“I really believe,” I told Sosigenes, “that my true task has nothing to do with helping you with the calendar, which I could not do anyway, but rather to convince the Roman people that it will be beneficial. We are very attached to our ancient institutions, you know.”
“All too well. Well, let me explain a bit.” He took my arm and began to stroll among the instruments and the others followed us. Like a great many Greek philosophers, Sosigenes liked to expound while walking. This originated with the Peripatetic school of philosophy, but spread to many of the others. Among other advantages, it saved the rent of a lecture hall.
“For all of your history you Romans, along with most of the world, have been using a calendar based upon the phases of the moon.”
“Naturally,” I said. “It is a measuring of time observable by everyone as the moon waxes and wanes and disappears and reappears.”
“Precisely. As such it is what we might call an intuitive way to measure the year, and it works after a fashion, but far from perfectly. The moon has a phase of twenty-eight days, but, alas, the year cannot be divided into a certain number of discrete twenty-eight-day segments. It is always off by a number of days because the year is 365 days long.”
“Are you sure? I always thought it was some number in that area, but I could never be sure exactly how many.”
“It is not easy to determine and a great deal of study went into ascertaining exactly that fact. It is now agreed by all astronomers that the year is about 365 days long.”
“‘About’?” I said.
He looked at the others. “Did I not say that the senator is extremely quick of apprehension?” Then, back to me, “Yes, no matter how many experiments were done, it was found that the year is never quite exactly 365 days long. It is always a few hours longer than that, about one-quarter of a day.”
“So it cannot be divided evenly into any number of days at all?” I asked.
“Not with perfect precision. However, we have worked out a new calendar based upon the solar year, using the winter solstice as the beginning and ending point.”
“Everyone starts the year at the beginning of January or thereabouts,” I said.
“Yes, but using months of twenty-eight days, taken together with the fact that there are a few extra hours every year, means that if you use a certain number of months to the year, you always end up with a number of extra days. You Romans have made up this anomaly by having the priests give varying numbers of days to the months and by adding an extra month from time to time.”
“We’ve found it a useful political tool,” I told him. “If you have an in with the pontifexes, you can get them to extend your term in office by an extra month or two.”
“Well, yes. Useful for politicians and for generals looting provinces, I am sure, but terribly inconvenient for everybody else.”
“You’ll find that Romans of the ruling class don’t care much what inconveniences other people.”
“It seems that Julius Caesar is an exception, then,” he said dryly.
“I can’t argue with you there, but I still fail to see how this can be an improvement. It is impossible to divide the year into an even number of months and the year in any case can’t be measured to the last hour.”
“That,” he said, “is where subtlety and unconventional thinking are called for. You see, people have been so fixated upon the lunar phase of twenty-eight days that they have always wanted each month to contain the same number of days, even knowing that that is impossible. Upon reflection, though, there is no necessity for this. Why should a month not be twenty-nine days? Or thirty days? And why should each month have exactly the same number of days?”
“Eh?” I said brightly.
“Think about it. Why should each month have the same number of days?”
“Why, because it would be convenient, I suppose.”
“Exactly. People are bound by custom and tradition and convenience. It is this sort of thinking we must avoid if we are to break new philosophical ground.” Here the crowd of astronomers made approving sounds, as if he were an advocate who had just made a telling point in court. “What is far more important, for everyday convenience and for the regulation of both public and agricultural life, is that the year start and end upon exactly the same day, and have exactly the same number of months as every other year, and that each month start and end on exactly the same days each year, with no variation.”
“I suppose that is logical,” I said, trying to get my mind around the concept of such a year. I, like everyone else, was used to the months wandering around a bit, and never knowing exactly how many days a month would have until the pontifexes announced the number.
“Very logical,” he concurred. “To that end we have devised a solar calendar based upon this concept. It consists of seven months of thirty-one days each, four of thirty days each, and a single month of twenty-eight days.”
I did some quick arithmetic in my head. “All right, that adds up to 365 days, but you still have that quarter day left at the end of each year.”
Sosigenes beamed triumphantly. “That is where that short month comes in. It will be the only month that does not adhere to the rule that each month have the same number of days every year. Every fourth year, it will have an extra day added, making it a twenty-nine-day month for that year.”
“And this structure will be stable, from year to year?” I asked him.
“Yes, with very slight discrepancies. That quarter day I spoke of is not precisely one-quarter of a day.”
“So adjustment will be necessary, from time to time?”
“Yes, but not as frequently as now. In about a thousand years it will be a few days off and require correction.”
“Oh. Well, let it be somebody else’s problem, then.”
“For the sake of convenience and respect for tradition, the twelve months will retain their customary names, even though some of these make little sense. Your most ancient calendar had only ten months, and those months named fifth through tenth are now the seventh through twelfth months.”
“True, ‘December’ just means ‘number ten,’ but we’ve been using the names so long that they are just sounds to us. Nobody notices the illogic.”
At that moment a slave summoned us to the midday meal, which was served on tables brought out from one of the temple buildings. We sat while one of the astronomers, who was a priest of Apollo, pronounced a simple invocation and poured a libation to that beneficent deity, and we launched into an austere meal of bread, cheese, and sliced fruit. The wine was, of course, heavily watered.
“Sosigenes,” I said, “something strikes me as odd here.”
“What might that be?” he asked.
“The fact that the year is arranged so haphazardly. Nothing seems to be very precise or consistent. There are the seemingly random numbers involved. Why 365 days, of all things? Why not a nice, even number easily divisible by a hundred? Then, why the disparity in the very length of the day, so that you end up with a partial day at the end of each year? We expect sloppy work from our fellow men. You’d think the gods would do better work.”
“This is a topic much debated,” Sosigenes admitted.
“There is some belief,” said the old fellow named Demades, “that human convenience is not of great concern to the gods.”
“Yet,” said the pseudo-Babylonian, “the cosmos seems to work according to rules of great complexity and precision, if we can just discover what those rules are.”
“That is the task of philosophers,” said another.