From: Ben Goertzel (ben@webmind.com)
Date: Tue Nov 28 2000 - 12:27:25 MST
> Perhaps this has given me a bad
> impression, but I did once try reading a book on computer-science
> mathematics - "Concrete Mathematics" (by Knuth, of course) - and what I
> saw there was amazingly awkward, confirming completely my initial
> impression that mathematics was simply not an appropriate description for
> computational systems.
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
> processes with major transitions of an if-then-else nature - are poison to
> mathematical descriptions. To be specific, complex structures built from
> if-then-else components, or from if-then-else operations acting to return
> different *structures* instead of different atomic elements, usually
> render any attempt at mathematical description completely useless. Not
> impossible, but "useless", because even if you come up with a description,
> it takes a form which cannot be analyzed using any of the mathematical
> tools you have available.
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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