Dear Hal,

    You make a very good point! Thank you for actually reading Calude et
al's paper. ;-) But, I have one nagging question: is the requirement of the
existence of an infinite superposition more or less "hard to swallow" than
Bruno's "arithmetical truth"?
     I don't see how "arithmetical truth" is a simpler assumption than the
existence of an infinite superposition (in Hilbert space?). It seems to me
that the former is a subset of the latter, not the other way around. Again,
I go back to Cantor's proof showing that the integers and the Reals have
distinct cardinalities and the simple question of "what breaths fire into
the equations?" (or Bruno's UD)?

    QM comp seems to operate in the space of the Reals (R) and TM operates
in the space of Integers (Z), is this correct?

    We must additionally account for, at least, the "illusion" of time and
concurrency of events.

Kindest regards,


----- Original Message -----
From: "Hal Finney" <[EMAIL PROTECTED]>
Sent: Monday, December 30, 2002 12:38 PM
Subject: Re: Quantum Probability and Decision Theory

> Stephen Paul King references:
> >
> whose abstract begins,
> "Is there any hope for quantum computer to challenge the Turing barrier,
> i.e., to solve an undecidable problem, to compute an uncomputable
> function?  According to Feynman's '82 argument, the answer is negative.
> This paper re-opens the case: we will discuss solutions to a few simple
> problems which suggest that quantum computing is theoretically capable
> of computing uncomputable functions."
> We discussed this article briefly in July.  Calude relies on infinite
> dimensional Hilbert space with the inputs prepared in an infinite
> superposition.  Without claiming to understand all the details, this
> looks to me like it would require an infinite amount of work to prepare.
> It is well known that under idealized classical Newtonian physics,
> computations are possible that break the Turing barrier if you have
> infinite precision in your inputs.  Of course, we don't live in a
> Newtonian universe.  This new result has something of the same flavor,
> applied to a quantum mechanical universe.  It still relies on infinities.
> When a finite quantum computer can break the Turing barrier, that will
> prove something.  But when your first step is to prepare an infinite
> superposition, that has no applicability to the physical universe.
> Hal Finney

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