Glitches in time

October 17, 1997

The millennium is a figment of the calendar - a human device which seeks to impose order on an essentially chaotic universe. Stephen Jay Gould ponders the history of time

A few diehards, instead of celebrating the inception of the new millennium on January 1 2000 will instead celebrate a year later, on January 1 2001. This is as the Royal Greenwich Observatory recommends, and as slavish compliance with a calculation rule requires. For, technically, modern time started on January 1 year 1 ad, and the first century therefore consumed year 100 for a finale, thus requiring the second century to wait until January 1, year 101, for a beginning. This pattern then continues, making year 2000 the last of our century rather than the first year of the new millennium.

But most people have chosen to celebrate the beginning of the new millennium on January 1, 2000 for the most charmingly simple and obvious of all reasons - 1999 to 2000 looks so much more interesting and significant than the passage from 2000 to 2001. I would defend the popular favourite of 2000 against the rule-bound sticklers for 2001 by simply reminding readers that calendrical transitions can only be imposed arbitrarily upon the temporal continuum of planetary motions. I also hasten to point out that this issue has been fiercely debated at the termination of every century - and never resolved because each side follows its own internally consistent logic, while the facts of nature easily accommodate either alternative. Thus, the popular feeling for 2000 does not derive from the invention of automobile milometers, but rather represents a preference of long standing.

We may be all worked up over the millennium but the passing of time in packages of 1,000 represents nothing more than an arbitrary human device for imposing order upon a chaotic universe that often seems so impervious to our hopes as well. Nothing in our solar system cycles in units of 1,000, and our attraction to this number only arises as a consequence of our decimal mathematics - while our decision to count by tens probably records an accident of our evolutionary origin with ten fingers, an event that can only be viewed as equally accidental on the unaccountable pathways of life's history (the first terrestrial vertebrates bore six to eight digits on each limb). Moreover, even ten fingers do not guarantee counting by millennia. The New World Mayan civilisation developed an elegant vigesimal mathematics based on 20 (perhaps they counted fingers and toes!) - a system full of meaningful cycles (20s, 400s, 1600s, etc).

We started counting by millennia as a specific consequence of a particular Christian myth - St John's vision in Revelation chapter 20, that Jesus would come again to rule the world for a millennium (or 1,000 year period) of bliss before God rang down the truly final curtain of the last judgement. When this apocalypse failed to materialise (or spiritualise), early Christians revised their estimates by arguing that the earth could endure for only 6,000 years, since God's day equals 1,000 human years (see Psalm 90) - and if God created in six and rested for a seventh, then the earth would cycle through six millennia before Christ's second coming initiated God's seventh day of restful bliss (the future thousand-year reign of Christ or the original meaning of the millennium). Thus, if one could figure out when the earth began, one could know the end of ordinary time by reckoning 6,000 years counted in millennia (or God's days). Archbishop Ussher's 17th-century date of 4004bc (at noon on October 23) for the origin of earthly time represents the most famous estimate ever made under this tradition of argument.

Given all this arbitrariness, and the historical tie to a biblical literalism that virtually no one now takes seriously in our secular age (at least as a factual claim), I find it somehow wonderful and exhilarating that most folks find our forthcoming millennial transition so fascinating (whenever it occurs). I can only view this millennial madness as a testimony both to humanism and to human foibles. Our brains work as pattern-seeking machines, and we yearn to impose meaningful order even upon truly random systems. (After all, we think we see constellations in the sky because stars are distributed at random - and truly random systems must produce some accidental and visually striking clustering!) How then can we fail both to love and pity ourselves for all our weaknesses, and for our struggles to wrest meaningful pattern from an uncaring cosmos? If we did not sometimes fight wars, kill and torture people over arbitrary differences in our preferred schemes for counts and calendars, I could endorse this blessed human peculiarity without any reservation at all. But, alas, we can also be cruel in trying to impose the "certainties" of our arbitrary decisions upon others.

My fellow scientists have oversold the public on the mathematical regularity of the universe. Some laws of nature do work by stunningly simple and precise formulae - but in the very domain where regularity would be of greatest value for the most immediate and eminently practical reasons, we find nothing but endlessly fractional complexity. Calendrics would be a boring subject - a matter of simple counting - if the natural cycles of days, lunar months, and years worked as simple multiples of one another. But these cycles could not be more out of synch and we must therefore struggle mightily to make sensible calendars, and to devise all manner of arbitrary conventions - including counting by millennia as a primary example - to make some sense of all this natural madness. God must be either arcane, mathematically incompetent, a jokester, or non-existent, to impose such difficulties upon the struggling creature supposedly crafted in His image.

