**From:** Ben Goertzel (*ben@webmind.com*)

**Date:** Tue Nov 28 2000 - 12:27:25 MST

**Next message:**Spudboy100@aol.com: "Jurgen Schmidhuber"**Previous message:**Harvey Newstrom: "Re: dawn of neurohacks"**In reply to:**Eliezer S. Yudkowsky: "Re: The mathematics of effective perfection"**Next in thread:**Eliezer S. Yudkowsky: "Re: The mathematics of effective perfection"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

*> Perhaps this has given me a bad
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*> impression, but I did once try reading a book on computer-science
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*> mathematics - "Concrete Mathematics" (by Knuth, of course) - and what I
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*> saw there was amazingly awkward, confirming completely my initial
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*> impression that mathematics was simply not an appropriate description for
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*> computational systems.
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Yeah, that book contains some famously ugly mathematics... I agree that it's

amazingly awkward, although it's useful for the analysis of the

computational

complexity of algorithms, and we have used this sort of thing for this

purpose once

or twice in designing the "lowest layers" of Webmind.

Not many mathematicians really likes the stuff in Knuth, because it is not

very elegant

*> If-then-else - not just the specific token-level IFJMP, but higher-level
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*> processes with major transitions of an if-then-else nature - are poison to
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*> mathematical descriptions. To be specific, complex structures built from
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*> if-then-else components, or from if-then-else operations acting to return
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*> different *structures* instead of different atomic elements, usually
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*> render any attempt at mathematical description completely useless. Not
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*> impossible, but "useless", because even if you come up with a description,
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*> it takes a form which cannot be analyzed using any of the mathematical
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*> tools you have available.
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But this is not really true, you just haven't studied automata theory, the

theory of

graph transformations, and so forth

For instance, my friends at supercompilers.com have written a program that

reads a Java

program, converts it into a mathematical data structure (a state transition

graph of all

possible execution flows), and then optimizes that data structure and

converts it back into

an optimized Java program. The program optimization uses all sorts of

advanced graph-theoretic

mathematics -- really deep and really cool stuff. This is precisely the

application of advanced

math to programs, including if-then-else and the whole kit and caboodle.

As you know, my plan for making Webmind rewrite its own sourcecode, a couple

years from now, is to

hybridize it with this supercompiler stuff. If this is the approach that

first brings about functional

self-modifying AI, then your idea about math being irrelevant to real AI

will be definitely

refuted ;>

ben

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