Alas, to wear the mantle of Galileo it is not enough that you be persecuted by an unkind establishment, you must also be right.
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Michael Richardson: Brian 2 is right -- Busy Beaver bb(n) grows faster than Ackermann or any other computable function f(n).
Wrong! There is no evidence to conclude that the Ackermann function is slower growing than the Busy Beaver Sigma.
The fact that a function is not computable doesn't necessarily mean it needs to be fast growing (e.g. convert the halting problem to a function that returns a boolean: not very fast growing, is it?)
Ackermann function is a computable function and for any computable function f(BBSigma(n)) < BBSigma(n+1).
Bill is right about there being no evidence that the Ackermann function grows slower than a non-computable function in general, but for the busy beaver function there is a proof that it grows faster than any computable function. See the wikipedia article for a proof.
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Peteris Krumins' blog about programming, hacking, software reuse, software ideas, computer security, browserling, google and technology.
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I love to read science books. They make my day and I get ideas for awesome blog posts, such as Busy Beaver, On Functors, Recursive Regular Expressions and many others.
Take a look at my Amazon wish list, if you're curious about what I have planned reading next, and want to surprise me. :)
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