When we were looking for astronomical support for our discovery that Roman time most probably is dated 218 years too old dendrochronologically, we found four dated observations in Pliny's "Natural History" (read about Pliny's quadruple here, opens in new window). Even though these observations strongly support the conventional chronology, there is an almost exactly matching second astronomical solution 232 years later than that conventionally assumed. Are there maybe more dated astronomical records which have a solution 232 years later in time?

Several Greek and Roman writers recorded a lunar eclipse that occured before the battle between Alexander the Great's army and Persian forces at Gaugamela near Arbela (todays Erbil in northern Iraq). The date of the battle is given by Arrian as during the month Pyanopsion when Aristophanes was archon at Athens. This means early in the autumn (October) RomBC 331 or 330 in our calendar. Plutarch mentions that the eclipse preceded the battle by 11 days.

There was a large lunar eclipse on -330 September 20, but also a second one on -98 October 6. Both eclipses would date the battle to October as Arrian says, and both were visible in northern Iraq, but at different hours of the night. A strange coincidence is the fact that the two solutions for Pliny's quadruple and the two candidates for the Arbela eclipse are offset by exactly the same number of days: 232 (Julian) years + 16 days = 84754 days.

A timing of the lunar eclipse at Arbela and a second place is given by both Pliny and Ptolemy. Both writers lived several centuries after Alexander. Therefore it is impossible that they made the observations themselves. However neither writer states the source for his timings and they give completely different hours of the night for the event. The difference is fully three hours. Read more about the astronomical details in Appendix A.

To summarize, Pliny's timing for the lunar eclipse at Arbela is fully compatible with the -330 event and just incompatible with the -98 event. However, Ptolemy's timing is not compatible with either of the two events, especially not with the -330 event which was already over at the time mentioned at Arbela. We might wonder how it is possible that Pliny, who was not an astronomer, could have more exact data than Ptolemy, who was a professional astronomer and had access to the best data available (in Alexandria). This is even more strange as Pliny lived about hundred years before Ptolemy.

Moreover, it seems that a Babylonian clay tablet mentioning the battle at Gaugamela has been preserved by a rare coincidence. Two cuneiform tablet pieces (BM 36761 + BM 36390) in the British Museum bear the official title "Astronomical Diary concerning month VI and VII of the fifth year of Artašata who is called Darius". The two pieces are from the same tablet, but they do not join. The references to the king, his regnal year and month are missing but can be deduced from the astronomical data given on the tablet.

To summarize the tablet: There was a battle 11 days after the lunar eclipse on -330 September 20. About three weeks after that battle the victorious "Alexander, king of the world" entered Babylon. It is most likely that the battle at Gaugamela is described in astronomical diary BM 36761 + BM 36390, and that this battle is dated by the tablet to -330 October 1 as conventionally assumed. Read more about the details in Appendix B.

Discussion
Even though there are two solutions with 232 years offset for both Pliny's quadruple and the lunar eclipse before the battle at Gaugamela, the Babylonian clay tablet tilts the scales in favour of the conventional solution. However, if our dendrochronological results are correct, something must be wrong with the astronomical records in some way.  Ultimately we have to decide which dating method we trust most. For the time being we rely on dendrochronology as this method is completely independent of historical considerations.

So what could be wrong with the record on the clay tablet found in the ruins of Babylon in 1880 (ref.5)?
The tablet is an astronomical diary, and it is a copy of an older damaged tablet. There is no doubt that the astronomical record describes the situation in the autumn of Astr -330, but the political record is a bit vague. The only explicite name mentioned is "Alexander", neither "Darius" nor "Gaugamela" or "Arbela" are preserved. The tablet could therefore describe another battle and another victorious Alexander.

However, the most plausible explanation (for the case that we are right) is that the scribe chose a set of suitable astrological omens when he handled the record of a decisive battle with far-reaching consequences for his society (see the commentary in ref.4). This he could achieve in two ways: either he could add the political record to a suitable existing astronomical record, or he could fabricate (i.e. retrocalculate) the entire astronomical record. That the Babylonians were fully capable of doing so is proven on the same clay tablet: the equinox on the twenty-first day was calculated as the astronomer comments "I did not watch". And the solar eclipse on the twenty-ninth day was expected after sunset (!) and moreover impossible to see in Babylon.

If already the Babylonians had these skills, also later ancient astronomers could have been experts in retrocalculation. This is exactly what Robert Newton (ref.6) suspects regarding Claudius Ptolemy and his Syntaxis (Almagest). Newton claims that all Ptolemy's own and most of the earlier "observations" made by others in the Syntaxis were fabricated. He goes so far that he states in his Final Summary:

It is clear that no statement made by Ptolemy can be accepted unless it is confirmed by writers who are totally independent of Ptolemy on the matters in question. All research in either history or astronomy that has been based upon the Syntaxis must now be done again.

