On 14 Aug 2009, at 18:55, Brent Meeker wrote:
>
> Bruno Marchal wrote:
>> Hi David,
>>
>> This is a nice post, but you are still putting the horse before the
>> cart.
>> Now I can see that you have not yet grasp the main UDA point. Hope
>> you
>> have no problem with being frank, and a bit undiplomatical, OK?
>>
>>
>> On 13 Aug 2009, at 23:01, 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,
>>
>> No, Turing tried to capture the notion of a human computer, working
>> with
>> a pencil and paper.
>> He tried to define mathematically what is human computable, and he
>> is,
>> with Post, and some other are the discoverer of a purely mathematical
>> notion of computation, and this before the appearance of concrete
>> computers. Computers have appeared after. Turing has played a role in
>> that later appearance.
>
> You are of course right about Turing. He was thinking of human
> computation. But he was
> preceded by some real computers, notably those of Charles Babbage.
I love Babbage.
>
> As an aside, when I was in college I worked during summers for a
> geophysical research
> company in Texas. I calculated subsurface distances from sonic
> echo records. My
> official job title was "Computer".
It is still an open problem for me if, for the english speaker,
computer really means automatically universal computer, or does it
means also some non universal device. In french we have the term
"ordinateur", but it has the connotation of big monumental machine.
People said "PC" today. The universal thing can take many shapes and
have many names.
>
>
>> A platonist could say those concrete beings are
>> just pale approximation of the real thing. Later this statement
>> will be
>> made precise, but with the step 8, we just cannot invoke any physical
>> things or physical reality.
>> To be sure, the fact that computer have been discovered in math,
>> before
>> "in nature" is not an argument, yet it helps a lot to see that,
>> especially for the grasp of the comp supervenience thesis. And that
>> is
>> the reason why I explain that absolutely fundamental mathematical
>> discovery. Computation has nothing to do with physics at the start.
>> Note that I abstract myself from the pioneer building of a computer
>> by
>> Babbage.
>>
>>
>>
>>> based on a tape
>>> (memory device) of potentially infinite length,
>>
>>
>> The human computer can use as many papers, or even the wall of its
>> cavern, or of its living room, ... He is a finite being embedded in a
>> non finite available memory-time space.
>>
>>
>>
>>> that has been shown to
>>> be capable of emulating any type of digital computer,
>>
>>
>> This has not been shown. But this follows from Church Thesis.
>>
>>
>>
>>> and hence any
>>> other TM.
>>
>>
>> What Turing has shown, is that there is a universal Turing machine,
>> capable of simulating all Turing machines. Then that Universal
>> machine
>> can be shown to emulate all existing universal machine, and by Church
>> Thesis: all universal (and particular) machines.
>>
>>
>>
>>
>>> The meaning of 'emulation' here entails transforming
>>> precisely the same inputs into the precisely same outputs, given
>>> sufficient time.
>>
>>
>> OK. But there is an intensional Church thesis, which can be deduced
>> from
>> Church thesis, saying that not only two universal systems can compute
>> the same functions, but they can compute them in the same way (same
>> algorithm).
>>
>>
>>
>>> 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.
>>
>> ... at some level. OK.
>>
>>
>>>
>>>
>>> 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.
>>
>> Step 08 forbids us to introduce anything physical. The reversal is
>> done
>> at that step. I guess you are right that it could be a better idea
>> to do
>> the step 8 before, but it is more difficult for most. Any way,
>> computational supervenience is defined after step 8.
>> Then we will discover that "Colin is right" no piece of matter
>> should be
>> Turing emulable. The mathematics of physics will have to escape the
>> turing emulable. The apparent turing emulability of the world
>> around us,
>> is a threat to indexical comp (the idea that "I am machine").
>> Of course I disagree with Colin's reasoning where he deduce the non
>> Turing emulability of nature from the non emulability of mind. UDA
>> deduces the non Turing-emulability of matter from the non
>> Turing-emulability of the mind. And the proof is constructive. It
>> redefines precisely what "matter" consists in.
>>
>>
>>>
>>>
>>> 3) Now we get into more controversial territory.
>>
>> Really? I don't think so. Difficult, not yet very well known, and
>> rather
>> subtle, no doubt.
>> But I don't think there is anything controversial. Nobody told me
>> that.
>>
>>
>>
>>> Bruno has shown (at
>>> least I agree with him on this) that for the mind to be regarded
>>> as a
>>> computation,
>>
>> The wording is a bit dangerous. All I know after UDA is that my
>> state of
>> mind at time and place (x,t) has to be linked to an infinity of
>> computations going through that state, and that my next state, from
>> my
>> first person point of view is indeterminate on the set of all those
>> computations.
>
> But don't you start with the hypothesis that saying yes to the
> doctor continues your mind?
Yes.
> Are you contemplating that the brain may do something that is not
> computable or only
> that the world is not computable?
Both. Below my substitution level. My histories does not care.
>
>>
>>
>>
>>> 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.
>>
>> True, but this excludes quickly that it can be conceived a priori as
>> computations. Immaterial relation between numbers, sure, but not
>> necessarily computable relation. Cf the first person indeterminacy.
>>
>>
>>> This is not universally
>>> accepted, but more on this in the next section.
>>
>> This is not universally understood, nor really studied. But it is
>> understood quickly or slowly when studied. To my knowledge.
>>
>>
>>> 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.
>>
>>
>> No. With the first person indeterminacy it would be more correct to
>> say
>> that it's got to be number all the way up. It makes the comp
>> immaterial
>> appearance of "stuffy matter" infinitely complex and non turing
>> emulable, a priori. I suspect you have not yet really see the role of
>> UDA1-6 in the step-7.
>>
>>
>>
>>>
>>>
>>> 4) If we don't accept 3) then we can keep stuffy matter,
>>
>> We can't by step 8; but by the whole UDA 'stuffy matter" does no more
>> make sense at all. The comp "stuffy" matter has to be made by a
>> infinite
>> sum of infinite computations including infinities of white
>> rabbits-computations. The apparent computability of the physical laws
>> *is* a problem for the indexical computationalist.
>>
>>
>>> but at the
>>> cost of losing the digital computational model of both mind and
>>> body.
>>
>> Most want introduce a stuffy matter because they believe they can
>> save
>> computation for both mind and body.
>
> I don't care where stuffy matter comes from, but whatever the TOE
> is, I want it to recover
> stuffy matter because that allows it to connect to all the science
> we have based on stuffy
> matter.
I am sure it will, or comp will appear to be false, and then UDA gives
a tool to measure the degree of non-computationalism. Don't worry, we
have to be very near the big one to escape the stuffy world.
Look at this in this way: may be it is because I like the stuffy stuff
so much that I want to assoir it on something more solid than
observations and guesses.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Aug 14 2009 - 22:03:41 PDT