# Re: The Rapidly-Accelerating Computer

From: <hal.domain.name.hidden>
Date: Thu, 14 Sep 2000 09:31:49 -0700

> 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
>
> ``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.

That's an interesting question. It gets into the question of whether
transfinite numbers "really" exist in some abstract mathematical sense.

The question is, under the AUH could you have a universe where there was
one subsystem which did an infinite amount of computation while another
subsystem did only a finite amount.

Obviously it would be possible to simulate the infinite calculation at
least in the limit. The universal simulator chugs along, and any given
step in the infinite computer (RAC) eventually gets hit by the simulator.

Then, would an observer in the non-infinite subsystem ever observe the
results of the RAC? That is, would the universal simulator ever finish
the calculation of the infinite result and be able to start simulating
events in the non-infinite subsystem which took place later?

In the field of transfinites, there is the concept of ordinal numbers
greater than infinity. The counting infinity is written as omega,
we can write it as w. The numbers go 1, 2, 3, ... w, w+1, w+2, w+3,
... 2w, 2w+1, ... and so on. So there is a notation to represent counting
numbers after infinity, and you can do math with them.

If we imagine that such numbers have a degree of abstract reality, and if
the AUH universal simulator is also abstract (assuming platonic realism),
then it could be said that the simulator is able to go through more than
w steps. It takes w steps to simulate the RAC, but then at steps w+1,
w+2, ... we would be able to simulate the non-infinite subsystems which
could contain observers who would witness the result of the infinite
calculation.

Normally in our probabilistic estimates we assume that the measure of a
universe is entirely due to the complexity of the program that runs it.
By this judgement, a universe containing an infinite subsystem (RAC)
would not be inherently of low measure. Therefore there would be no
reason to expect that observers who have witnessed the result of an
RAC would have low measure. Hence universes containing RACs could
exist and be reasonably probable. (Apparently not our universe though
because our particular physics don't seen to provide any mechanism for
infinite computation. Interestingly, an idealized Newtonian universe
with point masses can contain an RAC, I believe.)

Another perspective on the problem would be to abandon platonic realism
and say that the multiverse is actually being simulated by a real computer
somewhere, a Turing machine. This raises the philosophical question of
how the TM universe came into existence (it's turtles all the way down,
sonny). Awkward as this approach is, it suggests that no universe could
ever actually achieve an infinite amount of computation, that this could
only be approached in the limit. In that case the results of the RAC
could never be observed in any universe.

Hal
Received on Thu Sep 14 2000 - 09:39:12 PDT

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