[ExI] Can a single observer make an infinite number of computation in a finite time? (Was Mathematical Realism)

[John Clark]

On Sat, Oct 10, 2026 at 6:24 PM Jason Resch <jasonresch at gmail.com> wrote:

*>> In **Freeman Dyson's paper Time Without End
>> <https://suli.pppl.gov/2019/course/RevModPhys.51.447.pdf> he admits that
>> digital memory is limited by the number of particles available to construct
>> it, but he proposes that an expanding universe might permit analog memory
>> whose capacity grows without bound, even if the number of physical
>> components remains fixed. For that to work it would certainly help if space
>> was continuous, but even if it is measuring things with unlimited precision
>> would be, to say the least, challenging. *
>>
>
> *> For more memory, you don't need more particles, more volume with finite
> particles is enough. But more volume can runs into problems when space
> itself is expanding.*
>

*If space is continuous then the number of mathematically possible
positional relationships between two particles is infinite, but the number
of physically distinguishable positions might not be. That would depend on
some laws of physics that we don't know very well, like the rate of black
hole evaporation when they become very small. And as you use photons of
increasingly small wavelength and increasingly larger energy to distinguish
between a tiny change in distance between two particles, how do you keep a
photon from collapsing into a black hole? *

*Maybe you could get around that problem by encoding information in the
quantum phase between two particles instead of finding the distance between
them with ever increasing precision. If things are continuous then the
relative quantum phase between two particles can take any value between 0
and 2π, you wouldn't have the black hole problem when you tried to become
more precise in your measurements, but there would probably be
other difficulties.   *

*If space is not continuous but is still increasing in volume because the
number of cdiscrete cells of a fixed size is increasing then more possible
locations a particle could be in would also increase allowing you to encode
more bits. This does not require continuous space or an increasing number
of particles, but the computer must be able to read the stored information,
and as  particles become more distant information retrieval would become
slower and more difficult.  *


*John K Clark*
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.extropy.org/pipermail/extropy-chat/attachments/20261011/498a3601/attachment.htm>