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

[Jason Resch]

On Sun, Oct 11, 2026 at 6:39 AM John Clark <johnkclark at gmail.com> wrote:

> 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?*
>

Particle positions are smeared out (Compton wavelength). The only way to
reduce compton wavelength to 0 and attain infinite prevision in location
measurement is with infinite mass. Likewise, measuring ever smaller units
of time requires more and more energy.


>
> *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.  *
>

But how do you propose extracting that infinite real number?


>
> *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.  *
>

Yes that is what my previous e-mail said. Glad we agree.

Jason
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