# Re: Computability of consciousness

Nick Bostrom (bostrom@ndirect.co.uk)
Sat, 3 Apr 1999 12:10:02 +0000

Wei Dai wrote:

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