not be able to reconcile the unity and the diversity of things, the eternity and indestructibility
of nature as a whole with the obvious fact that many things are destroyed and disappear.
Thales discovered an approach that was open to development and improvement. His
water thesis not only introduces a logical scheme that overcomes the problem of the regress into
infinity, but also points to observable processes. Now the number of observations can be
increased and some of them can be interpreted differently. Those who want to make sure that
Thales is right or provide a better answer, receive stimulus for making observations and a basis
for incorporating their observations into the system. Thales’ thesis establishes the links between
specific properties (properties of transformations), and a particular bearer of these properties.
When discussing the thesis, it is possible to ask whether water is a specific bearer of these
properties, and if not, then whether it would be better to choose something else (as Anaximenes
chooses air with its condensation and rarefaction) – which involves, in turn, new aspects of
transformation processes to be considered.
So thought moves from one problem situation to another. Apart from other things, this
creates an important psychological mechanism for research activity: satisfaction derived from the
effectiveness of one’s efforts, indicated by a possibility of gradual advancement.
Thales’ approach to the cosmogonic problem was so fruitful that even problematic points
of his particular solution proved heuristically fruitful. There are several difficulties inherent in
Thales’ water thesis. If all things came to be out of water, this apparently means that there was a
time when there was nothing except water. But how is it possible, if water needs a reservoir or
container? Again, we are told that Thales’ earth rests on water (from which it emerged). Upon
what does water rest? One should not, of course, share belief of Aristotle (De Cael. 294 a 28; 11
A 14 DK) that Thales failed to recognize this difficulty. Thales would probably have replied:
what would then be the support for such a container? Upon what does this rest? Yet Thales
himself or his admirers were hardly happy to admit a limitless expanse of water. Anaximenes
substituted air for water, and this was a brilliant solution. Invisible, but proven to exist and resist
14
pressure in an inflated skin, Anaximenes’ air needed neither container nor support.
Some other difficulties involved were less specific, so they caused a long lasting, but
again fruitful discussion. Thales’ thesis left it unclear why the cosmogonic process should have
begun at all, since there was nothing other than water to trigger it. Thales would possibly have
replied that endless time is a sufficient explanation for something particular to happen one day.
Traces of geological catastrophes suggested to his followers a plausible solution in Thales’ own
style: a cycle of ever-recurring composition-and-destruction of the world was introduced, clearly
attested already by Xenophanes (A 33 DK). However, Parmenides pressed a difficult point: what
need would have driven the cosmogonic process to start “later rather than earlier” (B 8. 9-10
DK)? One may argue that major fifth-century systems are designed to take this problem into
account. According to the Atomists, the compositions and decompositions of atoms in infinite
space and time produce innumerable worlds. So one need not bother with the question why our
world began to grow at one moment rather than another if such things happen, so to speak, every
day. Empedocles minimizes the difficulty by assuming an eternal cycle of alternating structuring
and decomposition of the universe, so the cosmogonic start does not differ much from the
beginning of a season. Hippasus and Heraclitus combined a cyclical model with the idea of a
“definite time” for each phase of the cycle, with the idea of the world changing “according to
Number”. Anaxagoras introduces a special agent to trigger the cosmogonic process, calling it
Mind; thereby he makes the question of why at some particular moment inappropriate, for Mind
possesses a superior wisdom and thus knows, even if we do not, what particular moment is right
to start the cosmogonic process.
Again Parmenides, while considering the difficulties intrinsic in the approach Thales and
his followers employed regarding the cosmogonic process, arrived at the conclusion that change
is impossible. Heraclitus’ emphasis on flux (for the idea of constant transformation is already
implicit in the theories of the Milesians) can be seen as a solution to the problem, emphasized by
Parmenides, of how the process of change could begin. Heraclitus’ solution was that it never
began and it will never stop, since it is eternal and constant.
I would like to emphasize that it was Thales who opened up the possibility for critical
discussion in the field and the corresponding development of ideas. For one can hardly imagine
critical discussion between the adherents of different mythological stories, the one who says that
Chaos came first and the other who says it was Tiamat. Nor do I find very promising the
possibility of critical discussion among people disagreeing about whether it was water, or air, or
fire, or earth that came first in the world. They could with a comparable success discuss the
question which of the colors was the first to become visible – yellow, red, white or black. In
Thales’ construction, however, at one end are general premises that are commonly shared
15
(nothing comes out of nothing), and at the other end – a reference to particular experience
(transformations and circulation of water), the understanding and significance of which could be
reinterpreted.
Philosophy or science?
The task of Thales was to express a convincing assertion about something that no one had
seen or would ever see – the origin of the things in the world. A convincing assertion about the
unobservable needed to be rationally grounded, justifiable, and this was achieved by combining a
commonly shared premise (nothing is generated out of nothing) with commonly observable
phenomena (the transformations of water). The observable phenomena were assumed to have
been relevant to the past, while the problem of infinite regress pressed one to indicate something
that exists always. Cosmogony thus turned out to be inseparable from cosmology and Thales
became the author of the first theoretical postulate in the history of natural science: all things are
modifications of water, whether or not he formulated this principle explicitly. He also became
the author – implicitly, it is true – of the first general principle in the history of philosophy: the
unity of being.
In his highly stimulating essay, Jaap Mansfeld maintains that Thales was probably the
founding father of science, but certainly not of philosophy. He argues that philosophy begins
with Parmenides and in part with Heraclitus, for it is reasonable to take ‘philosophy’ as “those
activities and procedures which, at the moment, are assumed to be philosophical by the large
majority of professionals, and to exclude from consideration what is outside the field worked by
these professionals”. Since physics nowadays is no longer part of philosophy, “we should no
longer call the earliest Presocratics by the name of philosophers, but rather by that of
scientists”.23
Mansfeld is right to emphasize the scientific dimension of the activity of Thales and the
earliest Presocratics.24 It is clear, however, that Mansfeld refers to the practice of a quite peculiar
epoch in the history of philosophy and that physics was a part of philosophy for many
philosophers (rather than ‘professionals’) of previous generations. Further, I readily admit that
present-day philosophers would typically not bother themselves with the problem whether all
things derive from one, but I doubt that they will call this problem scientific rather than
philosophical. Furthermore, Thales assumes that there is something that exists always – his
23 Jaap Mansfeld, “Myth, Science, Philosophy: A Question of Origins”, in his Studies in the Historiography of
Greek Philosophy (Assen; Maastricht 1990) 1-21.
24 Similar view is expressed by Malcolm Schofield, in C. C. W. Taylor (ed.), Routledge History of Philosophy
(London; New York, 1997) 1, 47 ff. and (for Thales) by Stepen White, “Thales and the Stars”, in V. Caston and D.
W. Graham (eds.), Presocratic Philosophy. Essays in Honour of Alexander Mourelatos (Aldershot 2002) 3-18.
16
‘water’. Water, as an observable object, belongs clearly to the domain of science – but not the
principle of its eternal existence – a principle that is at variance with all established facts of
experience and achieved by purely logical reasoning.25 It is also not to be overlooked that Thales
suggested a new Weltanschauung according to which nature functions on its own, without the
intervention of the gods, and is subject to large scale regular processes. One usually speaks about
‘philosophy’ in such cases, and we will see in due course that the double identity of Thales and
his followers as philosophers and scientists is possibly their essential characteristic.
What motivated Thales’ approach and solution?
So far we have considered Thales’ problems and his solution; let us now involve
historical and psychological considerations as well.
The problem of a convincing assertion about cosmogonic matters could hardly occur
before contradictory versions confronted human minds; in this respect an acquaintance with
various Oriental cosmogonies could have played an important role.26 Also the publication of the
Theogony was of special importance. Hesiod’s initiative was taken up with characteristically
Greek competitiveness: we hear of theogonic constructions by Alcman (P. Oxy. 2390; fr. 5
Campbell), Alcaeus (fr. 327 Campbell) and Sappho (fr. 198 Campbell). Yet this very fact shows
that Thales’ solution was not predetermined by the encounter of divergent accounts of the initial
stage of the world. The idea of a convincing assertion required an additional motivation. One
cares about being convincing when one desires recognition by others. For one who was not a
poet, offering a convincing assertion was the only way to achieve public recognition of one’s
wisdom.
Both the search for new knowledge and the concern for recognition seem to me inherent
in Thales’ approach. For his solution to the cosmogonic question was not the only logical
possibility. It was, perhaps, natural that one familiar with various theocosmogonies recognized
the problem of an infinite regress; it is remarkable and yet not too surprising that one suggested
defining the oldest as that which was not born. But several options were open after that. One
might conceive never born matter along with a never born Master, or assume that the Master
emerged from the original stuff, if living beings did emerge from it at all events. One might
25 Those scholars who maintain that Parmenides discovered the independence of thought exaggerate. Parmenides
made the next (though, as it happens, very important) step. He was the first to argue something that was in striking
contradiction to the evidence of the senses. (Yet Parmenides still depends – and fortunately so – on such data of
experience as the recognition of the principles that nothing comes out of nothing and nothing happens without a
cause.)
26 Emphasized by Kurt von Fritz, “Der Beginn universalwissenchaftlicher Bestrebungen und der Primat der
Griechen,” Studium Generale, 14 (1961) 546-583, and his Grundprobleme der Geschichte der antiken Wissenschaft
(Berlin; New York 1971); also see Karl Popper, “The Myth of the Framework”, in Essays in Honour of A Schilpp,
ed. by Freeman E. La Salle (1976) 23-48.
17
postulate two rather than one sources of things or make one source inexhaustible so that there
would be no need to refill it. Thales avoided these possibilities, I suppose, because with them he
would hardly have impressed his audience – audience of the equals, ready to ask Thales why
they should believe him. To admit that the source is inexhaustible would be practically the same
as to admit generation out of nothing. Moreover, a one-way process of generating an everincreasing amount of things in the world would be counter-intuitive and would contradict
common experience. Furthermore, a mechanism of generating things (as opposed to living
beings) would be still required. To admit two sources, a scheme familiar from generation of
living organisms, would further imply an extra assumption – something that a person who
referred to transformations no longer needed. To admit an acting Master of things would mean
losing ground in competition between various proposals. Nothing in human experience indicates
that such a Master is possible. If he is to be accepted, then everything may be accepted, and one
explanation is no better than another. On the contrary, Thales makes his water thesis as far as
possible subject to critical examination. For having discussed things with people of equal social
status, he had to find things out: there is no recognition of an intellectual achievement, where no
examination is possible.27
On the other hand, there needed to be a readiness to accept a world picture compatible
with Thales’ solution to the cosmogonic question. Thales’ thesis could be advanced and could
contribute to its author's fame only in a social milieu that no longer tended to connect hopes and
fears with the interference of supernatural forces – a state of mind that one may recognize in
Mimnermos (fr. 8. 4-5 Gentili – Prato).28
But even that was probably not enough. One has to realize how extraordinary and how
bold Thales’ innovation was. He offered a responsible statement about something that he did not
see, that nobody saw and nobody could see; and, as if this were not enough, his statement
implied a new world outlook. There must have been something in his audience – a kind of
experience – to allow Thales to formulate his claim. Moreover, Thales himself must have
possessed a kind of experience that made him believe that he might be able to understand matters
that, one would think, are beyond the grasp of a human being. I will try to show in the next two
chapters that what he possessed was experience of an extraordinary scientific achievement and
that before removing the gods from cosmogony, which could not be the subject of direct
investigation, Thales eliminated them from their positions in cosmology.
27 Of the Nile floods
28
We
leave,
poet
says,
without
knowing
from
the
gods
either
evil
or
good
(     //  ). Archibald Allen, The Fragments of Mimnermus (Stuttgart 1993)
44 f. may be right that the talk is about the years of youth. However, Mimnermus does not say that in mature age, as
we are getting wiser, we turn to thinking about the gods.
18
Supplementary Notes
The alleged anticipation of Thales in Homer’s Okeanos passages
Many readers of Homer, both ancient and modern, regarded Il. 14. 201 (repeated at 14.
302) and Il. 14. 246 to be references to Okeanos as the origin of the gods (all the gods) and the
origin of all things, and so as an anticipation of Thales’ cosmogony and cosmology. Such an
understanding seems to me wrong.
In Il. 14. 246  points to  (streams), which has a clear parallel in Il. 21.
194-197. Moreover,  as neuter (referring to all things) would be unprepared and
without parallel, which would be strange for such a strong assertion. It is also strange that a
characterization proper to the highest deity (“the source of all things” or, on the other popular
interpretation, “of all the gods”) should have been applied to Okeanos precisely in a context (14.
244-248) in which the superiority of another deity, Zeus is emphasized. Thus Okeanos is said to
be the source of all the stream-gods.
The two passages of Book 14 seem to belong to a whole. Then  of line 201 (=302)
means just the stream-gods. As we learn from Il. 21. 194-197 (cf. Hes. Theog. 337-370),
Okeanos is the father of plenty of gods. Therefore he deserves the appellation  ,
which certainly need not mean “the source of all the gods”.29
The poet chooses the unusual  rather than  because the stream-gods are
gods of a special kind, for the rivers and streams are observable and palpable. The choice of the
word possibly indicates that the poet is careful about the difference between the realm of things
and the realm of persons, even when speaking about the divine powers. When Hera says that she
is disturbed by the endless strife between Okeanos and Tethys, so that they have avoided the
marriage-bed and love now for a long time (14. 205-207), it may reflect curiosity concerning the
fact that so many rivers and streams came to be once upon a time and so few if any come to be
now. In that case, there is still no anticipation of Thales’ train of thought, yet we have a hint of
that intellectual atmosphere which was conducive to inspire Thales and make his solution
welcome.30
Emergence-and-return in the Upanishads
One reads in the Chāndogya Upanishad (1. 9. 1):
29 As, for instance, the Ida mountain, called   (14. 283 at al.), is hardly thought to be the mother and
source of all animal life on earth.
30 For a more detailed discussion see Dmitri Panchenko, “The Iliad 14. 201 and 14. 246 Reconsidered”,
Hyperboreus 1 (1994) 1, 183-186.
19
‘What is the goal of this world?’ He replied, ‘Space, for all these creatures are produced from
space. They return back into space. For space is greater than these. Space is the final goal.’
Two similar passages appear in the Maitrī Upanishad (6. 14 and 17):
From time all beings flow, from time they advance to growth; in time they disappear.
Verily, in the beginning this world was Brahman, the infinite one, infinite in the east, infinite in
the south, infinite in the west, infinite in the north and above and below, infinite in every direction. For
him, indeed, east and the other directions exist not across, nor below, nor above. Incomprehensible is this
highest Atman – boundless, unborn, unimaginable, unthinkable this Atman of space … All that thinks
thinks because of him, everything disappears in him.
An independent parallel development seems to me unlikely. The dates of the Upanishads
are uncertain. There is nothing to show that any of them was composed as early as the sixth
century BC (though, of course, even earlier dates have been repeatedly suggested). As we saw,
the principle of emergence-and-return was developed in order to explain the coming into
existence of the material world. Since there must be an obvious connection between things as we
know them and their supposed source, such a source must have originally been thought to be
material itself – like Thales’ water. It would be strange if the principle of emergence-and-return
was originally conceived of in connection with space or time, or Being (Brahman). Logically, the
formulations found in the Upanishads are echoes and rearrangements of an earlier idea. The
principle of emergence-and-return is intrinsically connected with the principle of unity of things
and the principle of the conservation of the total amount of things. The authors of the Upanishads
used the Milesian way of thought to postulate ties of kinship between Being (Brahman) and the
Self (Atman) and to justify by that the hope that we may not die. One can easily point to an
intermediary development that bridges the idea of Thales with similar ones in the Upanishads: I
mean the Boundless of Anaximander and the Boundless Air of Anaximenes. The diffusion of
ideas from Ionia to India presents no real difficulty.31
31 See: D.R. Bhandarkar, Lectures on Ancient Indian Numismatics (Calcutta 1921) 24-32; A.K. Narain, The Indo-
Greeks (Oxford 1962) 1-5; cf. however: Paul Bernard, Fouilles d’ Aï Khanum. IV = Mémoires de la délégation
archéologique française en Afghanistan. T. 25 (Paris 1985) 19-32, 159-160. For a particular hypothesis of
transmission see: Dmitri Panchenko, “The City of the Branchidae and the Question of Greek Contribution to the
Intellectual History of India and China”, Hyperboreus 8 (2002) 2, 244-255. For a larger context see my “The
Phenomenon of the Achsenzeit”, in Drevnij mir i my (St Petersburg 2003) III, 11-43 (in Russian). A recent
interesting book addresses various similarities between the Presocratics and the Upanishads in respect to ‘the
problem of the One and the Many’: Thomas McEvilley, The Shape of Ancient Thought: Comparative Studies in
Greek and Indian Philosophies (New York 2002) 23–66. McEvilley is prone to accept Indian influence upon the
Presocratics for the reason of the surprisingly rapid transition “from polytheism through Orphic pantheism to
20
Animated water
Thales’ water was probably animated. Thales regarded the soul as the source of motion,
as follows from the fact that he believed a magnet to possess a soul because it is able to make
iron move.32 The ability of a magnet or amber to attract objects seems to indicate that even
apparently inanimate things can in fact have a soul. Indeed, soul is present in everything (Aristot.
De an. 411a7=11 A 22 DK). But everything is a modification of water. One infers that water is
not deprived of a soul either. This is all the more so since Thales had to consider water as the
source of life – for what else could be? Characteristically, both Aristotle and Theophrastus take
the view which makes water the source of life as suggesting itself; they cite corresponding
observations and accordingly conjecture that this was Thales’ reason for choosing water rather
than anything else as the arche (11 A 12; 13 DK). Now water existed always, from which it
follows that it is immortal. Everything that is immortal is, for a Greek, divine. Therefore
“everything is full of gods” (11 A 22 DK) and souls are immortal (D.L. 1.24=11 A1 DK).
According to Choerilus, Thales was the first to maintain that “souls are immortal” (11 A
1. 24 DK; the Suda s. v. ‘Thales’ has the formulation in the singular: “the soul is immortal”).
However, Ion of Chios connects with the wisdom of Pythagoras the hope than one’s soul will
live happily even after one’s death (36 B 4 DK). I suggest that the contradiction is only apparent
and that there is an essential connection between teachings of Thales and Pythagoras. Pythagoras
had in mind our personal souls, which means that we are in a way immortal – an exciting
revelation. Pythagoras taught that our souls do not die but migrate into another body.
Thales’ formula of emergence-and-return implies the principle of conservation: no thing
perishes into nothing, no thing is annihilated completely. As water cannot be annihilated, neither
can the soul that is inherent in water. Pythagoras applied Thales’ way of reasoning to our
personal souls. No soul came to be out of nothing, and no soul will turn into nothing. There will
be an eternal cycle of migrations, not dissimilar to the eternal circulation of water and its
derivatives. That is how, I guess, Pythagoras arrived at his doctrine of metempsychosis.
My hypothesis does not preclude the role of additional sources of inspiration – for
instance, from Egypt, where concern with the afterlife was so conspicuous. But it is hardly
compatible with the idea that the doctrine of metempsychosis was borrowed from India or that it
was a parallel independent development. The doctrine was a newcomer in both the Greek world
philosophical monism” in the Greek world (61). Since he overlooks the significance of the emergence-and-return
formula and the whole logic of Thales’ solution, he does not see that the transition to philosophical monism was
necessarily abrupt. It is characteristic that the gradualism assumed by McEvilley contradicts the actual course of
events, for Orphism came later than Milesian philosophy.
32 Aristot. De An. 405a 19; 11A 22 DK; Cf. H. Cherniss, Aristotle's Criticism, 296 and n. 26; J. Barnes, The
Presocratic Philosophers, 6ff.
21
and India. One cannot make a strong argument from its success and spread in India – the story of
the Buddhism inside and outside India is instructive. The doctrine of metempsychosis seems to
me a particular development of Thales’ teaching. That it took place in the Greek world rather
than India is clearly an easier assumption. Nor do I find much help in references to the fact that
the belief in the migration of a human soul into the body of an animal is attested by various
peoples. The Pythagoreans, the Orphics, and the Indians speak of the eternal cycle of migration,
which points to a philosophical origin of the idea.
Thales and the circumnavigation of Africa by the Phoenicians
There is a famous story in Herodotus (4. 42) of how the pharaoh Necho sent the
Phoenicians to circumnavigate Africa, starting from the Red Sea, and how they succeeded in
performing such a difficult task. The authenticity of the story has sometimes been doubted, but
no strong objection against it has ever been advanced. Necho’s reign falls in 610–595 BC. I
believe that Thales dared to formulate his water thesis in public after he acquired the reputation
of being an extraordinary person because of his successful prediction of a solar eclipse in either
585 or 582 BC (see below), that is, after the circumnavigation. Part of our tradition speaks
vaguely of a Phoenician ancestry of Thales. However, it has been repeatedly observed that the
name of Thales’ father, Examyas, does not confirm this claim. Whatever his relation to
Phoenicia, a Milesian such as Thales could easily have gotten information about a recent
circumnavigation of Africa at various occasions and places, and in particular in Egypt – whether
from the Egyptians or Phoenicians.
