I deliberately leave vague what is in the theory of the mind, but
simply assume a small number of things about consciousness:

1) That there is a linear dimension called (psycholgical) time, in which the
conscious mind find itself embedded 
2) The observations are a form of a projection from the set of subsets of
possibilities onto the same set. We identify a QM "state" with a
subset of possibilities.
3) The Kolmogorov probability axioms
4) The anthropic principle
5) Sets of observers are measurable

Also I assume the existance of the set of all descriptions (which I
call the Schmidhuber ensemble, but perhaps more accurately should be
called the Schmidhuber I ensemble to distance it from later work of
his). This is roughly equivalent to your Arithmetic Realism, but
probably not identical. It is the form I prefer philosophically.

(I think this is the exhaustive set of assumptions - but I'm willing
to have other identified)

I only treat continuous time in Occams razor (hence the differential
equation) however I do reference the theory of timescales which would
provide a way of extending this to other types of time (discrete,
rationals etc). In any case, contact with standard QM is only achieved
for continuous time.

The justification for assuming time is that one needs time in order to
appreciate differences - and differences are the foundation of
information - so in order to know anything at all, one needs to
appreciate differences hence the need for a time dimension.

Note - computationalism requires time in order to compute mind -
therefore the assumption of time is actually a weaker assumption than
computationalism. 

In terms of the above assumptions, 1) is a consequence of
computationalism, which I take is a basis of your theory (although
I've never understood how computationalism follows from COMP).

2) corresponds to your 1-3 distinction. Indeed I refer to your work as
justification for assuming the projection postulate.

3) Causes some people problems - however I notes that some others
start from the Kolmogorov probability axioms also.

4) I know the Anthropic principle causes you problems - indeed I can
only remark that it is an empirical fact of our world, and leave it as
a mystery to be solved later on.

5) Measurability of observers. This is the part that was buried in the
derivation of linearity of QM, that caused you (and me too) some
difficulty in understanding what is going on. I spoke to Stephen King
on the phone yesterday, and this was one point he stumbled on
also. Perhaps this is another "mystery" like the AP, but appears
necessary to get the right answer (ie QM !)

Of course a more detailed theory of the mind should give a more
detailed description of physics. For example - we still don't know
where 3+1 spacetime comes from, or why everything appears to be close
to Newtonian dynamics.

Stephen King is cooking up some more ideas in this line which seems
interesting... 

                                                Cheers

On Fri, Feb 27, 2004 at 02:55:33PM +0100, Bruno Marchal wrote:
> At 09:19 25/02/04 +1100, Russell Standish wrote:
> >I think that "psychological time" fits the bill. The observer needs a
> >a temporal dimension in which to appreciate differences between
> >states.
> 
> OK. That move makes coherent your attempt to derive physics,
> and makes it even compatible with the sort of approach I advocate,
> but then: would you agree that you should define or at least
> explain what is the "psychological time". More generally:
> What is your psychology or your theory of mind? This is (imo)
> unclear in your Occam Paper (or I miss something).
> I find that assuming time, and the applicability of differential
> equation (especially with respect to a psychological time)
> is quite huge.
> 
> Bruno
> 
> 
> 
> 
> >"Physical time" presupposes a physics, which I haven't done in
> >"Occam".
> >
> >It is obviously a little more structured than an ordering. A space
> >dimension is insufficient for an observer to appreciate differences,
> >isn't it?
> >
> >                                        Cheers
> >
> >On Tue, Feb 24, 2004 at 02:11:07PM +0100, Bruno Marchal wrote:
> >>
> >> Hi Russell,
> >>
> >> Let me try to be a little more specific. You say in your Occam paper
> >> at   http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html
> >>
> >> "The first assumption to be made is that observers will find themselves
> >> embedded in a temporal dimension. A Turing machine requires time to
> >> separate the sequence of states it occupies as it performs a computation.
> >> Universal Turing machines are models of how humans compute things, so 
> >it is
> >> possible that all conscious observers are capable of universal 
> >computation.
> >> Yet for our present purposes, it is not necessary to assume observers are
> >> capable of universal computation, merely that observers are embedded in
> >> time. "
> >>
> >> Are you meaning physical time,  psychological time, or just a (linear)
> >> order? I am just
> >> trying to have a better understanding.

-- 


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