Tuesday, October 20, 2009


Apparently the world is going to end in three years and some change.

Sony is making a movie about it. The date will be an almost-symmetric 12/21/2012. Also it's the end of the Mayan calendar or something. Some of my students last year were fascinated by this possibility.

Conjecture on the end of the world based on round numbers seems to be relatively common (remember Y2K?). But roundness of numbers is misleading.

1,000 is only round because we use a base ten number system (a choice almost certainly due to the fact that we have ten fingers). The choice of ten is otherwise arbitrary.

By base ten, I mean that each place in a number refers to a power of 10. The number 3,762, for instance, is shorthand for:
3x103 + 7x102 + 6x101 + 2x100
= 3x1,000 + 7x100 + 6x10 + 2x1
= 3,000 + 700 + 60 + 2
= 3,762
Computers are built on a base two number system, better known as binary. In this case each place refers to a power of 2. For instance, the binary number 10110 is shorthand for:
1x24 + 0x23 + 1x22 + 1x21 + 0x20
= 1x16 + 0x8 + 1x4 + 1x2 + 0x1
= 16 + 0 + 4 + 2 + 0
= 22
Any number can be represented in base ten, or in base two, or in base anything. This means that numbers which look round are only round in one particular number system. In base two, 1,000 is just 8. Some people find 8 a particularly appealing number, but most probably do not. But 1,000 in a base two system? That's 1111101000.

So to us, in our crazy base 10 mindset, 12/21/2012 looks mildly interesting. However, in another system, say base seven, the date is represented 15/30/5403. The year 2,000, which many more people got excited about, is just 13132 in base six. Not so round in either case.

Humans are superstitious as a rule, and it's easy to believe that round dates carry hidden significance. Whatever adjectives you might use to describe such a belief, it is if nothing else a tad anthropomorphic.

Side question: How would human history have differed as a function of the number of fingers we have?

*All of this is not to say that I am above celebrating the arrival of a round number.
** 2,000 in base 7 is actually 5555, which still has a certain roundness to it. We're so lucky the world didn't end at Y2K!

1 comment:

Ben said...

I would say so. If we had fewer, stronger fingers, digging may have been more practible, leading to earlier advances in metallurgy, potentially upsetting the order of bronze age nations.

More pertinantly, I've had some interesting mixed reactions over the years in explaining the base system to people. It can be really upsetting to have your counting system, generally a standard of absolute knowledge, be demonstrated to be rather arbitrary.