What lesson might have been drawn by Thales from the circumnavigation of Africa?
That it is likely that the earth is surrounded by a body of water – as is in Homer and in agreement
with what the Phoenicians claimed about the extension of the sea to the east, south, and west of
Africa. This made the idea that earth rests on water much more credible.
A person endowed with the curiosity of Thales could hardly fail to obtain more
knowledge from the Phoenicians about the surrounding body of water. I mean knowledge of
ocean tides. Thales must have been impressed by accounts of the rhythmic alternation of high
and low water. This will have sounded striking yet also agreed with what is observed on the
shores, on a much more minor scale, of the Aegean Sea. It was clear from the accounts (and
again, agreed with observations on the shores of the Aegean Sea) that the process was not caused
by the winds. The question arose, then, caused by what? The only natural hypothesis was that a
source of motion was contained within the body of water itself.33 We have seen that source of
33 The Phoenician settlers in Spain could have observed some (not very clearly patterned) correspondences between
the oceanic floods and the phases of the moon. However, it is not the case that floods reach its maximum along with
22
motion was called by Thales ‘soul’.
It seems to follow that both the idea that the earth rests on water (attested in the sources)
and the idea that water is animated (plausibly reconstructed from the evidence) were
significantly (of course only partly) rooted in the related data of experience.
One more comment is appropriate. Thales’ views were far more systematic than many
scholars believe they were. However scanty the information about Thales' ideas might be, they
often form complexes. For instance, his statement that earth is supported by water (Aristot. De
Cael. 294 a 28 ff.; 11 A 14 DK) is connected with his statement concerning the nature of
earthquakes: they happen because of the motion of the water (Ps.-Plut. Plac. 3.15.1) upon which
the earth rests like a huge and heavy ship (Sen. Nat. Quest. 3.14, 6.6; 11 A 15 DK).34 Another
complex is formed around the evidence concerning Thales' views on the nature of the soul.
Whether one accepts or denies the connections suggested above between this complex and the
complex of ideas related to water, Thales’ approach remains in any case highly systematic.
THALES’ EXPLANATION OF SOLAR ECLIPSES
The history of Greek science starts with an event which looks too emblematic to be true. We are
told about a prediction of a solar eclipse, made by a person who appears in our sources as the
founder of Greek astronomy, geometry and philosophy: Thales of Miletus. He perceived, it is
said, the cause of solar eclipses, he calculated the ratio between the size of the sun and its orbit,
he was able to determine the distance to a ship in the sea and the height of a pyramid, and he was
the first to formulate several theorems. We are not therefore surprised to hear that he received
public recognition by the Greeks as a Sage. One would rather wonder whether one should
believe in all, or any, of the achievements of this Thales.
Yet we will see that the evidence for all these facts is essentially reliable.
We will also see that Thales’ preoccupation with eclipses in particular played an
indispensable role in the intellectual development he gave rise to, and that we may safely select
the decade of 580s BC as the time when Greek and thereby all theoretical science was born.
waxing moon and its minimum with waning moon. A theory connecting the tides with the phases of the moon could
have been formulated only in the context of already existing science.
34 A comparison of the earth to a ship, preserved by Seneca, was most convincing: one could clearly see in the
example of a loaded and crowded ship how the things which were in themselves heavy and non-buoyant could,
when brought together (and forming, one would think, an even heavier mass), nevertheless be supported by water.
23
Ancient tradition versus the modern scholarship
Tradition has attributed to Thales the explanation of solar eclipses. We are told that
Thales explained these phenomena as being caused by the interposition of the moon between an
observer and the sun. Such is the assertion of many ancient writers, and this assertion is
contradicted by no ancient authority. If what the ancients say is true, Thales’ theory of solar
eclipses is the earliest scientific theory known to history.
While the ancients unanimously credited Thales with the essentially right explanation of
solar eclipses, modern scholars almost unanimously reject this tradition. Scholars argue that
evidence for it contradicts trustworthy testimonies of Anaxagoras’ priority in the field; and that
Thales could not have an essentially correct theory of solar eclipses, as is recorded, if succeeding
Ionian philosophers adopted ridiculous ones; they assume that all reports to the contrary are just
inferences from the story of Thales’ prediction of a solar eclipse.333555 Nevertheless, a critical
examination of the evidence leads to the conclusion that Thales undoubtedly had a theory of
solar eclipses; moreover, he held an essentially correct view. In other words, the ancient tradition
is right, while modern scholars have overlooked a crucial event in the entire history of theoretical
science.
Evidence
One can single out six assertions related to the evidence for Thales’ theory of eclipse. (1)
Thales “discovered the solar eclipse”; (2) the solar eclipse, according to Thales, is caused by
the interposition of the moon; (3) the moon is a body of earth-like nature; (4) the moon derives
its light from the sun; (5) the cause of solar eclipses is indicated by the day of their occurrences,
and one of the conventional names for this day is “the thirtieth”; (6) the term “the thirtieth day”
became conventional due to Thales.
It is clear that all these assertions are logically connected and mutually supportive.
The testimonies are as follows.
(1) Eudem. fr. 145 Wehrli (11 A 17 DK):
 (sc.  )  
“Thales was the first to discover the eclipse of the sun”.
35 Boll, “Finsternisse”, RE, VI (1909) 2329-2364; T. Heath, Aristarchus of Samos the Ancient Copernicus (Oxford
1913) 18: “if he had given the true explanation of the solar eclipse, it is impossible that all the succeeding Ionian
philosophers should have exhausted their imaginations in other fanciful explanations such as we find recorded”;
Burnet, Early Greek Philosophy, 41; Guthrie, A History of Greek Philosophy, I, 49; Kirk in The Presocratic
Philosophers, 82: “The cause was unknown to Thales' immediate successors in Miletus and, therefore, presumably
to him. If the contrary was implied by Eudemus ... then Eudemus was guilty of drawing a wrong conclusion from
the undoubted fact of Thales' prediction”.
24
cf. Schol. Plat. Rep. 600 A (11 A 3 DK):
       
“For he discovered that the sun suffers eclipse from having the moon running under it”.
(2) Aristarch. Sam. (P Oxy 3710 col. II 36-43; vol. 53 (1986) 97 Haslam):
                
             
         

  Haslam (indicating the space for c.6 more letters);
     Rea (in Haslam);
     Lebedev;
     Burkert3366
____________________
“That the eclipses happen at new moon is explained by Aristarchus of Samos who writes: ‘Thales
said that the sun suffers an eclipse when the moon comes to be in front of it, to which points the
(very) day when the sun suffers eclipses. Some people call this day the thirtieth and other people
call it the new moon.”
Cic. Rep. 1. 16. 25 :
Atque eius modi quiddam etiam bello illo maximo quod Athenienses et Lacedaemoni summa
inter se contentione gesserunt Pericles ille et auctoritate et eloquentia et consilio princeps civitatis suae,
cum obscurato sole tenebrae factae essent repente Atheniensiumque animos summus timor occupavisset,
docuisse civis suos dicitur, id quod ipse ab Anaxagora cuius auditor fuerat acceperat, certo illud tempore
fieri et necessario, cum tota se luna sub orbem solis subiecisset; itaque etsi non omni intermenstruo,
tamen id fieri non posse nisi certo tempore. Quod cum disputando rationibusque docuisset, populum
liberavit metu; erat enim tum haec nova et ignota ratio solem lunae oppositu solere deficere, quod
Thaletem Milesium primum vidisse dicunt.
“And a similar story is told of an event in that great war in which the Athenians and
Lacedaemonians contended so fiercely. For when the sun was suddenly obscured and darkness reigned,
and the Athenians were overwhelmed with the greatest terror, Pericles, who was then supreme among his
countrymen in influence, eloquence, and wisdom, is said to have communicated to his fellow-citizens the
information he had received from Anaxagoras, whose pupil he had been – that this phenomenon occurs at
fixed periods and by inevitable law, whenever the moon passes entirely beneath the orb of the sun, and
36 Walter Burkert, “Heraclitus and the Moon: The New Fragments in P.Oxy 3710”, ICS 18 (1993) 49-55, esp. 50, n.
8 relates the text to Herodotus’ account of Thales’ prediction of a solar eclipse, where  (‘the limit’) is a year,
and assumes that Aristarchus the astronomer “makes astronomical sense, tacitly correcting Herodotus”. But in such
a case (not very likely in itself) we would expect something like “indicated the day” and certainly not “indicated the
limits of the day” (Burkert’s translation).
25
that therefore, though it does not happen at every new moon, it cannot happen except at certain periods
(of the new moon). When he had discussed the subject and given the explanation of the phenomenon, the
people were freed of their fears. For at that time it was a strange and unfamiliar idea that the sun was
regularly eclipsed by the interposition of the moon – a fact which Thales of Miletus is said to have been
the first to observe” (C. W. Keyes’ translation).
Ps.-Plut. Plac. 2. 24 and practically the same text in Stobaeus, Eusebius and Ps.-Galen (Dox.
353, 627; 11 A 17 a DK; Eus, Praep. Ev. 15. 50):
            
  
(Some manuscripts have  instead of .)
“Thales was the first to say that the sun suffers eclipse when the moon, which is earthy by nature,
comes perpendicularly beneath it”.
See also Schol. Plat. Rep. 600 A (above).
(3) Stob. Ecl. 1. 1. 26 (Dox. 356, quoting also a similar text by Theodoretus):
    
“Thales maintained that the moon is earthlike”.
See also testimonies quoted or referred to above, under (2).
(4) Ps.-Plut. Plac. 2. 28 (Dox. 358; 11 A 17 b DK):
          
“Thales and his followers: the moon has its light from the sun”.
Stob. Ecl. 1. 26. 2 (Dox. 358; 11 A 17 b DK):
          
  
“Thales was the first to assert that the moon has its light from the sun. Pythagoras, Parmenides,
Empedocles, Anaxagoras, Metrodorus shared this view”.
(5) See the testimony of Aristarchus, above, under (2).
(6) Diog. Laert. 1. 24 (11 A 1 DK):
        
________________
  Scaliger
________________
“He was the first to give the last day of the month the name of Thirtieth”.
26
What is the value of these testimonies? The importance of the one by Aristarchus37 is
obvious: it comes from a competent professional and from a relatively early epoch (the first half
of the third century BC).
Eudemus of Rhodes, a disciple of Aristotle and the first historian of science, is usually
regarded as the best source on the subject.333888 Unfortunately, we do not have a direct quotation
from Eudemus' statement about Thales. The phrase quoted above is a part of a concise exposition
of Eudemus' information concerning the major discoveries in the history of astronomy, which
was derived by Theon of Smyrna from some other writer.
The imprecise formulation
“discovered the solar eclipse” has been the cause of divergent interpretations. Yet everything
points to the conclusion that it is an explanation of the phenomenon rather than the prediction of
a solar eclipse that is intended by the text. Putting aside for a moment the assertion itself, Theon's
summary gives a list of several facts and allegedly correct theories established by several
thinkers (Oenopides, Anaximander, Anaximenes, etc.); it has no reference to any predictions. If
a prediction was meant, it would have been easy and natural to express this unambiguously, as in
the case of references to Thales’ prediction, on the authority of Eudemus by Clement of
Alexandria and Diogenes Laertius (fr. 143, 144 Wehrli).333999 And – this point is decisive – we have
a parallel text in a scholium on Plato's Republic that does clarify what Thales ‘discovered’ about
the solar eclipse: he “discovered that the sun suffers an eclipse by the interposition of the moon”.
Thus the idea that Thales had a theory of solar eclipses is attested by the best authorities,
Aristarchus and Eudemus. It also follows from the testimony of Aristarchus and the combined
testimonies of Theon and the scholiast on the Republic that these authorities agree that Thales
connected the solar eclipse with the interposition of the moon. The doxographic writers
unambiguously confirm all this, though it is not clear whether their consensus goes back to
Theophrastus or to a later authority.
It is, furthermore, highly implausible that the idea of Thales having had an explanation of
solar eclipses arose as an inference from the story of the prediction, since the mere recognition of
the role of the moon in the phenomenon does not enable one to predict a solar eclipse.
It is also significant that there is no alternative candidate in our sources for introducing
the theory explaining solar eclipses by the interposition of the moon. No school of philosophy
made its claim. It was apparently regarded as known who had introduced this theory.
37 For this see: Andrei V. Lebedev, “Aristarchus of Samos on Thales’ Theory of Eclipses”, Apeiron 23 (1990) 77-
85.
38 See now the collection of essays: István Bodnár, William W. Fortenbaugh (eds.), Eudemus of Rhodes = Rutgers
University Studies in Classical Humanities, Vol. XI (New Brunswick; London 2002).
39 It is difficult to comprehend why many scholars assume that Eudemus spoke either about Thales’ prediction of a
solar eclipse or about its explanation and not about both.
27
Now neither Aristarchus nor Eudemus (as we have it), nor Cicero makes Thales assert
that the moon is an earthy body and that it borrows its light from the sun. It is pretty easy to
imagine that a basically correct statement like “the interposition of the moon causes an eclipse of
the sun” could be expanded into a detailed and correct statement which would explain how the
moon, apparently a luminous body, can cause the darkness accompanying a solar eclipse and
what is the nature of the moon’s light if it has none of its own. So points (3) and (4) of the
testimonies are suspect. We need not discuss here whether this part of the evidence is authentic
or wrong. We need only emphasize that the points (1) and (2) of the theory are perfectly possible
without (3) and (4). The moon is never seen at the junction of two lunar months. Thus at the only
time when a solar eclipse can occur the moon does not appear as a luminous body. Whatever the
nature of lunar light, the moon can screen the sun at such time without showing itself.
An examination of suggested objections
The frequently stated view according to which it was Anaxagoras who advanced the right
explanation of solar eclipses is simply an error. No ancient authority makes Anaxagoras the first
to explain solar eclipses.444000 Those very testimonies which emphasize the merits of Anaxagoras in
matters related to eclipses mention that the explanation of solar eclipses had been advanced
before him (Plut. Nic. 23) and explicitly name Thales (Cic. = T 2. 2, above).
The other argument against the evidence for Thales’ priority contrasts Thales’
precociously mature theory with the naive theory of Anaximander and other Ionian thinkers.
This argument is unconvincing on several counts. First of all, it is based on the assumption that
we know how the Ionians explained solar eclipses. But we do not. ‘Eclipses’ in doxographic
reports on Xenophanes are mostly sunsets. The testimonies on Heraclitus’ views are
contradictory and difficult to interpret. Anaximenes’ explanation of solar eclipses is not recorded
at all.
It is true that our sources ascribe to Anaximander quite an extravagant theory of solar
eclipses. But it is also true that scholars have failed to recognize that the doxographers, who were
not really interested in Anaximander’s antiquated views, have misrepresented them. We are told
that Anaximander’s sun is a wheel or a ring of air filled with fire and that what we see as the sun
is just a small aperture in this wheel or ring. We are further told that a solar eclipse happens
“when the aperture of fire is shut off”. One may concede that the doxographers’ description
suggests something like an automatic oven-door mechanism. But it is hard to invent anything
stranger than such a mechanism. The kyklos of the sun is fire within the envelope of the air. Now
40
There
is
only
a
general
and
imprecise
formulation
in
Hippolytus
(         – Ref. 1.8.10; 59 A 42 DK) where  is
the terminus technicus for lunar phenomena.
28
fire cannot hide the fire; and how can one imagine oven-door-like devices made of air? Would
not such a shutting result in an extinction of fire or in an explosion (cf. 12 A 22 DK)? And how
can an accumulation of air produce the well-defined shapes of the phases of a solar eclipse?
Moreover, a shutting off mechanism is incompatible with the fact that the same solar eclipses are
seen as total by people in one area, as partial in another, and not seen at all in yet another. It is
incredible that Anaximander would not have been aware of this fact. He was born in 611 or a
few years later. The eclipse of 28 May 585 was total for most of Ionia and yet partial in Miletus.
Few if any Ionian traders on the Black Sea north coast would have reported having seen a partial
occultation of the sun on 21 Sep 582, but this could hardly have passed unnoticed in Miletus and
especially in Naucratis, where it was nearly total. The eclipse of 19 May 557 was seen as total in
Miletus or a bit south of it but certainly not in Olbia or Naukratis.
The
original
idea
that
we
may
recover
behind
the
expression
       Dox. 354; 12 A 21) is that the
aperture of the real sun (= the visible sun) is screened, so that we cannot see it during a solar
eclipse.444111 It is not significant for the present purpose whether it was thought to have been
screened by the moon (which is below the sun in Anaximander – 12 A 18; A 11.5 DK) or in
some other way, but we have to take into account that an explanation of solar eclipses could not
be isolated from a thinker’s more comprehensive view of the universe. A system that was more
advanced as a whole might have included weaker solutions to particular problems. If Thales’
moon was earth-like, it was a solid and heavy body. The question that arises in that case is why it
has not fallen down. Anaximander, with his sun and moon composed of air and fire, avoided this
difficulty. There also were other difficulties, the most important of which were removed only by
Anaxagoras.444222 Thus if some of the Ionians did not share Thales’ explanation of solar eclipses,
they might have good (or seemingly good) reasons for that. At the same time it is worth
emphasizing that:
(1) There is nothing in the sky to immediately suggest whether the sun or the moon is
closer to us. One might even think that the sun is closer since its light is hot. Yet we hear of no
Greek thinker who put the moon above the sun (while many Indian thinkers did). All the relevant
evidence indicates that the earlier Ionians already located the moon below the sun (Anaximander
A 11.5, A 18; Heraclitus 22 A 1.10 DK). And the solar eclipse seems the only phenomenon the
explanation of which would require such a sequence.
41 Cf.     in Hdt. 4. 7.
42 Dmitri Panchenko, “Eudemus Fr. 145 Wehrli and the Ancient Theories of Lunar Light”, in Eudemus of Rhodes,
323-336, esp. 332.
29
(2) Greek cosmologists after Thales appear regularly to have a theory of eclipses. Why
must Thales have been an exception to the rule?
(3) The crucial evidence for the explanation of solar eclipses by the interposition of the
moon is the fact that solar eclipses occur only about the time of the new moon. Thucydides (2.
28) bears witness that this proof was recognized in his time by a larger group of educated people,
not by professional astronomers only. But how was this knowledge obtained by the Greeks?
This question, it seems, has never been asked. As soon as it is addressed, one immediately sees
that neither Anaxagoras nor anybody else was in a better position in this respect than Thales.
One cannot typically observe many solar eclipses during one’s life, especially if one does not yet
know that they are to be expected only on particular days. I do not assert that it is entirely
impossible for a single person to discover the regularity in question without having some
preliminary knowledge or without a series of dated eclipse records. If we knew nothing about the
observation of celestial phenomena outside of the Greek world, we would have to admit such an
astonishing scenario. But we do know that dated eclipse observations were carried by
generations of professionals in Mesopotamia at least since 747 BC.43 Moreover, we may safely
deduce from cuneiform sources that somewhere in the seventh century BC the regularity in
question was recognized. The question is then: Who of the Presocratics was in a position to
become acquainted with this discovery? The obvious answer is that all of them were.
As for Thales, he lived in an epoch that was especially conducive to the spread of
astronomical knowledge from Mesopotamia to Ionia. After being under pressure for a long time
by the Babylonians and the Medes, the Assyrian kingdom was not merely defeated but virtually
ruined (626–609 BC). Major cities of Assyria ceased to exist. Many people working for the
Assyrian kings lost their means of subsistence. Some of them would surely have chosen to
emigrate – either to the cities of Phoenicia and Palestine, where they could find a language and
culture similar to their own, or to the court of the pharaoh, the enemy of Babylon, the new superpower.444444 Skillful interpreters of celestial signs given by the gods were welcome everywhere. On
the other hand, an intense power struggle between Egypt and Babylon attracted many Greeks as
mercenaries. Many Greek traders came too. This was an epoch of close contacts between the
Greeks (the Ionians in particular) and Egypt. As a respectable Greek from the most important
43 Abraham J. Sachs, Hermann Hunger, Astronomical Diaries and Related Texts from Babylonia. Vol. I. Diaries
from 652 B.C. to 262 B.C. (Wien 1988) 12: “eclipse reports preserved on tablets go back to the second half of the 8th
century B.C., thus confirming the well-known claim of Ptolemy (Almagest III, 7) that he had at his disposal more or
less continuous eclipse records from the time of Nabonassar (747 – 734 B.C.) onwards”.
44 In 609/608 BC the Assyrian and Egyptian troops fought together against the Babylonian army of Nabopalassar;
this effort to save the Assyrian kingdom was in vain, the allies had to retreat – A. K. Grayson, Assyrian and
Babylonian Chronicles (Locust Valley 1975) 95 f., 212. But what happened with Ashur-uballit, the last Assyrian
king, and the people around him? A natural supposition is that they sought refuge in Egypt.
30
Ionian city, Miletus, Thales could easily have met various people from Assyria or Phoenicia at
the court of the pharaoh Necho (610–595 BC) and his successors.
