Tuesday 30 May 2017

Did Thales predict a solar eclipse?

In the late afternoon of 28 May 585 BCE, a total solar eclipse took place over central Anatolia. It is widely believed that a reference to this eclipse appears in Herodotus:
A war went on between the Lydians and the Medes for five years. The Medes often beat the Lydians, the Lydians often beat the Medes. There was even a night battle, of a sort. They were evenly matched in the war, and when there was an encounter in the sixth year, during the battle it happened that day suddenly became night.
-- Herodotus 1.74
Herodotus, writing about 160 years after the event, goes on to tell us that the Lydians and Medes were so impressed by this that they got two external arbitrators to broker a peace treaty between them, with marriage ties.

What are we talking about, exactly?

Even at this point, there’s room for endless quibbling:

Where did the battle take place?

It’s often claimed to have been at the Halys river (the modern Kızılırmak). Herodotus doesn’t actually specify the location. It’s the merest guess, based on the fact that the Halys was an important natural boundary to Lydian territory.

Which eclipse was it?

Several other candidates have been proposed. For the record, the 585 BCE eclipse is by far the best choice. Here are maps from Gautschy 2012 showing the path of the moon’s shadow for each of the eclipses that have been proposed: 30 Sep. 610; 18 May 603; 28 May 585; 21 Sep. 582; 16 Mar. 581. Note that e.g. ‘-584’ = 585 BCE. The path of the moon’s umbra (path of totality) is shown in red; surrounding lines indicate magnitude 0.9, or 90% totality; 0.8; 0.7; and 0.5. Around 600 BCE there’s about 2° uncertainty in longitude -- ΔT, as the astronomers call it -- and this is reflected in the multiple bands of red, for the possible paths of totality.

The trouble is that while the competing eclipses would have been visible, not one of them would have produced significant dimming. Hughes (2000) has calculated that, based on human perception of ambient lighting, anything less than a 3 point change in the sun’s apparent magnitude may go completely unnoticed unless you happen to look directly at the sun and directly observe that it is partly hidden. And, Hughes goes on to show, this corresponds to an eclipse of magnitude 0.937 or greater -- that is, concealing 93.7% of the sun. (Remember that stellar magnitude is a logarithmic scale.)

None of the other four eclipses achieved better than magnitude 0.7. That’s a change in the sun’s brightness of only 1 point of magnitude. That’s comparable to the edge of a cloud partially going in front of the sun. The dramatic dimming associated with total eclipses is very sudden, and only happens within about four minutes of totality.
Graph from Hughes 2000, showing eclipse magnitude (= α/2) versus brightness (sun’s apparent magnitude). Coloured elements are added by me, with approximate figures for eclipse magnitudes as seen in north-central Turkey based on Gautschy 2012.

Was it actually a solar eclipse?

Herodotus says ‘the day suddenly became night’ (τὴν ἡμέρην ἐξαπίνης νύκτα γενέσθαι). He uses the same phrasing about the same battle at 1.103. The trouble is that he uses the same phrasing again when talking about a different incident in 480 BCE at 7.37, and there was definitely no historical eclipse corresponding to the incident in 480. He uses slightly different phrasing at 9.10 (’the sun became dim in the sky’, ὁ ἥλιος ἀμαυρώθη ἐν τῷ οὐρανῷ), and while it’s conceivable that that lines up with a mag. 0.6 eclipse on 2 October 480 BCE, a 0.6 eclipse wouldn’t produce significant dimming, so it’s simply false to describe it as the sun ‘becoming dim’.

None of these are remotely as clear as Thucydides’ descriptions of partial solar eclipses. Thucydides uses explicit language like ‘the sun was eclipsed’ (ὁ ἥλιος ἐξέλιπε). He reports clear-cut eclipses on 3 August 431 (Thuc. 2.28; mag. 0.88) and 21 March 424 (Thuc. 4.52; mag. 0.71), and a lunar eclipse in the wee hours of 28 August 413 (Thuc. 7.50; total).

So it’s not at all clear that it was an eclipse, and there’s no particular reason to think that the battle happened at the river Halys.

Let’s move on to Thales now. Because that’s the thing that makes Herodotus’ eclipse famous -- let’s take it for granted for the following discussion that it was an eclipse. It’s that Herodotus also tells us that it had been predicted beforehand by Thales, a Greek sage.

Herodotus’ report

Herodotus isn’t the only source to tell us that Thales predicted an eclipse. But all the other relevant sources are very probably derived entirely from Herodotus, with some distortions along the way. So they’re not independent: they have very little corroborative value, if any. Still, here they are, for what they’re worth, in chronological order:
Clement, in particular, indicates that an important lost source, Eudemus of Rhodes (4th cent. BCE), was simply based on Herodotus. The only hint of independence here is in Cicero, who states that Astyages was on the Lydian throne at the time of the incident: in Herodotus, Astyages’ father Cyaxares was still around. In other respects, unfortunately, Cicero’s report is terse and vague.

The upshot is that we depend entirely on Herodotus for an account of what Thales actually predicted. So let’s take a look at what Herodotus actually says:
τὴν δὲ μεταλλαγὴν ταύτην τῇ ἡμέρης Θαλῆς ὁ Μιλήσιος τοῖσι Ἴωσι προηγόρευσε ἔσεσθαι, οὖρον προθέμενος ἐνιαυτὸν τοῦτον ἐν τῷ δὴ καὶ ἐγένετο ἡ μεταβολή.

