Re: A unique number for every "person" - can it be done?

spinoza1111_at_yahoo.com
Date: 03/16/05 

Date: 16 Mar 2005 03:09:38 -0800

Gerry Quinn wrote:
> In article <1110931111.988287.14620@o13g2000cwo.googlegroups.com>,
> spinoza1111@yahoo.com says...
> > Gerry Quinn wrote:
>
> > You were really taken in, and you don't understand Turing's
results.
> >
> > The higher speed of the (proposed: nonexistent) quantum computer is
> > IRREVELANT to whether it is in the same Turing class as the
> > supercomputer.
> >
> > A Turing machine is not measured in terms of physical speed or
> > parallelism because Turing's intent was not to design a computer
but to
> > show computation's limits, which aren't violated by the qc.
>
> On the contrary, I understand them quite well. Yes, the Turing
machine
> models the limit of a simplified Von Neumann architecture as the CPU

The von Neumann (aka Princeton) architecture is that of a
stored-program machine with both instructions and with data directly
addressed by ordinal numeric quantities. The Turing Machine doesn't use
addresses. Instead (as I rilly hope you know) it can move one space to
the left or right at a time.

The von Neumann (aka Princeton) architecture postdated Turing by ten
years, but John von Neumann did not use Turing's work at all, for the
very good reason that he was a mathematical consultant to an
engineering effort while Turing's design was NOT INTENDED to specify a
real machine.

The Turing machine does not ONLY model the limits of the Princeton
architecture. The Church/Turing thesis, for which no counterexamples
have been found, is that it models the limits not only of Princeton
architecture but of all other existent, and conceivable, computer
architectures.

> speed and memory size go to infinity. [Turing was not familiar with
the
> concept of a quantum computer, but he did in fact speculate about
> computational devices more powerful than a Turing machine.]

(Sigh) (Eye roll) (Crotch grab) The article you showed me ADMITS that
in the sense Turing intended, the quantum device is NOT more powerful
than a Turing machine.

If you mean "gawrsh, faster", then almost any computer, including the
Princeton IAS machine on which von Neumann worked, and that Trash 80 in
your garage, is not Turing compatible with a Turing machine in your
incorrect sense.

>
> The limit of a quantum computer, in theory (no useful one has been
made
> in practice, and I personally doubt any useful general purpose one
will
> ever be) is different. As a quantum computer operates on a larger
set
> of entangled qubits, its essential computational power increases
> exponentially with the size of the set. By contrast, that of a
> conventional computer increases linearly.
>
You're comparing apples and oranges. Turing did not care about speed
and it is NOT a criterion for Turing compatibility.

Your essential confusion is discovered in the word "power", a phrase
rhetorically appealing but meaningless when talking about Turing
machines, which form an equivalence class as regards what you mean by
"power".

> In Cantorian set theory, two raised to the power of an aleph yields a

> higher aleph. Since we are talking about limiting models, not real
> physical machines, this is really what is relevant.

Please explain. I don't think you are on to anything. But if you can
describe genuine mathematical results in terms of a nondenumerable
Turing machine able (let's say) to partition its tape into unboundedly
small "squares", and to fill each "square" with a "symbol" consisting
of a variable and real-valued voltage, which is able to calculate
something that the ordinary TM cannot, expound by all means.

>
> What you are claiming, in effect, is that the limit of x as x goes to

> infinity is the same as the limit of 2^x as x goes to infinity. In
> ordinary algebra, this is neither true nor false, as both are
undefined.
> In systems that can rigorously deal with analogous quantities, the
> identity is false.
>
> Comparing the ultimate, infinite, theoretical quantum computer with
the
> ultimate, infinite, theoretical Turing machine, we see that a single
> state of the former corresponds to every state of the latter; they
are
> not commensurable. If you like, the former can work with real
numbers
> of infinite precision, while the latter is limited to finite
integers.
> One can still quibble about finitude of data entry, but I think the
> point is made. The Turing machine is not a particularly useful model

> for discussing the properties of such a computer. The student who
> understands this is not wrong, even if we grant that your objections
> have some force.

OK. This is reasonably cool. Perhaps if we apply Cantorian
nondenumerability to a TM, and hypothesize a "quantum" device (or one
implemented using great vats of melted butter), it is able to carry out
a computation that a Turing machine cannot ("given unbounded amounts of
time and memory").

Do recall that because Turing, unlike so many people, was independent
of the otherwise universal division of effort by time which capitalism
uses to factor labor power, he ASSUMED that the Turing Machine would
have what Andrew Marvell called "world enough, and time". This is often
a stumbling block for the tyro (which does not include present
company), deluded as he is by the notion of computing "power" (faster
results and the hell with bugs), thinks it fundamental which it is not.

Let me be precise. I do not care if the nondenumerable TM is faster.
The only meaningful question is can it carry out a computation which
the ordinary TM cannot?

>
> > You were taken in by an Americanism and by rhetoric. In the
paragraph I
> > quoted, the writer used "in theory" and "theoretically". This is a
> > rhetorical trick designed to appeal to Americans, many of whom
believe
> > that evolution is "only a theory".
>
> I googled for a useful article and posted the URL in the forlorn hope

> of explaining certain matters to you. I did not get my knowledge of
> quantum computing, such as it is, from this article. It is true they

> use 'theory' too many times in too many different contexts, but I
have
> been guilty of the same. These are rather theoretical ideas from a
> rather theoretical region of quantum theory. I don't believe that
"only
> a theory" in the sense of "unproven, even speculative" was used.

I wasn't thinking about quantum theory. All I know about quantum theory
is what I read in the funny papers, and George Gamow, and the
occasional popular scientific update on the quark.

I yam thinking about theoretical compsci given my comprehension of
same, and as far as I know, Church/Turing holds. It will hold no matter
how "powerful" computers become because it is refuted by the
performance of a calculation which cannot be performed by a TM.

Wake me up, in other words, when a qc is able to read the encodement of
another qc and determine whether that arbitrary qc will HALT.

Having said this, I do take away the idea that an "analog" TM with
divisible squares and "symbols" with continuous values might make a
nifty software simulation. I will get back to you on this.
>
> - Gerry Quinn

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