Tr: [music-dsp] [OT] human intellect

[Johan Boulé]

----- Message d'origine -----
De : "Michael Gogins" <gogins@pipeline.com>
À : <music-dsp@shoko.calarts.edu>
Envoyé : jeudi 10 mai 2001 02:11
Objet : Re: [music-dsp] [OT] human intellect


> ----- Original Message -----
> From: Olli Niemitalo <oniemita@mail.student.oulu.fi>
> To: <music-dsp@shoko.calarts.edu>
> Sent: Wednesday, May 09, 2001 4:13 AM
> Subject: Re: [music-dsp] [OT] human intellect
>
>
> >
> > On Mon, 7 May 2001, Michael Gogins wrote:
> >
> > > The problem is a contradiction between the normal presupposition that
> the
> > > human intellect is adequate (given enough time) to solve any arbitrary
> one
> > > of the infinite set of solvable Diophantine equations, and the fact that
> if
> > > we are Turing machines we can't do that.
> >
> > (Is it a fact?)
>
> It's much closer to being a fact than most facts. If a formal system is
> consistent, then there are true propositions that can be stated in the
> system that cannot be proved. Alternatively, given a universal Turing
> machine, there are other Turing machines that it can simulate; some of these
> will halt and others will not; there is no universal Turing machine that,
> given another Turing machine to simulate, can decide in advance whether it
> will halt.
>
> In short, if mathematics is consistent, then it is indeed a fact.
>
> >
> > My view is that the strength of human intllect comes from that we always
> > leave a slight possibility of being wrong. (Did debugging *really* kill
> > all the bugs in the program?) In a very strict sense, proofs by humans are
> > not proofs because we can make mistakes.
>
> This is related to the question of the consistency of mathematics. As a
> matter of fact, professional mathematicians normally assume that even if
> mathematics as we know it is perhaps not consistent due to some oversight,
> it can be made to be consistent - that it is possible for it to be
> consistent - that consistency is a real possibility in the strict sense. If
> this is the case (and it would be silly to do mathematics if it were not)
> then proofs by humans are still proofs even if we can make mistakes.
> Frequently proofs are overhauled and tightened up. They are still proofs -
> they are still the most certain things we know, except for the fact that we
> exist and we think, and the bare facts of daily life.
>
> > I see human intellect as a chaotic system consisting of a huge number of
> > simple (mechanical) building blocks, so basicly a machine from the
> > inside.
> >
> > About simulated humans.. Why not some day? It is impossible to do an exact
> > simulation of the physics, but numerical approximation could be taken far
> > enough given enough processing power. This should happen about a century
> > after we have a full-scale simulation of a cell. (Today we can do some
> > rough simulation of biomolecule interactions, which is not much)
>
> This is the question at issue. You cannot ASSUME what we are trying to
> DECIDE.
>
> You have collapsed a large number of questions into one. The advantage of
> thinking in terms of formal systems and/or Turing machines is that it is a
> reasonable view that any scientific theory can be represented by a formal
> system or a Turing machine. Consequently, things that can't be done with
> formal systems or Turing machines can't be done with scientific theories.
>
> As I have said elsewhere, it is an open question in physics, the philosophy
> of science, and general philosophy whether in fact Nature IS a Turing
> machine or CAN BE DESCRIBED BY a Turing machine (not quite the same thing).
> Formal systems and Turing machines are discrete entities; they make
> decisions based on discrete inputs. Consequently, they have a limited
> complexity. Their complexity is either finite or, at most, countably
> infinite (like the integers or fractions). If Nature is not discrete but
> continuous, or in some other way has a complexity that is uncountably
> infinite (like the real numbers), then it cannot even be described by a
> Turing machine or formal system.
>
> If this is the case, then it is POSSIBLE that human beings nevertheless are
> Turing machines even if Nature as such is not, yet of course it is not
> NECESSARY that human beings are Turing machines.  If Nature is of finite
> complexity, or of countably infinite complexity that can be described by a
> Turing machine, then human beings NECESSARILY can be described by Turing
> machines (a simulated machine).
>
> This is a fundamental question that cannot be answered a priori.
>
> In general, in spite of the usual tone of responses to my remarks and the
> common beliefs of scientifically educated people, the evidence for Nature
> being a machine, or describable by a formal system or Turing machine, is
> distinctly less than it was at the beginning of the 20th century. At the
> same time, the abilities of computers have obviously increased; they can
> beat anyone at chess, for example, and do clumsy routine language
> translation.
>
> In my opinion, this question, if it can be resolved at all, will be resolved
> either at the level of fundamental physics, or by another advance in
> philosophy of logic on the order of Goedel's theorems, the halting theorem,
> and the work of Gregory Chaitin.
>
> I do not think the question can be resolved by producing a machine that acts
> human. It is obviously possible or at least conceivable to do that by means
> quite different from thse we actually use to act human, and that would fail
> outside of the test situation.
>
>
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