5. Computation Matters

32. Lots of Times

Standard everyday time is based on the rotation of the earth. This Universal Time (UT) is unsuitable for astronomical calculations, because the earth's spin is slowing down in an irregular manner.

Astronomers use a uniform time called Ephemeris Time (ET) in their calculations. Delta-T = ET-UT is a measure of the difference between the two ways of tracking time.

According to historians, the mean solar day in Diary times was about 1/20th of a second shorter than today. The minuscule difference added up over the nearly million days since 500 BCE and now amounts to several hours. This accumulated clock difference equals delta-T.

33. Delta-T

A great deal of effort has gone into working out delta-T for the epoch of the Diaries, but no solution satisfies the precision astronomers expect.

For year 0, one recent calculation puts delta-T at 2hr 34min, another at 2hr 38min, and TheSky offers 2hr 44min. In year -400, the difference widens: a contemporary canon of eclipses estimates delta-T at 4hr 5min -- 17 minutes off from TheSky's 4hr 22min. An error of 17 minutes can affect the dating of phenomena observed near the horizon and alter the description of an eclipse.

34. Better than Good

The eclipse dates recorded by the Babylonians closely match the computed dates tabulated in modern eclipse canons. Additionally, the eclipse characteristics documented in the ancient texts are generally consistent with the computed descriptions.

Historians are sometimes sanguine about their computations. They have been known to attribute an excessive scatter in computed results to inaccurate Babylonian clocks, rather than to the elusiveness of determining delta-T and other variables.

35. Circular Reckoning

A detailed study of lagtime (See frame 20, Lagtime) by Fatoohi et al led to remarkable findings. The authors searched the Diaries and found 136 records that register an observed lagtime. Analysis of the records determined that the time difference between the observed lagtime (by Babylonian astronomers) and the computed lagtime (by Fatoohi et al) is less than 16 minutes, except for only 9 records.

The computations involved a massaging of the data. The question arises: Is the excellent match between Babylonian observations and modern computation due to a circular reckoning?

36. Adjusting Delta-T and Other Fixes

Fatoohi et al computed delta-T based on historical records of astronomical events, including eclipses from Babylon. Their delta-T works out to 4h 40m in the year -500, a figure close to the 4h 31m determined by a contemporary investigator.

Lunar acceleration is another input the researchers fine tuned. Generally accepted values range from -23.895" to -26.0"/cy2 [seconds of a degree per century per century]. The authors found that -26.0''/cy2 delivers superior results.

They even revalued the cubit. Instead of 2.0 degrees, Fatoohi et al concluded that 2.2 degrees provides better agreement with Babylonian measurements of planetary conjunctions.

37. Confluent Findings

The computations of Fatoohi et al entail elements of circular reckoning. Possibly the aimed for end result unduly influenced the work. Their findings seem too good to be true.

However, the concurrence between lagtime observation and computation is not surprising. The excellent match is comparable to the box score toted up in the section Testing the Diaries. (See frame 24, Box Score) TheSky does not equal the accuracy claimed by Fatoohi et al, but Feat of Clay used the software mostly to test observations of planets. They move slowly across the background of fixed stars, and hence the observations are not sensitive to delta-T and other corrective factors.