Tuesday, June 19, 2012

The Y Conspiracy

Some phenomena are so outlandish that to explain them seems to require a conspiracy by the powerful.

For example, consider the modern computer chip. Is it really believable that a tiny piece of slightly adulterated silicon can, when an electric current is passed through it, compute millions of digits of pi? Well, maybe you can swallow the pi, but doesn't it burst the bounds of credulity to accept that it can also show you videos of cute kittens dancing?

Surely there's a more plausible explanation for the technology we all enjoy, preferably an explanation involving wickedness and shadowy forces. Is it possible that the computer companies of the world have made a deal with Satan, and imprisoned damned souls inside their machines, forcing them to do billions of calculations per second under threat of intensified torment?

Alas, my theory doesn't stand up to examination. There are conspiracies in the world, but they don't explain all hard-to-believe phenomena. For a conspiracy theory to be plausible, the conspiracy has to have a small enough number of participants that its details could reasonably remain secret—or at any rate, that has to be more reasonable than the alternatives. Given how much difficulty most people I know have in keeping a secret, my minions-of-Satan hypothesis falls apart if more than about three people are involved in the computer industry. Lacking a better explanation, then, I'll just have to accept the information-processing abilities of dirty sand.

Even more mind-bending are the properties of fixpoint combinators. No matter how many times I step through a demonstration of the Y combinator turning a nonsensical up-by-its-own-bootstraps lambda expression into a tidy well-behaved function, I can't quite convince myself that it could ever really work.

The problem with disbelief in stuff that can be demonstrated mathematically is that you have no freedom to invoke a conspiracy. Not even the Trilateral Commission with a fleet of black helicopters could fool us into putting our faith in the Y combinator if it didn't actually perform as advertised.

I'll just have fall back on the idea that The Lambda Calculus Is Magic.

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