The significance of Thales’ theory
A solar eclipse is an extraordinary and spectacular event. It was considered in prescientific cultures to be caused by the will of a mighty deity. But Thales no longer speaks of it in
terms of who orders, he addresses instead the question of what causes the event. One of the
major intellectual revolutions in the entire history of mankind took place in sixth-century Ionia: a
new Weltanschauung emerged, call it scientific or what you will. The most important document
of this revolution, Anaximander’s book, has been lost. Yet we know enough to get an idea of the
scale of the transformation involved. Wind and rain, lightning and thunder, earthquakes and
eclipses – all these things were explained by Anaximander as natural phenomena (12 A 11; 2224; 28 DK). He used the same approach to explain the origin of animal and human life (12 A 10;
11 DK) as well as the formation of celestial bodies, the earth and sea (12 A 10; 11; 18; 21; 22; 27
DK).
Anaximander seems to have taken the new Weltanschauung for granted, while our
sources relate the earliest manifestations of this Weltanschauung to his teacher – Thales. This is
logical since a rational explanation of eclipses involves a set of questions about the composition
of the sun and moon, their illumination, their movement and relative sizes and heights; it is the
paramount step in the elaboration of a systematic view of the universe. Moreover,
Anaximander’s theories, however ingenious and sometimes even correct, could not have been
proven and therefore could not unambiguously justify the new approach to phenomena. On the
contrary, Thales’ theory of solar eclipses was repeatedly confirmed since solar eclipses happened
invariably at the time of a new moon. This was the first success and therefore the basic
justification of the emerging theoretical science.
Another justification was provided by Thales’ successful prediction of a solar eclipse. But
before we turn to this fascinating story, we have to answer a pressing question of why the
discovery of regularity in the occurrence of eclipses, made by Mesopotamian observers of
celestial phenomena, did not bring about theoretical cosmology in Mesopotamia itself? Or –
Why did theoretical cosmology emerge in Ionia and not in Assyria or Babylonia?
A plausible conjecture seems available. The fact is that the Babylonian and Assyrian
observers worked for the temples and the kings. They got their bread precisely because they had
something to say about the will of the gods and the signs given by them through the
31
interpretation of celestial omens.444555 Some individuals might have had their doubts, but the group
interest must have effectively prevented the development of thought in the direction of
naturalistic conclusions. If some person outside of the group had tried to use the regularity in
question while speculating about cosmological issues, his efforts would have been easily
dismissed due to the fact that there were competent professionals to form opinions about
everything related to celestial phenomena.
The situation in Ionia was much different. Religious beliefs follow a certain logic. The
gods are supposed to give signs to mighty kings and not to the elected officers of tiny republics.
Accordingly, the Greeks had no professional interpreters of celestial omens and were much more
open to accepting a naturalistic view of a celestial phenomenon such as a solar eclipse.
Furthermore, the absence of professional experts in matters related to heavenly bodies made
possible the emergence of individuals characterized by a new type of intellectual activity. These
individuals, traditionally called the philosophers, combined that intellectual curiosity which is
natural for a number of people in any society with some specialized knowledge, first acquired
from abroad and then inherited and enhanced. Because they were free citizens of a free city-state
and typically from its upper stratum, and because they were not professionals, the philosophers
were free to apply their intellectual curiosity to any question they wanted to. And because they
possessed some special knowledge (in what later will be called astronomy and mathematics),
which the common people did not, their innovative ideas were not to be dismissed easily.
Finally, because they were able to demonstrate the power of their knowledge and the advantage
of their new approach, they found around them both the admirers and emulators.
In other words, there was no room for philosophers in Assyria and Babylonia; yet only
those Greeks initially were and could become philosophers who possessed special knowledge
and were thus scientists. That is why I consider essential the double identity of Thales and his
immediate followers.
45 Hermann Hunger, Astrological Reports to Assyrian Kings = States Archives of Assyria VIII (Helsinki 1992) #
316: “The evil of an eclipse affects the one identified by the month, the one identified by the day, the one identified
by the watch, the one identified by the beginning, where (the eclipse) begins and where the moon pulls of its eclipse
and drops it; these (people) receive its evil”; # 336: “[If] there is an eclipse, and the north wind blows: the gods will
have mercy on the land … If the moon comes out darkly and is like the command of the sky: the king will
overthrow all lands in defeat … If the moon is eclipsed in Sivan: later in the year, Adad will devastate the harvest of
the land”; # 384: “If the sun is eclipsed in Iyyar on the 28th day: the days of the king will be long; the land will enjoy
abundant business … If the sun at its rising is like a crescent and wears a crown like the moon: the king will capture
his enemy’s land; evil will leave the land, and (the land) will experience good. If there is a solar eclipse in Iyyar on
the 29th day, it begins in the north and becomes stable in the south, its left horn is pointed, its right horn long: the
gods of all four quarters will become confused … rise of a rebel king; the throne will change within five years”, etc.
32
THALES’ PREDICTION OF A SOLAR ECLIPSE
Evidence
The story is told by Herodotus:
‘There was war between the Lydians and the Medes for five years; each won many victories over the
other, and once they fought a battle by night. They were still warring with equal success, when it chanced,
at an encounter which happened in the sixth year, that during the battle the day was suddenly turned to
night. Thales of Miletus had foretold this loss of daylight to the Ionians, setting as its limit the year in
which the change did indeed happen. So when the Lydians and the Medes saw the day turned to night
they ceased from fighting, and both were the more zealous to make peace’ (1. 74).
Herodotus wrote about a century and a half after the event, but his account seems to be an
abridgement of a more comprehensive one. We are told that Thales predicted an eclipse to the
Ionians, but it is not specified under which circumstances this happened and who these Ionians
actually were. Herodotus' source was probably one of the Milesian writers active c. 500 BC.
Thales was not yet a figure of a remote past in their time.
Herodotus' account is nevertheless detailed. It states not only the addressee of the
prediction, but also specifies that the prediction was formulated in terms of years (and not
months or days). It is significant that Thales' prediction was addressed to neither side at war.
This lack of involvement distinguishes our case from such fictional predictions as the one
ascribed to Anaximander, who is reported to have convinced the Spartans to leave their homes
because of the coming earthquake (12 A 5 DK), which is the story of a sage who is able to divine
the future and thus save a city.444666
It is true that there is an example of a fictional eclipse in the Histories, namely Herodotus'
story about the solar eclipse which occurred at the beginning of the march of Xerxes' army
(7.37).444777 But the difference between the two accounts is evident. In the case of Xerxes' eclipse,
46 Anaxagoras' prediction of the fall of the meteorite at Aegospotami provides the only real parallel (Plin. NH
2.149; D.L. 2.10; Amm. Marc. 22.16.22, cf. 22.8.5; Philostr., Vit. Apoll. 1. 2; cf.: Plut., Lys. 12; D.L. 2.11-12).
Yet the story of Anaxagoras' prediction lacks any concrete detail. We are never told to whom he predicted the
event, whereas Herodotus' account implies that Thales made his prediction publicly: he addressed it to the
Ionians (the comparison with Herodotus 1.170 gives the impression that it was made at the Pan-Ionian meeting).
Furthermore Thales' real prediction could easily have provided a pattern for a number of fictional prediction stories.
47 This was emphasized by Alden A. Mosshammer, “Thales’ Eclipse”, TAPA 111 (1981) 145-155, esp.152 f.
33
the motive is quite clear: ‘to provide Xerxes with a celestial omen commensurate with his
ambitions’;444888 whereas in the case of Thales, there is no such motive.444999
It is worth noting that Herodotus does not want to believe that Thales enabled the
crossing of the river Halys for the army of Croesus without building a bridge (1. 75). This shows
that he was quite capable of taking a critical attitude towards reports about the achievements of
Thales. In the case of the prediction of a solar eclipse, the historian apparently had no reason to
mistrust his sources.
Turning to other testimonies, one may infer from the account in Diogenes Laertius that
Thales' prediction became a subject of critical examination already in antiquity:
‘He seems by some accounts to have been the first to study astronomy and to predict both eclipses and
turnings of the sun, as Eudemus says in his History of Astronomy. It was this which gained for him the
admiration of Xenophanes and Herodotus; Heraclitus and Democritus testify this too’ (1. 23).
The plural of ‘eclipses’ is not to be taken literally. Such inaccuracy of formulation was
provoked by the principle of economy, characteristic of a compiler's style. One solar
phenomenon, the solstices, was linked with the other, the eclipse. The plural for ‘solstices’ was
predetermined (since there are two every year) and thus was expanded to ‘eclipses’.
We should take into account that Eudemus, cited by Diogenes Laertius, ought to have
thought Thales' ability to predict a solar eclipse as astonishing as we do. Besides, Eudemus'
teacher, Aristotle, regularly shows considerable caution regarding the information received about
Thales,555000 and so it is most unlikely that Eudemus would uncritically credit Thales with the
prediction of a solar eclipse. On the contrary, his search for additional confirmation of the story
told by Herodotus reflects a critical attitude. Such confirmation was to be found in the writings
of early philosophers like Xenophanes and Heraclitus, and so Eudemus accepted the story as
trustworthy.
Xenophanes, born c. 565 BC, lived during the same century as Thales. He had a very
critical mind; he ridiculed common views, and criticized Homer and Hesiod as well as
Pythagoras. His testimony therefore bears much weight.
Furthermore, the question should be asked: who could have invented the legend of the
prediction, if it were just a legend? An explanation in terms of folklore is not appropriate here,
48 Ibid., 153.
49 It is likely, moreover, that the eclipse reported in 7. 37 is not entirely fictional. It might originally belong to the
story of the first Persian expedition against the European Greeks in 492 BC (Hdt. 6. 43-45). When this expedition
was apparently in state of preparation, a very impressive solar eclipse took place in Persia, 24 Nov 493 BC (max.
phase 0.99 in Persepolis, according to Manfred Kudlek, Erich H. Mickler, Solar and Lunar Eclipses of the Ancient
Near East from 3000 BC to 0 (Neykirchen-Vluyn 1971).
50 De an. 405 a 19; 411 a 7; cf. Metaph. 983 b 20.
34
for in order to invent a prediction of a solar eclipse, one must first accept that a solar eclipse is a
predetermined event rather than one that happens by divine command. Ordinary people of the
period would not have invented the story, nor would they have believed in it unless they were
confident that the prediction had actually occurred.
Everything points to this conclusion: the evidence for Thales' prediction is too strong to
be denied. In the words of Sir Thomas Heath, ‘it remains to inquire in what sense or form, and
on what ground, he made his prediction.’555111
Problem
A solar eclipse is not a rare event; it happens two to five times every year. However, a
solar eclipse is visible only within a relatively narrow band on the earth's surface. In order to
predict a solar eclipse visible in a given location, one has to take into account various data, many
of which were not available in Thales' day. As far as we know, the first man on earth able to
calculate a solar eclipse for a given location was Hipparchus of Nicaea, who lived in the second
century BC, more than four hundred years after Thales.
This difficulty was emphasized already in 1864 by Thomas-Henri Martin.555222 His
arguments were not ignored. However, scholars assumed that Thales had obtained the necessary
knowledge from Mesopotamian sources. Otto Neugebauer passionately criticized this approach:
‘In the early days of classical studies one did not assume that in the sixth century BC a
Greek philosopher had at his disposal the astronomical and mathematical tools necessary to
predict a solar eclipse. But then one could invoke the astronomy of the “Chaldaeans” from
whom Thales could have received whatever
information
was
required.
This hazy but
convenient theory collapsed in view of the present knowledge about the chronology of
Babylonian astronomy in general and the lunar theory in particular. It is now evident that even
three centuries after Thales no solar eclipse could be predicted to be visible in Asia Minor – in
fact not even for Babylon. There remains another vague hypothesis: the prediction by means of
cycles (if need be again available upon request from Babylon). But unfortunately there exists no
historically manageable cycle of solar eclipses visible at a given locality...”555333
Furthermore, the accuracy of the main evidence for the story has been largely discredited:
Thales is said to have determined the year of the eclipse (or so Herodotus' account is usually
51 Sir Thomas Heath, Aristarchus of Samos the Ancient Copernicus (Oxford 1913) 15.
52 Thomas-Henri Martin, "Sur quelques predictions d'eclipses mentionnees par des auteurs anciens", Revue
archeologique, nouvelle serie, 9 (1864) 170-199.
53 Otto Neugebauer, A History of Ancient Mathematical Astronomy (Berlin; New York 1975) pt. 2, 604.
35
understood), but this is odd, for one would think that if one can predict an eclipse at all, one can
predict it to the day.
Previous attempts at the reconstruction of Thales' method
We have no ancient account of the method which facilitated Thales’ extraordinary
achievement, and all modern attempts at the reconstruction of such a method seem to fail.
The typical attempts can be characterized by the words of Asger Aaboe: “The proposed
solutions of the problem have very often been sought in eclipse cycles, most notably the
‘Saros’ period of 18 years or, more precisely, 223 lunations (about 6585 1/3 days)”. Yet, to
continue the quotation, “though there are excellent cycles for lunar eclipses ... there are no such
cycles or periodic recurrences of solar eclipses for a given location on Earth.”555444
The most popular idea, of associating the prediction based on the Saros with the eclipse
of 28 May 585 BC, was certainly misleading. The fact is that the solar eclipse of 18 May 603
BC, the predecessor of the eclipse in the Saros, itself had no predecessor in the Saros that was
observable in the Mediterranean or the Near East. Who would have predicted that a solar eclipse
must happen 18 years later if there was no eclipse 18 years earlier? And why should Thales have
counted 18 years from the eclipse of 18 May 603 BC and not, say, from those of 13 Feb 608 BC
or 29 Jul 587 BC?
B.L.van der Waerden proposed that Thales used a correlation between the occurrences of
solar and lunar eclipses.555555 His proposal was commented on by Willy Hartner: "The circumstance
that a solar eclipse may follow a lunar eclipse after 23 1/2 lunations does not of course suffice to
make a prediction."555666
In his own study of Thales' prediction, Hartner attracted attention to such an important
eclipse period as the Exeligmos. He also emphasized that Thales "had to proceed with the
greatest possible circumspection so as to avoid being ridiculed." Yet, on the one hand, Hartner
postulates in an arbitrary way
the
existence of systematic observational data recorded in
Miletus for decades before Thales' birth (which is most unlikely since the Greeks did not know
any astronomer earlier than Thales), and credits Thales with too much knowledge about too
many cycles; while on the other hand, Hartner's train of thought offers no reason why Thales
should have chosen one cycle
rather
than
another. Moreover, Hartner’s reconstruction
54 Asger Aaboe, "Remarks on the Theoretical Treatment of Eclipses in Antiquity", Journal for the History of
Astronomy 3 (1972) 105-118, esp. 105.
55 B.L.van der Waerden, Science Awakening II: The Birth of Astronomy (Leiden 1974) 120-22.
56 Willy Hartner, "Eclipse Periods and Thales' Prediction of a Solar Eclipse", Centaurus 14 (1969) 60-71, esp. n.
14. However, van der Waerden’s approach was taken up and developed by Patricia O’Grady, Thales of Miletus. The
Beginnings of Western Science and Philosophy (Burlington 2002). For detailed criticism see Dirk L. Couprie, “How
Thales Was Able to ‘Predict’ a Solar Eclipse without the Help of Alleged Mesopotamian Wisdom”, Early Science
and Medicine 9 (2004) 4, 321–337, esp. 323–328.
36
requires that Thales, in order to justify his prediction, resorted to manipulations with the official
calendar in Miletus, but such manipulations are highly implausible for many reasons. In short,
the story told by Hartner is untenable. It was even asserted that "Hartner's ingenious approach
only serves to demonstrate how utterly fictional the story of Thales' prediction is."555777 But such a
conclusion was premature.
Thales' likely method: preliminary remarks
It is hardly contestable that neither the Greeks nor the Babylonians possessed the
knowledge necessary for reliable prediction of a solar eclipse visible in a given location before
the time of Hipparchus. Nevertheless, successful predictions have been recorded. Plutarch in the
Life of Dion, 19 ascribes such an achievement to Helicon of Cyzicus. The date of this eclipse is
either 12 May 361 or, as I believe, 29 February 357 BC. Helicon’s success was sensational, yet
Aristotle admits the possibility in principle of predicting a solar eclipse (Top. 111 b 30).555888 Sixty
one Babylonian solar eclipse predictions with indication of the exact time of the expected event,
from 358 BC to 35 AD, were considered by J. M. Steele.555999 It has been found that "all of the
predictions correspond to a date when a solar eclipse occurred upon the Earth's surface", though
"only 28 examples relate to eclipses that were visible at Babylon, or would have been if the Sun
had been above the horizon."666000 The sun was in fact below the horizon in about half of these 28
cases. Steele believes that the solar eclipses he studied "were predicted purely by use of a
cyclical procedure."666111 Because the written records of eclipses were kept in Mesopotamia at least
since 747 BC, it is likely that important eclipse cycles were discovered as early as in the seventh
century. In any case, expectations of a solar eclipse on a certain day are attested to in the letters
sent by Babylonian and Assyrian observers to Assyrian kings. Perhaps there were methods in
ancient astronomy that, while not permitting reliable predictions (otherwise successful outcomes
would not have been as episodic), did allow reasonable attempts to foretell the phenomena.
Neugebauer’s assertion that “there exists no historically manageable cycle of solar
eclipses visible at a given locality” needs qualification. For instance, the Exeligmos (or the triple
Saros), the period of 669 lunations or 54 Julian years and 1 month, was well known in antiquity
at least as a lunar period. Geminus ascribes its recognition to ‘the Chaldaeans’ (Isag. 18).
According to Ptolemy, this period was in use in the remote past: Ptolemy relates it to ‘more
57 Mosshammer, “Thales’ Eclipse”, 147.
58 I am grateful to Leonid Zhmud for drawing my attention to this passage,
59 J. M. Steele, "Solar Eclipse Times Predicted by the Babylonians", JHA 28 (1997) 133-139.
60 Ibid. 135 f.
61 Ibid. 133. One could also consider the possibility that the exact time of the eclipses was predicted from
observations made not long before the expected time of conjunction. J. K. Fotheringam , "Cleostratus", JHS 39
(1919), 164-184, esp. 180 (following Kugler) believes that this was the typical procedure of the Assyrian predictions
of both solar and lunar eclipses in the seventh century BC.
37
ancient’ astronomers as distinguished from ‘ancient’ (Synt. 2. 4, p. 269 f. Heiberg). Since the
Saros involves 1/3 day and since Mesopotamian observers regularly noted whether a lunar
eclipse took place in the evening or in the morning, it was easy to deduce a new useful period by
multiplying the Saros by 3.666222 Statistical data makes it plausible that the Exeligmos, as a solar
eclipse period, was discovered in Mesopotamia in the seventh century BC. For instance, we
know that the eclipse of 15 Apr 657, with the maximal magnitude 0.84 at 11.09 h for Nineveh,
did not pass unnoticed for professional observers in Assyria.63 It has both a predecessor and
successor in the Exeligmos – 14 Mar 711 (0.66 at 11.78) and 18 May 603 (0.76 at 9.36). One can
cite another triplet: 9 Dec 744 (0.80 at 11.58), 11 Jan 689 (0.83 at 12.22), and 12 Feb 635 (0.88
at 11.38).64 For the reasons indicated in the previous chapter, this knowledge could have been
available to Thales.
We turn now to another important point. Herodotus says that Thales predicted a solar
eclipse to the Ionians. Does this necessarily mean that Thales predicted an eclipse that would be
spectacular in Ionia? Such a conclusion is by no means unavoidable. The Assyrian empire
existed long enough to enable the discovery that a total solar eclipse was not experienced by the
all subjects of an Assyrian king. Thus, the already mentioned eclipse of 15 Apr 657 hardly
attracted the attention of common people in Nineveh, but it was total for a large part of Egypt,
and Egypt was at that time under Assyrian rule. As to the Egyptians, the eclipse of 19 Aug 636
was total for Thebes, but not for the Delta. It is not impossible that Phoenician or Egyptian
traders observed the total eclipse of 18 May 603 in the Red Sea and that the story reached
Thales. And it must have been known in Miletus that the total eclipse of 6 Apr 648 did not cause
sudden darkness for all Greek settlements around the Aegean Sea. Now, the maritime routes
regularly employed by the Milesians by the end of the seventh century extended for several
hundred kilometers. Milesian settlements or trade posts appeared in the Nile Delta as well as on
the northern shores of the Black Sea. Thales addressed his prediction to the people who had
relatives, friends or partners far in the south and far in the north. To predict a solar eclipse to be
spectacular somewhere within the large area between latitudes 31° and 48° N is not quite the
same as to predict it for ‘a given locality’.
But the question cannot be solved, of course, through general considerations only. For
centuries, Thales' achievement remained unique. This suggests that the clue is not to be found in
62 Cf. Ptol. loc. cit.: “In order to obtain a period with an integral number of days, they tripled 6585 1/3 days,
obtaining 19756 days, which they called Exeligmos”. Ptolemy has in mind Greek rather than Babylonian
astronomers.
