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

[Jason Resch]

On Sat, Oct 10, 2026 at 4:51 PM John Clark <johnkclark at gmail.com> wrote:

> On Sat, Oct 10, 2026 at 10:55 AM Jason Resch via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
> *>> not just because only 62 digits of pi would be necessary to compute
>>> the circumference of the observable universe with an error of less than
>>> the Planck length. The big question is whether it's possible, even in
>>> theory, for an individual observer to make an infinite, and not just very
>>> large, number of computations in a finite amount of time. If the universe
>>> is only capable of calculating a particular finite number of digits of pi
>>> then talking about a digit larger than that number is meaningless. *
>>>
>>
>> *> I would say it is independent of us, but not meaningless. We speak of
>> other possible universes in a greater multiverse that we will never access,
>> but that idea is not meaningless. For example, without that idea how else
>> does one explain fine tuning without invoking intelligent design?*
>>
>
> *As I mentioned before Hugh Everett's Many Worlds can explain that, and
> yet it doesn't say everything conceivable must exist, it says something
> much more modest, it only says that everything that does not violate
> Schrodinger's equation must exist. So the answer to the fine-tuning problem
> comes from physics not  mathematics. *
>
> *> The amount of memory available is also an important consideration when
>> talking about infinite computations, as eventually you will need to repeat
>> states after exponential time.*
>>
>
> *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.

Jason
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