Newsgroups: sci.math,comp.ai.neural-nets,sci.philosophy.tech
From: ohgs@chatham.demon.co.uk (Oliver Sparrow)
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Subject: Re: Limits to neural networking and Do circles really exist? [LONG]
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Date: Fri, 10 Feb 1995 09:26:41 +0000
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I suspect that there are a number of ways that distributed systems can  detect 
patterns; by which I mean more than different kinds of back propagation. 
Imagine, for example, an array of cells that have some simple rules and 
capabilities. 

* The cells receive filtered input from a percept filed in ways which preserves 
  the spacial information in that field.

* The cells have the ability to detect the presence and absence - and 
  orientation - of bars (let us say) in the percept field.

* The cells are hard wired together in ways which reflect the spacial 
  information which they receive. When a bar is detected by any one cell, 
  it emits a signal which excites (lowers the detection threshold of) all of 
  the cells which lie along a line parallel to the orientation of the bar which 
  has been detected.

* Excited cells which detect a bar begin to emit signals of their own.

* Several different systems are evoked by paired foci of excitiation. One of 
  these might "warm up" the immediate neighbours of each of the pairs; and if 
  these sparked off each other, then this system would extend excitation to 
  their neighbours: behold - a parallel line detector; where the level of 
  resonant excitation would say "Here!: it parallel. It's long, goes this way 
  and is thus and so intense.." Similar system scould detect circles, blocks 
  and the like.

One characteristic of these systems is that they play on the rules of geometry. 
The cellualr automata approach does not work if there are not deep structures 
which validate the processes which they evoke. If circle detection was not 
useful - or cellular happenstance like likely to generate circle detectors - 
then nothing would happen in evolutionary terms to hardwire this pattern of 
propinquity into our nervous systems.

To (finally) respond to the interesting entry which heads this thread, 
therefore, I suspect that geometrical functions are important to our perception 
because they are easy to perceive *and also* fundamental to the nature in which 
we live; and are easy to perceive *because* they are fundamental to the nature 
in which we live. That they may be less germane to the Reimann (etc) space in 
which we may live is as relevant as the Euclid to bacteria. That there can be 
proven to be no such thing as a perfect circle in nature does not prevent 
circles encircling us in our daily circuit.

 _________________________________________________

  Oliver Sparrow
  ohgs@chatham.demon.co.uk