63 Hermann Hunger, Astrological Reports to Assyrian Kings, # 104.
64 The values for Nineveh (and also for Babylon and Memphis) here and hereafter are taken from Manfred Kudlek,
Erich H. Mickler, Solar and Lunar Eclipses of the Ancient Near East; those for Miletus derive partly from Willy
Hartner, “Eclipse Periods and Thales’ Prediction”, 66 and partly were calculated for me by Marina V. Lukashova
(Institute for Applied Astronomy, Russian Academy of Sciences, St. Petersburg).
38
the discovery of some general method. The clue to such a particular achievement is to be found
in particular circumstances. In order to grasp these circumstances, we have to situate Thales'
prediction in time.
Chronological questions
The relevant chronological questions are not as easy to deal with as it may seem.65 One
has to approach the ancient chronographic tradition with greater caution than scholars usually do
(and than I myself did at an earlier stage of this study). In the brief discussion that follows, I will
mostly rely on astronomy and modern chronology, based essentially on the cuneiform sources.
Assuming that the battle was interrupted by a total eclipse (as Herodotus’ account clearly
implies), the date of the battle is 28 May 585 BC. The fact is that there were only two total solar
eclipses in the epoch in question visible in Asia Minor beyond the Halys – the other being that of
19 May 557 BC. Sources disagree as to who was the Median king at the time of the battle –
Cyaxares (as Herodotus believes) or his successor Astyages (according to some later authors).
Yet they agree that the Lydian king was Alyattes, and Alyattes was no longer king in 557 BC.
Moreover, the reign of Cyaxares, as far as we know, lasted exactly until 585 BC.
If one suspects exaggeration in Herodotus and admits that a crescent-like sun was an
omen impressive enough to stop fighting, then also the eclipses of 27 Jul 588, 21 Sept 582 and
possibly 16 Mar 581 are to be taken into consideration. But we are still left in the 580s BC.
Although it is likely that the Greeks participated in the battle as mercenaries or as Lydian
allies and that some of them heard about Thales’ prediction, one may still suspect that the eclipse
predicted by Thales and the battle happened on different days, and were later linked to make a
better story. We would then need an independent chronology for Thales and his prediction.
However, from the independent chronology that is available it is not clear whether or not it was
derived from the accepted date for the battle.66 In any case, tradition dates both Thales’
prediction and his recognition as a sage to the 580s as well.
It is, further, reasonable to assume that only experience of a total eclipse could have
impressed the Greeks so much as to make Thales one of the most famous persons of his epoch.
Our choice is, then, limited to the eclipses of 28 May 585, 21 Sept 582 and 19 May 557 BC. It
should be specified that the eclipse of 21 Sept 582 was possibly total only for Greek settlers and
visitors in the Nile Delta and Cyrene.
65 See: Alden A. Mosshammer, The Chronicle of Eusebius and Greek Chronographic Tradition (Lewisburg;
London 1979), esp. 255-273.
66 Dmitri Panchenko, “Democritus’ Trojan Era and the Foundations of Early Greek Chronology”, Hyperboreus 6
(2000) 1, 31-78, esp. 67.
39
I proceed from the most natural hypothesis that both Thales’ prediction and success took
place in the 580s, though in due course I will also consider the possibility of his having predicted
an eclipse for 557 BC.
Now, we have to remember that a sudden statement of the kind we are talking about
could make a man appear ridiculous or arrogant. We must therefore look for a situation in which
such an initiative would be acceptable or even welcome. The general public usually shows no
special interest in celestial phenomena. Their interest is aroused when an extraordinary celestial
event affects people's emotions. The usual reaction to a solar eclipse in the period in question
was fear that it was a bad omen. Thales' extraordinary statement would have been welcomed
rather than ridiculed, if it followed a solar eclipse and if Thales was able to assuage the anxiety of
the Ionians by explaining that there was no reason for fear – for a solar eclipse is no omen at all,
it is a natural event that happens from time to time, and he even dares to predict that another
solar eclipse is coming rather soon.
No impressive solar eclipse was visible in Ionia from 12 Feb 635 to 29 Jul 588 BC. Thus,
there was neither anxiety about solar eclipses nor a situation favourable for prediction. The
Greeks of Ionia and culturally-related areas were hardly very superstitious in that epoch, yet in
the 580s they confronted an unusual course of events: obscurations of the sun followed one after
another. The eclipse of 29 July 588 must have been quite conspicuous for it reached maximum
occultation (0.87) about half an hour before sunset. Seventeen months later, on 14 Dec 587, the
Ionians again saw the crescent-shaped sun (0.84 for Miletus). The occurrence of two consecutive
occultations provided a favourable situation for Thales’ extraordinary statement about a
forthcoming eclipse. I take 14 Dec 587 BC as terminus post quem for Thales’ prediction.
Thales' likely method
We read in Herodotus that Thales, while predicting a solar eclipse, “set as its limit this
year
in
which
the
change
actually
occurred”
(          ).
A reference to
the ‘limit’ implies the notion ‘not later than’. Thus the prediction was expressed in terms of a
period of time spanning from a given moment (probably that of the prediction) to another; this
time-span was defined either as one year or as a series of years. If Herodotus' formulation is
more or less accurate, it follows that Thales' prediction was based not on the observation of
relative positions of the sun and moon a short time before their next conjunction, but on the use
of a cyclical procedure.
So what was Thales' method?
I will suggest two different possibilities and then compare their merits and shortcomings.
40
Version 1
Two occultations of the sun in 588–587 BC were separated by just seventeen months.
Then, after only a further eighteen months, there occurred an eclipse that was total for the most
of Ionia (and close to total for Miletus). If Thales had something to say in order to assuage the
fear of the Ionians and at the same time to demonstrate the brilliance of his mind, this was the
time to do so. At the Pan-Ionian festival (cf. Hdt. 1. 170), he declared that the Ionians will see a
solar eclipse again in no longer than x number of years. Perhaps, he added: "or, at least, you will
hear about one".
His prediction came true. In the last year of the period specified by Thales, a solar eclipse
occurred, that of 21 Sept 582 BC. It was not very spectacular, and yet, with its magnitude c. 0.8
and the low altitude of the sun about eight in the morning, the crescent-shaped sun must have
attracted common attention. Moreover, the Ionians from the Nile Delta reported a total solar
eclipse. The man who predicted the eclipse became the subject of common admiration. We are
told that in the archonship of Damasias, that is, 582/581 BC, Thales became “the first to receive
the name of Sage”.67
I assert that a solar eclipse could have been predicted for the year 582/581 BC on the
basis of the Exeligmos, and also on the basis of a particular 27-year cycle.
The immediate predecessor of the eclipse of 21 Sept 582 in the Exeligmos (19 Aug 636)
was total in the region of Egyptian Thebes (0.8 for Babylon). Further, one has to bear in mind
that the Greek year typically began some time after the summer solstice, and so the eclipses of
21 Sept 582 and 16 Mar 581 would fall on the same year 582/581. Now the eclipse of 16 Mar
581 BC had three consecutive predecessors in the Exeligmos, all within the period of regular
records kept in Mesopotamia:
February 12, 635 BC (0.88 in Nineveh);
January 11, 689 BC (0.83 in Nineveh);
December 9, 744 BC (0.80 in Nineveh).68
Furthermore, the same eclipse of 16 Mar 581 BC had six consecutive predecessors in a particular
27-year period as illustrated by the following series:
Dec. 9, 744 BC (0.80 in Nineveh)
Dec10, 717 BC (0.56 in Nineveh)
Jan 11, 689 BC (0.83 in Nineveh)
Jan 12, 662 BC (0.97 in Nineveh)
67 D.L. 1. 22, with reference to Demetrium of Phalerum.
68 The corresponding values for Memphis: 0.93; 0.81; 0.62.
41
Feb 2, 635 BC (0.88 in Nineveh)
Feb 13, 608 BC (0.59 in Nineveh).69
The knowledge of these facts would have allowed Thales to venture a prediction of a
solar eclipse for the year 582/581 BC. Possibly, he even had the chance to check the reliability of
the 54-year cycle. The eclipse of 14 Dec 587 BC had a predecessor in the Exeligmos (11 Nov
641 BC), and the eclipses of 23 Dec 596, 18 May 603 and 13 Feb 608 BC had such predecessors
too (21 Nov 650, 15 Apr 657, and 12 Jan 662 BC respectively). A simpler approach is also
conceivable. Suppose Thales knew about the 54-year cycle and made an inquiry in Egypt as to
the dates of the most recent impressive eclipses. Suppose he established that there had been two
such eclipses –a total one in Thebes (19 Aug 636), the other, however annular, with a path of
centrality in the Nile Delta (12 Feb 635). Their successors in the 54-year cycle were to be
expected for the same Greek year 582/581.
A prediction in terms of years was due to the insufficient records for the eclipses of the
past. To be sure, Mesopotamian observers indicated the exact date of an eclipse. But the calendar
year in Mesopotamia was composed of lunar months, and a strict system of intercalation was not
yet established in the seventh century.70 An Assyrian astronomer in exile was hardly in a
position to determine which years had an additional month and thus establish with certainty the
number of lunations between two eclipses separated by many years. We cannot say what kind of
Egyptian records Thales could find, and probably none by his compatriots were available except
the recollection of the number of years elapsed since a remarkable event. Moreover, the eclipses
of 29 Jul 588 and 28 May 585 had no predecessors either in the Exeligmos or 27-year cycle, so
Thales had to take into account the possibility that a solar eclipse could intervene before the date
of the expected one. It was, thus, natural for Thales to formulate his prediction in terms of years.
The very detail in Herodotus' account which caused suspicion supports in fact the reliability of
what he says.
If Thales' method was as described, it is easy to see why his achievement remained rare
or unique for centuries, even if Thales revealed the secret to his disciples. The coincidence of
two series of eclipses was exceptional as was the success of a prediction based on such a
coincidence. As for the prediction on the basis of the Exeligmos only, further observations
would have shown that the method was disappointing – either absolutely or (more typically) in
69 I cite the magnitudes for Nineveh on the hypothesis that Thales’ knowledge was ultimately due to an Assyrian
émigré (see above). Nineveh no longer existed in 608 BC. The annular eclipse 13 Feb 608 BC could be quite
conspicuous for the Greek settlers in southern Italy (c. 0.9 with the late afternoon sun low above the horizon); it
could be observed in Miletus (max. magnitude over 0.7).
70 Richard A. Parker and Waldo H. Dubberstein, Babylonian Chronology 626 B.C. – A.D. 75 (Providence 1956) 1.
42
the sense that anticipated eclipses were of too small a magnitude to be appropriate for a
prediction addressed to the public.
Thales could have had one more reason to expect a solar eclipse in Mar 581. The eclipse
of 28 May 585 was separated from the two previous eclipses by intervals of 18 and 17 lunations
respectively, while the eclipse of 30 Jul 607 was also separated by the intervals of 18 and 17
lunations from the two preceding eclipses.71 Thales could, therefore, have discovered that not
only one interval between two consecutive eclipses previously encountered had been repeated,
but a series of two intervals between consecutive eclipses. Such a ‘regularity’ might have
allowed him to venture a prediction. There were 47 lunations between the earlier sequence and
the subsequent eclipse, of 18 May 603 (conspicuous in Egyptian Thebes). Thales might have
concluded that there would be the same number of lunations between later sequence and the
forthcoming eclipse. For the reasons explained above, Thales would have given a broad
formulation, something like ‘no later than four years’. The eclipse of 21 Sept 582 fell within the
fourth year, even though it happened six months earlier than expected.72
The weak point of the suggested reconstruction of Thales’ method is that it either
dissociates the predicted eclipse and the battle eclipse or requires corrections to Herodotus’ story
(partial eclipse instead of total, and probably Astyages instead of Cyaxares). Moreover, it implies
that Thales acquired fame because of the eclipse that was total only for the Greeks of Egypt and,
perhaps, Cyrene.73
Version 2
If one believes, as Thales did, that a solar eclipse is caused by the interposition of the
moon, how would one try to use such a hypothesis for the prediction of the phenomenon?
71 See Table 2 in Dmitri Panchenko, “Thales’s Prediction of a Solar Eclipse”, Journal for the History of Astronomy
25 (1994), 275-288, esp. 281.
72 An improvement upon my proposal (cf. paper cited in the previous note, 283 f.) was suggested by Dirk L.
Couprie, “How Thales Was Able to ‘Predict’ a Solar Eclipse without the Help of Alleged Mesopotamian Wisdom”.
He replaces 23 lunations interval between Nos. 7 and 8 in my Table 2 with correct 17 lunations. This makes him
suggest that Thales could have concluded that solar eclipses come in clusters of three, the second appearing 17 or 18
months, and the third 35 month, after the first one. The advantage of Couprie’s version is that he uses the repetition
of two clusters to account for predicting the eclipse of 28 May 585. However, Couprie assumes that Thales was not
aware of Nos. 4 and 6 of the Table and, further, his clusters are not exactly identical: a series of 17 and 18 lunations
alternates with the one of 18 and 17 lunations.
73 I have also to admit that this reconstruction depends to some degree on the map for the eclipse of 21 Sept 582
drawn by K. F. Ginzel, Spezieller Kanon der Sonnen- und Mondfinsternisse (Berlin 1899) Karte IV. Kudlek and
Mickler as well as F. Richard Stephenson and Louay J. Fatoohi, “Thales’s Prediction of a Solar Eclipse”, JHA 28
(1997) 279-282, esp. 281 draw the track of totality a bit south of the Delta. As far as I can see, the necessary
precision is still beyond the reach of science. Assuming that more recent work of science is likely to be closer to the
truth, one may nevertheless observe that the Greeks in the Delta would have certainly heard about the total eclipse
and that the obscuration of the sun as they saw it themselves was in any case quite impressive.
43
Thales certainly had to address the question why a solar eclipse did not occur at every
new moon. Part of the answer was simple: half of the conjunctions of the sun and moon take
place during the night. As for the other half, a careful observer of how the moon changes its
position each night with reference to a certain belt of the stars would discover that the moon
sometimes moves in a higher region and sometimes in a lower one – or, in modern terms, the
moon changes its position not only in longitude, but also in latitude. The moon, then, will not fall
in a direct line between us and the sun at every conjunction; sometimes it will pass too low and
sometimes too high. While the track of the moon among the stars can be directly observed, that
of the sun cannot. To get an idea of how the tracks of sun and moon are related to each other, one
had to observe which of the stars rise just before sunrise and set just after sunset on those points
of the horizon where the sun appears or disappears. Observations taken in the course of several
years would show that the sun, unlike the moon, does not deviate from its path among the stars.
The principal technique of such observations was known in Mesopotamia before the fall of
Nineveh (609 BC), for it is explicitly stated in the Mul. Apin: “The Sun travels the (same) path
the Moon travels.”74
Thales knew that the sun rises and sets every day at a new point on the horizon and yet
with a certain periodicity it repeats all its daily tracks. The moon, too, returns to the same stars.
Since the two luminaries move at different speeds, they meet in conjunction at a different point
each time. Yet a day must come when their conjunction will be repeated at the points where this
has already happened. To predict a solar eclipse on such a theory was to establish the time when
both the sun and the moon would simultaneously return to the points where they were at a
previous solar eclipse.
The task was difficult. Ancient testimonies, however, suggest that Thales was not
completely unprepared to address it.
D.L. 1.23; Eudem. fr. 144 Wehrli; 11 A 1 DK:
Thales was the first to predict the sun's eclipses and solstices (literally: the turnings of the sun), as
Eudemus says in his History of Astronomy.
Eudem. fr. 145 Wehrli; 11 A 17 DK:
Thales was the first to discover the eclipse of the sun and the fact that its passage with respect to
the solstices is not always of the same length.75
74 Hermann Hunger and David Pingree, MUL.APIN. An Astronomical Compendium in Cuneiform = Archiv für
Orientforschung. Beiheft 24 (Horn 1989) 70.
75 (sc.
 )               Diels
does not indicate that he prints the emended text:  instead of . D.L. 1.24 has . Cf. Aristot.
De Cael. 296 b 4:   
44
D.L. 1.24; 11 A 1 DK:
He was the first to determine the course of the sun from solstice to solstice.
Schol. in Plat. Rep. 600 a; 11 A 3 DK:
He was the first among the Greeks to discover … the solstices.
D.L. 1.27; 11 A 1 DK:
He is said to have discovered the seasons of the year and to have divided them into 365 days.
D.L. 1.24
He was the first to give the last day of the month the name of Thirtieth.
These testimonies present Thales’ dealing with the course of the sun, the solstices, and
the calendar, none of which is likely to be the subject of legends. His preoccupation with the
solstices is especially well recorded.
According to the best authority, Eudemus, Thales determined that the time during which
the sun travels its course with respect to the solstices is not always the same. It follows that
Thales could not have taken the length of the year as equal to 365 days and that the evidence we
have on this point is quite a usual simplification, all the more natural in our case because the
Greeks would frequently refer to the year as containing 360 days even centuries after Thales.
Apparently, Thales was able to establish that a four year-cycle comprises 1461 days and thus one
year has 365 1/4 days.
Thales could believe that he succeeded in establishing the length of a solar year with
sufficient precision, but he was hardly able to establish with confidence the time at which the
conjunction of the sun and moon takes place at the same point. Fortunately, he could have
received assistance from elsewhere.
Otto Neugebauer and Abraham Sachs published a remarkable cuneiform text, apparently
from Babylon.76 They do not date it, but one may infer from several of their remarks that it
belongs to the period from about 500 BC or even earlier, since a variant in the text reflects the
metrological basis of the Old-Babylonian period. Section 4 of the text begins as follows:
“In 19 years the moon will approach the place of the Normal Stars where it approached
before. Where there was a lunar eclipse, it takes place (again)”.
According to the editors of the text, “the mention of the 19-year cycle is surely a mistake
for the 18-year eclipse cycle, as the next sentence shows”.77 But both assertions of the text
essentially correspond to reality (see below), whereas the consecutive eclipses of the 18-year
cycle do not occur in the same place among the stars, as the text requires. It is, thus, the
76 O. Neugebauer and A. Sachs, “Some Atypical Astronomical Cuneiform Texts, I”, JCS 21 (1967) 183-218, esp.
200-208.
77 Op. cit. 205.
45
comments that are mistaken and not the mention of the 19-year cycle.78 The importance of the
text was emphasized by Kristian Peder Moesgaard.79 His study concerns, however, a question
which is not relevant here. We are interested here in the very observation that in “19 years the
moon will approach the place of the Normal Stars where it approached before.”
This observation is very nearly correct. The other assertion is certainly an exaggeration,
yet lunar eclipses are frequently repeated after 19 years. To illustrate this, I will cite just a few
lunar eclipses with their maximal magnitudes computed for Babylon:80
May 714 (1.78) and 1 May 695 (0.73)
27 Feb 711 (0.78) and 27 Feb 692 (1.62), and 27 Feb 673 (0.40)
23 Aug 711 (0.85) and 23 Aug 692 (1.64)
22 May 678 (1.51) and 22 May 659 (1.00)
21 Apr 667 (1.78) and 21 Apr 648 (0.62)
13 Jul 653 (0.81) and 13 Jul 634 (1.63)
2 Jul 652 (1.51) and 2 Jul 633 (0.31)
11 May 650 (0.59) and 11 May 631 (1.87).
Since eclipse records and astronomical diaries were kept already in the first half of the
seventh century, we may safely conclude that the repetition of lunar eclipses in 19 years did not
escape the attention of Assyrian and Babylonian observers of the celestial phenomena. They had
also to discover that usually only two consecutive lunar eclipses repeat in 19 years and that many
eclipses had no successors in a 19-year cycle. The unqualified formulation in our text may be
due to an early stage of research. One has, however, to bear in mind that a mistaken prediction
was a minor fault for an observer working for a king; it was much more important for him to not
let an eclipse occur unexpected. Therefore, any rule that pointed to a plausible date of an eclipse
was welcome. And there are signs that the 19-year rule was indeed used in the seventh and sixth
centuries.
B.L. Van der Waerden discusses the prediction of an “omitted” lunar eclipse for 4 Jul
568.81 He observes that the expectation could not be based on the Saros, and suggests quite a
complicated method of prediction.82 But there was a lunar eclipse on 4 July 587 BC, with a
78 Neugebauer and Sachs also try to support their conclusion with a reference to the unspecified “corresponding
passages in the first section”. A better correspondence is provided, in fact, in section 3 which immediately precedes
the text under discussion and which considers planetary periods as established with reference to the Normal Stars.
79 K. P. Moesgaard, “The Full Moon Serpent. A Foundation Stone of Ancient Astronomy?”, Centaurus 24 (1980)
51-96.
80 Manfred Kudlek, Erich H. Mickler, Solar and Lunar Eclipses of the Ancient Near East from 3000 B.C. to O
(Neukirchen – Vluyn 1971) 146.
81 Bartel L. van der Waerden, Science Awakening II: The Birth of Astronomy (Leyden; New York 1974) 117 ff.
82
46
magnitude of 1.54 for Babylon. The prediction, then, could have been based on the 19-year
cycle.
Hunger # 42 speaks of a lunar eclipse that “will pass by”. According to modern
calculations, this eclipse did not completely “pass by” and actually took place on 23 Aug 673
BC. But it reached its maximum magnitude (0.27) about half an hour after moonset and thus was
hardly observed. The eclipse could have been expected on both the Saros and the 19-year cycle.
However, its predecessor in the Saros, the eclipse of 12 Aug 691 BC, had a maximum magnitude
of 0.18, while its predecessor in the 19-year cycle, occurring on 23 Aug 692, had a magnitude of
1.64. The eclipse of 23 Aug 711 had a magnitude of 0.85.
Hunger # 250 predicts a lunar eclipse that occurred on 27 Feb 673 BC. It had no
predecessor in the Saros, but two in the 19-year cycle – 27 Feb 692 (1.62) and 27 Feb 711 (0.78).
Hunger # 251 predicts a lunar eclipse that occurred on 3 Sept 674. It had predecessors
both in the Saros, on 23 Aug 692 (1.64), and the 19-year cycle, on 3 Sept 693 BC (0.78).
This is not to say that all the mentioned eclipses with no predecessor in the Saros were
expected exclusively in the 19-year cycle. They could have been expected for other reasons as
well, but the cited data are enough, I believe, to make it highly probable that the recognition of
the return of the moon to the same place every 19 years was part of seventh century
Mesopotamia’s knowledge. And we have seen many reasons to believe that such knowledge
could have reached Thales.
If Thales accepted the 19-year period of the moon as reliable and if he believed the length
of the year to be 365 1/4 days, the only thing he had to do in order to establish the date of the
return of both the sun and moon at the same place was to multiply 19 years by four. Thus, he
received the repetition of a conjunction on the same day and under the same circumstances as
had existed 76 years before.
Although my reasoning supplies Thales with no method or fact beyond his reach, I
anticipate that it will be criticized as anachronistic since a 76-year cycle was introduced by
Callippus of Cyzicus in 330 BC, and its use in the time of Thales therefore seems a strange,
premature development. This objection is not valid. The Callippic cycle was introduced for a
particular purpose (to provide a fixed framework for dating astronomical observations) and
under particular circumstances. The very idea of a 76-year cycle (on the basis of the specified
facts) is very simple, and it does not require the level of astronomical knowledge achieved in the
time of Callipus.
The method that I reconstruct is actually documented in ancient astronomy. The evidence
comes, however, from China.
47
“The sun and moon start off together from the Establishment star. The moon's degrees are rapid,
and the sun's degrees are slow. The sun and moon meet again in between 29 and 30 days, when the sun
has moved a little over 29 du round heaven, the amount of this fraction is not being fixed.
So after 365 [days] the sun is [once more] at its southernmost point and the shadow is long[est].
The next day it shortens again, and at the end of the year the solar shadow is at its long[est] again.
Therefore we know in three periods of 365 days and in one period of 366 days [the solstice occurs
at the same time of day as before].
Therefore we know that one year is 365 1/4 days; ‘year’ means ‘conclusion’.
The moon has an accumulated lag behind heaven amounting to 13 revolutions, plus a little over
134 du, ignoring [the fact that] the [daily] lag behind heaven of 13 du and 7/19 du is not constant.
So, [when] the sun has made 76 circuits, the moon has made 1016 circuits, and they reach
conjunction [once more] at the Establishment star.”8833
The quotation comes from the Zhou bi, an ancient Chinese treatise (“The gnomon of
Zhou”) which was probably composed early in the first century AD, but which represents a
number of astronomical conceptions and techniques that were certainly known some centuries
earlier. Three particular points are to be emphasized.
First, the passage describes something different from the Calippic cycle. The 76-year
cycle is cited as an exact return of both luminaries to the same star; it operates with sidereal and
not synodic periodicity – which is also the case with the above cited cuneiform text as well as the
suggested method of Thales.
Second, the Zhou bi has no particular name for the 76-year cycle, but elsewhere it is
called the Obscuration Cycle.84 No Chinese text, it seems, connects the Obscuration Cycle with
the eclipses, but the name suggests an abandoned idea according to which the 76-year cycle is
suitable for predicting solar eclipses.
Third, the information available from the Zhou bi is of interest not only as a good
illustration of the methods employed by the ancient astronomers, the Zhou bi and related Chinese
texts display striking parallels to the late sixth-century Greek astronomy. Moreover, as I argued
elsewhere, there is good reason to suppose a Greek origin for the Zhou bi's core ideas and
techniques.85
If Thales arrived at the idea that a solar eclipse will repeat in 76 years, he would have
done his best to search for records of the impressive solar eclipses that occurred about two
83 Christopher Cullen, Astronomy and Mathematics in Ancient China: The Zhou bi suang jing (Cambridge 1996)
205.
84 N. Sivin, Cosmos and Computation in Early Chinese Mathematical Astronomy (Leiden 1969) 20; Cullen 25.
85 Dmitri Panchenko, “The City of the Branchidae and the Question of Greek Contribution to the Intellectual
History of India and China”, Hyperboreus 8 (2002) 2, 244-255.
48
generations before. For the reasons explained above, Thales could not have hoped to be sure
about the meaning of even a precisely recorded date of an eclipse that occurred long ago. Thus,
his prediction would again be in terms of a year or years. As a matter of fact, the span of exactly
76 years does not constitute cycle for solar eclipses. However, 76 years minus 1 month does
constitute a valid one. The idea of the return of both luminaries to the same place with reference
to the stars in exactly 76 yeas was based on data of insufficient accuracy on the motion of the sun
and the moon, but, in a stroke of good luck, this could be compensated by insufficient accuracy
in determining the time of recorded eclipses. Thus, the alleged cycle would have been applied in
the case in question with the same effect as a true cycle.
Now, we placed Thales' prediction in any case after the eclipse of 14 Dec 587 BC. This
eclipse had quite a conspicuous predecessor in the 76-year cycle – the annular eclipse of 12 Jan
662 (0.85 in Miletus; 0.97 in Nineveh; 0.94 in Memphis). One can imagine how Thales was
impressed if his theoretical expectations were confirmed!
If Thales knew about the eclipse of 12 Jan 662 BC, he apparently also knew about the
eclipse of 27 Jun 661 BC (0.96 in Miletus, 0.93 in Nineveh; 0.74 in Memphis).86 Its successor in
the 76-year cycle was to have been expected in 586/585, and Thales dared to predict an eclipse
for this term. The solar eclipse that occurred on 28 May 585 and was total for most of Ionia as
well as for the battlefield in Asia Minor brought Thales great fame. This is my second version.87
If one would like to imagine Thales as a more cautious person, one may suggest that he
first gained fresh confirmation of his theory and then ventured a prediction after 28 May 585; he
had in mind, then, an eclipse for 582/581 as the successor of the eclipse of 15 Apr 657 BC
(which was total in the parts of the Nile Delta and Cyprus). It follows that an eclipse for 582/581
could be predicted with all the methods described, but predicting an eclipse for 586/585 is in
better agreement with all circumstances.
The eclipse of 19 May 557 could have been also expected with both the Exeligmos and
76-year cycle. However, the corresponding predecessors (17 Apr 611 and 17 Jun 633) were not
visible in Mesopotamia, nor were they spectacular in either the Aegean or Egypt. And this
eclipse does not fit well with either preserved information about the battle or the likely
circumstances of the prediction.
86 Note also the combination of two impressive eclipses in Nineveh within 17 months. What is more, these eclipses
were the most impressive there since that of 15 Jun 763 BC (0.99).
87 The idea that the eclipse of 28 May 585 BC could have been predicted on the 76-year cycle was suggested by L.
Schlachter, Altes und Neues über Sonnenfinsternis des Thales und die Schlacht am Halys (Bern 1898; Separatdruck
aus dem 28. Programm des Freien Gymnasiums in Bern), esp. 15-18. Schlachter has in mind only true cycle, that is,
76 years minus 1 month. He assumes that this cycle was recognized by “Chaldaean and Egyptian statisticians” and
that the eclipse of 27 Jun 661 BC was recorded by priests in Miletus. Both assumptions are neither confirmed nor
impossible, yet Schlachter’s recourse to statistics is problematic since one had to look for a 76-year cycle in order to
discern it among the records. For the 76-year cycle see also F. K. Ginzel’s remarks in his Spezieller Kanon, 265 and
in a long footnote in Schlachter, 15 ff.
49
From the experience of revising my own suggestions concerning the method employed
by Thales, I do not claim to have succeeded in establishing the final truth about the secret of his
success. However, I believe that I have demonstrated that the prediction of a solar eclipse by
Thales was not impossible. Combining this result with the discussion of the evidence presented
above, one has to conclude that Thales’ prediction is not a legend.
It is gratifying to save a beautiful story. But we gain something more. Since Thales’
prediction brought him fame, it must have been made in public. And since Thales was not
considered by the Greeks to be a miracle-worker or a prophet, his prediction must have been
accompanied by explanations that made it possible to pay proper attention to his extraordinary
claim. Thus, there is strong confirmation of our previous conclusion that Thales advanced a
theory of solar eclipses. We may now date the earliest public formulation of a scientific theory:
this happened no earlier than 14 Dec 587 and no later than shortly after 28 May 585 BC.
HOW BIG ARE THE SUN AND MOON?
In his enthusiastic passage devoted to Thales, Apuleius tells us a beautiful story:
“The same Thales in his declining years devised a marvelous calculation about the sun, which I have not
only learnt but verified by experiment, showing how often the sun measures by its own size the circle
which it describes. Thales is said to have communicated this discovery soon after it was made to
Mandrolytus of Priene, who was greatly delighted with this new and unexpected information and asked
Thales to say how much by way of fee he required to be paid to him for so important a piece of
knowledge. ‘I shall be sufficiently paid’, replied the sage, ‘if, when you set to work to tell people what
you have learnt from me, you will not take credit for it yourself but will name me, rather than another, as
the discoverer” (Flor. 18; A 19 DK).
Similar information is preserved by Diogenes Laertius in a passage that is corrupt yet
plausibly restored by Hermann Diels:
50
“According to some, Thales was the first to declare the size of the sun to be one seven hundred and
twentieth part of the solar circle, and the size of the moon to be the same fraction of the lunar circle”
(D.L. 1. 24; 11 A 1 DK).88
“The size of the sun” appears in yet another list of Thales’ intellectual preoccupations and
achievements (Schol. Plat. Rep. 600 a; 11 A 3 DK).
Scholars usually ignore this achievement of Thales. However, the core evidence seems to
me adequate. Someone who studied solar eclipses and who advanced a theory such as is
recorded for Thales should have been preoccupied with the question of the size of both
luminaries. To see why this is so, let us suppose that all eclipses of the sun are total. How large,
then, must be the moon according to Thales’ theory? It must not be smaller than the sun, while
both luminaries could be as large as we see them. In reality, the same solar eclipse is experienced
as total in one area of the earth and seen as partial in adjoining regions. One concludes from this
that the moon is much smaller than the sun. But since a solar eclipse appears as total within an
area of many hundred stadia, it also follows that the moon is at least as large as that and the sun
is much larger still. Anaxagoras estimated that the moon was about as large as the
Peloponnese,89 and there is no reason to assume that Thales’ estimate was of essentially different
scale.
Although everybody knew that objects appear smaller as distance increases, the
consequences of Thales’ theory were too much at odds with the evidence of the senses to be
accepted without challenge. If people around Thales were bright enough to appreciate his
innovation and continue theoretical inquiry and even, as Anaximander did, to advance it further,
they were surely able to raise doubts about it. If Thales claimed the recognition of his wisdom,
he would have had to meet such doubts.
How can one prove that the sun and moon are immensely larger than they appear? A
simple proof, moreover one that does not depend on any particular theory of eclipses, is found in
Cleomedes (2. 1): as soon as we know a ratio between the apparent size of the sun (or the moon)
and its orbit, we realize that our eyes deceive us; for if the sun and the moon are about one foot
in length, we establish that their daily course would amount just to several hundred feet, which is
patently absurd.
We now see that the testimonies on Thales’ preoccupation with the size of the sun and
moon logically belong to his theory of solar eclipses. Moreover, we are now in a better position
to appreciate the degree of Thales’ innovation and realize what it was to make the first steps in
88               
      
89 See Dmitri Panchenko, “Eudemus Fr. 145 Wehrli and the Ancient Theories of Lunar Light”, 333 and n. 24.
51
creating theoretical cosmology. On the basis of the solar eclipses of 28 May 585, total in Ionia
and Aeolia, Thales would not have estimated the diameter of the moon as less than 150 km (in
modern measures). At a ratio 720 : 1 between the size of the moon and its orbit, the moon then
passes a distance of c. 150 km in two minutes and 4500 km per hour. The sun appears to us as
about the same size as the moon, but since it is further away both its size and its orbit must be
proportionately greater. Hence the sun is not only much larger than the moon, but it also rotates
much faster. So not only did Thales replace traditional stories of uncertain reliability told about
special kinds of beings (like Helios and Selene) for arguable and responsible statements about
physical bodies, but he also suggested a revolutionary image of the world around us. For we now
see that incredibly large celestial bodies rotating at an unbelievable speed were already a part of
Thales’ cosmology.
It is interesting to observe that the method of proving that the sun and moon are
immensely larger than they appear cited by Cleomedes – and one can hardly envisage for Thales
any other method – involves an indirect proof. Scholars have debated whether it was philosophy
or geometry that brought indirect proof about. One may now claim priority for astronomy. I am
not willing, however, to press this point. Particular forms of argumentation emerge to meet
particular problems and tasks. Therefore, I guess, indirect proof was rediscovered on many
occasions when one had to show that something was not what we would think or be prepared to
admit.
It is not easy to say how Thales determined the ratio between the diameter and the orbit
of the sun. In Cleomedes, the measurement is obtained by observing the amount of water passing
through a water clock between the first appearance of the upper limb of the sun on the horizon
and its complete rising, and comparing it with the amount passing through the clock in the course
of a full day and night. However, the ratio specified by Cleomedes differs from that attributed to
Thales, and no testimony links Thales to the use of the water clock. Archimedes (Aren. 4)
measured the angle subtended by the sun. It was suggested that Thales obtained his result by
angular measurement rather than time-measurement.999000 One may also suppose that Thales, using
a thin bar that exactly covered the visible disc of the sun or opening the legs of a compass (or
some other device), constructed two similar triangles with their common vertex in his eye. It was
easy, then, to obtain the ratio between the diameter of the sun and the radius of its orbit. And
Thales is said by some to have used similar triangles to determine the height of a pyramid (11 A
21 DK).
90 A. Wasserstein, “Thales and the Diameter of the Sun and Moon”, JHS 76 (1956) 105. Wasserstein’s proposal
involves, however, elements that are clearly anachronistic for Thales.
52
One may object that the method implies that the observer is thought to be at the centre of
the solar orbit. But such an assumption was likely – and almost inevitable – for one who
combined an interest in geometry with a study of the yearly course of the sun by observing the
points of its rising and setting on the horizon. For it is difficult to see what Thales’ methods of
determining the length of a year and the timing of solstices could be, if they did not involve
fixing the solstitial points on the horizon by means of alignment. The task of determining the
exact day of sun’s turning back southwards or northwards is difficult. It requires more than an
open horizon. For several days surrounding both solstices an unequipped observer would hardly
perceive any change in the points on the horizon where the sun rises and sets. However, simple
alignment achieved with the use of two sticks would allow quite a good estimate.999111
Now, one making such observations was likely to find himself within the circle of the
horizon – moreover, at its centre. One would not fail to observe that the points at which the sun
seems to rise and set display remarkable symmetry: on an open horizon, the points of rising and
setting are always seen at equal angles. For a person with an interest in geometry, it would be
natural to conclude that each day the arc described by the sun from its rising until midday is
equal to the arc from midday until the sunset and that he himself is on the line that divides the
daily tracks of the sun into two equal parts – this is the north–south line. Further, there are two
days every year when the sun rises due east and sets due west. And these are the days when day
and night are of equal duration. It follows (from the most natural assumption of the essentially
uniform rotation of the sun) that on these two days the sun describes from sunrise to sunset a half
of its daily circle. Thus the line connecting equinoctial points of sunrise and sunset divides this
circle into two halves; and the observer is to be located on this line. But the line which divides a
circle into two equal parts is its diameter – a proposition the converse of which is said to have
been an achievement of Thales (11 A 20 DK). So our observer finds himself on two different
diameters of the same (the sun’s daily) circle, that is, at their intersection. But it is clear that two
diameters of the one circle intersect at its centre. Hence the observer is at the centre of the solar
track. And we are told, incidentally, that “the followers of Thales assume the central position of
the earth” (Dox. 377; 11 A 15 DK).
91 For an accurate result, the alignment method is more reliable than measuring noon shadows, at least for the
summer solstice. However, an open horizon is not available everywhere – for instance, in Sparta where
Anaximander is reported to have set up a gnomon. The popular idea that Meton determined the day of the summer
solstice by observing shadows is neither likely nor compatible with the ancient testimony, preserved in the
Almagest, according to which the observation was made at the beginning of the day (3. 1, p. 205, 1 Heiberg:
). “A device aligned to a solstitial rising-point” is an obvious option – as recognized by Alan C. Bowen and
Bernard R. Goldstein, “Meton of Athens and Astronomy in the Late Fifth Century B.C.”, in Erle Leichty et al.
(eds.), A Scientific Humanist. Studies in Memory of Abraham Sachs (Philadelphia 1988) 39-81, esp. 72 f. (though
with unnecessary caution and without a necessary reference to Ptolemy).
53
It was repeatedly denied that such a good estimate as 720 to 1 has something to do with
Thales. According to Heath, “from the statement of Archimedes that Aristarchus discovered
() the value of 1/720th, we may infer with safety that Aristarchus was at least the first
Greek who had given it.”999222 But Archimedes does not speak about a ‘discovery’ since in the very
same phrase he starts to describe his own method of determining the apparent size of the sun
(A      ). His words imply only that Aristarchus cited this
ratio on his own authority. And Aristarchus could have followed a well-established tradition.999333
At the same time it should be specified that neither geometry nor a water clock would
certainly yield such an accurate result. 720 is a consciously chosen value within a range of, say,
650 to 750. This is a convenient number divisible by 12, 30, 60, etc. It also corresponds to the
number of hours in a calendar month (24 x 30). Whatever the reason for this particular number, it
is of no consequence for our present purpose.
THE FOUNDER OF GREEK GEOMETRY
Thales is the founder of Greek geometry. This statement implies not only that he introduced
geometrical studies into Greek usage, but also that he founded a special kind of geometry. The
geometry of Mesopotamia and Egypt was largely an accumulation of recipes. It was a
distinctively Greek contribution that general propositions and proofs became inalienable parts of
geometry.
Evidence
According to the standard Greek view, geometry originated in Egypt, but it was Thales
who “first went to Egypt and introduced this study to Greece,” as Proclus states in his
Commentary on the First Book of Euclid's Elements. He continues, “Thales discovered many
propositions himself, and instructed his successors in the principles underlying many others, his
method of attack being in some cases more general, in others more empirical” (65. 7. Friedlein).
Proclus preserved more specific information as well:
“Thales is said to have been the first to demonstrate that a circle is bisected by its
diameter” (157. 10 Friedlein; 11 A 20 DK).
“We are indebted to old Thales for the discovery of this and many other theorems. For
92 Heath, Aristarchus, 312.
93 See further my “Aristarchus of Samos on the Apparent Sizes of the Sun and Moon,” Antike Naturwissenschaft
und ihre Rezeption 11 (2001) 23-29.
54
he, it is said, was the first to notice and assert that in every isosceles [triangle] the angles at the
base are equal, though in somewhat archaic fashion he called the equal angles identical” (250. 20
Friedlein; 11 A 20 DK).
“Thus this theorem shows that, if two straight lines cut one another, the vertically
opposite angles are equal; Eudemus says that Thales was the first to discover this” (299. 1
Friedlein; Eudem. fr. 135 Wehrli; 11 A 20 DK).
“Eudemus in his History of Geometry attributes the theorem itself999444 to Thales, saying that
the method by which he is reported to have determined the distance of ships at sea shows that he
must have used it” (352. 14 Friedlein; Eudem. fr. 134 Wehrli; 11 A 20 DK).
Some information about Thales’ achievements is naturally missing from Proclus’
commentary on Euclid’s First Book. Thus, Diogenes Laertius quotes Pamphila, who states that
“having learnt geometry from the Egyptians, Thales was the first to inscribe a right-angled
triangle in a circle, whereupon he sacrificed an ox.” Diogenes specifies that “others tell this tale
of Pythagoras” (1. 24; 11 A 1 DK), but a number of parallel passages suggest that the disputed
point is the sacrifice of an ox on the occasion of a geometrical discovery rather than the
discovery in question itself.999555
A reconstruction of ‘Thales’ basic figure’, which would be sufficient for the proof of all
theorems ascribed to him, has been suggested: it is only necessary to inscribe a rectangle into a
circle and link its apexes with diagonals (Fig. 1).999666
Fig. 1.
The rest of the evidence pertains to the measurement of the height of a pyramid.
According to one version, it was accomplished by measuring the shadow of the object at the time
when a body and its shadow are equal in length (Plin. HN 36. 82; Hieronymus in D.L. 1. 27; 11
A 21 DK). According to the other, Thales set up the stick at the extremity of the shadow cast by
a pyramid and, having thus made two triangles from the impact of the sun’s rays, showed that the
94 Eucl. 1. 26: “If two triangles have the two angles equal to two angles respectively, and one side equal to one side,
namely, either the side adjoining the equal angles, or that subtending one of the equal angles, they will also have the
remaining sides equal to the remaining sides and the remaining angle to the remaining angle.”
95 Sir Thomas Heath, A History of Greek Mathematics (New York, 1981 [original publication: Oxford 1921]) I,
133 f.
96 Oskar Becker, Das mathematische Denken der Antike, 2nd ed. (Göttingen 1966) 37-39.
55
pyramid has to the stick the same ratio which the shadow has to the shadow (Plut. Conv. sept.
sap. 147 A; 11 A 21 DK).
The origin of geometrical proofs
While our predecessors have overlooked Thales’ decisive contribution to the emergence
of theoretical astronomy, his role in the formation of Greek geometry was denied by only a few
and emphasized by many scholars, most notably Jürgen Mittelstraß who argues an essential
connection of Thales’ geometry to what he calls ‘the discovery of the possibility of science’.97
Yet many questions remain unanswered.
A. I. Zaicev defines Thales’ achievement as a “real revolution in the forms of human
cognition”, to wit: “first, Thales realized the necessity or at least desirability of proving
geometrical statements that seemed self-evident, and second, he gave those proofs.”999888 We may
ask, why Thales (unlike the Egyptians and Babylonians) began to prove theorems? “The first
mathematical proofs”, Zaicev writes, “were the natural fruit of a social climate where the
discovery of a new truth not only gave immediate satisfaction but could also bring fame. For it is
clear that in these conditions, mathematical truths confirmed with proof became a particularly
attractive object of search; one who found a faultless proof could as a rule count on public
recognition, while the achievements in any other field of knowledge could as a rule be
disputed”.999999
This ingenious and heuristically valuable explanation does not, however, agree with the
neighbouring assertion that the revolution accomplished by Thales consisted of proving
statements that seemed self-evident. Who would have disputed something self-evident? Who
would have admired the proof of something that was already clear?
B. L. van der Waerden tried to explain the origin of proving geometry by the fact that
Thales was acquainted with both Egyptian and Babylonian mathematical traditions; having
found some discrepancy between them, Thales wondered who was right and how to ascertain
this.100 Such an approach does not work in the given case since the geometrical problems
considered by Thales did not concern such matters as the formula for the area of a circle, for
which the data of the two Near Eastern traditions were at odds.
I assert that proof comes from the demand for proof. The demand for proof arises, on the
one hand, in connection with solving a problem, the answer to which cannot be obtained by
97 Jürgen Mittelstraß, Die Möglichkeit von Wissenschaft (Frankfurt am Main 1974) 29-55; Idem, Neuzeit und
Aufklärung. Studien zur Entstehung der neuzeitlichen Wissenschaft und Philosophie (Berlin; New York 1970) 1832.
98 Alexander Zaicev, Das griechische Wunder: Die Entstehung der griechischen Zivilisation (Konstanz 1993) 167.
99 Ibid.
100 B. L. van der Waerden, Science Awakening.
56
means of immediate observation or measurement, and, on the other hand, in connection with the
need to submit the answer in the form of an arguable and not arbitrary statement.
The information preserved in our sources allows us to suggest how the first geometrical
proofs could be given. We are told that Thales determined the distance of ships in the sea and
also the height of a pyramid. In both cases it was impossible to take measurements, and if Thales
nevertheless gave answers he needed to prove their correctness.
Yet this was probably not enough to predetermine the specific development of Greek
geometry. One can easily imagine geometry of a Near Eastern type, supplemented by sporadic
proofs for particular cases. Ancient Chinese geometry provides one example.111000111 It also makes us
see that the solving of problems concerning the distance of an inaccessible object could be
presented in textbooks as recipes and not as statements derived from general characteristics of
corresponding geometrical figures and accordingly proven. And if we still wish to select a proof
as a decisive event, we should perhaps prefer the proof of the incommensurability of a square’s
diagonal with its side – an achievement by Hippasus of Metapontum111000222 – to the first proofs given
by Thales. Here, a problem arose that was analogous to one whose solution initiated theoretical
cosmogony: it was necessary to ascertain something that was absolutely impossible to observe. I
cannot believe that “the deductive mathematics begins just at that very moment when the
knowledge obtained only from practice ceases to be considered convincing: when the need ... of
proof appears even in cases when everyday practice gives, one would think, a full
explanation.”111000333 On the contrary: what is called deductive mathematics begins when the
knowledge that can by no means be obtained empirically is nevertheless recognized as
convincing. It is not the proof of something self-evident, but the proof of something that cannot
be seen (or checked by any available empirical device), that produces argumentative and
systematic knowledge, consecutively brought into correlation with what has already been
ascertained.
The proof of irrationality, further, promoted a stricter approach to geometry. For it
showed that the evident and the trustworthy do not necessarily coincide. And again – to oppose
an influential view – when choosing between trustworthiness and evidence, the mathematicians
preferred the principle of non-contradictory reasoning not because they adopted it from Eleatic
101 E. I. Berezkina, Matematika drevnego Kitaia [Mathematics of Ancient China] (Moscow 1980).
102 Kurt von Fritz, “The Discovery of Incommensurability by Hippasus of Metapontum,” in David J. Furley and R.
E. Allen (eds.), Studies in Presocratic Philosophy (London; New York 1970) 1, 348-412. The author assumes that
ancient tradition dates the discovery to the middle of the fifth century (411 et al.). In reality ancient tradition
suggests a date c. 500 BC, if not earlier. For according to the Suda, Heraclitus was a listener of Hippasus (18 A 1 a
DK) and a passage in Aristotle seems to confirm that Hippasus was older than Heraclitus (Metaph. 984 a 7; 18 A 7
DK).
103 Á. Szabó, “Wie ist die Mathematik zu einer deduktiven Wissenschaft geworden?”, Acta Antiqua, 4 (1956)
130. See also Árpád Szabó, The Beginnings of Greek Mathematics (Budapest 1978).
57
philosophy, but because otherwise they would be unable to answer the question: “Where did you
get it from?” It is true that the philosophical poem of Parmenides shows highly nontrivial use of
logical reasoning, but we have no relics of the early mathematical treatises. The idea that
deductive mathematics arose from Parmenides’ discussion of Being is not only unnecessary, but
also unlikely. Parmenides argued that change and movement are illusory. Did the
mathematicians find his claims so convincing that they decided to imitate his style of
argumentation? But this is what the train of thought of Árpád Szabó, Walter Burkert and other
champions of this idea imply.111000444
The demonstration of the incommensurability of a square’s diagonal with its side
involves the distinction between odd and even numbers (for if they are commensurable, the same
number is both odd and even). But they are such by definition, and so the demonstration of
incommensurability was an important step towards the definitional basis of deductive
mathematics. Further, the discovery of incommensurability was attended through indirect proof.
Now, geometrical truths are not deduced consecutively from a single, fundamental fact, but from
a complex of facts. The complex-forming properties are not deduced one from another, but
should be ascertained in their interdependence. The totality of the visually evident truths tends to
coincide with such a complex. What an indirect proof can do is show the indispensable
concomitance of some fundamental properties. Thus, strict proofs of the evident correlations and,
above all, the formation of the punctiliously arranged deductive system are hardly conceivable
without indirect proof. So, if such a proof entered geometry for the first time with the
demonstration of incommensurability, the significance of the latter must again be emphasized.
In a new context, at a relatively advanced stage, the proving of even evident statements
became appropriate. In the course of demonstrative reasoning it was necessary to come to
premises that the opponent could agree with, and then show the inevitability of the correlation
between these premises and the consequence being upheld; since such premises belong to the
sphere of the evident, there would be no need for further persuasion – though if the listener
happened to be a follower of Zeno, one had to expect some cavils. On the other hand, a person
arranging the material of his proof in chains so that the transition from one link to another would
leave no room for doubt and would win common recognition111000555 would certainly want every link
to be solid; after all, the boundary between the evident and the not-quite-evident is not always
unequivocal.
But what is to be done with Proclus’ assertion that Thales proved that a circle is halved
104 The opposite view – that Parmenides’ style of argumentation derives from Greek mathematics – is more likely,
but neither proven nor necessary. For the most recent defense of this view see posthumous paper by Alexander
Zaicev, “Encore une fois à propos de l’origine de la formalisation du raisonnement chez les Grecs”, Hyperboreus 9
(2003) 2, 265-273.
105 N. Bourbaki, Elements d'histoire des mathémathiques (Paris 1969) 10.
58
by its diameter? Heath suggests we should not take Proclus' words too literally, for even Euclid
does not prove this statement but takes it as a fact.111000666 Zaicev rejects the idea that Thales simply
advanced the geometrical statements that have been ascribed to him, while the subsequent
tradition attributed to him their proof; he points out that the talk is about visually evident
truths.111000777 It seems that a compromise can be found: “Undoubtedly, many ratios were first
discovered by means of drawing figures of different kinds and lines inside them along with the
concomitant observation of the evident ratios of equality and so on between the parts.”111000888 In the
course of various constructions of this kind it was possible to observe ratios of different degrees
of evidence. Since within the limits of one diagram they appeared interdependent, the study of
problematic ratios could entail the formulation and demonstration of all ratios. Moreover, it is
only within the limits of a special diagram that many obvious geometrical truths (like the
equality of vertical angles or that of two triangles with equal bases and adjoining angles) could
be realized and formulated as facts.
Furthermore, it can be that the original context of Thales’ assertion pertained not so much
to one diameter bisecting a circle as it did to two diameters, each of them dividing a circle into
two halves. The relevant construction is implied in the Aristotelian proof of the proposition that
in every isosceles triangle the angles at the base are equal (An. Pr. 41 b 13-22), which involves
the equality of two ‘mixed’ angles, each formed by the circumference of a semicircle and the
diameter. The proof referred to by Aristotle has long been recognized as a pre-Euclidean one,
and since Proclus attributes the discovery of this proposition to Thales, many scholars are
prepared to admit that Aristotle preserved for us the demonstration employed by Thales (Fig. 2).
Fig. 2.
Since one would hesitate to maintain that the equality of four (or more) segments formed by two
(or more) diameters is self-evident. Therefore Thales’ general assertion would constitute new
knowledge.
106 T. L. Heath, A History of Greek Mathematics, 131.
107 Alexander Zaicev, Das griechische Wunder, 166.
108 T. L. Heath, A History of Greek Mathematics, 136.
59
It is possible that Proclus transmitted to us a recollection of how Thales commented on
the property of the diameter to bisect a circle. Proclus’ remark, “Thales is said to have been the
first to demonstrate that a circle is bisected by its diameter” continues as follows: “And the
reason of halving is that the straight line passes through the center unflinchingly. For passing the
centre and always preserving the same movement, being indifferent to both sides, it separates the
equal towards the circumference of the circle on both sides and in all its parts”. The passage goes
on: “And if you want to prove the same in scientific way ...” – which is followed by an indirect
proof. Thus, Proclus, while commenting on the seventeenth Euclidean definition (“The diameter
of a circle is any straight line drawn through the center and bounded at both ends by the
circumference of the circle, the same line cutting the circle in halves”), first gives a general
commentary, then states that the correctness of the second part of the definition discussed was
first proved by Thales, gives a proof, and finally opposes it with another proof, a scientific one. It
appears that Proclus is attributing the first proof to Thales.111000999 If that is the case and if Proclus is
correct, one may observe that Thales deals here with a kind of etiology rather than deduction. At
the same time we have before us reasoning, and not a primitive demonstration by means of
folding and superposing the figures (which, in spite of the ancients’ habit of drawing on the
ground, is generally supposed to have been used by Thales).111111000 What we have here is a study,
and not a crafty answer.
Geometry as a study of correlations and its likely origin within the study of celestial
bodies
The interest in the properties of figures expressed in various correlations comes to the
foreground in Thales’ geometrical studies. Thales is interested in what is the relation between the
diameter and the circle, which triangles are equal, what happens to angles when straight lines
cross. It was this way of thinking that led to the formation of geometry as a system of
interdependencies and eventually as a deductive system.
Fortunately, we are in a position to be more specific as to what particular set of
correlations was of special interest for Thales. This can be seen from the already mentioned
‘Thales’ basic figure’ – a circle crossed by two intersecting diameters that at the same time are
the diagonals of a rectangle inscribed into the circle. In other words, it is a study of certain
geometrical correlations within a circle. But we already know something about Thales and the
circle. As someone who had studied the yearly movement of the sun between the solstices and
109 Proclus' text as an account of Thales' proof is quoted by S. J. Lurje, Ocherki po istorii antichnoi nauki [Essays
on Science in Antiquity] (Moscow; Leningrad 1947) 38; the attribution of the proof to Thales is also assumed by
Jürgen Mittelstrass, Neuziet und Aufklärung (Berlin; New York 1970) 31.
110 For instance, K. von Fritz, “Die Archai in der griechischen Mathematik”, in his Grundprobleme der Geschichte
der antiken Wissenschaft (Berlin; New York: De Gruyter, 1971) 335-429, esp. 402.
60
who fixed the time of rising and setting of particular stars Thales was concerned with the circle
of the horizon. What are we dealing with: a chance coincidence or an essential connection
between the astronomical and geometrical studies of Thales? A testimony related to an
outstanding follower of Thales seems to speak in favour of the latter option.
Proclus comments on Eucl. 1. 12 (“to draw a perpendicular to a given straight line from a
point outside it”): “This problem was investigated by Oenopides, who thought it useful for
astronomy. He, however, calls the perpendicular in the archaic manner a line drawn with the
gnomon, because the gnomon is also at right angles to the horizon” (283. 7-10 Friedlein; 41 A 13
DK). This testimony is frequently cited by scholars, but I do not recall any attempt to explain it.
Let us start with what is at hand – Euclid’s proof of the theorem (Fig.3).
C
A G
H
E
B
D
Fig. 3.
“Let a point D be taken at random on the other side of the straight line AB, and with center C and
distance CD let the circle EFG be described; let the straight line EG be bisected at H, and let the
straight lines CG, CH, CE be joined. The triangles CHG and EHC have three respectively equal
sides; they are equal and therefore the angle CHG is equal to the angle EHC. Since they are
adjacent angles, each of them is right”.111111111
One finds mention of the gnomon in combination with a drawing analogous to that
presented by Euclid in a book by a great mediaeval scientist and polymath – Al-Biruni. In 4. 15
of his Al-Qanunu’l-Mas´udi, Al-Biruni addresses the problem of the exact determination of the
meridian line.112 He explains various methods with both their advantages and drawbacks.
Almost all methods employ a gnomon erected on carefully leveled ground. One of the methods
is of particular interest for our purpose. Al-Biruni refers to it as constructing ‘the Indian circle’.
This circle is to be drawn on the leveled ground; the gnomon occupies the centre of it. The
111 The Thirteen Books of Euclid’s Elements, transl. with introd. and comm. by Sir Thomas L. Heath. 2nd ed. (New
York 1956) 1, 270 f.
112 I used a Russian translation by P. G. Bulgakov and B. A. Rosenfeld (Tashkent 1973).
61
shadow cast by the gnomon shortens during the first half of the day and increases after the
midday. One observes – the day of the winter solstice is recommended – the moments when the
shadow enters the circle and when it leaves the circle. The points of both entrance and exit are
marked and connected by a straight line. This line is bisected by the line drawn through the
centre of the circle (occupied by the gnomon). One thus obtains the meridian line, while the
diameter drawn at the right angle to this line makes the equinoctial line. Al-Biruni provides an
illustration (Fig.4).
S
W
E
N
Fig. 4.
A similar method is described in the Zhou bi (#F7 Cullen): “When the sun first rises, set up a
gnomon and note its shadow. When the sun sets, note the shadow again. The line between the
two ends fixes east and west, and if one splits [the distance] between them in the middle and
points to the gnomon it fixes south and north.”
The Zhou bi offers no demonstration of the validity of the method, but it is clear that this
would require a construction either identical or analogous (with an equilateral triangle in the
‘southern’ part of the circle) to that employed by Al-Biruni. As a matter of fact, the next section
of the Zhou bi describes the use of a graduated circle drawn on level ground for fixing stellar
positions, and it was suggested that the cited passage originally belonged to this section.111111333
Furthermore, the method stated in the Zhou bi is hardly possible without a circle drawn on level
ground. For no shadow from a gnomon can be observed when the sun rises or sets, so it is left to
fix two points at which the shadows touch a circle drawn in advance. In reality, thus, the Zhou bi
offers a cruder formulation of the method described by Al-Biruni
To be sure, it is not Thales, but Anaximander who is linked in our sources with the
gnomon, and it is likely that combining this device with geometrical constructions for an
astronomical purpose was Anaximander’s innovation. Yet Anaximander was the immediate
113 Christopher Cullen, Astronomy and Mathematics in Ancient China: the Zhou bi suan jing (Cambridge 1996)
190 and 193.
62
follower of Thales, and it is possible that Thales was already familiar with some of the
techniques involving the gnomon since this instrument at all events came to the Greeks from the
Near East and since the observation of a shadow appears in the accounts of Thales’ measurement
of the height of a pyramid. More importantly, the alignment can be effectively substituted for the
observations of shadows in the method as described in the Zhou bi.111111444 And we saw that
alignment was almost certainly the technique which allowed Thales to fix the solstitial points on
the horizon. If because of weather conditions these observations were made around the summer
(rather than winter) solstice, the demonstration of the validity of the method would require some
additional – and characteristic – considerations (Fig. 5).
N
B
A
C
D
F
E
S
Fig. 5.
A and B are the points on the circumference of a circle with centre C; they correspond to the
points of the sunrise and sunset on the horizon; D and E are the points at which the projections of
AC and BC touch the circle; DE is halved at F. The triangles DCF and ECF have three
respectively equal sides; they are equal and therefore the angle ACD is equal to the angle BCD.
But one has actually to show that the arc BS is equal to the arc AS. They are equal if the angle
BCS is equal to the angle ACS. Since it is shown that the angle ACD is equal to the angle BCD,
one has only to prove that the angle BCD is equal to the angle ACE. But they are equal as the
vertical angles – a proposition the formulation of which our sources explicitly attribute to Thales.
One can also observe that the same drawing and a very similar way of reasoning are used in the
above-mentioned pre-Euclidean demonstration of another of Thales’ discoveries – that in every
isosceles triangle the angles at the base are equal. One can further see that it is enough to join D,
B, A, E to get the so-called ‘Thales’ basic figure’.
114 Characteristically, the technique of alignment is repeatedly employed in the Zhou bi.
63
There is indirect confirmation of the assumption that Thales was interested in
determining the exact north–south line. He is said to have discovered Ursa Minor (11 A 1. 23; 3;
3a DK), which points to the task of determining the position of the North Pole. One should not
forget that no bright star was visible close to the North Pole in the middle of the first millennium
BC. Also Callimachus’ wording (if one may rely on it) implies something more specific (and
scientific) than practical problems of navigation.111111555
If the characteristic features of Greek geometry were initially taking shape in the context
of astronomical research, one need no longer account for another near miracle – that a single
person happened to be the founder of both Greek geometry and astronomy. Further, it explains
well why astronomy appears in our sources as the most typical activity of the mathematikoi; why
the study of angles, in contrast to Near Eastern geometries, became prominent in Greek
geometry; and why one observes the remarkable expansion of the term gnomon in Greek
mathematics, even into arithmetic.
With this hypothesis, we are also in a better position to see how Greek geometry emerged
as a system of correlations or interdependencies in which general propositions and proofs played
an essential role. It started with a study of a natural system of correlations, framed by the circle
of the horizon as well as the circles and arcs described by rotating celestial bodies. All the
objects within this frame were inaccessible. Therefore any assertion about them that went
beyond the immediately observable must have been proved. The system of rotating bodies could
not be formulated in simple recipes; it was not like measuring and re-measuring land. There was
nothing to add or subtract or transform in this arrangement. Particular truths about particular
aspects of this arrangement could have been established only on the basis of general principles,
established and formulated as general propositions.
Supplementary Notes
How did Thales determine the distance of a ship at the sea?116
The question was discussed at length by Sir Thomas Heath: “The most usual supposition
is that Thales, observing the ship from the top of a tower on the sea-shore, used the practical
equivalent of the proportionality of the sides of two similar right-angled triangles, one small and
one large … The objection to this solution is that it does not depend directly on Eucl. I. 26.
Tannery therefore favours the hypothesis of a solution on the lines followed by the Roman
agrimensor Marcus Junius Nippus in his fluminis varatio.” This means constructing two equal
115      – “measured (or: drew the outline of) the little stars of
the Wagon”.
116                
            
64
right-angled triangles, one of which is situated on land and therefore can be measured (Fig.6).
Fig. 6.
Heath realizes, of course, that, “as a rule, it would be difficult, in the supposed case, to get a
sufficient amount of free and level space for the construction and measurements”. He suggests
simplifying the technical aspect of the solution without changing its geometrical essence, by
means of a simple device fixing the angle, so that the distance equal to that of the ship from the
shore can be measured “from the foot of the tower” along the shore.111111777
The methods referred to by Heath are clumsy. They require either a particular landscape
or the presence of a tower.111111888 None of these methods would have impressed people so much as
to bring fame to Thales. A more plausible solution involves a combination of mathematics and
philology. I suppose that Proclus made a mistake because of too much knowledge. He knew that
Thales “had called the equal angles identical”. When he read in Eudemus that the method by
which Thales is reported to have determined the distance of ships at sea involves two triangles
with o angles, he interpreted this as a reference to the use of two triangles with
 angles, that is, Eucl. 1. 26. But Eudemus was not commenting on Euclid. He had in mind
two similar triangles, the use of which allows an easy solution to the task – without erecting a
tower or involving any equipment but a walking stick for the sake of alignment (Fig. 7).
117 T. L. Heath, A History of Greek Mathematics, 132 f.
118 Burkhard Gladigow, “Thales und der ”, Hermes 96 (1968) 264-275 points out that the device
described by Heath is proven archaeologically and would have probably been called by the ancient , and
that our tradition connects Thales with the use of . Nevertheless the method remains clumsy. As to
, the term designates a kind of compass, and Thales’ geometrical studies are unthinkable without a
compass; there is no thus specific connection with the determination of a distance from a particular point to a ship.
65
Fig. 7.
It is certainly true that Eudemus must have understood whether similar or equal triangles were
involved. But those scholars who advance this as an objection against the use of similar
triangles111111999 miss the simple point that Proclus was not necessarily in a position to realize
adequately the words of Eudemus.111222000 One may also recall that similar right-angled triangles are
used in one of the versions concerning Thales’ measurement of the height of a pyramid. Many
scholars find more probable the alternative version – measuring the shadow of the pyramid at the
time when a body and its shadow are equal in length. This version could, however, have
originated because of its narrative value; in any case, the person able to find the height of a
pyramid through observing the shadows and who is interested in geometrical figures in general
could hardly have failed to notice the remarkable properties of similar right-angled triangles.
Cosmology and the proof of the incommensurability of a square’s diagonal with its side
The ancient proof of the incommensurability of a square’s diagonal with its side is based
on the distinction between odd and even numbers. This distinction seems to us so natural that we
forget to ask what could have brought it about. What was the problem situation of the person
who introduced the notions of odd and even numbers?
The odd and the even figure in the Pythagorean series of opposites (Aristot. Metaph. 986
a 13). Since the opposites (hot and cold, dry and wet, etc.) play a prominent role in Presocratic
cosmogonies and cosmologies beginning with Anaximander I suggest that the one who
introduced the notion of odd and even numbers was extending the principle to a new area. He did
119 Most categorically Burkhard Gladigow, Op. cit. 266.
120 One may consider the possibility of a method based on constructing two similar triangles with the help of a
compass. One points the compass at the ship and then measures the distance from one’s eye to the compass. In that
case, however, Proclus’ misinterpretation requires additional assumptions – that he was well familiar with the
method known to us from Marcus Junius Nipsus and interpreted the words of Eudemus under the influence of this
knowledge.
66
so because he believed that the ratios expressed in numbers were essential constituents of the
world fabric, so he needed to find opposites in the realm of numbers. Tradition says this was
Pythagoras.
According to a standard view, the proof of incommensurability destroyed the whole
Pythagorean philosophy. But the alleged crisis is not confirmed by our sources,121 and the idea
itself seems to me wrong. Pythagorean philosophy claimed that there are certain ratios behind all
things, but not that all things have a common measure. The geometer who studied right-angle
triangles must have been well aware of the fact that it is very often impossible to express in
integer numbers the length of the hypotenuse and sides. He certainly knew that in a right-angle
triangle with sides of 4 and 3 units, the length of the hypotenuse is 5 units. Yet every time he
considered an isosceles right-angle triangle, with sides of 2 or 4, or 6, etc. units, he had to face
the difficulty of expressing the length of the hypotenuse in integer numbers. He was very happy
and proud to overcome this difficulty by proving that their squares have a ratio. ‘Rational only in
the square’, later Greek mathematicians would say. And clearly the ratio of a side to the
hypotenuse of a right-angle isosceles triangle is much the same problem as the ratio of a square’s
side to its diagonal. Thus, the proof of incommensurability hardly affected philosophy even if it
employed a distinction that, I suppose, originated in philosophy.
The philosophy that assigned such an important role to numbers was essentially
connected with the discovery that the realm of the invisible, of sounds, displays ratios that are
expressed in numbers. This was a new field of research and not a legacy of Thales. This is worth
keeping in mind for several reasons. One of them is that our tradition appears once again
essentially correct: we have competing claims for Pythagoras, Hippasus and, perhaps, Lasus of
Hermione, but no attempt has been recorded to include this kind of study among those initiated
by Thales.
HOW DO WE KNOW ABOUT THALES?
The books by Anaximander and Anaximenes have not been handed down to us. Yet ancient
expositions of their views are ultimately based on the accounts of people (one thinks first of all
121 The stories usually cited report that the person who divulged the discovery of the incommensurability was
punished by the gods. The stories imply only the recognition of the importance of the discovery, but they contain no
hint of the idea that the discovery was considered important because it undermined the teaching of the Master.
67
of Theophrastus) who read the originals. Thus, our knowledge of the ideas of Anaximander and
Anaximenes, on the one hand, is very deficient, possibly even distorted in a number of points,
and we are hardly in a position to appreciate their intellectual accomplishment as it deserves
(though strangely, many scholars believe that the nature of our sources results in an exaggeration
of their achievements); on the other hand, our knowledge rests ultimately on a safe foundation.
The case of Thales seems different since he left no book at all. Many scholars would deny or
doubt the very possibility of establishing what Thales thought, studied and maintained. Caution
in respect to transmitted information about Thales is certainly reasonable, but a priori skepticism
is not justified.
During the first hundred years of its existence, Greek astronomy and geometry had no
textbooks to educate new generations. Knowledge of both astronomy and geometry could spread
only by personal contacts, by transmission from a teacher to a disciple. And because Greek
astronomy and geometry developed in quite a specific way from the start, they must have
originated from a very limited circle, from the people immediately surrounding Thales. And we
should not underestimate the power of oral transmission. Even now we hear from our teachers
stories about the teachers of their teachers. Thales made an extraordinary impression on his
contemporaries. Under such circumstances it is no miracle if some of his views and formulations
were orally transmitted until they were recorded by competent people able to admire their
predecessors. As a matter of fact, Diogenes Laertius (1. 22-24) cites Xenophanes, Heraclitus,
Democritus (twice) and Hippias among the authorities who mentioned Thales. Modern scholars
proposed to include in the list Anaximenes and even Anaximander.
It is, further, worth emphasizing that the tradition attributes to Thales not only
indisputable achievements but also ideas and assertions rejected by later Greek authorities.
Thales is said to have advanced the view according to which the floods of the Nile are caused by
the so-called Etesian winds that hinder the outflow of water to the sea (Diod. 1.38.2; Dox. 384;
634). This theory was repeatedly criticized in antiquity, and it actually belongs to the epoch
when the Greeks knew little of Egypt beyond the Delta – it does not take into account the fact
that the flood occurs in Upper Egypt earlier than in the Delta. Again, Pliny gives us a number of
opinions about the length of time separating the autumnal equinox and the setting of the
Pleiades, and the assertions of Thales and Anaximander differ significantly from those of later
authorities.111222222
122 HN 18, 213; 11 A 18; 12 A 20 DK: occasum matutinum Vergiliarum Hesiodus – nam huius quoque nomine
exstat astrologia – tradidit fieri, cum aequinoctium autumni conficeretur, Thales XXV die ab aequinoctio,
Anaximander XXIX, Euctemon XLIIII, Eudoxus XLVIII. We need not discuss this difficult passage here. It is
remarkable that D. R. Dicks, a passionate fighter against what he believes is the myth of Thales, does not mention
this testimony in his general paper – “Thales”, CQ N.S. 9 (1959) 2, 294-309 – nor in “Solstices, Equinoxes, and the
Presocratics”, JHS 86 (1966) 26-40. Nor does he mention testimonies of Xenophanes, Heraclitus, and Democritus.
68
Furthermore, some information about Thales is very specific. The most striking example
is Proclus' assertion that Thales “in somewhat archaic fashion called the equal angles identical”
(250. 20 ff. Friedlein).111222333 Proclus could not, of course, have invented the peculiar formulation he
mentions. Since he refers several times to Eudemus' History of Geometry and twice to Eudemus'
reports on Thales (299.1-5; 352.14-18 Friedlein = fr.135;134 Wehrli = 11 A 20 DK), scholars
assume that Proclus' information goes back to Eudemus.111222444 This conclusion can be confirmed.
Proclus provides us with one more instance of a reference to a formulation ‘in archaic
fashion’. As we remember, Oenopides of Chios “in archaic fashion called the perpendicular a
line drawn with the gnomon” (283. 7-10 Friedlein; 41 A 13 DK). When Proclus speaks about
another achievement of Oenopides, he refers explicitly to Eudemus' authority (333. 5-6 Friedlein
= fr.138 Wehrli = 41 A 14 DK). While Thales left no book, Oenopides did. If Proclus had had
direct access to Oenopides' book, he would not have needed to resort to Eudemus. Consequently,
it was almost certainly Eudemus who preserved Oenopides' old-fashioned formulation. This is
clearly an additional reason to believe that yet another report on ‘archaic’ terminology was
borrowed from Eudemus.111222555
Yet there were two and a half centuries between Thales and Eudemus. The question
remains of how Thales’ original wording reached the historian. Several possibilities can be
indicated. Bruno Snell and Joachim Classen argued that a book by Hippias of Elis was a link
between Thales and Aristotle.111222666 Alexander Zaicev extrapolated their conclusions to the case of
Eudemus.111222777 And good reasons can be advanced in favour of such an extrapolation. Hippias was
known as a person who praised his predecessors (Plat. Hip. Mai. 282 a) and was regarded as an
expert about everything related to ancient times (ibid., 285 d) as well as a teacher of geometry
(Plat. Prot. 318 e; Hip. Mai. 285 c) and an able mathematician.111222888 Moreover, Proclus allows us
123 Characteristically, Dicks makes no comment on this testimony. He tells us instead a very strange story of how
Thales’ geometry was constructed as “the amplification and linking together of separate notices in Herodotus”
(“Thales”, 304). Otto Neugebauer, The Exact Sciences in Antiquity (Providence 1957) 148, without discussing this
testimony, just tell us that “the traditional stories of discoveries made by Thales or Pythagoras must be discarded as
totally unhistorical”.
124 Sir Thomas Heath, A History of Greek Mathematics, I, 130 f.; Charles Mugler, Platon e la recherche
mathématique, 54; Oskar Becker, Das mathematische Denken der Antike, 39; B. L.van der Waerden, Science
Awakening (New York 1961) 87; Kurt von Fritz, Grundprobleme 473 f.; Neuenschwander E. "Die ersten vier
Bucher der Elemente Euclids", Archive for history of exact sciences 9 (1973) N 4-5 360; H. D.Rankin, “
in a fragment of Thales”, Glotta 39 (1961) 73-76. Burkhard Gladigow, "Thales und der ", 264 and some
other scholars suggest that Eudemus believed that he had a book by Thales, but we will see that there is no need to
resort to such a guess.
125 Moreover, we are even in a position to understand why Eudemus might be attentive to Thales' out of date
formulation – see: Dmitri Panchenko, “ and  in Anaximander and Thales”, Hyperboreus 1 (1994)
1, 28-55, esp. 38 f.
126 Bruno Snell, "Die Nachrichten über die Lehren des Thales und die Anfänge der griechischen Philosophie- und
Literaturgeschichte", Philologus 96 (1944) 170-182; C. Joachim Classen, "Bemerkungen zu zwei griechischen
"Philosophiehistorikern", Philologus 109 (1965) 175-181, esp. 175-178.
127 Alexander Zaicev, Das griechische Wunder: Die Entstehung der griechischen Zivilisation (Konstanz 1993) 165.
128 Any history of Greek geometry should have an account of Hippias’ quadratrix.
69
to realize that Hippias recorded some information pertaining to the history of geometry (65.1115 Friedlein = 86 B 12 DK).
Thus it is easy to imagine that Hippias had occasion to say Thales brought geometry from
Egypt. Nor is it difficult to conceive of Hippias making a catalogue of geometric items in which
Thales was regarded as their discoverer; but was there room for commentary on peculiar
terminology in such a catalogue? It seems that the information about particular formulations
must have come from an occasional remark within a special treatise. This might also have been
the work of Hippias, yet there are two more plausible candidates – Oenopides and Hippocrates of
Chios.
Hippocrates, a mathematician and physiologos, who was active in Athens in the middle
of the fifth century BC111222999 and was the first to compose a book of Elements, became famous as a
geometer able to approach the fascinating problem of the squaring of the circle by a method
known as Hipppocrates' quadrature of lunes. A Eudemian account of this method has been
preserved by Simplicius, and its detailed and illustrated exposition can be found in any general
history of Greek geometry. What is of special interest for our purpose is that Hippocrates'
method involves several propositions established, according to our sources, by Thales. So the
preliminary part of Hippocrates' argument has a reference to the proposition that angles of all
semicircles are right, and the basic construction used by Hippocrates for demonstrations is a
semicircle circumscribed about an isosceles right-angled triangle. Hippocrates obviously used
the proposition about the equality of the angles at the base of an isosceles triangle, so he had
occasion to mention that this was established by the famous Thales. Moreover, Hippocrates had
good occasion to say a word about terminology. The fact is that a clear distinction between
 and  was indispensable for his demonstration.
He proved that a lune, a crescent-
shaped figure, was equal to a triangle (      – Eud. fr.140, 1617 Wehrli). It was just impossible to say that they were  because, having different shapes,
they were not. On the other hand, he needed a special term to designate similarity because one of
his starting propositions said that “similar segments of circles have the same ratio to one another
as have the squares on their bases.”
One may, accordingly, guess that Thales was mentioned by Hippocrates in a context
related to the problem of the squaring of the circle. Interestingly, Thales does appear in such a
129 Walter Burkert, Lore and Science in Ancient Pythagoreanism (Cambridge, Mass. 1972), 314, n. 77 is right to
observe that Hippocrates’ theory of comets must have been published before 427 BC, but he is hardly correct to date
Hippocrates to about 430 BC. For the comet observed in Athens in early 427 BC is referred to by Aristotle to refuse
a theory advanced by “Hippocrates and his disciple Aeschylus” (Met. 342 b 29; 42 A 5 DK). One may think that
Aeschylus published the theory when his teacher was no longer alive. In any case a shared claim implies that
Aeschylus was not just a beginner, and Hippocrates had to gain prominence before starting to teach. Thus
Hippocrates must have become prominent a good number of years before 427 BC. On the other hand, Proclus dates
him after Anaxagoras and Oenopides (66.4 Friedlein; 42 A 1 DK).
70
context, in Aristophanes' Birds (414 BC.). The poet introduces Meton, whom we know as a
distinguished astronomer, but who is shown in the comedy as a geometer. Meton comes with a
ruler and compasses in his hands eager to plan the city of birds. He makes a certain construction
"so that your circle may become square" (1005). It has been remarked many times that the
passage points to the problem of squaring the circle, which was very popular at that time. Indeed,
we are told that not only Hippocrates of Chios but also Anaxagoras (59 A 38 DK; the evidence is
dubious), Hippias (86 B 21 DK) and Antiphon (87 B 13 DK) dedicated themselves to its
solution. As for Aristophanes, he introduces a scientist in order to make fun of him. Meton is
finally beaten by Peisthetaerus. While dramatizing the episode, the poet makes Peisthetaerus first
express his admiration: "this man is a Thales" (  – 1009).
Thales appears elsewhere in Aristophanes as a famous geometer. In the Clouds (423
BC), a student of Socrates praises his teacher's ability to use the compass in order ... to steal a
piece of clothing. Strepsiades, impressed by such a profitable skill, exclaims: "Why, then, do we
admire that Thales?" (   – 180). Now we should ask: what made Thales, the
geometer, so famous as to be used in comedy? I propose it was the propaganda of geometers
themselves, especially those working in Athens.111333000 And if this was the case, Hippocrates is the
first person to consider.111333111
Hippocrates came to Athens from Chios, a good place to have been trained in geometry.
There was a flourishing school of Oenopides on the island. We are told that Oenopides was a
little younger than Anaxagoras, but older than Hippocrates (Procl. 65. 21 Friedlein; 41 A 1 DK)
and that he was mentioned by Democritus (41 A 3 DK). Hence he must have been active in the
second quarter of the fifth century BC.111333222 Unfortunately, we do not know much about this other
outstanding Ionian. But what we do know shows that Oenopides was preoccupied with the same
set of disciplines and even issues as Thales.
He was both an astronomer and a geometer, he
studied the tropai of the sun (41 A 9 DK) and had his own theories of archai (41 A 5 DK), of the
world psyche and God (41 A 6 DK), and of the Nile floods (41 A 11 DK). The teachers of
Oenopides' teachers must have been Thales' audience. Why should they not have transmitted
some of Thales' words to later generations?
130 It is strange to believe that a geometer could be the subject of folklore (an assumption by K.J.Dover, p.XXXVI
in his edition of the Clouds ).
131 Curiously, another report of Proclus on Thales is marked by a special intonation: "They say, that Thales
( ) was the first to demonstrate that the circle is bisected by the diameter" (157. 10-11 Friedlein). Is
it just by coincidence that both Proclus and Aristophanes use the same expression to describe the same person?
Don’t we hear echoes of the same phrase, though the intonations are different?
132 Traditional dates for Anaxagoras are not reliable: Dmitri Panchenko, “Democritus’ Trojan Era and the
Foundations of Early Greek Chronology”, Hyperboreus 6 (2000) 1, 31-78, esp. 45, n. 29. His teaching was well
known in 460s. Anaxagoras seems not to have been aware of Oenopides’ astronomy which, however, influenced
Archelaus (who was older than Socrates, born in 470/69 BC) – see my “Who found the Zodiac?”, Antike
Naturwissenschaft und ihre Rezeption 9 (1999) 33-44, esp. 43 f.
71
Moreover, we are told that Oenopides was “the first to present in a treatise the methods of
astronomy” (       ).111333333 It is clear that
in such a book Oenopides had to present not only his own achievements, but also those of his
predecessors. Eager to compete, the Greeks were therefore quite sensitive to plagiarism; one
should not, of course, imagine the scrupulous registration of individual contributions in
Oenopides’ book, yet it would have been reasonable of him to mention some of Thales’
achievements in astronomy and geometry. As we saw in the previous chapter, Oenopides
explained in his book how to draw lines due north, south, east, and west. His solution was not
irrelevant to Thales’ proposition that the diameter divides a circle into two equal parts; it also
involved constructing an isosceles triangle formed by two radii. This was an occasion to say that
in every isosceles triangle the angles at the base are o and also note that this truth was a
discovery of Thales. It was left for Eudemus to use this information in his History as well as to
observe that Thales’ terminology differed from that which was accepted in his own day.111333444
We are, thus, in a position to indicate various possibilities of how the information about
Thales’ studies in astronomy and geometry was recorded in an epoch when the memory of them
was still alive. It should be added that we are explicitly told that Hippias recorded Thales’ views
on the soul (11 A 1. 24; 86 B 7 DK) and that Xenophanes, Heraclitus, and Democritus
mentioned his prediction of a solar eclipse. Democritus had also something to say about the
alleged (or genuine) Phoenician ancestry of Thales (11 A 1. 22; 68 B 115 a DK; Democr. fr. 156
Luria). Democritus was not a biographer, so he talked about Thales’ ancestry in connection with
some of his achievements, and these were not necessarily the prediction of a solar eclipse.
Democritus, “speaking of Anaxagoras, declared that his views of the sun and the moon were not
original but ancient, and that he had simply stolen them” (D.L. 9. 34; 59 A 5 DK; Democr. fr.
159 Luria). The famous views of Anaxagoras were that the sun is a mass of red-hot iron (or
stone) and the moon is another earth (Plat. Apol. 26 d; D.L. 2. 8; Dox. 349, 356). Since
Democritus held essentially the same views, he was interested in emphasizing that there was a
long tradition behind them and it was not the case that he was simply not able to suggest
anything better than Anaxagoras. Now similar comparable views are attributed (rather
surprisingly) to Anaximenes about the sun (13 A 6 DK), and to Thales about the moon.
