Re: Arthur O'Dwyer on the feasibility of simulating a Turing Machine
From: Edward G. Nilges (spinoza1111_at_yahoo.com)
Date: 28 Feb 2004 17:29:23 -0800
Calum <email@example.com> wrote in message news:<firstname.lastname@example.org>...
> Edward G. Nilges wrote:
> > Willem <email@example.com> wrote in message news:<firstname.lastname@example.org>...
> >>)> This has already shown to be false; there's only a finite amount of matter
> >>)> in the universe.
> >>Edward wrote:
> >>) However, do we know if there is a finite amount of time? For by simply
> >>) having the simulator act as a sort of virus we can exchange raum for
> >>) zeit, space for time.
> >>Each operation of any TM-like machine increases the entropy of the universe
> >>by some amount (with a fixed nonzero minimum), therefore an UTM needs to be
> >>able to increase the entropy of the universe by an unlimited amount.
> >>But a finite universe has a finite maximum entropy.
> > In fact, this is false. For any calculation that halts, the universal
> > turing machine will execute necessarily a finite number of operations.
> But, you can always devise a computation that requires more
> time/energy/space/memory/tape than the universe is capable of. Even one
> that halts.
If the universe goes on indefinitely this is wrong.
> bool array[NUM_PARTICLES_IN_UNIVERSE+1];
> for(int i=0; i<NUM_PARTICLES_IN_UNIVERSE+1; ++i)
> array[i] = is_prime(i);
> Your assertion that any desktop PC can compute anything is of course
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.
> > All you're affirming is that BOTH the simulator and the "ideal" will
> > consume the universe if they loop. The UTM and the simulator are in
> > fact exactly equivalent in this regard.
> > The UTM, *qua* UTM, has no special permission to continue looping in
> > the formalism merely because it is either a Turing Machine or a
> > Universal TM: to think so is to confuse the designation TM or UTM with
> > some sort of honorific which (again) somehow raises Turing's mere
> > contrivance ABOVE writing and into speech, where the UTM is allowed to
> > loop.
> > In fact, the formalism is silent on a number of issues including how
> > the tape is expanded, how long the computation will take as a cardinal
> > number and not a function of its input, and here, whether the machine
> > in a nonhalting state is permitted to loop.
> Of course, it is important to realise that a UTM is a thought
> experiment, a mathematical entity. Its purpose is primarily to discuss
> the mathematical nature of computation. The point is it DOES NOT MATTER
> how the tape is extended, or whether it is performed by a computer or
> by pencil and paper. That's what's nice about mathematics, you always
> get the same result.
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.
> 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:
"…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."
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
For as Ian Smith claims, a consensus seems to be that no "Turing
Machine simulator exists that is a full simulation of a Turing
This seems wrong, or wrongly phrased, for there is no one TM. For
starters, there exist in the theory multiple machines, categorized
into two sets, one large and one "small". The first is the set of all
special purpose TMs, armed with a tape that doesn't perform the
calculations of a Universal Turing Machine, which is able to simulate
any other TM including UTMs when its tape contains a suitably encoded
list of the quintuples of the simulated machine.
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. Furthermore, any UTM that contains instructions to halt when
its tape length or computation time approaches a limit can be
Now, I concede that a computer simulation of a Turing Machine may fail
on storage limitations for arbitrary TM. But this (empirical) fact
fails to prove that "it is not possible to simulate a TM with
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.
But there are two deeper issues here than such contrivances…such
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.
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.
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.
The Pop, ignorant reading of Kant is that in so many tedious words,
Kant showed that ultimate reality is unknowable and, of course, Kant
did nothing of the sort. Instead he actually takes the patient reader
of the Kritik der Reinen Vernunft of the only ultimate reality
accessible to experience, and this is the way experience necessarily
takes place in space and time.
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 cock-crow they are dispelled by Kant himself who shows that
language adequate to ordinary experience is inadequate to describing
the abstraction itself.
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.
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.
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. Thus the "scope" is the same as
experience itself. But he doesn't imagine for a minute that TMs
already exist in God's computer room and for this reason the
intuitionist would probably be friendlier towards the idea of
simulating a Turing Machine.
He would demand, however, that the Turing Machine not preallocate its
tape as TM_TAPE tape, or any fixed number but would demand
instead that the tape be expandable UNTIL malloc failure (to speak in
the barbarisms of the C language).
The Intuitionist would not I think infer from the TM's mortality any
failure to simulate a "real" TM.
