Conventional wisdom has it that although the new millennium was celebrated popularly and in the mass media on January 1, 2000, the "true" new millennium only begins January 1, 2001. Advocates of this "2K1" view say it is the one and only "purist" position supported by history and numerical common sense because of the lack of a year 0 in the globally-accepted Gregorian calendar.

But I would advocate that the lack of a year 0 makes the historical calendar itself a numerically incorrect standard and therefore 2K1, as based on it, cannot claim to be "pure". In my view, the only "pure" approach is to acknowledge an alternate calendar used by astronomers which does include a year 0, and to say that for purposes of this debate at least, the alternate calendar makes it reasonable for us to designate either 2000 or 2001 as inaugurating the new millennium.

No year 0 only because zero itself wasn't yet invented.

According to the U.S. Naval Observatory, at http://astro.nmsu.edu/~lhuber/leaphist.html, the Gregorian calendar was established by Dionysius Exiguus, a sixth-century scholar who started his count with the year 1 A.D., considered to be the year of the birth of Christ. (We now believe that date is off by a few years, but it makes no difference in this discussion.) Two centuries later, the English historian Bede began the practice of counting backwards from 1 A.D. beginning with 1 B.C. without any intervening year 0.

Did Dionysius and Bede omit a year 0 from their tallies because of some deep historical rationale and conscious choice? No, it was because the number system they were using, roman numerals, didn't have any zero. The arabic numerals we use today, incorporating 0's, didn't enter into common use in Europe until much later, around the thirteenth century.

Absence of year 0 corrupts the standard on which "pure" 2K1 is based

The zero-less Gregorian calendar works great if you want year-groupings that appear logical, at least at first glance. Let's consider decades instead of centuries or millennia for which the principles are the same.

Here are our decade groupings without any year 0:

----TABLE ONE----

(etc. on up) 14 A.D. 13 A.D. 12 A.D. 11 A.D.

10 A.D. 09 A.D. 08 A.D. 07 A.D. 06 A.D. 05 A.D. 04 A.D. 03 A.D. 02 A.D. 01 A.D.

01 B.C. 02 B.C. 03 B.C. 04 B.C. 05 B.C. 06 B.C. 07 B.C. 08 B.C. 09 B.C. 10 B.C.

11 B.C. 12 B.C. 13 B.C. 14 B.C. (etc. on down)

By this approach there’s only one way to group years into decades that makes any sense at all. The first decade A.D. is 1-10, the second is 11-20, and so on. Larger groupings work the same way. The first century A.D. is 001-100, the second is 101-200, and so on. The first millennium A.D. is 0001-1000, the second millennium is 1001-2000, and so on. Decades, centuries, and millennia B.C. are mirror images of the A.D. ones.

It looks clean and neat. As far as members of the "2K1" camp are concerned, the discussion ends there. Our new millennium has to be 2001-3000, and can't possibly be 2000-2999.

So what's the problem ... what's the corrupt standard I'm talking about?

The problem is that numerically there does indeed exist a number between +1 and -1: the number 0. Any numbering system which omits 0 is arithmetically defective and causes all sorts of problems and confusion. Let's look at some examples.

Off by one year every time

If a dog was born, say, May 20, 2 B.C., how old was it on its birthday, May 20, 2 A.D., by the Gregorian calendar lacking a year 0? The dog was 3 years old, not 4 years old. Huh? That's right. From 2 B.C. to 1 B.C. makes one year, then 1 B.C. to 1 A.D. makes two years, then 1 A.D. to 2 A.D. makes three years. In other words, 2+2=3. Now, I've got to admit I have a problem with this. How about you?

Julius Caesar died March 15, 44 B.C., and the Nazarene died on the cross, say, March 15, 33 A.D. (for discussion's sake; not known precisely historically). How far apart were those two events? They were 76 years apart, not 77 years, even though 44+33=77.

Let's imagine we're in ancient Bethlehem, and today is, say, April 25, and we know that Mary will give birth in a manger exactly one year from today on April 25 (some say it was historically in the spring because sheep and their lambs were in the meadows). Well then, what year are we in now? We have to be in the year 1 B.C., don't we, since there's exactly one year to go? Then, let's say two years pass, and it's April 25 again, and the holy child is now exactly one year old. We must be in the year 1 A.D., right? So what about that year in between? Without a year 0 we can't make sense of it.

In A.D. every fourth year is a leap year (except three out of four century years), such as 4 A.D., 8 A.D., etc.. Likewise in B.C. every fourth year is a leap year, but it's 5 B.C., 9 B.C., etc., instead of the 4 B.C., 8 B.C., etc. we would intuitively expect.

Quick! As of January 1, 2000 A.D., what day occurred exactly four thousand years ago on the Gregorian calendar? January 1, 2000 B.C.? No ... January 1, 2001 B.C.

Astronomers' solution

To eliminate such problems of calculating intervals, astronomers and others use an alternate calendar that includes the missing year 0. This corresponds to the Gregorian year 1 B.C. The year -1 is the same as 2 B.C., -2 is 3 B.C., and so on. Meanwhile 1 A.D. is the year +1, 2 A.D. is +2, and so on, as you would expect.

