On Friday, January 18, 2019 at 7:36:34 AM UTC-6, Bruno Marchal wrote:
>
>
> On 17 Jan 2019, at 21:02, Philip Thrift <[email protected] <javascript:>>
> wrote:
>
>
>
> On Thursday, January 17, 2019 at 12:45:31 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 1/17/2019 12:22 AM, [email protected] wrote:
>>
>>
>> *Later I'll post some questions I have about your derivation of the
>> Planck length, but for now here's a philosophical question; Is there any
>> difference between the claim that space is discrete, from the claim or
>> conjecture that we cannot in principle measure a length shorter than the
>> Planck length? *
>> *TIA, AG *
>>
>>
>> The theory that predicts there is a shortest measured interval assumes a
>> continuum. There's no logical contradiction is this. But physicists tend
>> to have a positivist attitude and think that a theory that assumes things,
>> like arbitrarily short intervals, might be better expressed and simpler in
>> some way that avoids those assumptions. This attitude does not assume the
>> mathematics itself is the reality, but only a description of reality; so
>> there can be different descriptions of the same reality.
>>
>> Brent
>>
>
>
>
> *A* theory that does this assumes a continuous mathematics.
> But that doesn't mean *every* theory has to.
>
> As Max Tegmark's little lecture to physicists says:
>
> Our challenge as physicists is to discover ... infinity-free equations.
>
>
> http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/#.XEDdLs9KiCQ
>
> Unless he is wrong in his premise, of course!
>
>
>
> That assumes non-mechanism, and thus bigger infinities. Tegmark is right:
> we cannot assume infinity at the ontological level (just the finite numbers
> 0, s(0), s(s(0)), …). But the physical reality is phenomenological, and
> requires infinite domain of indetermination, making some “observable”
> having an infinite range. The best candidate could be graham-Preskill
> frequency operator (that they use more or less rigorously to derive the
> Born rule from some “many-worlds” interpretation of QM.
>
> Bruno
>
>
>
I think it is possible some of this can be approached with what is referred
to as *higher-type computing*, where
higher-type computing is about
- *the characterization of the sets that can be exhaustively searched [1]
by an algorithm, in the sense of Turing, in finite time, as those that are
topologically compact*
- *infinite sets that can be completely inspected in finite time in an
algorithmic way, which perhaps defies intuition*
[1] Exhaustible sets in higher-type computation
https://arxiv.org/abs/0808.0441
[2] A Haskell monad for infinite search in finite time
http://math.andrej.com/2008/11/21/a-haskell-monad-for-infinite-search-in-finite-time/
from Martin Escardo's page
http://www.cs.bham.ac.uk/~mhe/
- pt
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