David Nyman wrote:
> Colin's recent interesting (not to say impassioned!) posts have - yet
> again - made me realise the fundamental weakness of my grasp of some
> of the discussions that involve Turing emulation - or emulability - on
> the list.  So I offer myself once more as lead ignoramus in
> stimulating some feedback on this issue .  Anyway, here's what I think
> I know already (and I beg you patience in advance for the
> inaccuracies):
> 1) A Turing machine is an idealised digital computer, based on a tape
> (memory device) of potentially infinite length, that has been shown to
> be capable of emulating any type of digital computer, and hence any
> other TM.  The meaning of 'emulation' here entails transforming
> precisely the same inputs into the precisely same outputs, given
> sufficient time.  In effect, digitally 'emulating' a computation is
> conceptually indistinguishable from the computation itself; or to put
> it another way, computation is deemed to be invariant under emulation.
> 2) Insofar as the causal processes of physics are specifiable in the
> form of decidable (i.e. definitely stopping) functions, they are
> capable of finite computation on a TM - i.e. they are TM emulable.
> What this amounts to is that we can in principle use a TM to compute
> the evolution of any physical process given the appropriate
> transformation algorithm.  Since we're dealing with QM this must
> entail various probabilistic aspects and I don't know what else: help
> here please.  But the general sense is that the mathematics of physics
> could in principle be fully Turing-emulable.
> 3)  Now we get into more controversial territory.  Bruno has shown (at
> least I agree with him on this) that for the mind to be regarded as a
> computation, essentially everything else must also be regarded in the
> same light: IOW our ontology is to be understood entirely from the
> perspective of numbers and their relations.  This is not universally
> accepted, but more on this in the next section.  Suffice it to say
> that on this basis we would appear to have a situation where the
> appropriate set of computations could be regarded not as mere
> 'emulation', but in fact *as real as it gets*.  But this of course
> also renders 'stuffy matter' irrelevant to the case: it's got to be
> numbers all the way down.
> 4) If we don't accept 3) then we can keep stuffy matter, but at the
> cost of losing the digital computational model of both mind and body.
> Not everyone agrees with that radical assessment, I know; but even
> those who don't concur presumably do hold that everything that happens
> finally supervenes on something stuffy as its ontological and causal
> basis, and that numbers and their relations serve merely to model
> this.  The stuffiness doesn't of course mean that the evolution of
> physical systems can't in principle be specified algorithmically, and
> 'emulated' on a TM if that is possible; we still have mathematics as a
> model of stuff and its relations.  But it does entail that no digital
> emulation of a physical system can - as a mere structure of numbers -
> be considered the 'real thing': it's got to be stuffy all the way
> down.

A good summary, David.  However, there are some other possibilities.  
Physics as now conceived is based on real and complex numbers. It can 
only be approximated digitally.  QM supposes true randomness, which 
Turing machines can't produce.  Again it may just be a matter of 
"sufficient approximation", but the idea of a multiverse and 
"everything-happens" assumes real numbers.
> 5) We might call 3 the numerical (necessary) model, and 4 the stuffy
> (contingent) model of reality - but of course I don't insist on this.
> Rather, it seems to me that in our various discussions on the
> emulability or otherwise of physics, we may sometimes lose sight of
> whether we are interpreting in terms of numerical or stuffy
> ontologies.  And I think this has something to do with what Colin is
> getting at: if your model is stuffy, then no amount of
> digital-numerical emulation is ever going to get you anything stuffy
> that you didn't have before.  A physical-stuffy TM doing any amount of
> whatever kind of computation-emulation remains just a physical-stuffy
> TM, and a fortiori *not* transmogrified into the stuff whose causal
> structure it happens to be computing.

I can look at it either way.  A sufficiently detailed, accurate and 
predictive numerical model is as good as the stuff it models.  But also 
a sufficiently accurate, detailed and predictive stuffy model is as good 
as the consciousness it models.

> Now of course this stricture wouldn't necessarily apply to model 3).
> But the 'comp' that Colin claims to refute is, I suspect, not this but
> stuffy-comp - i.e. the comp based on stuff rather than numbers, that
> Olympia, in her lazy but decisive way, dismisses as ephemeral.  This
> is also the comp that I have argued against, but I don't intend this
> merely to be a re-statement of my prejudices.  I know that Colin isn't
> precisely a proponent of model 3) nor model 4), arguing strenuously
> for a distinctive alternative; so it would be interesting (certainly
> for me) if he'd care to characterise precisely how it diverges from or
> extends the foregoing stuffy-numerical dichotomy.
> Be that as it may, the punchline is: do we find this analysis of the
> distinction between numerical 3) and stuffy 4) to be cogent with
> *specific* respect to the significance and possible application of the
> concept of 'emulation' in each case?
> David
> >

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