> This brings a question to mind: are there any qualitative properties
>> of systems that are provably _not_ representable in terms of bits?
Depends. If you mean a finite number of bits - yes, for example real
numbers and certain kinds of computation using reals (see Siegelmann, H.
(1995). Computation Beyond the Turing Limit. Science 268: 545-548.).
Otherwise no - I don't think you can *prove* this due to the finitary
nature of proof itself. This does not mean all properties can be so
represented (depending what you mean by "represented" etc.)
>> The theory of computation says that anything computable can be
>> computed using a finite state machine (if I understand it right) so
>> I suppose such properties - if they exist - must not be computable.
>> If so what are they, and are they socially interesting?
Not quite - it says anything "effectively computable" can be computed by
a finite state machine with infinite memory.
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But why would you want to *prove* such a thing? Proof is a matter of
internal/formal reasoning - you can't *prove* anything about the natural
world. With respect to this one has to look at evidence - this is not
clear cut but is much more informative.
I deal with some of these issues in:
Edmonds, B. (1999). Pragmatic Holism, Foundations of Science, 4:57-82.
(http://bruce.edmonds.name/praghol)
and
Edmonds, B. (2000). The Constructability of Artificial Intelligence (as
defined by the Turing Test). Journal of Logic Language and Information,
9:419-424. (http://cfpm.org/cpmrep53.html)
Regards.
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Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University
Aytoun Building, Aytoun Street, Manchester M1 3GH, UK.
Tel. +161 247 6479 Fax. +161 247 6802
http://bruce.edmonds.name
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