Thales of Miletus had advised the Ionians in advance that this transformation would happen, setting this year as a boundary, in which the change did in fact take place.
-- Herodotus 1.74
‘Setting this year as a boundary’? This isn’t a report of someone predicting that an eclipse -- or whatever it was -- would happen on a specific day. What Herodotus actually claims is that Thales predicted in which year this ‘transformation’ would occur. To call that ‘predicting an eclipse’ is a colossal stretch.

How could Thales have predicted an eclipse anyway?

The simplest customary answer to this question is: he must have discovered that solar eclipses come in saros cycles, just like lunar eclipses do.

A saros cycle is a period of 223 lunar months which governs all eclipses, both solar and lunar. This period is determined by three simultaneous periodic movements of the earth-moon-sun system (the moon’s orbit relative to the sun, the moon’s orbit relative to the stars, and orbital precession) which which come very close to coinciding with one another after 223 lunar months.

In other words: if you have an eclipse at t = 0, you will have another eclipse at t = 18 years, 11 days, 7 hours, and 42 minutes. (Subtract one day if that period includes five leap years.) A saros series doesn’t last forever, but it’s pretty close: it will last for 1230 to 1550 years. Plenty long enough for ancient astronomers to notice it!

And, indeed, long before Thales came along, the Babylonians had already discovered the saros cycle as it relates to lunar eclipses. So, hey, it’s obvious: Thales must have discovered that solar eclipses follow the same cycle, right?

And that would be absolutely completely dead wrong. Here’s why. A lunar eclipse is when the earth casts its shadow on the moon. As a result, the eclipse is visible from anywhere on that side of the earth. A solar eclipse is when the moon casts its shadow on the earth. As a result, the eclipse is only visible on that part of the earth which happens to be shadowed by the moon.
The solar eclipse of 8-9 March 2016, as viewed by the NASA-NOAA Deep Space Climate Observatory (DSCOVR). (source: Space.com)
If you see a solar eclipse at the start of month 0, it’s possible to see another eclipse 223 months later. But, because the saros cycle isn’t a round number of days, you’ll only see the second eclipse if you move south and west far enough to compensate for that. The end of the lunar month will fall 7 hours and 42 minutes later in the day. Solar eclipses may happen every 223 months, but there’s absolutely no possible way for an ancient astronomer to have seen them every 223 months.

But wait, not so fast. If the 223 month period means that each eclipse is 7 hours and 42 minutes later in the day, that’ll eventually wrap round, right? After three saros cycles, you’ll get another eclipse that’s 23 hours and 7 minutes later -- pretty close to 24 hours. Put another way, you’ll get an eclipse that’s 53 minutes earlier in the day. That could be a realistic way to see solar eclipses! And in fact Greek astronomers had a technical term for this period of three saros cycles, 669 lunar months or 54 years and 32 days: they called this period an exeligmos.

But wait again: yes, the exeligmos cycle was known to Greek astronomers -- 500 years after Thales’ time, mind -- but to predict an eclipse on 28 May 585 BCE using the exeligmos cycle, you would need to have observed the eclipse one exeligmos earlier on 26 April 639 BCE. Unfortunately, that eclipse never got as far as Thales. Sunset intervened. The eclipsed sun set below the horizon while the moon’s shadow was still over Estonia. Eclipses before that are even worse: the earlier in the exeligmos series you go, the earlier sunset puts an end to the eclipse.

This is why many people who have faith in Thales -- or rather, Herodotus’ vague and poorly described version of Thales -- tend to opt for other eclipses. The 28 May 585 BCE eclipse is actually pretty hard to predict. But as we saw earlier, none of the rival candidates would have darkened the sky noticeably.

No one has any good theories on how Thales might have predicted the 28 May 585 eclipse. The astronomer Miguel Querejeta (2011) has rejected two leading candidates, and one of the targets of his criticism, Couprie (2004), rejects several more.

One thing is certain: there were no genuine techniques in Thales’ time for predicting solar eclipses. Genuine predictions didn’t start to emerge until around the 4th century BCE in Babylonian astronomy, and the 3rd century CE in Chinese astronomy (Steele 1997, 1998). The simple reason is that solar eclipses are really sodding hard to predict: because they are very localised, they require an awful lot of very precise observations, and observations of them are very tightly constrained by the geographical location of the observer.

We’d better not go too hard on Thales, though. He may not have predicted an eclipse -- and there’s not much reason even to think he did, given how vaguely Herodotus describes his ‘prediction’ -- but he was a creature of his time. Like all Greek thinkers until the late 400s BCE, he imagined the earth as a flat disc: he believed the earth was like a wooden disc floating in water, as Aristotle and other later writers report (Couprie 2011: 63-7; see Thales frs. A.14, A.15 Diels-Kranz). On the other hand, we have testimony suggesting that he did get some things right. We have (1) two reports that Thales explained the light of the moon as the moon being illuminated by the sun (fr. A.17b D-K; p. Oxy. 3710, col. ii lines 38-43); (2) one report that he explained solar eclipses as being caused by the moon screening the sun (fr. A.17a D-K); and (3) one report that he discovered the periodic nature of eclipses and how ‘they are not always exactly equal’ (fr. A.17 D-K). What does the last of these mean? Maybe the fact that the saros cycle isn’t an integer number of days. He was no eclipse-predictor, but if half of these reports are true, he was not half bad as an astronomer.