If this is valid for the Almagest, which is regarded as the most eminent support for our conventional chronology, it could as well be valid for Pliny's astronomical statements in his "Natural History". So what makes even modern astronomers convinced that the conventional solution is correct?  First there is the eclipse timing mentioned above and second there is one explicite date in Pliny's quadruple which clearly point out the conventional solution as the right one. These two statements happen to appear in the same passage  (ref.3, ch.72):

Consequently inhabitants of the East do not perceive evening eclipses of the sun and moon, nor do those dwelling in the West see morning eclipses, while the latter see eclipses at midday later than we do. The victory of Alexander the Great is said to have caused an eclipse of the moon at Arbela in the second hour of the night while the same eclipse in Sicily was when the moon was just rising. An eclipse of the sun which occurred the day before the calends of May, in the consulship of Vipstanus and Fonteius a few years ago, was visible in Campania between the seventh and eighth hour of the day but was reported by Corbulo commanding in Armenia as observed between the tenth and eleventh hour: this was because the curve of the globe discloses and hides different phenomena for different localities. If the earth were flat, all would be visible to all alike at the same time; also the nights would not vary in length, because corresponding periods of 12 hours would be visible equally to others than those at the equator, periods that as it is do not exactly correspond in every region alike.

What if a later copyist with astronomical skills made some "minor changes" in that passage for some reason? We get a hint that something is wrong when Pliny about hundred years before Ptolemy gives a far better timing of the eclipse at Arbela. Maybe Ptolemy's "Geography" contains some genuine information about the eclipse (i.e. that it was seen around midnight), while Pliny's "Natural History" has been amended with later "improved" information?

Further it is interesting that the 232 years offset apparently was invented in Babylon, if we are right. It could have been rediscovered and used for some special purposes by later colleagues, maybe as the ultimate hard to detect and therefore longlasting fraud.

 

Appendix A: Astronomical details about the lunar eclipse candidates
Several Greek and Roman writers recorded a lunar eclipse that occured before the battle between Alexander the Great's army and Persian forces at Gaugamela near Arbela (todays Erbil in northern Iraq). Details see ref.1, ch.10.5.

The date of the battle is given by Arrian (Anabasis, II, 7.6) as during the month Pyanopsion when Aristophanes was archon at Athens. This means early in the autumn (October) RomBC 331 or 330 in our calendar. Plutarch mentions (Life of Alexander XXXI) that the eclipse preceded the battle by 11 days.

The Nasa Eclipse Web Site (ref.2) shows that there was a large lunar eclipse visible at Gaugamela on -330 September 20:

This would date the battle at Gaugamela to -330 October 1.

Exactly 232 years later, we find another large lunar eclipse on -98 October 6:

This would date the battle at Gaugamela to -98 October 17.

Both eclipses would date the battle to October as Arrian says, and both were visible in northern Iraq, but at different hours of the night. According to the NASA Eclipse Web Site the partial eclipse in Arbela began: in -330 at 19:46 when the moon was 19 degrees above the horizon (i.e. in the night's second hour), and in -98 at 00:50 when the moon was 54 degrees above the horizon (i.e. in the night's seventh hour). So there is a five hours difference between the timings of the two events, see also the tables below.

A timing of the lunar eclipse at Arbela and a second place is given by both Pliny (ref.3, ch.72) and Ptolemy (Geography, I, 4). Both writers lived 400 resp. 500 years after Alexander. Therefore it is impossible that they made the observations themselves. However neither writer states the source for his timings and they give completely different hours of the night for the event. The difference is fully three hours. Both realize correctly that the eclipse would start about two hours local time later in Arbela than in the middle of the Mediterranean, because Arbela's position is about 30 longitudinal degrees farther to the east.

Pliny says that the eclipse was seen at Arbela in the night's second hour, and the same eclipse was seen in Sicily when the moon was just rising.
According to NASA, the partial eclipse began in Syracuse on Sicily in -330 at 17:46 when the moon was 4 degrees below the horizon (i.e. the moon rose eclipsed), and in -98 at 22:50 when the moon was 53 degrees above the horizon (i.e. in the night's fifth hour), see also the tables below.

Ptolemy says that the eclipse was seen at Arbela in the night's fifth hour, and at Carthage in the night's second hour.
According to NASA, the partial eclipse began in Carthage in -330 at 17:31 when the moon was 8 degrees below the horizon (i.e. a little before sunset, the moon rose almost totally eclipsed), and in -98 at 22:35 when the moon was 52 degrees above the horizon (i.e. in the night's fifth hour), see also the tables below.

