Path: utzoo!attcan!uunet!zephyr.ens.tek.com!uw-beaver!milton!wcalvin
From: wcalvin@milton.u.washington.edu (William Calvin)
Newsgroups: comp.ai.philosophy
Subject: Re: emergence and rigour
Message-ID: <8893@milton.u.washington.edu>
Date: 10 Oct 90 04:13:35 GMT
References: <2100@scott.ed.ac.uk>
Organization: University of Washington, Seattle
Lines: 76


CFoster@cogsci.ed.ac.uk (Carol Foster) writes:
>A well-worn example from Dewan (1976) described by Hooker (1981)
>and repeated by P.S. Churchland (1986, 'Neurophilosophy'):
>
>   'Consider a set of electrical generators G, each of which
>    produces alternating current electrical power at 60 Hz but
>    with fluctuations in frequency of 10% around some average 
>    value.  Taken singly, the frequency variability of the 
>    generators is 10%.  Taken joined together in a suitable 
>    network, their collective frequency variability is only 
>    a fraction of that figure because, statistically, generators
>    momentarily fluctuating behind the average output in
>    phase are compensated for by the remaining generators, and
>    conversely, generators momentarily ahead in phase have
>    their energy absorbed by the remainder.  The entire system
>    functions, from an input/output point of view, as a 
>    single generator with a greatly increased frequency 
>    reliability, or, as control engineers express it, with a
>    single, more powerful, 'virtual governor'.  The property
>    'has a virtual governor of reliability f' is a property
>    of the system as a whole, but of none of its components.'

     That's a nice example (the original version BTW is E. M.
Dewan, "Consciousness as an emergent causal agent in the context
of control system theory," pp. 181-198 in _Consciousness and the
Brain_, edited by G. Globus et al, Plenum, 1976).
     I did something similar on the emergence of precision timing
from noisy neurons.  To hit a target twice as far away requires
reducing timing jitter by eight-fold; you can do that by
averaging together the timing recommendations of 64 times as many
timing neurons as sufficed at the closer target distance.  While
at some distance and target size (what in baseball country is
known as a "side of the barn" throw), the jitter of a "command
neuron" might suffice, known throwing abilities of even children
requires that projectile release be timed to a precision orders
of magnitude less than the best single neurons can manage.
     So precision timing is an emergent property of neuron
networks.  And while precision timing isn't so interesting in
itself, some of the secondary uses of movement sequencers are. 
See:
 
Calvin, W. H. (1983).  A stone's throw and its launch window: 
     timing precision and its implications for language and
     hominid brains.
     Journal of Theoretical Biology 104:121-135.

     I'd appreciate hearing of other examples of emergent
precision.  I have modeled precision differential depth
discrimination (takes 16-fold to double the distance, rather than
the 64-fold for throwing) and suspect that it applies to all
difficult jobs, i.e., that the more neurons that you can assign
to the task as you "get set", the better the precision
performance.  The neuropsychologist Marcel Kinsbourne noted in
1988 that:
     When wide areas of the [cortex] are involved in one
     mental operation...  [they] can be used either for a
     wide-ranging but shallow encoding, or for a single but
     difficult mental operation.
The "virtual governor" of the AC generators (these are all really
just applications of the Law of Large Numbers) may help explain
some of the more interesting phenomena of human-style parallel
computing used for language and our scenario-oriented
consciousness.  A short version of this is in:

Calvin, W. H. (1987).  The brain as a Darwin machine.  Nature
     330:33-34 (5 November).

It is discussed in more detail in my books, especially _The
Cerebral Symphony:  Seashore Reflections on the Structure of
Consciousness_ (Bantam 1989), and the forthcoming _The Ascent of
Mind:  Ice Age Climates and the Evolution of Intelligence_
(Bantam, xmas '90 in the US).

                                   William H. Calvin
                                   wcalvin@u.washington.edu