Re: Arthur O'Dwyer on the feasibility of simulating a Turing Machine
From: Malcolm (malcolm_at_55bank.freeserve.co.uk)
Date: Sun, 29 Feb 2004 18:37:34 -0000
"Edward G. Nilges" <email@example.com> wrote in message
> The assertion is that given enough time and memory space, a
> desktop PC can compute anything. This assertion is true and
> equivalent to Church's thesis re the Turing machine.
This is true. In practise an infinite machine cannot be built in a finite
universe. However the memory and backing store can be arbitrarily large, and
frequently is in real desktop systems.
> This is true so far as it goes. But the description of the TM needs to
> be rephrased depending on your philosophy of mathematics.
> The TM is an "entity" only to the Platonist who ground the truth of
> mathematics in the existence of Forms. To an Intuitionist or Marxist
> the TM is a text and a set of construction instructions.
This is the heart of it. Just say a TM is an "abstraction". It's amazing
that Marxists would attempt to get involved in mathematical philosophy.
> > And as for "how long the computation will take", does the phrase
> > "Halting Problem" have any meaning to you?
> Yes, and it doesn't apply, since this NG is collectively dazzled by
> HALTING Turing Machines that take up all the matter in the
> universe for the deconstructive reasons I've explained in the
> following paper:
That's because you've tried to claim that one can implement an infinite tape
in a finite and discrete universe. Obviously most people will home in on
that and ignore anything else you might have to say.
> ".writing is not only an auxiliary means in the service of science-and
> possibly its object-but as Husserl in particular pointed out in The
> Origin of Geometry, the condition of the possibility of ideal objects
> and therefore of scientific objectivity."
There are plenty of non-literate cultures. Writing is practically necessary
for anything approaching modern science, but it is not philosophically
> I do find this discussion of "the feasibility of simulating a Turing
> Machine with actual software" interesting because it shows how
> Jacques Derrida's so-called deconstruction applies to a critical
> theory of computer science.
You'd be better off sticking with conventional literary criticism.
> I've already shown, as against the rather simple-minded objection
> that "the simulator will run out of memory at some point for some
> computation", that to address this problem, all you have to do is (1)
> assume that the universe and the Internet are from this day immortal
> and (2) implement the simulator not as a program running on a single
> machine but as a computer virus.
Here we go again. The Turing machine tape can be advanced or, crucially,
reversed. This means that there is no engineering trick you can use to
> The first is that one, and only one, completely unexamined
> philosophy of mathematics dominates the discourse cascade, and, as
> far as a philosophy can be discredited, this philosophy is discredited.
Though folk-psychology is discredited, but this doesn't necessarily
discredit discourse about people's motives.
> This is logicism, or Platonism, which baldly assumes that
> mathematical objects have reality independent of the mind, exist in a
> World of Forms and furthermore that real infinities exist. It was
> refuted by the paradoxes, Godel's result and in general Bertrand
> Russell's failure to derive mathematics from logic.
> The Platonist hypostatizes the Turing Machine as existing, in a
> fashion which "can't be simulated by a mere program", in a World of
> Forms, and one sense in the consensus here that the very idea of
> "simulating" a Turing machine, even for such a humble task as
> teaching, is a form of farting in the Church of Reason.
A Turing machine has a status similar to a circle. It has properties we can
talk about, it can be approximated closely enough for those properties to be
of practical use, but it cannot be constructed. Plato would say the the
Turing machine exists in the world of ideal forms. However we don't need to
go into that to understand the concept and to use it. Similarly
schoolchildren are taught how to calculate the area of a triange before they
are introduced to philosphy.
> More strongly a Marxist philosopher of mathematics would say that > what
Turing actually did was to abstract from the praxis of actual
> working people a model of what it means to mechanically compute,
> whether by watching clerks at work or observing simple office
> machines of the1930s in action.
We don't know enough about how the mind works to answer this. It is entirely
possible that Turing was inspired by watching industrial machinery. The
Marxist seems to be trying to diminish his achievement.
> the surprising source of the glimmer of understanding is Jacques
> Derrida's Of Grammatology.
> This extraordinarily difficult book
You need to read about the poststructuralist hoax. It's very easy to write
write-only code, similarly write-only philosophy.
> Thus in both theoretical linguistics and the practical teaching of
> language the need to address the spoken word is so foregrounded
> that it is claimed that written symbols actually represent speech, a
> claim which isn't argued for as much as it is axiomatic.
Initially writing represents speech, and it is very unusual to know how to
read without knowing how to speak. However written language has its own
rules that are slightly different from spoken language. In particular, if
you try to transcribe speech literally, you get um, er, kinda, this sort
thing, know what I mean? So journalists usually clean up quotes.
> Thus in the
> practical teaching of language the students are rather overwhelmed
> with written texts which use grammatical tables and illustrations of
> the spoken word only to be told both at the start of the class and at
> its end that of course, the living, vibrant, spoken language is never
> mastered by such contrivances but by dwelling among the peasants
Are you talking about foreign languages? At school the problem is that it is
practically difficult to provide contact with native French speakers. At
university, the focus is not on learning to ask for a cup of coffee in
french, but on French literature. However university students do usually
spend a year abroad to mix with native speakers.
If you are talking about lessons in one's native language, then of course
everything becomes much more interesting. Do adult speakers normally make
grammatical errors, for example?
> Derrida speaks in terms of "oppositions" which structure Western
> thought such as "the Letter killeth but the Spirit giveth life", which
> are undercut because the very text is transmitted not through the
> Spirit but through the Letter.
That's a problem for Protestants. Catholics would say that the Church is
inspired by the Holy Spirit, which tells her how to recognise and interpret
> I think in this discussion an erroneous result is arrived at (a Turing
> Machine can't be simulated) because of the completely unconscious
> operation of the Western binary opposition between speech and
This is a stretch. No-one recognises such a binary opposition between speech
and writing except yourself. We can say that the Turing machine exists ina
Platonic world of real forms, or we can say that Turing machines don't exist
but instructions for making a Turing machine do exist. Whichever position
you take, an infinite tape cannot be provided in a finite universe.
> A mere intuitionistic construction rule is merely a piece of writing,
> a set of instructions and a story which the reader can then use, in an
> unbounded fashion, to create new Turing Machines:
"merely a piece of writing" or "merely language" leads us into very deep
waters indeed. For the writing to be effective, the reader must have some
idea what a machine is, what a tape is, etc.
> Derrida has long interrogated the prescientific and barbaric pose
> struck by he who like the Heathfield man, Rousseau or de Saussure
> would set himself up to patrol the boundaries of a discipline.by
> making sure that the very technology of the discipline is not used in
> full and for the purposes intended. Thus deSaussure rages in the
> Course of General Linguistics against orthography and gives secret
> satisfaction to boneheads in many lands who are actually proud of an
> inability to spell, while they condemn mispronunciation.
Here's another stretch. Pronunciation is something we have adapted to over
evolutionary time, whilst spelling is novel. There is no connection with
Heathfield's inability to construct a Turing machine.
> Indeed, it was only at the "better" universities that I perceived at
> all any interest in such contrivances and the demand for
> "practicality" at inferior universities has the effect of separating
> theoretical constructs from working individuals.
Sure. People of middling intelligence are generally interested in things of
immediate relevance to their chosen careers.
Out of time.