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Май 28 Солнечное затмение Геродота/ФалесаMay 28 Solar Eclipse Herodotus/Thales



https://www.academia.edu/6355805/THALES_AND_THE_SOLAR_ECLIPSE_OF_28_MAY_585_BC 
THALES AND THE SOLAR ECLIPSE OF 28 MAY 585 BC
Dirk Couprie
 
 
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THALES AND THE SOLAR ECLIPSE OF 28 MAY 585 BC
Lecture held at the Research Center for Theory and History of science of the
University of West Bohemia in Pilsen, 3rd March 2014, and at the Institute of
Philosophy of the Czech Academy of Sciences in Prague, 6th March 2014
Several sources, of which Herodotus is the most famous, report that Thales predicted an
eclipse of the sun. We may ask:
1) did he really predict an eclipse?
2) if so, which one did he predict?
3) if so, how did he do it?
The answers to the first two questions will appear to follow from the answer to the third one.
If we are able to discover which method Thales could have used, it follows immediately that
he predicted an eclipse and also which one it was he foretold.
We will answer these three questions: yes, he did predict a solar eclipse; it was the eclipse of
28 May 585 BC, and he did it by making a brilliant mistake. Here is the path of the eclipse of
28 May 585 BC:
The path of the eclipse of
28 May 585 B.C.
As you see, Miletus lies just outside the path of the full eclipse, which means that what Thales
saw was actually a great but partial eclipse:
The solar
eclipse of
25 May 585
BC, seen
from
Miletus
2
But let us hear first some sceptical voices.
The main source, Herodotus, says that Thales foretold the eclipse, “fixing as its term the sixth
year of the battle between the Medes and the Lydians”. This can hardly be called a prediction.
Dmitri Panchenko rightly remarked: “If one can predict an eclipse at all, one can predict it to
the day”. Herodotus’ remark shows, how little he understood of eclipses and their prediction.
The most disappointing is the search for a method that Thales could have used for his
prediction, the search for some regularity in the occurrences of eclipses. It has been argued
that Thales must have had knowledge of ancient Babylonian wisdom about cycles of solar
eclipses.
In 1969 Willy Hartner examined fifteen possible cycles, of which the Saros (a cycle of 223
lunar months or lunations) and the Exeligmos (or triple Saros of 669 lunar months) are the
most important, but his conclusion was that none of them could have been a base for a
prediction of the eclipse of 28 May 585 BC.1
Dmitri Panchenko tried the Exeligmos for the eclipse of 21 September 582 AD.2
The solar
eclipse of
21
September
582 BC,
seen from
Miletus
Panchenko calls this eclipse “impressive”, but in 1997 Stephenson and Fatoohi, two experts
on eclipses, pointed out very clearly that this eclipse may very well have passed unnoticed.3
And they are right, as I could observe myself at the eclipse of 11 August 1999 AD, which was
in Holland (actually Maastricht) even bigger (0.95) than the eclipse of 21 September 582 BC,
which was 0.85 at Miletus.
The solar
eclipse of
11 August
1999 AD,
seen from
Maastricht
In Maastricht, the atmosphere became spooky, as if a heavy thunderstorm was coming. At
Miletus, the only thing ordinary people may have noticed is that daylight was somewhat
dimmed. A skilled observer like Thales, however, could have observed its reflection in a bowl
filled with oil or water. This conflicts with Herodotus’ report that the day turned into night.
Perhaps the most ingenious attempt has been made by Patricia O’Grady in 2002.4 She
noticed – as van der Waerden did before5 – that sometimes a solar eclipse occurs 23½ months
after a lunar eclipse.
3
However, she based her analysis on eclipses, visible at Ninive instead of Miletus, and
her list contains some other dubious points. When we make the list for Miletus it appears that
no more than 5 out of the 22 lunar eclipses took place 23 1/2 month before a solar eclipse.
This is too small a base for a prediction that is more than a guess, as Hartner already
remarked.
Moreover, in Thales’ time even the Babylonian astronomers were not able to predict
eclipses. The only thing they were capable of was to find out the dates of possible eclipses,
based on a very simple rule of thumb. Of this rule of thumb we will come to speak later.
Our conclusion can be that Thales did not depend on ancient wisdom, whether
