Steve Richfield wrote:
> Differential equations describe a system. Errors in the equations
> map to errors in the system being described, and can be directly
> corrected by adjusting the equations to eliminate the differences
> between simulated/solved and observed results.
You may not be getting as much engagement on this as you hope for because,
perhaps, others are as baffled as me by what you are even aiming for here.
Differential equations are *one* way of describing a system. We care about
that particular way because it has very cool and important correspondences with
certain aspects of physics, which makes it a very useful way to model those
physical phenomena. Why this should be so is rather an awesome question (see
of course "The Unreasonable Effectiveness of Mathematics in the Natural
Sciences" and subsequent discussion)...
But what does that have to do with AGI? "Differential Equations" are composed
of particular types of terms representing particular mathematical functions...
in domains that are readily described in those exact terms there is a chance
for diffy-Q's to make a decent model, but thoughts aren't numerical, concepts
aren't continuous; the whole idea looks like a giant category error.
Of course it is true that neurons are made of atoms and brains are made of
neurons and (biological) thoughts are the product of brains, so there is a
sense that a good modelling method for the lowest level kind of models the
higher level as well, but in practice this kind of reductionism very rarely
actually works and when it does it is because the higher level is naturally
described with the same kind of language as the lower level, so you get
occasional useful cases like the fluid dynamics of weather prediction, but
barring some revolutionary new perspective on cognition, it just isn't the case
for the things we are interested in on this list.
It's exactly why Cybernetics never went very far.
If you want to revive or extend that avenue of investigation you have to
explain how to fit cognitive phenomena into that particular mathematical
construct, and why it would be appropriate to do so. Nobody has ever been able
to do it, even a little bit -- beyond some vague analogies leading to
simplistic models that were abandoned because nobody could get them to
correspond to the cognitive "territory" even as well as languages of logic or
statistics (which also haven't yet proven adequate but seem at least to have
gotten somewhat further).
I do find it a consistent and possibly correct hypothesis that there can in
fact be no such higher-level model of cognition that has sufficient
correspondence with the "territory" that we vaguely see and describe in
terminology of cognitive psychology (etc) -- the Physical Symbol System
Hypothesis (and other similar assumptions underlying AGI work) could be wrong.
But if that is so, then there is no language about thinking or intelligence
that has any use whatsoever. Stick to physics at the level for which there
seems to be principled correspondence between map and territory, and figure out
how to make it scale by 25 or so orders of magnitude, and good luck with that!
I'm even skeptical of approaches that want to use such modelling language
applied to intermediate levels of description -- like neuron modelling. On
what principled basis do we decide that the "important" features of those blobs
of atoms are adequately described by any particular mathematical formalism?
All we have is empirical justifications supporting pet intuitions. It could
work out, but there already is a field called "neuroscience" that is working on
that with billions of dollars of resources. You could try telling *them* to
use differential equations; maybe they haven't thought of it, I don't know.
This got rather long... but put more briefly, if you want anybody to engage
this (or any!) idea, you have to explain what you are trying to do a little
better, because it is baffling. In this case, differential equations are
specific kinds of expressions involving specific mathematical constructs. So,
just to start: what exactly are you thinking the variables in differential
equations should refer to, such that they can model anything of interest to AGI
researchers?
Derek Zahn
-------------------------------------------
AGI
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