Bingo, all the numbers which were messed up before now make sense. Our dog, born May 20 in the year -1, is three years old not four years old as of May 20 in the year +2. Caesar died in -43 and Christ died in +33, 76 years apart, not 77. The year before Mary gives birth is -1 and two years later her son has his first birthday in +1. Leap years occur in -4, -8, etc., just as they do in +4, +8, etc.. From January 1, +2000 counting back four thousand years takes us to January 1, -2000.

Decades, centuries, and millennia as "either-or"

Now that we have retrieved our year 0, which decade do we put it into? In my view, we have two possible choices.

One choice is that we can treat 0 as "+00" and group it with the "+" years:

----TABLE TWO----

(etc. on up) +14 +13 +12 +11 +10

+09 +08 +07 +06 +05 +04 +03 +02 +01 +00

-01 -02 -03 -04 -05 -06 -07 -08 -09 -10

-11 -12 -13 (etc. on down)

Doing it this way, the first "+" decade is +00 +09, the next is +10 +19, and so on. The first "+" century is +000 +099, the second is +100 +199, and so on. The first "+" millennium is +0000 +0999, the second is +1000 +1999, and so on.

Aha! This makes our third millennium +2000 +2999, in other words, beginning on January 1, 2000.

Our other choice is that we can treat 0 as "-00" and group it with the "-" years:

----TABLE THREE----

(etc. on up) +14 +13 +12 +11

+10 +09 +08 +07 +06 +05 +04 +03 +02 +01

-00 -01 -02 -03 -04 -05 -06 -07 -08 -09

-10 -11 -12 -13 (etc. on down)

Doing it this way, the first "+" decade is +01 +10, the next is +11 +20, and so on. The first "+" century is +001 +100, the second is +101 +200, and so on. The first "+" millennium is +0001 +1000, the second is +1001 +2000, and so on.

Aha! This makes our third millennium +2001 +3000, in other words, beginning on January 1, 2001, just as the 2K1 crowd insists.

In my opinion, either of the two choices is equally reasonable, once the year 0 omission has been corrected.

That's why I say it's fair to regard the third millennium as starting either January 1, 2000 or January 1, 2001. That's why I say there should not be any dogma that either of the two choices is "absolutely" the correct one.

Certain astronomers wish to have it both ways

Surprisingly, three astronomers who are dear friends of mine told me the new millennium must be considered as starting January 1, 2001. There's no debate, they said, because the conventional calendar has no year 0. Yet these same astronomers, for their own purposes of calculating intervals, turn right around and use the alternate calendar that does include the year 0.

Therefore I maintain that I am free to, and hereby declare that I do, refer to that calendar as well, for the purpose of deciding when, for me at least, the new millennium begins. I believe such calendar's year 0 makes it reasonable for me to choose either 2000 or 2001. I hereby choose the former, 2000. Someone else referring to the same calendar might choose 2001, but I choose 2000.

The point is, once again, that either choice is justifiable, and neither should be proclaimed out of the running.

The mirror image concern

In Table Two above, the "+" decades (and centuries and millennia), beginning with +00 +09, are unfortunately not mirror images of the "-" decades (and centuries and millennia), beginning with -01 -10.

Likewise, in Table Three above, the "+" decades (and centuries and millennia) are not mirror images of the "-" decades (and centuries and millennia).

However, we can eliminate the perceived need for the corresponding sets to be mirror images by separating the ten's and the units and turning around the "-" units to go in the same direction as the "+" units. From your high school math you may recall a similar stratagem applied in logarithms so that the same tables can be used for logs less than zero as are used for logs greater than zero. Here's what the reformulated year numbers look like:

----TABLE FOUR---- EQUIVALENT TO TABLE TWO

(etc. on up) (+10)+4 (+10)+3 (+10)+2 (+10)+1 (+10)+0

(+00)+9 (+00)+8 (+00)+7 (+00)+6 (+00)+5 (+00)+4 (+00)+3 (+00)+2 (+00)+1 (+00)+0

(-10)+9 (-10)+8 (-10)+7 (-10)+6 (-10)+5 (-10)+4 (-10)+3 (-10)+2 (-10)+1 (-10)+0

(-20)+9 (-20)+8 (-20)+7 (etc. on down)

Or alternatively for symmetry, though it might seem a tad far-fetched, we could even turn around the "+" units to go in the same direction as the "-" units:

----TABLE FIVE---- EQUIVALENT TO TABLE THREE

(etc. on up) (+20)-6 (+20)-7 (+20)-8 (+20)-9

(+10)-0 (+10)-1 (+10)-2 (+10)-3 (+10)-4 (+10)-5 (+10)-6 (+10)-7 (+10)-8 (+10)-9

(-00)-0 (-00)-1 (-00)-2 (-00)-3 (-00)-4 (-00)-5 (-00)-6 (-00)-7 (-00)-8 (-00)-9

(-10)-0 (-10)-1 (-10)-2 (-10)-3 (etc. on down)

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This article was published on this Hermetic Systems website on 2000-12-30 CE.

To contact John Beattie by email: jrbt*(at)*ix.netcom.com     [Remove the asterisks "*" in this email address and replace the "(at)" with "@" — sorry for the inconvenience, I am trying to foil netbots and reduce spam.]