Pliny's timing for the lunar eclipse at Arbela is fully compatible with the -330 event and just incompatible with the -98 event. However, Ptolemy's timing is not compatible with either of the two events, especially not with the -330 event which was already over in the night's fifth hour at Arbela. We might wonder how it is possible that Pliny, who was not an astronomer, could have more exact data than Ptolemy, who was a professional astronomer and had access to the best data available (in Alexandria). This is even more strange as Pliny lived about hundred years before Ptolemy.

 

For those who want to look at more details:
Time tables generated by using ref.2, Javascript Lunar Eclipse Explorer, for the appearance of the total lunar eclipses at Arbela, Syracuse and Carthage.

 

Appendix B: A Babylonian clay tablet mentioning the battle at Gaugamela?
Two cuneiform tablet pieces (BM 36761 + BM 36390) in the British Museum bear the official title "Astronomical Diary concerning month VI and VII of the fifth year of Artašata who is called Darius". The two pieces are from the same tablet, but they do not join. The references to the king, his regnal year and month are missing but can be deduced from the astronomical data given on the tablet.  Moreover, the tablet is a copy of an older one which was damaged. We use a recent translation of the tablet by Bert van der Spek and Irving Finkel (ref.4) for the following discussion.

As the tablet is very incomplete, we have to verify which information actually is extant, and which information is filled in by the translators. The tablet contains (as a Babylonian astronomical diary usually does) information about prices for staple goods, weather etc. besides astronomical data and political events. We are only interested in the latter two types, and only the significant statements.

Astronomical data
The thirteenth, Moonset to sunrise: 32 minutes ... lunar eclipse, in its totality covered. 40 minutes of the night ... Jupiter set; Saturnus ...
The twenty-first: Equinox. I did not watch.
Night of the twenty-ninth: Solar eclipse which was omitted; (it was expected for) about the 4th minute of the night after sunset.
At that time, Jupiter was in Scorpius; ...

This information is a fully sufficient description of the total lunar eclipse on -330 September 20. The penumbral eclipse at Arbela started 18:49 local time, which was about 40 minutes after sunset (18:05). At that time Jupiter, which was in Scorpius, set. All this can be simulated with a modern planetarium software, we use Stellarium. We can also see that Saturn was in the vicinity of the moon.

Moreover, if the 13th day in that month was September 20, the 21th day would have been September 28. In the (Julian) year -330 the autumnal equinox would have fallen on this date. And there was indeed a solar eclipse on -330 October 6, but that one was visible in Greenland and North America only.

On the other hand, the eclipse described on the clay tablet has nothing to do with the total lunar eclipse of -98 October 6. At that time Jupiter was in Cancer, and the autumnal equinox had been passed ten days ago. Though there was a solar eclipse on -98 October 20 which was visible in Antarctis.

Political events
The twenty-fourth, in the morning, the king of the world ... standard ... Opposite each other they fought and a heavy defeat of the troops ... The king, his troops deserted him and to their cities ... land of the Gutians they fled.
That (next) month, from the first until ... came to Babylon, saying as follows: 'Esagila ... and the Babylonians ... to the treasury of Esagila ...
On the eleventh, in Sippar an order of Al...  'Into your houses I shall not enter.' On the thirteenth day ... la gate, the Outer gate of Esagila and ...
The fourteenth day, these Greeks a bull ... short ... fatty tissues ... Alexander, the king of the world, entered Babylon ... horses and equipment ... and the Babylonians and the people ... a parchment letter to ...

To summarize the tablet: There was a battle 11 days after the lunar eclipse on -330 September 20. About three weeks after that battle the victorious "Alexander, king of the world" entered Babylon. It is most likely that the battle at Gaugamela is described in astronomical diary BM 36761 + BM 36390, and that this battle is dated by the tablet to -330 October 1 as conventionally assumed.

 

References:
1. Stephenson F.R.: Historical Eclipses and Earth's Rotation, Cambridge 1997.
2. NASA Eclipse Web Site Eclipse Predictions by Fred Espenak, NASA/GSFC
3. Pliny, Natural History, Book II, trans. Rackham read here. However, we inserted own translations of dates and timings from Latin because Rackham's statements contain too much interpretation. E.g. he translates pridie Calendas Maias with "April 30", and inter horam diei decimam et undecimam with "between 4 and 5 p.m".
4. Van der Spek R.J. and Finkel I. (2010, as per 2015-12-04). An Astronomical Diary mentioning Gaugamela. read here, or here (p.17-28)
5. The British Museum, Collection online (as per 2015-12-27). read here, and here
6. Newton R.R.: The Crime of Claudius Ptolemy, The John Hopkins University Press 1977.