Newsgroups: comp.ai.philosophy
From: ohgs@chatham.demon.co.uk (Oliver Sparrow)
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!MathWorks.Com!europa.eng.gtefsd.com!howland.reston.ans.net!pipex!demon!chatham.demon.co.uk!ohgs
Subject: Re: Penrose's new book
References: <1994Oct11.200236.25598@oracorp.com> <CxJAKr.Dxu@unocal.com>
Organization: Royal Institute of International Affairs
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Date: Mon, 17 Oct 1994 07:57:46 +0000
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Two fascinating entreies prompt a thought. Ingemar Hultage made the point, 
effectively that a system which has bifurcations in it which make it 
uncomputable remains understandable; and that each path of bifurcating (tile-
laying, for example) system is entirely "post-rationalisable": we can 
understand why it happened. Daryl MacCullough made the point that whilst any 
lemma is subject to the Godel/ Wittgenstein/ etc school which points to the 
inadequacy of any system in which we attempt modeling, this does not equate to 
the impossibility of using such a system for the purposes of computing. As he 
points out, every statement - even Godel's theorum - is subject to Godel's 
theorum.

There seem to me to be two questions at work. 
   
*  One question is concerned with the degree to which systematic knowledge 
   representation *in engineering* needs to be a unitary system (and thereby 
   subject to attacks that the knowledge is incomplete, ungrounded or the 
   like). 'Unitary' here means a mixture of three things: 
     (1) that the system should be understandable at a single level of 
     abstraction - that all of its constituent parts (such as symbols) are at 
     least in principle capable of direct interaction. 
     (2) that it has an algorithmic road map associated with it which is 
     understandable in terms of the symbols and other operaters which it uses 
     and 
     (3) that there is a clear priority focus (say, a single processor or multi-
     processor hierarchy manager) from which all systems branches flow. 
   In other words, a "unitary" system is open to ex ante proof of reliability. 
   The other side of this question asks how our understanding of how "real" 
   knowledge structures in real heads - that this strutures seems to lie in 
   the association of loose domains of connectivity, to lie over an 
   architecture which in no way resembles a single-processor logic engine - can 
   be (or should be) be brought into the domain of practical design. 
   
   If you buy the unitary architecture as essential and you dump the loose 
   association, many layer, many processor model, then you do indeed bump in 
   the problems with which I began. Nature doesn't; and nature does not. There 
   seems to be a lesson in that.

*  The other question is concerned with the degree to which a system of order 
   needs to be determined: or, to put it another way, the way in which 
   biological freedoms to exercise apparent choice, to innovate and to create 
   can be understood in ways which allow these to be mapped into a frame of 
   reference which will allow some of these capabilities to be built into the 
   design of created structures of knowledge representation. 
   
   The idea of a determined system is that, known or not, knowable or not, a 
   system has a set of underpinning laws; and that the working of these laws 
   define the outcome which results from a particular state, known or not, 
   knowable or not. Exceptional to this are instances where the state is 
   perturbed by factors driven by quantum indeterminacy or where the 
   system has chaotic bifurcations which are either at the Plankt limit such 
   that their state is indeterminate (which is, effectively, the same thing as 
   the random event case) or that they are so deeply rooted in the complexity 
   of their context that they are effectively indeterminate; which is actually 
   true of most things: science spends its existence finding cases where this 
   is not true or can  be made untrue.

I sugest that between the ticking of predetermined clockwork and random events 
there is a middle way; and that this is how biological intelligence may well 
operate and is how we might resolve some of the issues which we have been 
discussing. This boils down to the notion of hierachical, self modifying 
systems. If we seek to understand what happened when a particular frog 
jumped at a given moment, our model extends from the way in which physics and 
genes underpin metabolism, physical design and motor neuron function; 
underpinning an understanding of how frogs learn about flies; how there was a 
fly; lunch. 

Note that this hierarchy goes the wrong way for a good explanation: it is hard 
toi find a lemma that you could construe in the term sof reference of the 
underlying physics which would encapsulate the idea of "learning about flies" 
and, whilst we can understand why this particular sodium atom is whizzing out 
of that particular gate in terms of the "learning downwards" architecture, it 
is impossible to proceed usefuly the other way up this hierarchy. This would 
not matter in practical terms, save that the elements of the hierarchy can 
interact with each other in ways which are determined solely in the terms of 
reference of that level. What happens when a frog learns changes things which 
effect how a frog subsequently learns, explores, behaves; and the poor old 
sodium atom trails along, disregarded in the framework in which this occurs. 
One should note that lemma busting does not work here as a constraint: indeed, 
this is lemma busting in action. Now write a heuristic that does the same; run 
lots of them in parallel with different but overlapping data streams and 
objective functions: let them vote, squash the weak and re-inforce the strong 
contributors, change each others' access to data, objective functions; and 
what do you get? Godel, the Movie.

_________________________________________________

  Oliver Sparrow
  ohgs@chatham.demon.co.uk
