From: Ben Goertzel (ben@goertzel.org)
Date: Mon Feb 12 2007 - 22:14:28 MST
****
For some time now, I've been considering the idea of defining many
-typically hard to define- cognitive functions (such as though, memory
recollection, consiousness, pain, desire) using a rationally concrete
mathematical model. That is, defining the above functions as states,
transformations or relations within this mathematical model.
****
I have attempted such a thing in a series of book written over the last
15 years.
For a summary of my perspective see my recent book "The Hidden
Pattern." Most of the book is nonmathematical, but there are two
Appendices that put some of the foundational concepts in the book in
mathematical form. Then, if you're still curious, you can dip back into
earlier works such as The Structure of Intelligence, The Evolving Mind
and Chaotic Logic (which alas are more riddled with typos as I was an
even messier copy-editor back then...) for more detailed models of
things like different types of memory and different kinds of learning.
I spent a long time trying to mathematize different aspects of
cognition. What I arrived at was a bunch of mathematical equations that
represented my intuitive understanding of how mind works, but were not
tractable or solvable using contemporary mathematical tools! So, the
formalizations so far have not been much use for anything except
refining and guiding my intuitive understanding. Of course, that is a
significant use and I think if I hadn't gone through this extended
mental exercise of cognitive formalization, I would not have been able
to come up with a workable AGI design (although that also took me many
years of effort ... the challenge being that the first AGI design my
formalizations led me to, the Webmind design, was workable-in-principle
but overly complex from a practical implementation standpoint...)
-- Ben Goertzel
Anthony Mak wrote:
> Not sure if these pointers are mathematical enough.
> But I am currently looking into cognitive psychology as part of my study.
>
> In "The Architecture of Cognition", Anderson, there are two chapters
> called
> Spread of Activation and Control of Cognition and there seems to be some
> differential equations in it.
>
> And I am having a look at this interesting book called "Cognitive
> Psychology:
> A Neural-Network Approach", Martindale. Even though it does not seem to
> contains any mathematical equations.
>
> Sorry, I can't give much details yet as I haven't gone through them yet :)
>
> (I am a phd student in ANU working on hybridization of machine
> learning and
> automated reasoning methods)
>
> Anthony
>
> -----Original Message-----
> *From:* owner-sl4@sl4.org [mailto:owner-sl4@sl4.org] *On Behalf Of
> *Konstantinos Natsakis
> *Sent:* Tuesday, 13 February 2007 8:05 AM
> *To:* sl4@sl4.org
> *Subject:* Definitions of cognitive functions - Any pointers?
>
> Hello all,
> I've been reading this list for the last couple of months, and I
> enjoyed reading about novel (and new to me) ideas in fields that I
> consider as the frontiers of the human intellect.
>
> For some time now, I've been considering the idea of defining many
> -typically hard to define- cognitive functions (such as though,
> memory recollection, consiousness, pain, desire) using a
> rationally concrete mathematical model. That is, defining the
> above functions as states, transformations or relations within
> this mathematical model.
>
> For example defining thought as a state of a neural state machine
> with particular properties. Memory recollection as a state change
> and a slight transformation of the underlying state machine
> structure. Concious thoughts as a subset of thoughts with certain
> properties etc
>
> I find it a bit hard to believe that noone has ever thought this
> way before, but I have found nothing similar at any of the
> resources I've read so far (which is not much).
> Do you know of any work that has been done in this field? Or any
> arguments supporting that this is just as useless way of thinking? :-)
>
> Any pointers will be greatly appreciated.
>
> I'm currently doing the first year of a "Computer Science" BSc at
> the University of Sheffield, UK.
>
> --
> cyfex
>
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