Re: continous universes

From: Hal Finney <hal.domain.name.hidden>
Date: Wed, 28 Jan 1998 14:37:15 -0800

Wei Dai, <weidai.domain.name.hidden>, writes:
> Schmidhuber's paper explicitly assumes that only discrete universes exist,
> so that theories of computation can be applied. But this assumption may
> not be necessary. Consider a TM which implements an algorithm for
> numerically solving a fixed system of partial differential equations
> defining some continous universe. The TM would take as input a set of
> arbitrary-precision coordinates defining a region in this universe and a
> parameter specifying the precision of the output, and produce as output
> the content of that region to the specified precision.
>
> Under the interpretation I proposed earlier, the regions of this continous
> universe would have physical existence as the output of the TM and
> therefore the universe as a whole would have physical existence.

Very interesting. It would seem though that you could only input
rational numbers, so that the universe's granularity would not extend
to the reals?

Perhaps Schmidhuber's interpretation could be similarly enhanced. First,
you could remove the restriction that there must be only a finite number
of bits at each time slice, by writing the universe states one under
another to form an array, and then outputting the array in some diagonal
order. This would allow each time interval to have a countably infinite
number of bits, to allow for spatially infinite universes and/or for
countably dense ones.

You could then reorder the rows to correspond to some countable ordering
of the rational numbers, like 1, 1/2, 2, ..., so that you could have
a countably infinite number of time slices.

> On a different note, I'm trying to learn enough quantum mechanics to
> figure out what a program for our universe might look like. Does anyone
> have suggestions for a good quantum mechanics text book?

It's been too long for me to remember, unfortunately. I don't think any
of the ones I used in college were very good.

Hal
Received on Wed Jan 28 1998 - 15:30:23 PST