Babylonian or not.
It could be asked, whether a prediction of an eclipse does not presuppose a knowledge of the
true mechanism of eclipses. However, it must be stressed that the prediction of an eclipse does
not presuppose any knowledge whatsoever of what a solar eclipse really is.
Even Anaximander was not acquainted with this, for he explained eclipses as the partially or
totally closing of the apertures in the celestial wheel of the sun or the moon. In other words:
Thales did not need to know that an eclipse of the sun occurs when the sun is blocked by the
moon.
The only thing that matters that he observed eclipses when they occurred and tried to
find some regularity in their occurrences. These regularities Thales could have noticed
without having the faintest idea why they occurred.
Our conclusion can be that Thales did not depend on knowledge about the true
mechanism of eclipses.
At best, the sceptics say, Thales made a lucky guess. I will argue that his guess was brilliant
and based on an observed regularity.
From Willy Hartner I took the idea of looking at “the statistical material at Thales’
disposal”, as he called it. Let us suppose, then, that Thales knew nothing about alleged
Babylonian wisdom, but just started observing and registrating eclipses of the sun and the
moon during his lifetime. Fortunately, he lived in a time in which relatively many eclipses
were visible at Miletus.
The first thing he could have discovered – if this was not already common knowledge – was
that both lunar and solar eclipses can be partial or full.
The second thing he could have discovered – if this was not already common knowledge –
was that lunar eclipses occur at full moon and solar eclipses at new moon.
This was helpful, because it meant that he did not need to look out for a possible
eclipse every day and night, but only twice a month. Mark that whenever I speak of months,
lunar months or lunations are meant, from one new moon until the next, about 29 1/2 days.
The third thing he could have observed was that the dates of possible solar eclipses
always fall within the same month as possible lunar eclipses. This will become more clear
when we will see the table with possible and real eclipses during Thales’ lifetime.
The fourth thing he could have learnt after some years of observation, was that not
every full or new moon an eclipse occurred, but that they came at longer intervals, of
multiples of six months, sometimes minus one. This is the rule of thumb the Babylonians of
his time also were acquainted with.
This rule presents the data of possible eclipses, days on which it is worth while to look
at the heavens. As you can see, actually the rule has a certain rhythm or pattern, which repeats
itself after 38 lunar months:6
4
The 6-months/5-months rule
of thumb of possible eclipses
This knowledge made observation still easier, because he had to observe the sky only twice a
year.
Together this is the knowledge that Thales could have been gathered simply from a
careful observation of the heavens during his lifetime. When put into a table, it looks like this:
YEAR
B.C.
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
610 1   30 28 28
609 27 24 26 25 24 23 22 21  19 18 17 16
608 15   15 14 13 12 12 10  9 8 7 6
607 4 3 5 3 3 1 1  29 28 27 26 25
606  24 22 23 22 21 20  19 18 17 16 15 15 
605 13 12 12 10 10 8 7 6 5 4 3 3 
604 31 2 31 29 29 27 28 25 24 23 22 22
603 21 19 21 19  17 16 14 13 12  11 11
602 10 9 10 9 8 6 6 4 2 2 31 30 30
601 28 27 28  26 26 24 24 22 20 20 18 18
600 17 16 17 16 15 14 13 12 10 9 8 7
599 6 5  6 5 4 3 2 1  31 29 29 27 26
598 25 23 25 24 23 22 21 20 18 18 17 16
597 15 13 13 12 11 10  8 7 6 5 5
596 3 2 2 1 1 30  28 27 25 25 24  
595 22 21 22 20 20  18 17 16 14 14 13  13
594 12 10 12 10   8 7 5 4 3 2 2 31
593 30 29 30 28 27 26 25 23 22 21 20 19
592 18 17 19  17 17 15 15 13 11 11 9 9
591 7 6 8  7 6 5 4 3 1 30 30 28 28
590 26 25 26 25 25 23 23 21 20 19 18 17
589 16 14 15 13 13 12 11 10 8 8 7 6
588 4  3 4 3 2 1 30  28 27 27 25 25
587  4 22 23 22 21  19 19 17 16 16 15 
586 13 12 13 11 11 9 8 7 5 5 4 3
lunar ()
and
solar
eclipses
( = full,
 = partial)
visible at
Miletus
from 610-
586 B.C.
The cells of the months in which an eclipse of the moon or the sun was visible at Miletus are
colored red. The numbers in the cells of the months are the data of new moon.
I took the idea of this table from Joachim Herrmann, who in 1969 drew a similar one
