Wednesday, May 16, 2012

"In the long run..."

"In the long run, we're all dead" is a famous quote attributed to John Maynard Keynes. The context was his arguments with economists of the time: he was trying to argue for government intervention in the markets to control inflation, rather than just letting it play out.

It's an apt response also to occasional claims that asymptotics will eventually win out, especially with large data. Asymptotics will eventually win out, as long as everything else stays fixed.

But that's the precise problem. Everything else doesn't stay fixed. Well before your $C n \log n$ algorithm beats the $c n^2$ algorithm, we run out of memory, or local cache, or something else, and the computational model changes on us.

We come up with external memory models, and are informed that in fact even a factor of log N is too much. We design streaming models and Mapreduce and so on and so forth, and realize that all this communication is burning a hole in our atmosphere.

Lesson to be learned (and re-learned): asymptotic analysis is a powerful tool, but it's only as good as the model of computation you're REALLY working with.
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