Babylonians again

If you ever took an astronomy class and paid attention, you know that there are two different ways of defining a month:  sidereal month and synodic month.  Frankly, these tax my retention.  But the real picture is even more complicated.

Shlomo Sternberg, Celestial Mechanics (1969), p. 26:

The return [of the moon] to maximum velocity  takes slightly longer than a sidereal month, and slightly less than a synodic month.  The period of return to maximum velocity is known as the anomalistic period or anomalistic month.

Thus far, a curiosity of astronomy;  one which, one might venture at hazard, was discovered by some persistent fellow with a telescope, prior to the discoveries of quasars or the Red Shift, but probably not all that long before.

But no.   The facts were known in the second century B.C.E. -- and this, in dizzying detail:

Hipparchus gives the relation that 251 synodic periods  are almost exactly equal to 269 anomalistic periods.

Now, at this point, things become seriously weird:

What is most striking is that we find this ratio 251/269 used in a theoretical way in Babylonian tables.

            This startlingly early anticipation does not mean that the ancient Babylonians had been informed of the facts by visiting Space Aliens, as the New Agers would no doubt have it (if they have heard of this story at all).  But it does suggest a preternaturally diligent interest in astronomical niceties.

            And indeed, preternatural is here the operative word.  For as Sternberg several times mentions, the desire for extraordinarily precise knowledge of the celestial facts  stemmed, among the ancient Hebrews, from necessities of religious observance.   Islam likewise has such requirements, a fact perhaps not unconnected with another blazingly insightful observation of the late 9^th/early 10^th century (p. 20):

The motion of the apogee (beyond the effect due to precession) was apparently first discovered by the Arabian astronomer al-Battani.

These, then, are instances in which religion was the midwife of science.  Other instances are familiar from the field of linguistics, where the preservation and explication of sacred Scripture (the Vedas, the Bible, the Koran) was the motivation.

Credo (concluded)

Bishop Berkeley famously quipped, in his (cogent) critical article on Newton’s fluxions (infinitessimals), that “he who can digest a second or third Fluxion,  need not, methinks, be squeamish about any Point in Divinity.”  Conversely,  might not a certain intellectual tolerance for points of Divinity, pre-dispose one towards seeking the reality behind such initially ill-presented abstractions as the infinitessimals, that they might be put upon a sound footing?  Indeed this has, since Berkeley’s time, been done, for the Calculus as inherited from Leibnez and Newton; and since that time, those very infinitessimals, once spirited away in the new Cauchy formulation, have shown up again unexpectedly at our door, no longer in rags, but smartly outfitted by Robinson.  And indeed these originally disreputable and now revived entities (very small ones, to be sure, but still entities) – which originally, I confess, struck me as rather a sterile abstraction, no doubt true enough in their way, but probably no part of the Palace – have latterly been suggested as just the broom for cleaning out the Augean stables of perturbation theory, of all massively practical things..  Is there nothing the mind of math may dream up, which may not prove someday as routinely serviceable as a hammer?

            Consider again the ill-fated squeamishness of Pythagorus, concerning what we now think of merely as the complement in R of Q.   Might his bias of nominalism been somehow connected to the limits of his theological horizons – Olympus and its rabble of godlings, with their petty jealousies and sordid couplings?  You are not likely to get much of an ontological leg-up from a shag-shanked goatgod; whereas God  the creator of all things visible and invisible…nay, Who dies and yet rises… a God who is One, and yet Three…