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[ontolog-forum] non-linearity and AI

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
Date: Tue, 12 Feb 2008 22:27:32 +0800
Message-id: <7616afbc0802120627t6e810s9541a1cacaf7fc36@xxxxxxxxxxxxxx>

A new thread, to try and keep the issues clear.

I agree there may be some systems usually expressed in terms of reals which seem to have the property I want. Chaos and catastrophe theory would be two. But I'm not sure that "reals" sums them up. Frankly my own intuitions about them come almost entirely from the contemplation of assemblies: solid-state physics or the properties of gases.

The dialogue you have pointed us to is very interesting. I have often wondered at the connection myself. Though usually from the point of view of computational theory. It struck me that the power of computation might explain certain odd properties of these non-linear systems (their "random" character, to be frank :-) Perhaps the dialogue can be productive the other way round as well. But let us be specific what it is about either which is important.

For instance, all the "real" systems which interest me seem to be "non-linear". Would that narrow it down a bit?

On Feb 12, 2008 9:53 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

 1. What is important is not the real numbers themselves, but the
    much richer mathematical structures that can be built with
    multi-dimensional spaces with real number coordinates instead
    of just the combinations of Boolean {0,1}.

 2. Holograms and catastrophe theory are just two examples of
    powerful techniques that can be supported with real numbers.
    Blum, Smale, et al., discuss the advantages of the wider range,
    but they admit that there are still vastly more kinds of
    structures that have yet to be explored -- many of which may
    be much better suited to modeling cognitive mechanisms than
    the ones explored so far.

My suggestion is that coding over combinations of elements, leaving the value of each element indistinct, gives us a model for the power and character of "meaning" which is superior to anything to date, and provides an explanation for the appeal of the several "non-linear" techniques which have been mentioned in the context of cognition: catastrophe theory, chaos, holograms to name three.

It also suggests why probabilistic formulations are equally popular. For language, but also for AI. E.g. Schmidhuber:


Perhaps non-linearity captures this. If there is some other concrete property of these "real" models which is directly explanatory of something we see in cognition, please mention it.


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