Re: The Rapidly-Accelerating Computer

From: David Seaman <drseaman.domain.name.hidden>
Date: Fri, 15 Sep 2000 14:36:46 +0100

Maybe the RAC could be a sort of quantum computer which continually
expands itself deeper into the multiverse.

In any case the plenitude should allow all logical possibilities - so
every observer is sure to experience (with very low measure) the
result of every computation however long it takes.

David


At 17:58 +0200 14/9/00, Saibal Mitra wrote:
> Question: Does the AUH exclude universes in which a RAC can be
>built? The following text explaining the RAC is from the website:
>
>
><http://www.ix.de/tp/english/inhalt/kolu/2414/1.html>http://www.ix.de/tp/english/inhalt/kolu/2414/1.html
>
>``Just to see how extreme the Turing-Church Thesis actually is, a
>few years ago mathematician Ian Stewart half-jokingly suggested the
>idea of what he called, The Rapidly-Accelerating Computer (RAC). His
>goal was to show what it is exactly about computing machines that
>gives rise to things like the unsolvability of the Halting Problem
>and uncomputable numbers. Basically, the problem is the assumption
>that it takes a fixed, finite amount of time to carry out a single
>step in a computation. For his idealized computer, Turing assumed an
>infinite amount of memory. Stewart, on the other hand, considers the
>RAC, whose clock accelerates exponentially fast, with pulses
>separated by intervals of 1/2, 1/4, 1/8 ...seconds. So the RAC can
>cram an infinite number of computational steps into a single second.
>Such a machine would be a sight to behold as it would be totally
>indifferent to the algorithmic complexity of any problem presented
>to it. On the RAC, everything runs in bounded time.
>
>The RAC can calculate the incalculable. For instance, it could
>easily solve the Halting Problem by running a computation in
>accelerated time and throwing a switch if and only if the program
>stops. Since the entire procedure could be carried out in no more
>than one second, we then only have to examine the switch to see if
>it's been thrown. The RAC could also prove or disprove famous
>mathematical puzzles like Goldbach's Conjecture (every even number
>greater than 2 is the sum of two primes). What's even more
>impressive, the machine could prove all possible theorems by running
>through every logically valid chain of deduction from the axioms of
>set theory. And if one believes in classical Newtonian mechanics,
>there's not even a theoretical obstacle in the path of actually
>building the RAC.
>
>In Newton's world, we could model the RAC by a classical dynamical
>system involving a collection of interacting particles. One way to
>do this, suggested by Z. Xia and J. Gerver, is to have the inner
>workings of the machine carried out by ball bearings that speed up
>exponentially. Because classical mechanics posits no upper limit on
>the velocities of such point particles, it's possible to accelerate
>time in the equations of motion by simply reparameterizing it so
>that infinite subjective time passes within a finite amount of
>objective time. What we end up with is a system of classical
>dynamical equations that mimics the operations of the RAC. Thus,
>such a system can compute the uncomputable and decide the
>undecidable.
>
>Of course, just like Turing's infinite-memory machine, the RAC is
>impossible in the real world. The problem is that at the
>nitty-gritty level of real material objects like logical gates and
>integrated circuits, there is a theoretical upper bound to the rate
>of information transfer (i.e., velocities). As Einstein showed, no
>material object can exceed the velocity of light. Thus, there is no
>RAC and, hence, no devices to complete the incompletable.
>
>But the fact that we can never construct a RAC in no way precludes
>the possibility that some analogue device like a DNA computer or a
>quantum machine cannot be made that will allow us to transcend the
>Turing limit, and, hence, compute the uncomputable.
>
>Saibal
>
>
Received on Fri Sep 15 2000 - 06:42:45 PDT

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