for the years 1968 to 1990 AD.7 As we see, in such a table the rule of thumb expresses itself
as a series of strings or garlands through the calendar. This is even better visible when the
table is folded into a cylinder.
5
However, the extrapolation of this table will lead to no more than the fixation of two
possible data for solar eclipses in 585 BC: one at new moon in May and one at new moon in
November. For a real prediction, more is needed.
Let us suppose that Thales looked more carefully into the data he had gathered during
his lifetime. Then he could have noticed a curious regularity in the series of the last eight
successive eclipses of the sun before the year 585 BC. I will show you them in a table:
After how many months do you think the next
solar eclipse is to be expected?
I left out eclipses amaller than 0.50, because they could easily have escaped observation,
unless Thales had a special reason to expect one. If you were Thales, what would you have
put as the next item in the last column?
YES !!
And which date do you think will appear in the last row?
6
YES !!
This is, I think, how Thales predicted an eclipse.
Note that the apparent 17/18 months regularity is not one of the fifteen real cycles discussed
by Hartner.
Why haven’t other scholars discovered this method? One reason is that scholars were
looking for really existing regularities, such as the Saros cyclus and the Exeligmos cyclus. No
one (with one exception) ever thought about a non-existing but only apparent regularity that
could have deceived Thales.
Another reason is a silly mistake. In 1969 Hartner presented a table of possible
Milesian records, similar to the one I showed you, but by a curious mistake he omitted the
solar eclipse of 23 December 596 BC, and took instead the small eclipse of 28 June 596 BC
(maximum phase 35) that almost certainly passed by unnoticed. This resulted in the numbers
of 12 and 23 lunations instead of 18 and 17 between two successing eclipses.
Hartner’s mistake
28 June 596 0.35 12
23
From Dmitri Panchenko I took the idea of looking for apparent regularities, and more
in particular the intervals of 17 and 18 months. In 1994 he wrote; “an astronomer (like Thales)
would naturally have searched for (…) eclipses with the same interval”. And also he wrote:
“the eclipse of 28 May 585 was separated from the two previous eclipses by intervals of 18
and 17 lunations respectively. But this sequence had taken place once before! The eclipse of
7
30 July 607 was also separated by intervals of 18 and 17 lunations from the two preceding
eclipses.”
Why didn’t Panchenko not discover the other interval of 17 and 18 months? Because
he blindly copied Hartner’s mistake and put the number 23 instead of 17 at the eclipse of 9
May 594:
Hartner’s and Panchenko’s mistake
23
Because of this mistake Panchenko favored the eclipse of 21 September 582 BC, as we
already saw.
The only thing I had to do was to correct Hartners’s and Panchenko’s mistake.
And now for the last question: Did Thales really predict the solar eclipse? The answer
must be: no. The regularity he saw was only a lucky coincidence. When we look at eclipses
later than the year 585 BC, no such regularity as the 17 and 18 lunations occurs.
This explains why Thales “predicted” only one eclipse, and also why others could not
copy his method. After all, his preciction was a lucky guess, although it was based on
thorough research and careful observation. His prediction was an example of the not
uncommon situation in science that a right conclusion is based on a false presupposition. Such
mistakes happen in science and their exposure brings science further.
The End
1 Willy Hartner, “Eclipse Periods and Thales’ Prediction of a Solar Eclipse”. Centaurus 14 (1969), 60-71.
8
2 Dmitri Panchenko, “Thales’s Prediction of a Solar Eclipse”. Journal for the History of Astronomy 25 (1994), 275-88.
3 Francis R. Stephenson & Louay J. Fatoohi, “Thales’ Prediction of a Solar Eclipse”, Journal for the History of Astronomy 28 (1997), 279-82.
4 Patricia F. O’Grady, Thales of Miletus. Aldershot: Ashgate 2002.
5 Bartel L. Van der Waerden, Science Awakening II: The Birth of Astronomy. Leiden: Brill 1974, 122, n. 1.
6 Cf. John M. Steele, “Eclipse Prediction in Mesopotamia”. Archive for the History of Exact Sciences 54 (2000), 421-54.
7 Joachim Herrmann, Gesetze des Weltalls, Stuttgart: Franckh’sche Verlagshandlung , W. Keller & Co. 1969.
 
