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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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It would be nice if you left your e-mail address. Sometimes I want to send a private message, or just thank for the great comment. Having your e-mail really helps.
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(Your twitter handle, if you have one.)
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Peter 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.
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