From: J. Andrew Rogers (andrew@ceruleansystems.com)
Date: Fri Mar 18 2005 - 11:37:58 MST
Ben wrote:
> I believe what Marc really wants to say here is NOT
> that Bayes theorem is "broken" (clearly it's correct
> math), but rather that explicitly applying
> Bayesian inference is not a computationally feasible
> strategy in most cases. So it's the idea that
> "intelligence should be achieved primarily via
> explicit application of Bayes Theorem" that is broken.
Marc said what Marc said. If he wanted to say something else, then he
should be a little more thoughtful before pressing the "Send" button.
Even if he had written exactly what you had written above, I would still
disagree with the reasoning. Just because some implementations of Bayes
may be intractable does not mean that it is *necessarily* intractable in
this domain. Even you use the "most cases" weasel words, which makes
the idea that "Bayes theorem is broken" a real stretch even if Marc
merely meant "infeasible".
It is not obvious to me that some fairly pervasive application of Bayes
is always going to be intractable for this application. It would seem
to me to be making some implicit assumptions in the design,
implementation, and problem space that are not warranted. I'll simply
make the observation that people don't implement mathematics on
computers, they implement finite approximations that often have
different properties than the pure math description would suggest. As
an obvious example, useful lossless data compression algorithms do a
pretty fine job on ordinary computers even though a perfect
mathematically pure implementation of data compression would be
generally intractable in this universe.
j. andrew rogers
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