Re: Arthur O'Dwyer on the feasibility of simulating a Turing Machine

From: Michael Mendelsohn (keine.Werbung.1300_at_michael.mendelsohn.de)
Date: 02/29/04 

Date: Sun, 29 Feb 2004 12:05:35 +0100

I have some question regarding your writings.
Could you enlighten me?

"Edward G. Nilges" schrieb:
> 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.

Was Turing a Platonist or an Intuitionist?

> We can see pace Ian that most special purpose Turing Machines can be
> simulated as long as their computation and tape is bounded, and known
> to be so.

I do not understand what "pace" means.

> 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 is enough that mathematical objects have reality dependent on minds
for them to exist and make meaningful discussion worthwhile. A UTM
simulator would have reality independent of mind.

A euclidic circle has a reality in mind only; in a discrete universe, it
can have no reality outside it. BUt it does have that; and that is
useful because what we learn about circles helps our minds copy better
with the imperfect similes of circles we find in the world.

> Completely unexamined is the intuitionistic alternative which based on
> Kant posits mathematical reality as "real" but so embedded in
> experience as not to be meaningful once abstracted from experience.

This seems to me to deny that one can experience mathematics. As
mathematical thought has existence dependent on mind, and since we have
minds and can experience them, this seems a flawed assumption.

> In this tour, entities outside of experience seem to emerge like
> Hamlet's father from the general murk of Kant's style, but like ghosts
> at ***-crow they are dispelled by Kant himself who shows that
> language adequate to ordinary experience is inadequate to describing
> the abstraction itself.

I should say that no language is adequate to describe ordinary
experience, and that there is language at least as adequate to
describing mathematical experience. In fact, mathematical language tries
to limit itself to say only these things that can be said without
misunderstandings; while this excludes a large part of mathematical
experience (which can or cannot be expressed in ordinary language), it
is much more explicit about this than ordinary language, which usually
makes no such distinction.

> In mathematics, a succession of triangular shapes suggested to Euclid
> a common three-sided figure which when sufficiently abstracted by the
> necessary operation of memory and anticipation was seen to be at once
> "perfect", and unattainable, even on a computer screen: and one reason
> for the vicious return of a barbaric Platonism (which doesn't deign to
> even consider alternatives) is that software presents what seems to be
> (but is not) the Form.

There is a form to think about software, and that is the UTM. The form
allows us to make deductions about software that are mostly true/useful;
and limitations of the UTM will certainly be limitations of software.
There is no software that can be sure to halt if its UTM form is not.

> 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.

For example, the UTM never has to deal with bit errors on its tape,
which no existing mechanical memory technology can be assured of being
free of, _especially_ over an unbounded amount of time.

> The Intuitionist regards the TM instead as a set of instructions for
> building something (zuivere beelding) which unlike a house is without
> apriori or aposteriori bounds.

I do not understand the meaning of "zuivere beelding", or what it
references.
I do not know a single thing or concept that is without apriori or
aposteriori bounds, and cannot imagine one exists, except maybe god in
some theologies.
A TM machine is unlike a house in many ways.

> 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 the
> 1930s in action.

But would he be right about that?

> But be that as it may, Ian reaches an absurd conclusion, that
> computers cannot simulate Turing machines. The conclusion is absurd
> because it denies Church's Thesis, that Turing Machines express the
> limits of what is computable.

No, it does not.
The idea is that while Church's Thesis sets a formal limit to that which
can be computed, it does not grant that you can compute everything
within its purview in reality; much as what can be constructed using
ideal circles could perchance not be constructable in reality.

> 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.
>
> The Turing Machine becomes speech to software writing. On the side of
> the TM is hypostatized the academy, Truth, and disinterest in
> commercial gain. On the side of software is cast the demons of
> commerce and the disabling nature of writing which is assumed without
> argument to cripple its adepts and make them at best a convenient, but
> disposable, class of scribes who write down the commands of kings.

>From this writing I conclude that the TM is a theoretical construct
which should not be separated from working indivuduals; that working
individuals would do well to understand it; and realize what bearing it
has on their work. Whether a UTM could be simulated in a way that is
thoroughly impractical make no difference at all. What is important is
what the theory of TMs and UTMs tells them about the real software they
are working with. Whether you could, by some eternal process, expand the
above series of ratios in infinity, is of no concern to the practician,
who derives from theory that the series cannot reach or exceed 1 even in
practice.

> This seems to be happening because precisely as the West globalizes
> Western ways using the Internet, the consumers regurgitate the content
> in their own way: Chinese shall be the dominant language on the
> Internet by 2008.

Viewing dominance in numbers only seems shortsighted.

mendel 

-- 
Feel the stare of my burning hamster and stop smoking!