Just consider the earth's two great cycles of days (rotations) and years (revolutions). Why could we not have a nice, convenient and even number of days in a year, rather than the 365, and just-a-teeny-little-bit-less-than-a-quarter daily rotations that actually occupy one earthly revolution about the sun. What kind of a sensible calendar can such nonsense provide?

Julius Caesar tried his best by adopting the Julian calendar of exactly 365.25 days - that is, a leap year every fourth year to make a simple cycle of 365, 365, 365, and 366. This device overestimates the solar year by a mere 11 minutes and some change (the "teeny little bit less than a quarter" mentioned above) - so you might think that such a slight discrepancy would not matter. But Caesar did live a rather long time ago, and extra days began to pile up. By the 16th century, errors had accumulated to the alarming extent of some extra ten days - so Pope Gregory XIII, on the advice of a star-studded committee of clerics and astronomers, proclaimed the Gregorian reform that we still use today. He first dropped those pesky ten days, allowing October 15 to follow October 4 in 1582. (Yes, October 5-14, 1582, just fell into a black hole of human decisions, and never occurred at all). Second, Gregory tweaked the leap year rule slightly to correct the small over-estimate of the Julian calendar.

Henceforward, every fourth year would be a leap year except for century boundaries not divisible by 400. Thus, 1700, 1800, 1900 were not leap years - but 2000 will be, and we shall enjoy the rare privilege of an extra day that comes but once in 400 years. Use it in good health! At this point, political realities intervened to make a subject already rendered complex enough by nature's inconveniences, even more tricky. In Anglican England, the Gregorian reform smelled like a Popish plot - and you Brits would have none of it, at least initially. By the time reality jolted you into acquiescence in 1752, yet another needless day had accreted - so Britain dropped September 3-13 to institute the Gregorian reform.

When we imbibe these little tidbits of history, other tiny but annoying anomalies fall into place. George Washington, America's national hero for our parting of the ways, was born on February 22, 1732 - or so I learned in school. But contemporary sources cite February 11, 1731 - the "correct" Julian date in a British colony that had not yet adopted the Gregorian calendar, and that also celebrated the new year in March. Did you ever wonder why the Soviets always celebrated the "October revolution" in early November? (Remember those annual news photos of the grim old men of the Politburo, standing atop Lenin's tomb in their tall fur hats, and reviewing the troops?) Well the Russian Orthodox Church, and the Tsarist state as well, were then still using the Julian calendar - and the key days of Julian October fell in Gregorian November. And if you think these arcana are bad enough, it only gets worse when you add the moon to the mix - for the lunar month runs 29 and a half days and the lunar "year" (12 lunations of about 354 days, or 13 of about 383 days) could not be more out of whack with the solar year.

Societies that must reconcile the lunar and solar calendars - as many do because they fish or farm, or because they need to coordinate a religious lunar calendar with the secular solar year - all manage to invent some version of the so-called and God-awful Metonic cycle (named for a fifth century bc Athenian astronomer), which adds a "leap month" to any seven of 19 years in order to synchronise these two cosmic orders. (For this reason, Jewish holidays, set by the religious lunar calendar, creep back about ten days each year on our secular calendar, but then "shoot forward" some 30 days or so, every once in a while. These forward rushes mark the insertion of required leap months in seven years of each ten-year cycle.) The devices of the Gregorian reform and the Metonic cycle may sound like principled laws of nature - but they represent no more than eminently practical "rules of thumb" to make our calendars work in a universe of such inconveniently uncoordinated natural cycles. But order we must have - and order we have constructed and imposed - to make sense of our accidental lives in this funny little space that Omar Khayyam described so well in his famous Rubaiyat - as translated by Fitzgerald in 1859, the same year that Charles Darwin's Origin of Species taught us the natural reasons for human heartache and wonder:

Into this universe, and why not knowing

Nor whence, like water willy-nilly flowing.

So we keep one step ahead of chaos by imposing the arbitrary order of millennia and other human devices upon a calendar made more rational than nature's own cycles permit. The psalmist advised as well in a classic prayer of intellectual life: "Teach us to number our days, that we may apply our hearts unto wisdom."

Stephen Jay Gould is professor of geology and Alexander Agassiz professor of zoology at the Museum of Comparative Zoology, Harvard University.

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