RE: The mathematics of effective perfection

From: Ben Goertzel (
Date: Mon Nov 27 2000 - 14:51:16 MST

It's all undergraduate mathematics...

Designing the higher-order inference component did involve some mathematical
logic ... it's all done using
nodes & links & self-organization, but still, we needed to confirm that the
particular node/link dynamics
we were using would have universal expressive power, by creating a mapping
from our structures into n'th order
predicate logic. This process revealed some subtle shortcomings in the way
we were doing things, which weren't
so hard to remedy. (They had to do with Skolem functions representing
quantifier dependency... the kind of thing
that seems really obscure until you realize how it relates to very simple
things like learning how to act...)

Getting the dynamics of the system's "attention allocation" right required
application of some dynamical
systems theory -- analysis of fixed points, basins of attraction, and so
forth. We saw that some of the equations
we were using to adapt various parameters, while they looked intuitively
right, actually had odd dynamical
properties that could be seen by a simple dynamical systems type analysis.

Don't get me wrong, we have a host of engineers, and a handful of
mathematicians, and a handful of cog.
scientists. WM is not mathematically founded in a strong sense. But as I
said, math has been crucial to
getting many of the system components to work right...


> -----Original Message-----
> From: []On Behalf
> Of Eliezer S. Yudkowsky
> Sent: Monday, November 27, 2000 4:38 PM
> To:
> Subject: Re: The mathematics of effective perfection
> Ben Goertzel wrote:
> >
> > Don't get me wrong -- there's more intuition than math in the Webmind
> > design. But without mathematical
> > analysis applied to key parts -- not just system-level parts like memory
> > pool allocation -- it just
> > wouldn't work.
> I can't say this convinces me, but it does surprise me. If there's any
> concrete example you can give without giving away something proprietary,
> I'll shut up and listen.
> -- -- -- -- --
> Eliezer S. Yudkowsky
> Research Fellow, Singularity Institute for Artificial Intelligence

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