Re: Elegant simplicity
- From: Ben Rudiak-Gould <br276deleteme@xxxxxxxxx>
- Date: Tue, 25 Apr 2006 17:22:33 +0100
Tim Walters wrote:
The truth of the line "Beauty is the eye of the
beholder" seems unassailable. But surely simplicity is in a different
category. Surely objective standards can be applied.
Information theory is probably the branch of mathematics you want to look at, and comp.compression is the newsgroup. Don't expect to find a procedure to measure simplicity, though. There is a formula for the Shannon entropy, but to use it you need a model, and choosing a model is the hard part.
There's a family of models that work well for a lot of different kinds of data, and give similar entropy results, and which are used in compression programs like WinZip. If you want a measure of this kind of practical general-purpose entropy, just compress your file with something like bzip2, and see how large it ends up. This may coincide fairly well with what you think of as complexity.
Coming up with better compression algorithms means coming up with better models, and this is almost exactly the same problem as AI. Animals are intelligent to the extent that they can construct simple and accurate models of the external world. Experiments have shown (unsurprisingly) that expert chess players have a much easier time memorizing chess positions taken from actual games than random arrangements of chess pieces, while people who don't play chess have equal trouble with both. That's because the experts have a better model of the game, and need to memorize less; the non-players (and the experts on the random board) are using some sort of general model like bzip2. So in this sense simplicity is in the eye of the beholder. The tax code is easier to memorize if you're trained in accountancy or economics. If you're interested in simplicity from the average Joe's perspective, then you might be able to argue that bzip2 is a decent metric for text files.
As far as the broader issue goes, I should point out that it's a fallacy to argue that, because simplicity is desirable, therefore things should be as simple as possible. (I don't know if that's what you were arguing or not.) Simplifying the tax code has advantages and disadvantages, and what matters is whether the advantages outweigh the disadvantages, not whether there are advantages per se. To find the "best" tax code you have to choose a utility function, after which you can (hopefully) find a stable equilibrium point which represents the optimal tradeoff between simplicity and other desirable properties, with respect to that utility function. But utility is definitely in the eye of the beholder. So I think your debate is ultimately pointless.
-- Ben
.
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- From: Tim Walters
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