There was growing public interest in science in the fifth century. Oenopides and
Hippocrates published the first manuals in astronomy and geometry respectively. The sophists
133 DK, for no obvious reason, conceals this important truth. The importance of the evidence was recognized by
Walter Burkert, Lore and Science, 314, n. 79.
134 It may be that the only book of Oenopides that Eudemus used was devoted primarily to astronomy and not to
geometry. This may explain the deceptive impression that Oenopides’ geometry was rather primitive. It is, further,
quite possible that Eudemus’ and others’ information about Thales’ theory of solar eclipse goes back to Oenopides.
It is also worth noting that Aristotle never mentions Oenopides.
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taught science along with public speaking. These intellectuals whose main interests were far
from science committed themselves nevertheless to problems in astronomy and geometry.
Science was brought to the stage in Athenian theatre. It is not surprising that this growing
interest in science included Thales, the founder of Greek astronomy and geometry and a man of
extraordinary fame because of his successful prediction of a solar eclipse; it is not surprising that
in such an atmosphere Thales’ views and achievements were recorded by his successors. That
made them known to Aristotle and – more importantly – to Theophrastus, who composed a
survey of what had been suggested in ‘physics’, as well as to Eudemus, who composed surveys
of what had been done in both astronomy and geometry.
Supplementary Notes
An explanation of doxographic misattributions to Thales
The doxographers credit Thales with two ideas that, on the basis of what we know,
cannot be his. First, the sphericity of the earth. Dox. 376: “Thales, the Stoics, and the followers:
the earth is spherical”. Since Thales’ earth rests on water, it need not be spherical, it can have a
variety of shapes. Characteristically, there are alternative candidates for who first presented this
idea (Anaximander, Parmenides, Pythagoras).
Then, there is the division of the celestial sphere into five zones. Dox. 340: “Thales,
Pythagoras, and followers divided the sphere of the entire heaven into five circles, the so-called
zones”. Again, since Thales’ earth rests on water, his heaven is hardly spherical; a hemisphere
would be a more likely option.135
The two cases have something in common, and this is the involvement of Pythagoras. We
learn from Diogenes Laertius that despite the authority of Theophrastus, who maintained that the
idea of the earth’s sphericity originated with Parmenides, some people asserted that this
innovation was due to Pythagoras (D.L. 8. 48). Since there was an influential tradition according
to which Parmenides either had a Pythagorean teacher or was a Pythagorean himself, it was easy
to ascribe to Pythagoras anything found in Parmenidies’ poem. So one is not surprised to learn
that although Parmenides “is thought to have been the first to see that the Evening Star and the
Morning Star are the same …, others say it was Pythagoras” (D.L. 9. 23; cf. 8. 14). Furthermore,
Strabo (2. 2. 2) cites Posidonius as stating that it was Parmenides who originated the division of
the earth into five zones, while Pseudo-Plutarch gives, on the one hand, a report that agrees with
135 However, it is Anaximenes and not Thales who is cited for the view that celestial bodies rotate above (and not
below) the earth.
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Posidonius and that almost certainly goes back to Theophrastus,111333666 but on the other hand, he says
that “Pythagoras, in an analogy with the celestial sphere, divided the earth into five zones –
arctic, antarctic, summer and winter tropics, equinoctial” (Dox. 378).111333777 Scholars are probably
right to assume with Pseudo-Plutarch’s source that the division of the celestial sphere into five
zones preceded the analogous division of the earth, but it is not impossible that both divisions
were present in Parmenides’ poem. At all events we have a similar case of constructing
Pythagoras’ priority for yet another astronomical discovery: “Pythagoras is said to have been the
first to conceive the inclination of the zodiac circle, which was borrowed by Oenopides as if he
had conceived it himself” (Dox. 340; 41 A 7 DK).111333888 Some even dared to ascribe to Pythagoras
the 59-year cycle (Dox. 363 f.), safely attributed to Oenopides (41 A 8-9 DK).
It seems that some Hellenistic scholars treated the early Presocratics as if they were
favourite sports teams. Some backed the Italian school, while others supported the Ionian school.
Theophrastus said that Parmenides was the first to introduce the idea of the sphericity of the
earth. It was inferred by a Hellenistic scholar that Parmenides had got this idea from Pythagoras.
The opposing party replied by attributing this discovery to Anaximander (12 A 1) and Thales.111333999
Posidonius, certainly, and Theophrastus, probably, credited Parmenides with the division of the
earth into five zones. Someone inferred from this that Parmenides just elaborated upon the
division of the celestial sphere into zones and that this division was introduced by Pythagoras.
But again we have an analogous claim for Thales. Mainstream tradition attributed to Oenopides
the discovery of the zodiac and its obliquity, yet some people maintained that this had been in
fact a discovery of Pythagoras. Again, we find the same discovery ascribed to Anaximander as
well (12 A 5).111444000
I conclude that those (and only those) attributions to Thales are suspect for which there
are competing claims and that these competing claims are typically connected with the undue
enthusiasm of the admirers of Pythagoras. So such attributions can be isolated in a particular
group.111444111 It is certainly wrong (though rather common) to approach our information about Thales
136 Dox. 377. See further Hyperboreus 2 (1996) 1, 107, n.100.
137 Similarly Mart. Cap. 6. 609 (see Walter Burkert, Lore and Science, 306, n. 35).
138 The priority of Oenopides is clearly stated by Eudemus and confirmed by other sources.
139 Compare a transfer from a disciple to the teacher in the case of modeling a sphere – an achievement of
Anaximander, according to mainstream tradition (12 A 1-2 DK and Plin. HN, 7. 203), and of Thales, according to
Cic. Rep. 1. 14
140 Mere confusion, however, is also possible in this case – see my “Who found the Zodiac?”, 37.
141 Two more cases may belong to this group. The assertion “the followers of Thales assume the central position of
the earth” (Dox. 377; 11 A 15 DK) is to be compared with D.L. 9. 21 (28 A 1 DK): Parmenides “was the first to
declare that the earth is spherical and is situated in the centre” and D.L. 2. 1 (12 A 1 DK): according to
Anaximander, “the earth lies in the midst; being of spherical shape, it occupies the centre of the arrangement”.
Again, when we read in Stobaeus: “Thales was the first to assert that the moon has light from the sun; Pythagoras,
Parmenides, Empedocles, Anaxagoras, Metrodorus shared this view” (Ecl. 1. 26. 2; Dox. 358; 11 A 17 b DK), we
may certainly suspect that the only evidence available to the doxographers were Parmenides’ lines. However, we
have no separate claim for either Parmenides or Pythagoras as the first to advance this view. See further my
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and Pythagoras on equal footing. It is difficult to cite any achievement of Pythagoras in
astronomy for which there is no alternative claim.111444222 In the case of Thales, our tradition indicates
no competitors for being the first to predict and explain a solar eclipse or to discover that the
sun’s period in respect to the solstices is not always the same, or to advance a doctrine about the
size of the sun. There were the Pythagoreans and Neo-Pythagoreans, interested in exaggerating
Pythagoras’ greatness. But there were no ‘Thalesians’. Thales never claimed to possess
superhuman knowledge and abilities, nor was he ever the subject of the incredible stories of the
kind reported about Pythagoras.
Thales as a monopolist and the father of federalism
Aristotle in his Politics cites a story about Thales:
“He was reproached for his poverty, which was supposed to show the uselessness of
philosophy; but observing from his knowledge of astronomy (so the story goes) that there was
likely to be a heavy crop of olives, and having a small sum at his command, he paid down
earnest-money, early in the year, for the hire of all the olive-presses in Miletus and Chios; and he
managed, in the absence of any higher offer, to secure them at a low rate. When the season came,
and there was a sudden and simultaneous demand for a number of presses, he let out the stock he
had collected at any rate he chose to fix; and making a considerable fortune he succeeded in
proving that it is easy for philosophers to become rich if they so desire, though this is not the
business which they are really about. The story is told as showing that Thales proved his own
wisdom; but … the plan he adopted – which was, in effect, the creation of a monopoly –
involves a principle which can be generally applied in the art of acquisition” (1259 a 3; 11 A 10
DK).111444333
The story has a distinct post-Socratic colour. However, it is essentially authentic. A
constructed parable would either not be specific about the location of the olive-presses rented by
Thales or would locate them in Thales’ own city. The mention of Chios proves that the core of
the story was not invented. Apparently traditional political ties between Miletus and Chios made
possible the situation described. The involvement of astronomical knowledge is clearly a later
addition – one need not foresee particular crop in order to use Thales’ scheme, the creation of a
monopoly; Aristotle is right speaking of its general applicability.
“Eudemus Fr. 145 Wehrli and the Ancient Theories of Lunar Light”.
142 Pythagoras’ contribution to astronomy is thus very problematic. However, it seems to me likely that he proved
the theorem that bears his name.
143 Aristotle indeed gives examples. A concise version of the story appears in D.L. 1. 26 (from Hieronymus of
Rhodes).
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The story is of interest from a sociological point of view. In many societies, such a trick
would bring hatred rather than admiration upon a man acting like Thales. The story illustrates
well a society with a high level of the so-called need for achievement.144
The other story is told by Herodotus. This is the story of the counsel that Thales had
addressed to the Ionians at some unspecified time before they were conquered by the Persians:
“He would have had the Ionians make one common place of counsel, which should be in Teos,
for that was the centre of Ionia; and the state of the other cities should be held to be no other than
if they were but townships” (1. 170; 11 A 4 DK).
Since scholars fear to appear credulous, they typically treat the story as fictitious, as a
post factum suggestion of how it was possible to prevent the military defeat and subsequent
subjugation to Cyrus. But the proposal seems too detailed to be fictitious. And if one admits that
the idea itself came from “the keener minds of Ionia”,111444555 why not attribute it to Thales?
Moreover, if one takes into account the competitive pattern so characteristic of Greek
civilization, one will see that it is very strange to assume that a certain Ionian arrived at a bright
idea only to ascribe it to someone else.111444666
It is no wonder that the man with such an innovative mind conceived new methods in
politics and realized new approaches to business. There is good reason, however, to believe that
these new ways were repeatedly rediscovered under the appropriate circumstances. The case of
theoretical science is different. Its formation was a unique event, and therefore we cannot be
certain than anybody else, even the great Anaximander, would have performed the task of
triggering theoretical science as efficiently as Thales did.
THEORETICAL KNOWLEDGE AND INTERPESONAL INTERACTION
Thales was the first Greek scientist and philosopher, but certainly not the last. We have already
had occasion to see why his particular ideas were either accepted or formed the basis for
subsequent development. Now it is appropriate to address more general questions: Why were the
activities introduced by Thales taken up by others? How could it happen that he introduced such
amazingly fruitful intellectual developments?
144 David Clarence McClelland, The Achieving Society (1961).
145 Arnold J. Toynbee, A Study of History (London, etc. 1939) 4, 22, n. 1.
146 The historicity of both stories is admitted (without particular argumentation) by Andrew Robert Burn, The Lyric
Age of Greece (London 1978) 332, 334-6. Markus Asper, “Mathematik, Milieu, Text. Die frühgriechische(n)
Mathematik(en) und ihr Umfeld”, Sudhoffs Archiv 87 (2003) 1, 1-31, esp. 10 even uses the latter story as an
indication that Thales belonged to the upper stratum of the society – as I also did in Hyperboreus 2 (1996) 1, 85.
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Alexander Zaicev, the only scholar to my knowledge who has dared to approach the socalled Greek miracle with a comprehensive explanation rather than separate observations and
thoughts, focuses on the mechanism for releasing the brakes on creative potential and for
creating a social climate in which every success of intellectual activity receives encouragement
independent of its practical applicability.147
However, the emphasis on ‘brake release’ and intellectual stimulation is good for
accounting for the rise of creative activity, but not for the ways in which that activity is realized.
First, it is not yet clear how the demonstration of a geometrical proposition or the formulation of
an astronomical theory could bring fame (for the general public is typically neither in a position
to evaluate such things, nor typically interested in them). Further, the problem remains as to why
curiosity, once encouraged, should necessarily lead to non-contradictory, systematic, and
advancing knowledge. Furthermore, the efforts themselves, no matter how encouraged, will fade
if an adequate form for their application is not found. In other words, there remains the question
of the mechanism that organizes the theoretical knowledge.
Such a mechanism seems to have been named by Karl Popper, who emphasized the role
of critical discussion and the resulting critical tradition in the amazing development of early
Greek philosophy and science:
“The early history of Greek philosophy, especially the history from Thales to Plato, is a splendid
story. It is almost too good to be true. In every generation we find at least one new philosophy,
one new cosmology of staggering originality and depth. How was this possible? Of course one
cannot explain originality and genius. But one can try to throw some light on them. What was the
secret of the ancients? I suggest that it was a tradition – tradition of critical discussion.”148
To explain what made the critical tradition possible, however, Popper simply assumed the happy
temper of Thales, who encouraged Anaximander to criticize his own ideas. But one cannot
accept his reference to Thales’ ability to tolerate criticism as an explanation of a practice that
lasted for many generations. To be sure, it is not an easy task to explain the rise of the critical
tradition. However, it is hardly necessary to resort to guesses about the good temper of Thales or
anybody else.
147 Alexander Zaicev, Das griechische Wunder: Die Entstehung der griechischen Zivilisation (Konstanz 1993).
Original Russian edition was published in 1985.
148 Karl Popper, The World of Parmenides: Essays on the Presocratic Enlightenment, ed. by Arne F. Petersen with
the assistance of Jørgen Mejer (London; New York 1998) 20. The text originally belongs to Popper’s essay “Back to
the Presocratics” (1958).
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The notion of the critical tradition comprises ideas of criticism, tradition, and a
combination of the two. Only the first of these aspects has enjoyed much scholarly attention. The
majority of scholars would approach it in terms of the political dimension of Greek life, citing
the polis and democracy. But this is of little help. The experience of argumentative debate
acquired at the assembly or the court could be useful, of course. However, the strategy of legal or
political debate differs greatly from that of scientific inquiry, as it aims to convince listeners at a
particular moment rather than establishing an ‘eternal’ truth. Furthermore, the polis and
democracy as such have nothing to do with an interest in cosmology or demonstration of
theorems.149
Some scholars refer to the encounter of divergent truths, particularly Greek and nonGreek (Kurt von Fritz, Sir Karl Popper, B.L. Van der Waerden). This explanation has, no doubt,
heuristic value and may be relevant to the interpretation of the emergence of philosophical
cosmogony. Yet conflicting truths frequently supported skeptical and agnostic conclusions. In
the epoch in question, moreover, not only the Greeks, but also other peoples (including the
Assyrians, Babylonians, and Egyptians), had experience of hearing conflicting accounts of gods,
cosmogony, and institutions.
When we speak of critical discussion, we mean by ‘critical’ something more than one’s
readiness to doubt the correctness of an assertion. We rather mean a procedure employing factual
and/or logical examination of an assertion. To conduct critical discussion means to exchange
arguments. Critical discussion deals, accordingly, with arguable statements. An arguable
statement anticipates questions, such as why should we believe what you are saying?
Consequently, a particular form of human interaction is impressed on the very logic of critical
discussion and its outcome – theoretical knowledge.
And the corresponding pattern of interaction is natural for the upper stratum of Greek
society with its free and relatively equal individuals. If Thales, or Anaximander, etc. claimed the
recognition of equals, they had to answer the question of why their unusual assertions were to be
met with approval.
The demand for an arguable statement pertains, however, to a specific set of problems.
There is no need for proof or argumentation when one can just go to see or measure. Such a need
arises only when the subject is unobservable or (in the case of mathematics) that which cannot be
149 As the most representative work of the criticized type I can suggest the book by J. P. Vernant, Les origines de la
pénsee grecque (Paris1969). On Vernant’s approach "the birth of natural thought" appears to be only a change in
images following a change in the environment and not the formation of a new mode of reasoning about nature. For
a more flexible and diverse treatment of the political dimension in the development of Greek science and
philosophy, see G. E. R. Lloyd, Magic, Reason and Experience (Cambridge1979), and The Revolutions of Wisdom
(Berkeley 1987).
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measured. Thus theoretical knowledge emerged as a set of arguable statements about matters that
could not be observed (or measured).
We may plausibly suppose that an interest in such matters and the interactional pattern
characteristic of free and equal individuals were brought together within small associations –
both formal and, more typically, informal. Such associations emerged on the basis of common
intellectual interests, friendly connections, or perhaps around a distinctively bright person. The
associations thus formed were far from suppressing the initiative and aspirations of their
members, for whom, on the contrary, the prospect of gaining distinction among their fellows was
one of the motives for participation in the association. The fellows, therefore, provided each
other with both encouragement and critical control. If the demand for a responsible statement
became a rule within such associations, it was not because the participants in intellectual
communication had inherited the pattern of argumentative debate from the court or the assembly.
The fact is that they found themselves in a similar interactional situation in the court, in the
assembly, and in a discussion of the nature of things: they interacted as free and relatively equal
individuals. For the same reason, they were not in need to enjoy the freedom of criticism with a
kind permission from a master.
On the other hand, Presocratic philosophies were usually strongly connected with
astronomy. Therefore the transmission of some technical knowledge must have taken place too.
And this implies both tradition and a school-like relationship between a teacher and disciple. We
have no reliable information about details of a teacher-disciple relationship among the
Presocratics, but we may be sure that a former disciple was financially independent from the
teacher and school. Only good manners would prevent him from criticizing the teacher if he
wished to, and nothing could prevent him from replacing the teacher’s ideas with his own if he
felt that they were superior. Whatever Thales’ or anybody else’s temper, we may safely
eliminate the teacher’s encouragement of criticism from the account. The encouragement came
from elsewhere. I mean the agonistic spirit, so characteristic of the Greeks. The desire to surpass
one’s teacher and predecessors was an efficient driving force behind the critical tradition. It
invited improvement upon what had been done – and thereby continuity.111555000
To sum up, critical discussion and the demand for arguable statements were secured by the
interactional pattern characteristic of the independent and equal members of small associations
based on common intellectual interests. A distinguished member of such an association could
one day become a teacher. Critical tradition was maintained in part through the transmission of
the special knowledge he passed to his disciples as well as through subsequent attempts of some
150 The role of the agonistic spirit was emphasized by Zaicev, but he does not connect it with the critical tradition.
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disciple to surpass the achievements of the teacher, while addressing himself, once again, to
equals.111555111
And now I turn back to Thales. Competition cannot be kept alive in a field of no repute.
Among other things, the critical tradition was maintained because of the success of the earliest of
the Presocratics. To the astonishment of his contemporaries, Thales claimed to know the true
nature of a sudden disappearance of the sun during the day. But everybody who took care to
examine Thales’ claim would discover that solar eclipses occur only at the time of a new moon;
everyone who observed the phases of a solar eclipse through its reflection in water would see
with his own eyes how a dark circular body gradually covers and then releases the disc of the
sun. Moreover, this claim came from a person who managed to predict a solar eclipse.
Yet Thales’ personal contribution to the establishment of critical tradition is not limited to
his public success. Monumental edifice of theoretical knowledge requires a mighty foundation.
The critical tradition could not start with just anything. Imagine an Ionian Greek maintaining that
the sun and the moon are just bodies, no more divine than the clouds or rocks. It would be a bold
assertion, pointing towards a naturalistic outlook. We can imagine one who approves of such an
assertion, another who says, ‘I don’t know’, and yet another who thoughtfully asks, ‘How can
you know what is divine?’ The last question could lead to an attempt at defining the divine, and
in that case the initial statement could prove fruitful. But what I suggest is that an elaborate
definition of the divine could provide the basis for a critical tradition, but the assertion ‘the sun
and the moon are no more divine than the clouds’ could not. For this assertion taken as such is
too poor in content, it offers nothing to improve upon. The legacy of Thales was of a very
different kind. His water thesis solved difficult problems, on the one hand, and was open to
modification and development, on the other hand. His theory of solar eclipses took into account
various nontrivial facts and necessitated a comprehensive view with respect to the nature of both
luminaries, including their mutual disposition, their size and speed of rotation. In all probability,
he also succeeded in showing how geometrical constructions can be used in the study of
astronomy. In sum, it is likely that Thales’ personal contribution to the establishment of critical
tradition was indispensable.
151 Applying this approach to a later epoch (and at the same time checking its validity), one may say that the
divorce of philosophy and science (that is, advancing knowledge) significantly contributed to the conservatism of
Hellenistic philosophies.
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ACKNOWLEDGEMENTS
This study benefited much from my academic stays at Harvard University, 1991-92 (made
possible due to the generosity of the Daniel and Joanna S. Rose Fund), at the Center of Hellenic
Studies, 1993-94 (directed at that time by Kurt Raaflaub and Deborah Boedeker), and at the
University of Konstanz, 1997-98 and subsequent short visits (a fellowship from the Alexander
von Humboldt Foundation). I am very grateful to all the colleagues who supported me and
especially to Jürgen Mittelstraß, my academic host in Konstanz. My special gratitude is due to
Dionisis Mentzeniotis who inspired me to write this book. It is based on my previously published
studies, but is by no means confined to the presentation of my English and Russian papers. I am
proud and happy that this book appears in Greek.
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