Wednesday August 20, 2014

Uncooperative nature makes messy calendar


As a species, there are many things peculiar to Homo sapiens, perhaps none so much as our preoccupation with time.

With respect to living on planet Earth, there are really only two basic units of time that matter, the solar day and the solar year. That wasn’t good enough for our ancient forebears, though.

It makes sense in the context of civilization to want to break these basic units into smaller increments. There have been numerous schemes (calendars) for doing this over the millennia.

We get our modern concept of the 24-hour day from the Egyptians, who, for reasons I won’t go into, used a base-12 counting system. They divided the clock into 12 hours of daylight and 12 hours of darkness. Astute readers, of course, can instantly see the problem with this as the period of daylight varies on a daily basis throughout the year. Without a fixed number of even smaller units (minutes, seconds) having variable length hours didn’t seem to bother the ancient Egyptians.

It did bother mathematicians, however. The Greeks standardized the day for purposes of making refined theoretical calculations into 24 equal hours. Further complicating matters, the Ancient Babylonians used a base-60 counting system, which gave us 60-minute hours and 60-second minutes.

It winds up being a pretty good approximation of the time it takes the Earth to rotate once on its axis. The average length of a solar day is 23 hours, 56 minutes and 4.09 seconds, although, in reality, our days are variable lengths. Because the planet’s orbit is elliptical, when it is closest to the sun it rotates slightly faster and when it is furthest, slightly more slowly. Solar days can be about 15 minutes shorter or longer either side of the mean.

Early humans weren’t just interested in the sun, there’s also the moon to consider. The phases of the moon may have given us the seven-day week, although the argument has been made for a biblical origin. Another likely clue to the origin of the seven-day week comes from the names of the days. Babylonian astrologers named the days after their gods, which corresponded with the major celestial bodies, the sun, moon, Mercury, Venus, Mars, Saturn and Jupiter. The Romans carried this on and it is still apparent in the names of the days in Latin-derived languages. English retains Saturday, Sunday and Monday, but derives the rest of the day names from equivalent Norse gods.

The moon is also responsible for our months. The earliest Greek and Roman calendars were lunar calendars. Since the full cycle of the moon is actually around 29.53 days, months were either 29 days or 30 days. Reconciling a lunar calendar with the solar year created havoc, however, because no matter how you slice the year up into months of 29 or 30 days, you wind up with extra days. If you ignore the fact of the solar year, it does not take long before your months are completely out of whack with your seasons.

They dealt with this in various ways, occasionally adding intercalary days or months. One early Roman calendar-making attempt simply had 51 days that were not assigned to any month.

In 46 BC, Julius Caesar had had enough of this unwieldy situation and by Pontif Maximus (high priest) decree gave us the 365-day, 12-month calendar with an extra day added to February every four years accounting for the fact that it actually takes the Earth approximately 365.25 days to complete one orbit of the sun.

The Mayans also had a 365-day civil year with 18 months of 20 days and one month of five days. I asked one of our Mayan guides during a recent trip to Mexico how they dealt with the other .25 days. He said they didn’t, giving me a vague sort of answer that suggested they simply didn’t care if days were of variable length. This does not work; I did the math. What he was most likely getting at was that the Mayans took a much longer view (the long count or great cycle of roughly 5,125.36 years) and didn’t care that the seasons would drift through the civil year. Mayan astronomers estimated the seasons would complete two full cycles through the civil year every 1,101,600 days. When you do the math, that gives you a solar-year length of 365.242036 days, amazingly close to the 365.242190419 we now know from precise astronomical calculation and slightly better than Pope Gregory XIII’s basis for reforming the Julian calendar of 365.2425 days. Gregory recognized that this was still slightly off, which means that after 400 years of leap years the calendar would once again be off by approximately one day. He decreed a further adjustment of only having 97 leap years every 400 years instead of 100. To accomplish this, years that are divisible by both four and 100 are not leap years, unless they are also divisible by 400. What the Pope did not take into account was that after 3,200 years of this regime, the calendar will once again be off by approximately one day and there will need to be another adjustment. Interestingly, 3,200 years is pretty close to the Mayan’s 1,101,660-day seasonal drift cycle (3,016.08 years).

What we’re left with is a convoluted system of marking time derived from numerous base counting schemes, none of which work mathematically because the universe does not behave in a way conducive to our inherent human need to somewhat arbitrarily or superstitiously make sense of our world.

There have been many attempts to once again reform the calendar (and even the clock), none of which have met with much success for various reasons. Part of it is that there is no base counting system that can be crammed into the reality of the Earth’s movements. The proposals also rely on breaking the seven-day week, which is anathema to the religious traditions of all major religions, as well as, banking systems, international commerce and television broadcasters.

There is one proposal that has merit, however. It is described as a “permanent calendar” by its developers Richard Henry and Steve Hanke of Johns Hopkins University.

Henry and Hanke argue that it costs every organization in the world time and money to plan their annual calendars.

But, what if every year was exactly the same? It would simplify everything and, they say, save billions of dollars. Their proposal calls for the year to be divided into four quarters each having two months of 30 days followed by one month of 31 days. Of course, that means the year would be 364 days. In their new Calendar this would be reconciled by adding an intercalary week every five or six years.

It’s definitely worth considering and, I propose, that extra week be a week off for everybody.



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