Of counting schemes and end-of-century partying
It is the year 2020. I want to make a prediction. By the year 2030, we will have changed, in a fundamental way, how we count things. That probably sounds pretty unlikely, as well as fairly arcane and abstract, to you, and I would not be surprised if you yawned a little after reading that ®rst paragraph, and began to move on to read something else. But wait, now ± let me try to make this discussion come real and alive. Remember back to the turn of the century? Remember how all those staid and sophisticated calendar mongers said that the ocial turn of the century would not come until the year 2001? Remember what happened next? There was the most fantastic turn-of-thecentury/turn-of-the-millennium party beginning 31 December 1999, celebrating the arrival of the year 2000, exactly what those staid and sophisticated people had said was the wrong thing to do? (And remember what happened on 31 December 2000? There was some repeat partying (some people will use any excuse to party!), and the staid and sophisticated people held their ®rst party, celebrating the arrival of the year 2001, but it was Dull City compared to what had happened the year before!) The interesting thing about all of this is that there are broader implications here. And it is those broader implications that cause me to predict that we will change our counting scheme sometime in the next decade. Here is what I am talking about. The 2001 people, the ones who postponed their party a year, based their reasoning on their preferred counting scheme. And that counting scheme is one based on counting starting at one. The year one is the ®rst year, according to that scheme. The year 2001 is the ®rst year of this millennium, according to that scheme. It all makes sense. Except that there is another counting scheme. The party people, the ones who celebrated their socks o with the dawning of the year 2000, may not have realized it ± but they were using a counting scheme based on zero. The year zero is the ®rst year, according to that scheme. The year 2000 is the ®rst year of this millennium, according to that scheme. The funny thing is, that all makes sense, too. Which is the right counting scheme? It is not as obvious as it may seem. Although the 2001 folks quoted chapter and verse to convince us that new centuries will begin with a year ending in one, there is strong support for the zero position, as well. Try this on for size. When we are born, we are zero years old. We celebrate our ®rst birthday when we are one year old. For the whole next year, we say we are ``one''. You may never have thought of it much before, but that is a counting scheme starting with zero. During the ®rst year of our lives, we are zero years old. And we all live by that zero-based counting scheme. Try this on for size, also. In the US, when we count ̄oors in a building, the ®rst ̄oor is ``1'' and the second ̄oor is ``2.'' That, of course, is a counting from Scheme 1. But it is not the only ̄oor numbering scheme. In much of the rest of the world, the ®rst ̄oor is known as ``ground,'' and the next ̄oor up is ``1,'' then ``2.'' With ``ground'' being a surrogate for ``0,'' we see here a true zero-based counting scheme. Have you ever thought much about timepieces? There are, of course, two counting schemes for time. In the US, we use a 12 h scheme. Our clocks run from 1 to 12. That's a one-based counting scheme. But, once again, there is another counting scheme, the 24 h clock. You may not realize it, but that is a zero-based scheme. Try staying up till midnight some night with a 24 h timepiece. What time comes after 23:59? The answer, perhaps surprisingly, is 00:00. (The ®rst time I saw that, I thought my watch had broken!) Thus the 24 h clock is a zero-based, 0±23 h counting scheme. There is yet another example of zero-based counting. This century, the one our year 2020 is in, is the 21st The Journal of Systems and Software 47 (1999) 1±2 www.elsevier.com/locate/jss