For note that the "real" TM doesn't have an unbounded tape. It merely
has the ability, deliberately unspecified, to demand more tape. A
"real" program simulates this ability when it aborts on not enough
storage and thus demands that its programmer expands its arrays and/or
installs more memory.
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 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.
But we must explore more deeply why this absurd conclusion becomes the
ng consensus and the surprising source of the glimmer of understanding
is Jacques Derrida's Of Grammatology.
This extraordinarily difficult book is a meditation on an unnoticed
theme in Western philosophy, expressed in a simple and simple minded
fashion as the privileging of speech over writing. But this precis
needs to be expanded.
It seems that as a member of the generation of the 1960s Derrida was
troubled by the way in which so many learned disciplines, including
lingistics and philosophy, tend to cut away the ground on which they
stand at a key point, and this gesture becomes the central mystery of
the discipline…one which is maintained in a terroristic fashion
because it can always be used to ensure the subordination of truth to
power in the West.
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. 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
At one and the same time, an offer is made and rescinded in a gesture
which Derrida was the first to notice.
This gesture doesn't seem to be repeated by other cultures of writing.
It appears that at least traditionally in China, no idea existed that
speech was logically prior to writing and as in Moslem cultures, the
traditional high regard for literacy, coupled with its absence, means
that "more writing" was naturally prized, without second thoughts. In
fact, the more recent emphasis on China on language change and reform,
and the literal attack on cultures of the book in the Cultural
Revolution may be due to western influence, and part of the tension
between the West and Islam may be due to the way in which incompetent
Western translators and journalists translate written metaphors as
vulgar spoken attacks.
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.
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 writing.
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: just as the reader
of Stephen Wolfram's A New Kind of Science can use his related
formalism in an unbounded fashion. Wolfram while claiming that his
automata may be useful in physics certainly doesn't maintain that you
cannot simulate his automata on a computer for the very good reason
that he would not have been able to write A New Kind of Science
without writing simulators.
But note that in this ng the binary opposition so operates that the
abstract Turing Machine becomes "unwritable" in the sense of not being
simulated and the (literally false) claim is a command masquerading as
a truth value. Just as Aristotle had no good reason to say that
written symbols "symbolize" spoken sounds but said it anyway because
it simplified his task and policed the boundaries of his speech, a
division is maintained between theory and practice in mere computer
science between mathematical abstractions, which are immortal, it
seems, and are best spoken of, best whispered about, best muttered
about as Eleusinian mystery by adepts and not written about…and not
Derrida remarks that this gesture, which constructs the sociological
foundations of many disciplines, entails that the scientist, the
linguist in the case of de Saussure, drop the mask of scientific
courtesy and objectivity because he is, without being able to
acknowledge it, policing the frontiers of the grounds of the Palace of
Reason. Thus violations, including written programs which "simulate a
Turing machine" become not only incorrect but wrong, pernicious and
evil, monstrum horribilum which like Carthage delenda must have to be.
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.
Derrida was struck in his exchange with John Searle (who I learned
recently was a soured survivor of the wars in the 1960s at UCB) by the
lack of affect and humor which must preserve boundaries even at the
cost of common sense: even at the cost of a regression to barbarism
(as when the Heath man tells us that programming, has nothing to do
with programmers, being lef by security men weeping to their cars in a
layoff let us say).
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.
Thus the discourse cascade rages against the "simulation" of the TM in
precisely the same way Plato raged against representational art and
Software winds up with a bad or divided conscience in the West because
at one and the same time it must maintain the superiority of
self-present speech while it continually undercuts self-presence by
multiplying forms of writing. For example, the completely narcissistic
claim has to be made that "my protocols are ‘clearer' than thine" in
economic competition which when translated to the terms of the binary
opposition means that "my" protocols better serve the seen need for
openness and transparency.
The paradox is that in so moving towards that stated goal, the
protocols and standards become ever more opaque to end users and to
people considered as pure victims of operational systems.
Thus it is claimed that "my" Java Beans are better encapsulators of
business rules than your .Net but in both cases one will search the
actual data base in vain for the rules which are hidden from the
customer and supplier and "protected" against change or even
understanding by the CEO…who has now in America to nonetheless sign a
statement, risking prison, if his data processing people have misused
the hidden business rules (cf Sarbanes-Oxley).
Derrida has no "cure" for the ailment he describes for he so describes
the ailment as (like a bug in a compiler on which the users now rely)
so constitutive of Western thought that to cure the ailment would kill
the patient. And in the case of software, the writing has fulfilled
Plato's worst fears, for his worst fear was that the writing would
take on a bad life of its own and destroy its host.
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.