From: ben goertzel (email@example.com)
Date: Thu Feb 28 2002 - 09:55:46 MST
> Normally I am quite irritated by people stating that they could
> formulate something mathematically,
> and use this as an argument. It is nornally used when running out of
> real arguments.
Christian, often the reason I turn to mathematical formalization is that I'm
frustrated with the ambiguity of natural language. I say something in words
that, to me, clearly represents my intuition. Then Eliezer (for instance)
slightly misinterprets it and rephrases it in a way that's (in my view)
almost but not quite right. And I feel like there's nowhere else to go with
the discussion *except* into the domain of mathematics, because ordinary
language is not precise enough to make the distinctions that need to be
made. Of course, one can do without special symbols, if one wants to
construct extremely complex sentences that effectively describe mathematical
structures and use specially defined terms, but that's not really preferable
I was not trying to use a potential mathematical formulation as an argument.
Rather, it was an excuse for bowing out of an argument temporarily! I felt
Eliezer's rephrasing did not fully capture the distinction I was making,
but, couldn't see how to fully explain my idea in ordinary language...
The point in question was not a new one to me. Pei Wang and I have been
discussing something similar. He doesn't believe there is an important
distinction between the different levels of self-modification, and we've
been going back and forth on this a bit.
I recently spent some time creating a (pragmatically useless so far)
mathematical definition of "intelligence", building on the one I gave in
1993 in my book The Structure of Intelligence. It is this that I would
build upon to formalize the notion of levels of self-modification. The
foundation here is algorithmic information theory (which means that one is
dealing with uncomputable quantities, and quantities that are meaningful
only for arbitrarily large computer programs, or else relative to some
specific reference UTM).
Anyway, all this back-and-forth dialogue is probably going to push me to
actually write up the formalization in question, at some point in the next
month or so. Unless, as sometimes happens, the idea dissolves along the
path from my unconscious mind to the language of mathematics ;-D
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