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In early 2004 a phenomenon occurred that happens only about four times in the course of a century: There were five Sundays during the month of February. Such an event can only be witnessed every seventh leap year, that is, once in 28 years. The last time this happened was in 1976; the next time will be in 2032.

A lot is odd about leap years. Astronomers have observed that the time between two spring equinoxes is 365 days, 5 hours, 48 minutes, and 46 seconds, or 365.242199 days, which in turn equals nearly, but not exactly, 365.25 days. As an approximation this is good enough, though, and in the middle of the 1st century Julius Caesar introduced the calendar that would henceforth carry his name. Every three years, with 365 days each, would be followed by a leap year, which would include an additional day. For the following millennium and a half, the years thus had an average length of 365.25 days.

But toward the end of the 16th century the gentlemen of the Catholic Church were no longer prepared to put up with an annual error of 11 minutes, 14 seconds. Consultants to the Vatican had calculated that within 1,000 years the annual mistake would accumulate to a difference of eight entire days. Thus, in a mere 12,000 years, they pointed out, Christmas would fall in the autumn season and Easter would have to be celebrated in January. Since the Church plans for the long term, such inaccuracies are unacceptable.

Pope Gregory XIII (1502–1585) had a long think about all this and eventually arrived at the conclusion that the Julian year—the year according to Julius Caesar—was simply too long. To compensate for the inaccuracy, the Pope decided to adjust the calendar by leaping over some of the leap years: for each 25th leap year the leap day, originally

added by Caesar, would be canceled. Thus, the month of February of the last year of each century—that is, each year that is divisible by 100—would only have 28 days, even though it should have been a leap year. The years whose leap days were being lopped off could thus be renamed as “lop leap years.” Every century would thus have 75 regular years with 365 days, 24 leap years with 366 days, and a lop leap year with, again, 365 days. On average, a year would then have a length of 365.24 days.

This, however, falls short again—albeit to a small extent, but short nevertheless. A further adaptation was called for. The Pope and his advisers put their thinking caps on yet again and hit on another idea: Reinsert the leap day into every fourth lop leap year. Thus the loop would be closed, so to speak, and those years that are divisible by 400 were to be “loop lop leap years.” Since the year 1600 was just around the corner, it was declared the first “loop lop leap year.” The next one would be the year 2000.

Thus the average length of a year was now precisely 365.2425 days (three centuries with an average length of 365.24 days; one century with an average length of 365.25 days). Well, wouldn’t you know it? This is just a wee bit too long. But by then Pope Gregory XIII had had enough. There would be no further corrections or adjustments. Not even the Church, known for its long-term planning, was prepared to go the extra … well, millimeter, considering the order of magnitude here discussed. The discrepancy of 26 seconds per year amounts to no more than a day every 3,322 years.

Future inaccuracies of the calendar had thus been taken care of, but what about the inaccuracies that had accumulated during the millennium and a half since Julius Caesar introduced his calendar? Pope Gregory’s ingenuity solved the problem with one ingenious stroke: In 1582 he struck 10 entire days from the calendar. This drastic step had an additional benefit to the pontiff. It was an opportunity to show the world and its rulers who the true master was. So what happened was that Thursday, October 4, 1582, was followed in most Catholic countries by Friday, October 15.

But the non-Catholic countries had absolutely no intention of obeying the Pope’s diktat. In England and its colonies (including America), the correction took place as late as 1752, at which point 11 days had to be struck from the calendar. The Russians stuck to their calendar until the Revolution but were then forced to cross out 13 days. The abstruse result was that the October Revolution in fact took place in November 1917.

Not all is well, however, and no one yet knows how it will all end. Even though everything seemed to run rather smoothly since Pope Gregory’s adjustments, 400 years later all is threatening to fall apart again. Science has made huge progress, and atomic clocks can nowadays measure time with a precision of 10⁻¹⁴.¹ This corresponds to an error of not more than one second every 3 million years. With such precise measurements, an annual surplus of 26 seconds becomes once again unbearable. So, what this writer wishes to propose is one further adjustment: Delete the reinserted additional leap day every eighth loop lop leap year. Hence, every 3,200 years, the month of February would again comprise only 28 days. This would be the final lap in the rounds of adjustments; hence, that particular year would be called the “lap loop lop leap year.” The average year would last for 365.242188 days. Based on painstaking calculations, it turns out that the first lap loop lop leap year would be upon us in AD 4400. So we still have some time to think this whole thing over. The average year would still be one second short, but it would take 86,400 years for this error to accumulate to a full day. This is an imprecision with which even the loopiest mathematicians and church people could lope … I mean cope.