Debate about the emerging of early astronomical calculations.
Around Michael J. Barany’s post Mathematicians Are Overselling the Idea That „Math Is Everywhere“ on SciAm appeared an interesting discussion on Tony Christies blog Some rather strange history of maths and again a response by Michael.
I became interested in the discussion about astronomical calculations in Babylon by the following paragraphs:
Michael: In the first agricultural societies in the cradle of civilization, math connected the heavens and the earth. Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies.
Tony’s objection: We are taking about the area loosely known as Babylon, although the names and culture changed over the millennia, and it is largely a myth, not only for this culture, that astronomical calculations were used to mark the seasons.
Spontaneously, I would have stated the same like Michael. Are the fallacies so widely spread? Here is the outcome of a quick check of Babylonian astronomical calculations though.
The first thing that comes in mind are the calendars in Babylon and Egypt. But, in fact Tony seems to make a point. We do not know exactly when the calendars came into use (at some point between the fifth and second millenium B.C.), and there is no proof that calendars have been derived originally from astronomical calculations.
But wait a second. It cannot be shown that there was knowledge of astronomical objects that allowed the theoretical derivation of a calendar. Nevertheless, the calendars reflect clearly periods appearing in the astronomical phenomena even if the precision did not allow to use them for predictions. Therefore, the priests must have had data and done something we would tag today as data fitting. They looked for patterns in the measurements, something that nowadays is tried by hordes of scientists in small and big data sets of all kinds.
Leaving calendars, another interesting question is what calculations do we know that have been carried out in Babylon at those times.
The collected data from the Moon observations could finally be processed by mathematical means. One realised that the Sun’s velocity is not constant and also the variable velocity of the Moon has been used in the calculations. This allowed to calculate the length of the synodic month with a precision of up to seven sexagesimal digits. Finally it was possible to predict moon eclipses. In order to do this, also the lateral movements of the moon had to be considered and have been represented as a linear sawtooth function. Furthermore, the Saros cycle of the eclipses has been known.
While the calendar was quite inexact in the beginning, increasing knowledge allowed to improve it. Finally, a precision of about 2 hours in a cycle of 19 years has been achieved (Metonic cycle).
Another interesting impression of the mathematical capabilities is possible from a tablet, created around 1700 B.C., showing a representation of the square root of 2. It has been discussed by Richard Elwes in his blog post Babylon and the Square Root of 2.
To cut a long story short, mathematics developed probably in parallel to the use of the first calendars, and there was not a straightforward way to the mathematics for astronomical calendar calculations. But, it can well be assumed that the mathematical processing of astronomical data improved calendars.