 
 
2But let us hear first some sceptical voices.The main source, Herodotus, says that Thales foretold the eclip
se, “fixing
as its term the sixthyear of the battle between the Medes and the Lydians
”.
 This can hardly be called a prediction.
Dmitri Panchenko rightly remarked: “If one can predict an eclipse at all, one can predict it tothe day”. Herodotus’ remark sho
ws, how little he understood of eclipses and their prediction.The most disappointing is the search for a method that Thales could have used for his prediction, the search for some regularity in the occurrences of eclipses. It has been arguedthat Thales must have had knowledge of ancient Babylonian wisdom about cycles of solareclipses.In 1969 Willy Hartner examined fifteen possible cycles, of which the Saros (a cycle of 223lunar months or lunations) and the Exeligmos (or triple Saros of 669 lunar months) are themost important, but his conclusion was that none of them could have been a base for a prediction of the eclipse of 28 May 585 BC.
1
 Dmitri Panchenko tried the Exeligmos for the eclipse of 21 September 582 AD.
2
 
The solareclipse of21September582 BC,seenfromMiletus
 
Panchenko calls this eclipse “impressive”, but
in 1997 Stephenson and Fatoohi, two expertson eclipses, pointed out very clearly that this eclipse may very well have passed unnoticed.
3
 And they are right, as I could observe myself at the eclipse of 11 August 1999 AD, which wasin Holland (actually Maastricht) even bigger (0.95) than the eclipse of 21 September 582 BC,which was 0.85 at Miletus.
The solareclipse of11 August1999 AD,seenfromMaastricht
 In Maastricht, the atmosphere became spooky, as if a heavy thunderstorm was coming. AtMiletus, the only thing ordinary people may have noticed is that daylight was somewhatdimmed. A skilled observer like Thales, however, could have observed its reflection in a bowlfilled with oil or water.
This conflicts with Herodotus’ report that the day turned into night.
 
Perhaps the most ingenious attempt has been made by Patricia O’Grady
 in 2002.
4
 Shenoticed
 – 
 as van der Waerden did before
5
 
 – 
 that sometimes a solar eclipse occurs 23½ monthsafter a lunar eclipse.
 
3However, she based her analysis on eclipses, visible at Ninive instead of Miletus, andher list contains some other dubious points. When we make the list for Miletus it appears thatno more than 5 out of the 22 lunar eclipses took place 23 1/2 month before a solar eclipse.This is too small a base for a prediction that is more than a guess, as Hartner alreadyremarked.
Moreover, in Thales’
 time even the Babylonian astronomers were not able to predicteclipses. The only thing they were capable of was to find out the dates of
 possible
 eclipses, based on a very simple rule of thumb. Of this rule of thumb we will come to speak later.Our conclusion can be that Thales did not depend on ancient wisdom, whetherBabylonian or not.It could be asked, whether a prediction of an eclipse does not presuppose a knowledge of thetrue mechanism of eclipses. However, it must be stressed that the prediction of an eclipse doesnot presuppose any knowledge whatsoever of what a solar eclipse really is.Even Anaximander was not acquainted with this, for he explained eclipses as the partially ortotally closing of the apertures in the celestial wheel of the sun or the moon. In other words:Thales did not need to know that an eclipse of the sun occurs when the sun is blocked by themoon.The only thing that matters that he observed eclipses when they occurred and tried tofind some regularity in their occurrences. These regularities Thales could have noticedwithout having the faintest idea
why
 they occurred.Our conclusion can be that Thales did not depend on knowledge about the truemechanism of eclipses.At best, the sceptics say, Thales made a lucky guess. I will argue that his guess was brilliantand based on an observed regularity.From Willy Hartner
I took the idea of looking at “the statistical material at Thales’disposal”, as he called it.
Let us suppose, then, that Thales knew nothing about allegedBabylonian wisdom, but just started observing and registrating eclipses of the sun and themoon during his lifetime. Fortunately, he lived in a time in which relatively many eclipseswere visible at Miletus.The first thing he could have discovered
 – 
 if this was not already common knowledge
 – 
 wasthat both lunar and solar eclipses can be partial or full.The second thing he could have discovered
 – 
 if this was not already common knowledge
 – 
 was that lunar eclipses occur at full moon and solar eclipses at new moon.This was helpful, because it meant that he did not need to look out for a possibleeclipse every day and night, but only twice a month. Mark that whenever I speak of months,lunar months or lunations are meant, from one new moon until the next, about 29 1/2 days.The third thing he could have observed was that the dates of possible solar eclipsesalways fall within the same month as possible lunar eclipses. This will become more clear
when we will see the table with possible and real eclipses during Thales’ lifetime.
 The fourth thing he could have learnt after some years of observation, was that notevery full or new moon an eclipse occurred, but that they came at longer intervals, ofmultiples of six months, sometimes minus one. This is the rule of thumb the Babylonians ofhis time also were acquainted with.This rule presents the data of
 possible
 eclipses, days on which it is worth while to lookat the heavens. As you can see, actually the rule has a certain rhythm or pattern, which repeatsitself after 38 lunar months:
6
 
 
4
The 6-months/5-months ruleof thumbof
 possible
eclipses
 This knowledge made observation still easier, because he had to observe the sky only twice ayear.Together this is the knowledge that Thales could have been gathered simply from acareful observation of the heavens during his lifetime. When put into a table, it looks like this:
YEARB.C.JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC610
 1

30228
609
2724262524232221
 
19181716
608
15
 
151413121210
9
 8
76
607
4353311
2928272625
606
 
242223222120
 
191817161515
605
13121210108765433
604
312 31292927282524232222
603
21192119
 
1716141312
1111
602
109109866422 313030
601
282728
 
262624242220201818
600
171617161514131210987
599
65
654321
3129292726
598
252325242322212018181716
597
151313121110
 
87655
596
32211 30
 
2827252524
  
595
2221222020
 
181716141413
13
594
12101210
  
8754322 31
593
302930282726252322212019
592
181719
 
1717151513111199
591
768
765431 30302828
590
262526252523232120191817
589
16141513131211108876
588
4
34321 30
 
2827272525
587
 
422232221
 
191917161615
 
586
13121311119875543
lunar(
 
)andsolareclipses(
 
= full,
= partial)visibleatMiletusfrom610-586 B.C.
 The cells of the months in which an eclipse of the moon or the sun was visible at Miletus arecolored red. The numbers in the cells of the months are the data of new moon.I took the idea of this table from Joachim Herrmann, who in 1969 drew a similar onefor the years 1968 to 1990 AD.
7
 As we see, in such a table the rule of thumb expresses itselfas a series of strings or garlands through the calendar. This is even better visible when thetable is folded into a cylinder.
 
5However, the extrap


 
 
 
 
 
5However, the extrapolation of this table will lead to no more than the fixation of two
 possible
 data for solar eclipses in 585 BC: one at new moon in May and one at new moon in November. For a real prediction, more is needed.Let us suppose that Thales looked more carefully into the data he had gathered duringhis lifetime. Then he could have noticed a curious regularity in the series of the last eightsuccessive eclipses of the sun before the year 585 BC. I will show you them in a table:
Afterhowmanymonthsdo youthinkthe nextsolareclipseis to beexpected?
 I left out eclipses amaller than 0.50, because they could easily have escaped observation,unless Thales had a special reason to expect one. If you were Thales, what would you have put as the next item in the last column?
YES !!
 And which date do you think will appear in the last row?
 
6
YES !!
 This is, I think, how Thales predicted an eclipse. Note that the apparent 17/18 months regularity is not one of the fifteen real cycles discussed by Hartner.Why
haven’t other scholars discovered this method? One reason is that scholars were
looking for really existing regularities, such as the Saros cyclus and the Exeligmos cyclus. Noone (with one exception) ever thought about a non-existing but only apparent regularity thatcould have deceived Thales.Another reason is a silly mistake. In 1969 Hartner presented a table of possibleMilesian records, similar to the one I showed you, but by a curious mistake he omitted thesolar eclipse of 23 December 596 BC, and took instead the small eclipse of 28 June 596 BC(maximum phase 35) that almost certainly passed by unnoticed. This resulted in the numbersof 12 and 23 lunations instead of 18 and 17 between two successing eclipses.
Hartner’s
mistake
28 June596 0.35 12
23
 From Dmitri Panchenko I took the idea of looking for
apparent 
 regularities, and morein particular the intervals of 17 and 18 months. In 1994 he
wrote; “an astronomer (like Thales)
would naturally have searched for
(…) eclipses
 with the same interval
”.
 And also he wrote:
“the eclipse of 28 May 585 was separated from the two previous eclipses by intervals of 18
and 17 lunations respectively. But this sequence had taken place once before! The eclipse of
 
730 July 607 was also separated by intervals of 18 and 17 lunations from the two preceding
eclipses.”
 
Why didn’t Panchenko not discover the other interval of 17 and 18 months? Becausehe blindly copied Hartner’s mistake and put the number 23 instead of 17 at the eclipse of 9
May 594:
Hartner’s
and
Panchenko’s
mistake
23
 Because of this mistake Panchenko favored the eclipse of 21 September 582 BC, as wealready saw.
The only thing I had to do was to correct Hartners’s and Panchenko’s
 mistake.And now for the last question: Did Thales really predict the solar eclipse? The answermust be: no. The regularity he saw was only a lucky coincidence. When we look at eclipseslater than the year 585 BC, no such regularity as the 17 and 18 lunations occurs.This explains why Thales
“predicted” only one eclipse, and also why others could not
copy his method. After all, his preciction was a lucky guess, although it was based onthorough research and careful observation. His prediction was an example of the notuncommon situation in science that a right conclusion is based on a false presupposition. Suchmistakes happen in science and their exposure brings science further.
The End
 
1
 Willy
Hartner, “Eclipse Periods and Thales’ Prediction of a Solar Eclipse”.
Centaurus
 14 (1969), 60-71.
 
8
2
 
Dmitri Panchenko, “Thales’s Prediction of a Solar Eclipse”.
 Journal for the History of Astronomy
 25 (1994),275-88.
3
 
Francis R. Stephenson & Louay J. Fatoohi, “Thales’ Prediction of a Solar Eclipse”,
 Journal for the History of Astronomy
 28 (1997), 279-82.
4
 Patricia F.
O’Grady,
Thales of Miletus
. Aldershot: Ashgate 2002.
5
 Bartel L. Van der Waerden,
Science Awakening II: The Birth of Astronomy
. Leiden: Brill 1974, 122, n. 1.
6
 
Cf. John M. Steele, “Eclipse Prediction in Mesopotamia”. Archive for the History of Exact Sciences 54 (2000),
421-54.
7
 Joachim Herrmann,
Gesetze des Weltalls
, Stuttgart: Franckh’sche Verlagshandlu
ng , W. Keller & Co. 1969
https://www.academia.edu/6355805/THALES_AND_THE_SOLAR_ECLIPSE_OF_28_MAY_585_BC 
 
 
THALES AND THE SOLAR ECLIPSE OF 28 MAY 585 BCLecture held at the Research Center for Theory and History of science of theUniversity of West Bohemia in Pilsen, 3
rd
 March 2014, and at the Institute ofPhilosophy of the Czech Academy of Sciences in Prague, 6
th
 March 2014
Several sources, of which Herodotus is the most famous, report that Thales predicted aneclipse of the sun. We may ask:
 
1) did he really predict an eclipse?2) if so, which one did he predict?3) if so, how did he do it?The answers to the first two questions will appear to follow from the answer to the third one.If we are able to discover which method Thales could have used, it follows immediately thathe predicted an eclipse and also which one it was he foretold.We will answer these three questions: yes, he did predict a solar eclipse; it was the eclipse of28 May 585 BC, and he did it by making a brilliant mistake. Here is the path of the eclipse of28 May 585 BC:
The pathof the eclipseof28 May 585 B.C.
 As you see, Miletus lies just outside the path of the full eclipse, which means that what Thalessaw was actually a great but partial eclipse:
The solareclipseof25 May 585BC, seenfromMiletus
 
 
2But let us hear first some sceptical voices.The main source, Herodotus, says that Thales foretold the eclip
se, “fixing
as its term the sixthyear of the battle between the Medes and the Lydians
”.
 This can hardly be called a prediction.
Dmitri Panchenko rightly remarked: “If one can predict an eclipse at all, one can predict it tothe day”. Herodotus’ remark sho
ws, how little he understood of eclipses and their prediction.The most disappointing is the search for a method that Thales could have used for his prediction, the search for some regularity in the occurrences of eclipses. It has been arguedthat Thales must have had knowledge of ancient Babylonian wisdom about cycles of solareclipses.In 1969 Willy Hartner examined fifteen possible cycles, of which the Saros (a cycle of 223lunar months or lunations) and the Exeligmos (or triple Saros of 669 lunar months) are themost important, but his conclusion was that none of them could have been a base for a prediction of the eclipse of 28 May 585 BC.
1
 Dmitri Panchenko tried the Exeligmos for the eclipse of 21 September 582 AD.
2
 
