When do the Teens End?

I’m in the mood for revisiting an over-10-year old issue.

It is now 2014, and when does the decade of the Teens end? Of course it is December 31 of 2019, and the new decade of the Twenties starts with January 1, 2020. And that is clearly how all the decades work. Yet, back in 1999 we were told we had to wait for 2001, and that there was this huge decade/century/millennium mismatch, supposedly “because there is no year zero.” Thus we were told by the pedantic. Supposedly, Arthur C. Clarke’s “2001” has that name for the same pedantic reason.

Well, the pedants were wrong. Here’s the right answer.

[A repost, with some minor editing.]

As mentioned, the problem arises because our dating system has no year 0 A.D.. Instead, the years go directly from 1 B.C. to 1 A.D., thusly:

One thing to realize to go about fixing this dilemma is that, while there was no year 0, there really was no year 1, or 2, or 3. In fact, the method of dating A.D. and B.C. wasn’t really created until the Sixth Century (525 A.D., according to Wikipedia). We’re free to look at the period before then with fresh eyes, and a bit of logic.

The other thing to realize is that the dating system is really a pastiche of two different dating systems, the A.D. dating system, and the B.C. dating system. In other words, what is really going on is that two different dating systems have been pasted together. We have the A.D. number line:

and the B.C. number line:

Note that the B.C. number line is oriented such that the positive direction points to the left.

Once we realize that these are two completely different number lines, that these are two overlapping coordinate systems (in MathGeek-Speak, two coordinate patches covering a 1-manifold, though that is really overkill in more ways than one), we are free to extend them over all numbers. The A.D. number line really looks like this:

and the B.C. number line really looks like this:

To overlap them fully, we have this:

So, of course there was a year 0, or, I should say, 0 A.D.. It happens to be the same year as 1 B.C.. And there was a -5 A.D., the same as 6 B.C..

Once one realizes that there really are two overlapping coordinate systems in use here, all the problems about weird 9-year decades, or a weird 999 year millennium, disappear. Better yet, it all lines up with our intuitive sense that the 2nd millennium ended on December 31, 1999, and the new one started on January 1, 2000. We’re no longer stuck with this goofy 2001 stuff, and the zeroes on the ends of our years properly line up.

And there is no reason we cannot decide to do this. It is not as if the numbering system was handed down by God. It is all convention, and we are perfectly capable of defining convention for ourselves so as to make sense. We are just as capable as anybody else to do so, and in fact are almost assuredly more capable than some guy over 1500 years ago in that regard.

One other thing: what is it about authoritarians? (Yes, this is related.)

A few years back I presented this to an acquaintance who is really quite
authoritarian in nature. In conversations, it rarely seemed to be about what he could actually figure out for himself, but a search for authorities to tell him the answer (and usually an answer that agreed with him). Life wasn’t a search for truth, but a system of dueling authorities. When I presented this to him, his answer was not substantive, just a pointer to some article from the Naval Observatory, an “authority”. Life should be more than just acceding to authority, particularly when that authority may or may not have the right answer.