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.
5) We might call 03 the numerical (necessary) model, and 04 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.
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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Received on Thu Aug 13 2009 - 22:01:55 PDT