John, (01)
Thanks for the references. I wasn't aware of them. They look excellent. (02)
The extension to chaos theory was purely a guess on my part based on
the patterns you see forming when you try to learn classes from raw
text. (03)
At a quick glance what Thom and Wildgen seem to be doing is coming at
it from the other direction and showing how semantics etc. can be
thought of as behaving that way. (04)
So they are arguing that is how language and semantics behave, while
I'm saying that is the kind of behaviour you get when you abstract
classes from flat text. (05)
I wonder that no-one has tried to model classes abstracted from flat
text in this way before. All existing machine learning work I know of
assumes classical classes. Do you know of any machine learning work
which assumes the classes will be chaotic? (06)
-Rob (07)
P.S. Thanks for the reference to Ramsey, Jakub. I understand this to
be a proof chaotic systems are not empty. Do you know of any work
which looks at the amount of information which can be coded in a
chaotic system as opposed to a classical system? (08)
On Feb 6, 2008 2:58 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> Ed, Randall, and Rob,
>
> The mathematics of catastrophe theory has many relationships to
> chaotic phenomena. It depends heavily on nonlinear mathematics,
> and it can be studied quite well with digital computers without
> extraordinary degrees of precision.
>
> René Thom, who founded catastrophe theory and received the Fields
> Medal for his efforts, was firmly convinced that all areas of human
> perception and cognition -- language, in particular -- depend on
> features that are closely related to catastrophe theory.
>
> Wolfgang Wildgen is a linguist who developed Thom's ideas on
> catastrophe theory applied to of semantics. For various papers
> and PowerPoint slides (in English, German, and French) see
> the list on his website:
>
> http://www.fb10.uni-bremen.de/lehrpersonal/wildgen.aspx
>
> Wildgen also published several books in English that present
> Thom's ideas and Wildgen's extensions in some detail.
>
> I won't say that I am 100% convinced of the Thom-Wildgen approach
> to semantics, but I will say that I have more faith in it than I
> have for many other things that have been discussed in this forum.
> (Of course, one might say that is not a strong claim.)
>
> John
>
> Footnote: For anyone who is not familiar with the Fields Medal,
> mathematicians regard it as the equivalent of a Nobel Prize.
> Of course, there are many people who have been awarded a Nobel
> Prize in one field and then made fools of themselves in other
> fields. But I think that Thom was on the right track in his
> ideas about cognition. (09)
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