Broca's Brain - Carl Sagan [51]
There is an alternative explanation, which derives from the fact that there are not a whole number of lunations in a solar year, nor a whole number of days in a lunation. These incommensurabilities will be galling to a culture that has recently invented arithmetic but has not yet gotten as far as large numbers or fractions. As an inconvenience, these incommensurabilities are felt even today by religious Muslims and Jews who discover that Ramadan and Passover, respectively, occur from year to year on rather different days of the solar calendar. There is a clear whole-number chauvinism in human affairs, most easily discerned in discussing arithmetic with four-year-olds; and this seems to be a much more plausible explanation of these calendrical irregularities, if they existed.
Three hundred and sixty days a year provides an obvious (temporary) convenience for a civilization with base-60 arithmetic, as the Sumerian, Akkadian, Assyrian and Babylonian cultures. Likewise, thirty days per month or ten months per year might be attractive to enthusiasts of base-10 arithmetic. I wonder if we do not see here an echo of the collision between chauvinists of base-60 arithmetic and chauvinists of base-10 arithmetic, rather than a collision of Mars with Earth. It is true that the tribe of ancient astrologers may have been dramatically depleted as the various calendars rapidly slipped out of phase, but that was an occupational hazard, and at least it removed the mental agony of dealing with fractions. In fact, sloppy quantitative thinking appears to be the hallmark of this whole subject.
An expert on early time-reckoning (Leach, 1957) points out that in ancient cultures the first eight or ten months of the year are named, but the last few months, because of their economic unimportance in an agricultural society, are not. Our month December, named after the Latin decem, means the tenth, not the twelfth, month. (September = seventh, October = eighth, November = ninth, as well.) Because of the large numbers involved, prescientific peoples characteristically do not count days of the year, although they are assiduous in counting months. A leading historian of ancient science and mathematics, Otto Neugebauer (1957), remarks that, both in Mesopotamia and in Egypt, two separate and mutually exclusive calendars were maintained: a civil calendar whose hallmark was computational convenience, and a frequently updated agricultural calendar—messier to deal with, but much closer to the seasonal and astronomical realities. Many ancient cultures solved the two-calendar problem by simply adding a five-day holiday on at the end of the year. I hardly think that the existence of 360-day years in the calendrical conventions of prescientific peoples is compelling evidence that then there really were 360 rather than 365¼ rotations in one revolution of Earth about the Sun.
This question can, in principle, be resolved by examining coral growth rings, which are now known to show with some accuracy the number of days per month and the number of days per year, the former only for intertidal corals. There appears to be no sign of major excursions in recent times from the present number of days in a lunation or a year, and the gradual shortening (not lengthening) of the day and the month with respect to the year as we go back in time is found to be consistent with tidal theory and the conservation of energy and angular momentum within the Earth-Moon system, without appeal to cometary or other exogenous intervention.