Numerical Precision? Mother Nature Laughs!

Everything is number? Pythagoras supposedly said so although scholarly consensus disagrees. The best proof that Nature is sovereignly indifferent to number is discernible from the enormous difficulties humanity has had with keeping its calendars straight. Leap days, leap years, leap centuries (but only those divisible by 400) have disfigured our tools, and still do, and, in the early Julian calendar, we even had an intercalary month. That word itself is a mongrel, coming from inter (between) and calare (to proclaim or to call out). Things that don’t come around regularly need to be—called out.

Devilishly indifferent nature! The lunar year is 354.37 days—not 354, mind you, an even number, but fractional. The lunar phase is also a tricky 29.53 days (the period between two full moons) but is, observed against the fixed stars (the sidereal lunar month), 27.32 days. Not a whole number in sight. The 365.25 day year holds 12.369 lunar cycles.

But that length of year above is also just a sorry approximation. The solar year (called tropical year) is actually 365.2422 days; the sidereal year†, thus the year measured against the fixed stars, is 365.2564 days (both numbers rounded).  Nothing divides properly into anything. One has to keep adjusting, leaping, intercalating, and so on.

All this because I noticed—purely by happenstance—that the Julian year, in vogue from 45 BC through 1582, when the Gregorian calendar “corrected” it, would today be 13 days out of date with the observable dates of the equinoxes—of which the next comes this December 21. Back in the days of Pope Gregory XIII (that number again), the calendar was out of whack by 10 days. Three more have been added since. Now that number, 13, is a prime, therefore indivisible by anything cleanly, except 1, which makes it devilishly natural.

Is the Gregorian calendar perfect—at least in marking the equinoxes? No. It has a built in error of 1 day every 7,700 years. This suggests that the Gregorian will probably be revised and abandoned not later than the year 78 582 AD, by which time it will also be 10 days out of whack and need revision. So, approaching 2013, I am relaxed. Plenty of time yet before times comes to revise a calendar by dropping ten days to make the vernal equinox come out around about March 20, 21. This year, in the Julian, it would have fallen on March 7.

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†For more on tropical/solar and sidereal times, see this post.