[FOM] The Lucas-Penrose Thesis

[Eray Ozkural]

On 10/10/06, Apostolos Syropoulos <asyropoulos at gmail.com> wrote:
> 2006/10/10, Eray Ozkural <examachine at gmail.com>:
> > I will reply to this part. I cannot know how Copeland has managed
> > to misread Turing's paper. However, it should also be fairly obvious
> > that humans do not have the role of oracles in the debugging process.
>
> No it is not obvious at all!  When I said the role I meant the role not that
> they are oracles. And in passing I would like to stress that it is one thing
> to say that there are no oracle machines and another to say that someone
> else has stated explicitly that there are no such machines. In the second
> case one has to say specifically where this statement appeared.

I don't know what you mean by "the role not that they are oracles", because
you clearly said the following sentence: "They operate more or less like oracle
machines, where a human person has the role of the oracle". Perhaps at
this point you would like to revise your claim because human debuggers are
not oracles at all, and as I have repeatedly said, any programmer will know
that. For being an oracle entails the capacity to solve the halting
problem in its
entirety. But of course, if you mean something like "knows something about
the halting problem", that is valid. I know that certain families of programs
will not stop. Thus, my brain contains _some_ information about the halting
problem.

On oracles, at least, we can afford to look at wikipedia:

http://en.wikipedia.org/wiki/Turing_machine#Choice_c-machines.2C_Oracle_o-machines
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An oracle machine or o-machine is a Turing a-machine that pauses its
computation at state "o" while, to complete its calculation, it
"awaits the decision" of "the oracle" -- an unspecified entity "apart
from saying that it cannot be a machine" (Turing (1939), Undecidable
p. 166-168). The concept is now actively used by mathematicians.
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You can follow around the references and see that the quote is from
Turing's 1939 paper "Systems of Logic Based on Ordinals" and
also his PhD thesis if I have got it correctly.

My problem is that, these so-called philosophers like Copeland,
are actually doing a disservice to the theory. I don't think they understand
an iota about the halting problem, oracles, or programming for that
matter. Yet, they have built an industry on "hypercomputation".

If you look at the following remarks about such "thinkers" as
Copeland, you will see how they have tried to "revise" history
by omitting Turing's above words:
http://www.turing.org.uk/philosophy/lecture1.html

So, that is how he managed to misread Turing, or more probably by
deliberately misrepresenting Turing.

The analysis on turing.org is sound. The oracle is not a machine.
And it definitely is not the brain according to Turing, who thought
that the brain can be simulated by an a-machine. Thus, all the
happy-going speculations are generated by vitalist philosophers
who came afterwards.

At any rate, it is also easy to see why an oracle is physically implausible.
Some models for a hypercomputer are listed in the following
wikipedia article, none of which seem to be plausible:

http://en.wikipedia.org/wiki/Hypercomputer

The basic idea is that you need either infinite space or time to
be an oracle. Very difficult in this world of quanta.

Regards,

-- 
Eray Ozkural, PhD candidate.  Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo  Malfunct: http://myspace.com/malfunct
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy