The Universe of Discourse

Sat, 15 Apr 2006

Doubling productivity and diminishing returns
I think I have a strange sense of humor. Other people tell me so, anyway. Here's something I found funny.

The website has an article by Mark Rosenfelder titled The last century: What the heck was that?. It's framed as a discussion of what intellectuals from around 1900 would make of the world 100 years later, what they expected, and why it did or didn't occur. That was one of the topics I planned to discuss when I started this blog. I was reading The Communist Manifesto a few years ago, and in chapter 2 there's a list of the reforms that will need to be effected in order to revolutionize production and bring us all into the new communist utopia. And item #6 is:

Centralisation of the means of communication and transport in the hands of the State.

Well, OK. Perhaps in 1848 that looked like a good idea. Sure, it might be a reasonable thing to try. Having tried it, we now know that it is a completely terrible idea. I was planning a series of essays about crackpot ideas, how there are different sorts. Some crackpot ideas are obviously terrible right from the get-go. But other crackpot ideas, like that it would be good for the State to control all communication and transportation, are not truly crackpot; they only seem so in hindsight, after they are tried out and found totally hopeless.

Another idea of this type: In 1668 John Wilkins wrote An Essay Towards a Real Character and a Philosophical Language, which, alas, goes back to the library this week. This is a really remarkable book. Wilkins recognizes that all languages are arbitrary and confusing, and wants to devise a language which is rational and perfect and logical. He wants each sound to have a unique letter, and vice versa. He wants the form of the letters to be logical. He wants the grammar to be logical and consistent. And, most amazingly, he wants the spelling and pronunciation of the words to be logical. In English, if you don't know what "trembling" is, you can only guess, or try infer it from the context. In Wilkins' language, the word "capop" tells you what you need to know: The "ca" words are all corporeal actions; "cap-" words are all outward signs of inner passion; "capo" is a bodily expression of hope or fear, such as a start or a quiver; the repeated "p" in "capop" suggests repeated and emphatic action. "Capos" means its opposite, to freeze with terror or to be stunned with surprise.

To accomplish all this, Wilkins must first taxonomize all the things, actions, and properties in the entire universe. (I mentioned this to the philosopher Bryan Frances a couple of weeks ago, and he said "Gosh! That could take all morning!") The words are then assigned to the concepts according to their place in this taxonomy.

When I mentioned this to my wife, she immediately concluded that he was a crackpot. But I don't think he was. He was a learned bishop, a scientist, and philosopher. None of which are inconsistent with being a crackpot, of course. But Wilkins presented his idea to the Royal Society, and the Royal Society had it printed up as a 450-page quarto book by their printer. Looking back from 2006, it looks like a crackpot idea—of course it was never going to work. But in 1668, it wasn't obvious that it was never going to work. It might even be that the reason we know now that it doesn't work is precisely that Wilkins tried it in 1668. (Roget's Thesaurus, published in 1852, is a similar attempt to taxonomize the universe. Roget must have been aware of Wilkins' work, and I wonder what he thought about it.)

Anyway, I seem to have digressed. The real point of my article is to mention this funny thing from the Rosenfelder article. Here it is:

You can double your workforce participation from 27% to 51% of the population, as Singapore did; you can't double it again.
Did you laugh?

The point here is that it's easy for developing nations to get tremendous growth rates. They can do that because their labor forces and resources were so underused before. Just starting using all the stuff you have, and you get a huge increase in productivity and wealth. To get further increases is not so easy.

So why is this funny? Well, if an increase from 27% to 51% qualifies as a doubling of workforce participation, then Singapore could double participation a second time. If the double of 27% is 51%, then the double of 51% is 96.3%.

It's funny because M. Rosenfelder is trying to make an argument from pure mathematics, and doesn't realize that if you do that, you have to get the mathematics right. Sure, once your workforce participation, or anything else, is at 51%, you cannot double it again; it is mathematically impossible. But mathematics has strict rules. It's OK to report your numbers with an error of 5% each, but if you do, then it no longer becomes mathematically impossible to have 102% participation. By rounding off, you run the risk that your mathematical argument will collapse spectacularly, as it did here. (Addendum: I don't think that the conclusion collapses; I think that Rosenfelder is obviously correct.)

OK, so maybe it's not funny. I told you I have a strange sense of humor.

The diminishing returns thing reminds me of the arguments that were current a while back purporting that women's foot race times would surpass those of men. This conclusion was reached by looking at historical rates at which men's and women's times were falling. The women's times were falling faster; ergo, the women's times would eventually become smaller than the men's. Of course, the reason that the women's times were falling faster was that racing for women had been practiced seriously for a much shorter time, and so the sport was not as far past the point of diminishing returns as it was for men. When I first started bowling, my average scores increased by thirty points each week. But I was not foolish enough to think that after 10 weeks I would be able to score a 360.

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