From: Nick Bostrom (bostrom@ndirect.co.uk)
Date: Sat Apr 03 1999 - 05:10:02 MST
Wei Dai wrote:
> Are you refering to _The Conscious Mind : In Search of a Fundamental
> Theory_?
Yes.
> I haven't read the book yet but would like to know if it is the
> one I should get. How does he define "causal structure"?
I found an old review I wrote on a floppy disc. Here is the relevant
part:
So we have the gulf between a physical process and an abstract
structure to be bridged. As a platform on the abstract side, Chalmers
chooses the notion of a combinatorial-state automaton. A CSA is
defined by giving a finite set of input vectors {(I1, ..., In)}, a
finite set of output vectors {(O1, ..., Om)}, and a finite set of
internal states {(S1, ..., Sk)} (where all the vectors can be
infinite, but Chalmers focuses on the finite case), and a set of
state transitions, i.e. a function f(((I1, ..., In), (S1, ..., Sk)))
= ((S1, ..., Sk), (O1, ..., Om)) from ordered pairs of an input
vector and a state vector to ordered pairs of a state vector and an
output vector. Finite CSAs are equivalent in computational power to
ordinary finite-state automata, but they have a richer inner
structure which Chalmers thinks he can exploit in his explication.
Then we can formulate the criterion for implementing a CSA as
follows:
"A physical system P implements a CSA M if there is a decomposition of
internal states of P into components (s1, ..., sn), and a mapping f
from the substates sj into corresponding substates Sj of M, along with
similar decompositions and mappings for inputs and outputs, such that
for every state transition rule ((I1, ..., Ik), (S1, ..., Sn)
[arrow-to-the-right] ((S'1, ..., S'n), (O1, ..., Ol)) of M: if P is
an internal state (s1, ..., sn) and receives input (i1, ..., in),
which map to formal state and input (S1, ..., Sn) and (I1, ..., Ik)
respectively, this reliably causes it to enter an internal state and
produce an output that map to (S'1, ..., S'n) and (O1, ..., Ol)
respectively." (p. 318)
Additional restrictions can be placed on the permissible
decompositions: for example, we might demand that the elements of the
vectors supervene on separate regions of the physical system. The
underlying idea is that a computation is implemented when there is a
structure of causal relationships that mirrors the structure of
formal relations in the computation that is implemented.
Nick Bostrom
http://www.hedweb.com/nickb n.bostrom@lse.ac.uk
Department of Philosophy, Logic and Scientific Method
London School of Economics
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