Monday, December 19, 2005

Numbers: A Cranky Editorial

Now I do not know a great deal about the mathematics of magnitude, partly because I saw fit to doodle during math class in high school. But I do know that editorializing forgives, and perhaps even necessitates, ignorance of the subject at hand; and that it further requires the production of an inordinate amount of verbiage concerning things that annoy you in passing. Put the two together, and you are Pulitzer material.

First a little uninteresting background: Lately Mrs Bleak and I found ourselves in the puzzling position of having ordered many packages from, not to mention any names, the world's largest online retailer. These were gifts having something to do with one of the holidays or something, and we might have ordered them wrappped, in dreadful paper and at extra cost, but we individually chose not to. Unfortunately, Mrs Bleak did what she called "a very stupid thing" (I suppose I could have dissented more forcefully from this judgment than I did), and had her gifts to me sent unwrapped and addressed This confronted us with the distressing difficulty of sorting out the packages that contained our gifts for each other without actually opening them.

I am not adept at practical problems, to put the matter generously, and this situation struck me as a classic instance of a logico-mathematical conundrum, whose solution could be a priori determined purely on the basis of the principles of formal logic. After wasting several hours determining that this was not remotely the case, I at last hit upon the empirical solution that should have leaped to mind in the first place: I would look up the "tracking numbers" and "order numbers" for the items I had requested, then match them against the numbers printed on the package labels, and thus separate out my packages from Mrs Bleak's.

Those who are expecting all sorts of comical events to ensue from this seemingly simple plan will be disappointed. The plan was perfect, and it worked flawlessly. We are concerned here with an even more trivial matter.

While I was looking up and writing down the appropriate numbers, I could not help but notice that they were difficult to transcribe without repeated checking of the computer screen, and that I was developing the initial symptoms of writer's cramp. (Not, as might be hoped by the restless reader, of writer's block, which is a painless way of doing nothing, unlike cramp.) These numbers were very, very long.

The largest tracking number was 22 digits in length (none of those ever-helpful dashes.) Idly, I started marking off that number in groups of three, just like you do with...well, numbers. Nine sextillion. As I said earlier about the mathematics of magnitude, I don't know much, but I do know that when you start adding numerals onto a number in base ten (which I use faithfully, mostly for convenience), the level of magnitude begins increasing very, very quickly. I began to wonder just what incredibly vast amount of information could conceivably be encoded using such a figure. You could assign a numerical code to every man, woman, and child, plus most of the dead, in the country, and you'd still be left...well, pretty much where you started. You could add a code for specific holidays and still be left with a pretty big number. You could code for hair color, eye color, clothing sizes, sexual preference, and political party affiliation, and still have made barely a dent. You could add a code for every day of the calendar year, and...still have an awful lot of digits. Then I started throwing in silly stuff like the amount of information contained in all of the Mahler symphonies, but my information theory is fuzzy, so I decided to skip this part, amusing though it might be to a certain type of mind.

Okay. Let's try something else. Let's say they've given an individual number to every order they've ever received. Further, let's stipulate that there have been on average multiple orders to a magnitude of ten for every person on the planet. Just for fun, let's further stipulate that they have been doing a rip-snorting business since the dawn of man, a million years ago. No, I don't think so. The sheer weight of the orders at a given point in time would have collapsed the planet, which would have bothered the environmentalists and they would have sued. Even the weight of the paper these orders were written on, assuming one sheet per...Well, we'd have long since cut down every tree, so forget that.

As I say, I'm not very good with orders of magnitude, but I do sense that if you used each of these numbers to encode a different particle in the known universe, you might not be able to get the job done, but you'd have made a good start.

The situation seems approximately better with the 18-digit tracking numbers. But, whoops, three of the spaces are taken up by letters. At worst, this means that an alphanumeric code is being used, and that the entire thing is in base 36 (0 through 9, plus A through Z, unless they use small letters, too.) Now you're getting into all the DNA from the dawn of time territory -- roughly, as I don't like to multiply figures out before April.) But probably only three spaces are used (so far) for alphabetical symbols, which means that three evenly spaced places -- well to the head of the figure, so we're talking very large -- are in base 26, while everything else presumably is in base 10. I'm really not sure what this works out to, because I've never wondered about mixed-base numbers before, but it's complicated, and maybe someone else with more idle time on his hands than I have can work out the math. Don't call me, I'll call you.

This is about as far as my thoughts on this matter have taken me. But I'd quickly switch my allegiance to a company that used order numbers of reasonable length, such as six or seven digits. And wouldn't it be thrilling to have an order with four or fewer digits - maybe with a letter of two on the end? It would make me feel really special. (There is also the problem with what happens when the current coding system starts to overrun the package labels that are used for it, but I'll leave that to the population explosion theorists to wet their pants over.)

In any case, I must end with the editorialist's eternal imprecation: Something must be done! Are you listening, Washington, D.C.?