The solareclipse of21September582 BC,seenfromMiletus
 
Panchenko calls this eclipse “impressive”, but
in 1997 Stephenson and Fatoohi, two expertson eclipses, pointed out very clearly that this eclipse may very well have passed unnoticed.
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 And they are right, as I could observe myself at the eclipse of 11 August 1999 AD, which wasin Holland (actually Maastricht) even bigger (0.95) than the eclipse of 21 September 582 BC,which was 0.85 at Miletus.
The solareclipse of11 August1999 AD,seenfromMaastricht
 In Maastricht, the atmosphere became spooky, as if a heavy thunderstorm was coming. AtMiletus, the only thing ordinary people may have noticed is that daylight was somewhatdimmed. A skilled observer like Thales, however, could have observed its reflection in a bowlfilled with oil or water.
This conflicts with Herodotus’ report that the day turned into night.
 
Perhaps the most ingenious attempt has been made by Patricia O’Grady
 in 2002.
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 Shenoticed
 – 
 as van der Waerden did before
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 – 
 that sometimes a solar eclipse occurs 23½ monthsafter a lunar eclipse.
 
3However, she based her analysis on eclipses, visible at Ninive instead of Miletus, andher list contains some other dubious points. When we make the list for Miletus it appears thatno more than 5 out of the 22 lunar eclipses took place 23 1/2 month before a solar eclipse.This is too small a base for a prediction that is more than a guess, as Hartner alreadyremarked.
Moreover, in Thales’
 time even the Babylonian astronomers were not able to predicteclipses. The only thing they were capable of was to find out the dates of
 possible
 eclipses, based on a very simple rule of thumb. Of this rule of thumb we will come to speak later.Our conclusion can be that Thales did not depend on ancient wisdom, whetherBabylonian or not.It could be asked, whether a prediction of an eclipse does not presuppose a knowledge of thetrue mechanism of eclipses. However, it must be stressed that the prediction of an eclipse doesnot presuppose any knowledge whatsoever of what a solar eclipse really is.Even Anaximander was not acquainted with this, for he explained eclipses as the partially ortotally closing of the apertures in the celestial wheel of the sun or the moon. In other words:Thales did not need to know that an eclipse of the sun occurs when the sun is blocked by themoon.The only thing that matters that he observed eclipses when they occurred and tried tofind some regularity in their occurrences. These regularities Thales could have noticedwithout having the faintest idea
why
 they occurred.Our conclusion can be that Thales did not depend on knowledge about the truemechanism of eclipses.At best, the sceptics say, Thales made a lucky guess. I will argue that his guess was brilliantand based on an observed regularity.From Willy Hartner
I took the idea of looking at “the statistical material at Thales’disposal”, as he called it.
Let us suppose, then, that Thales knew nothing about allegedBabylonian wisdom, but just started observing and registrating eclipses of the sun and themoon during his lifetime. Fortunately, he lived in a time in which relatively many eclipseswere visible at Miletus.The first thing he could have discovered
 – 
 if this was not already common knowledge
 – 
 wasthat both lunar and solar eclipses can be partial or full.The second thing he could have discovered
 – 
 if this was not already common knowledge
 – 
 was that lunar eclipses occur at full moon and solar eclipses at new moon.This was helpful, because it meant that he did not need to look out for a possibleeclipse every day and night, but only twice a month. Mark that whenever I speak of months,lunar months or lunations are meant, from one new moon until the next, about 29 1/2 days.The third thing he could have observed was that the dates of possible solar eclipsesalways fall within the same month as possible lunar eclipses. This will become more clear
when we will see the table with possible and real eclipses during Thales’ lifetime.
 The fourth thing he could have learnt after some years of observation, was that notevery full or new moon an eclipse occurred, but that they came at longer intervals, ofmultiples of six months, sometimes minus one. This is the rule of thumb the Babylonians ofhis time also were acquainted with.This rule presents the data of
 possible
 eclipses, days on which it is worth while to lookat the heavens. As you can see, actually the rule has a certain rhythm or pattern, which repeatsitself after 38 lunar months:
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