Matt Mahoney wrote:
Richard,
I looked at your 2006 AGIRI talk, the one I believe you referenced in our
previous discussion on the definition of intelligence,
http://www.agiri.org/forum/index.php?act=ST&f=21&t=137
You use the description "complex adaptive system", which I agree is a
reasonable definition of intelligence. You also assert that mathematics is
useless for the analysis of complex systems. Again I agree. But I don't
understand your criticism of Shane's work. After all, he is the one who
proved the correctness of your assertion.
The abstract on the AGIRI website is a poor shadow of the paper that
will be published in the proceedings: I will send a copy of that paper
to you offlist.
The term "complex adaptive system" has very specific connotations that I
think you have missed here: I was not using it as definition of
intelligence. It refers to a general type of system that has a very
particular kind of relation between the low-level mechanisms that drive
the system and the overall behavior of the system. In a CAS (or, if you
prefer, in a "complex system") there is no analytic relationship between
the low level mechanisms and the overall behavior. Basically, you
cannot solve the equations and derive the global behavior. This is the
sense in which "mathematics is useless for the analysis of complex systems".
In essence, I assert that "intelligence" is something that we can
observe in certain systems (namely, in us), but that it is a high-level
characteristic of what is actually a complex system, and so it cannot be
defined precisely, only observed. You can give "descriptive"
definitions, but not closed-form definitions that can be used (for
example) as the basis for a mathematical proof of the properties of
intelligent systems in general.
The full argument is much more detailed, of course, but that is the core
of it.
Oh, and: Shane is *not* the one who proved the correctness of my
assertion! I am not sure where you got that from. ;-)
Richard Loosemore.
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