The Other Millennium Bug

The Other Millennium Bug:

The obstinacy of human error

It’s all very well getting excited about the so-called Millennium Bug: our society is very dependent on computers, and date arithmetic errors will, in some situations, have far-reaching consequences. But I’m far more concerned about a widespread human problem: the apparent inability (or refusal!) to count correctly.

There are three common attitudes to "The Millennium":

The classical view, that the third millennium starts on 1 January 2001;
The popular view, that the third millennium starts on 1 January 2000;
The literalist view, that the third millennium really started in (about) 1995.

Only the first of these is correct. Why? Why are the others wrong? And does it matter anyway?

In the final analysis, no: it probably doesn’t matter. Whether next year is the last year of the 20th Century and 2nd Millennium, or the first year of the 21st Century and 3rd Millennium, isn’t going to make much difference to most things. Curtains will fade at the same rate; crops will ripen (or fail) at the same times; the depletion of the Amazon rain forest will continue at the same pace. But there is a lot of superstition about. Many people, believing that the end of the millennium will bring some sort of apocalyptic upheaval, will act in ways that tend to fulfil their own prophecies.

Besides, I’m reluctant to go to my grave knowing that I have witnessed history’s first 99-year century and 999-year millennium. Call me pedantic, by all means, but I believe that correctness has a virtue of its own.

At the risk of stating the obvious, let’s begin by reviewing some basic facts about space, time, and number. Some divisions of the "river of time" are based on natural phenomena: the (roughly) 24-hour day, defined by the rising and setting sun; the (roughly) 28-day lunar month, defined by the waxing and waning moon; the (roughly) 91-day seasons, defined by the equinoxes and solstices; and the (roughly) 365-day year, defined by the winter solstice. All shorter intervals—seconds, minutes, hours, weeks, calendar months—are arbitrary, whether considered in terms of length or in terms of how many of them make up the next larger interval.

What about the longer intervals—the decade, the century, and the millennium? They, too, are entirely arbitrary, being multiples deriving from the accident of humans having ten fingers. But, arbitrary or not, we still number the centuries and millennia just as we number the days of the month and name the days of the week. No doubt this is why, when journalists want to settle the question "When does the new millennium start?", they ask astronomers or historians. In fact, they should ask a primary-school teacher of arithmetic: it’s simply a question about counting. So what’s the difference between numbering the days of the month and numbering the millennia?

Essentially, it’s a matter of cycles—or the absence thereof. Once we have defined a day as the period from one midnight to the next, we have also defined starting and ending points for subdivisions and multiples of the day. Several conventions then apply, allowing us to repeat the cycles of minutes in the hour, hours in the day, days in the week, days in the month, and months in the year. Naming the days is a repetitive exercise we do every week. Naming the months is a repetitive exercise we do every year. And so on. But there is nothing repetitive about our numbering of the years, centuries, or millennia; nor is there anything fundamental about when we start that numbering. We have a convention here, too: a convention that gives a starting point in what is now the remote past, and adds 1 to the year number every New Year’s Day.

That starting point is, for our purposes, just as arbitrary as having seven days in the week. It’s based on an early estimate of the birth-date of Christ. This is where the literalist view arises: there’s a broad consensus among historians that the actual birth took place around what we now identify as 4 or 6 BC. Regardless of historical inaccuracy, that starting point is now accepted—for dating purposes—by many (perhaps most) societies regardless of whether they have a nominally Christian background. Hence the irrelevance of the literalist view, and hence the widespread use of CE and BCE—Common Era and Before Common Era—instead of AD and BC. But the original term, AD (for Anno Domini, Year of the Lord), gives us an important clue.

The numbering of years AD is ordinal (according to sequence), not cardinal (according to quantity). The year 10AD was not "when there are (or have elapsed) ten years", but "year number ten" or "the tenth year". A long time ago, another convention decreed correct notation as "AD10", which could be seen as supporting a cardinal rather than ordinal interpretation, though the simplest interpretation is "Year of the Lord number ten". The fact remains that there was never a "year 0": we started counting with the first year, so clearly the first century—the first hundred years—weren’t over until the end of the hundredth year, and the first two millennia won’t be over until the end of the 2000th year.

Just for fun, it’s worth thinking about the reverse process. Why do we call the years 100–1 BCE the "first century BCE"? In fact, it was the last—but we can’t identify the first, and talking about "the 13th-last century BCE", when we mean the period 1400–1301 BCE, is cumbersome, unclear, and far from elegant. (By the way, if you saw a purportedly Roman coin bearing the date 6BC, would you be tempted to buy it?)

But back to our theme. We can see that the popular view of the millennium is a bit like confusing years with anniversaries. We have our 30th birthday at the end of our 30th year. But that’s because we don’t count the date of birth as the first birthday. Just as well, really: we would still turn 30 at the end of the 30th year, but it would be on the 31st birthday. Not many of us could handle that. The same confusion appears when significant anniversaries of annual events are celebrated a year early: the tenth annual ASTC (NSW) Conference took place only nine years after the first.

Of course, the popular view of the millennium has an obvious emotional appeal: changing that high-order digit does look as though it "means something". Indeed, this view is reinforced by a pervasive piece of twentieth-century technology: the odometer in a car’s instrument panel (a cardinal, rather than ordinal, counter). We are accustomed to thinking, when the odometer clicks over to 2000, that "we’ve done 2000 kilometres". So we should not be surprised that Sydney’s Lord Mayor Frank Sartor, when asked when he thought the millennium would change, went on record as picking 2000 because "We’ll have done 2000 years." Understandable it may be, but I hope he uses sounder principles of arithmetic when he checks the Council budgets…

Still, we’ll go on calling that computer problem the "Millennium Bug" rather than the "Millennium Minus One Bug". It could be worse: in most computer parlance, a "K" is not 1000 (10³), but 1024 (2¹⁰)—so the "Y2K Bug" should be the "Y2K Minus 48 Bug". Or should that be "Y2K Minus 47"?