> On 18 Jan 2019, at 15:44, Philip Thrift <cloudver...@gmail.com> wrote:
> 
> 
> 
> On Friday, January 18, 2019 at 7:36:34 AM UTC-6, Bruno Marchal wrote:
> 
>> On 17 Jan 2019, at 21:02, Philip Thrift <cloud...@gmail.com <javascript:>> 
>> wrote:
>> 
>> 
>> 
>> On Thursday, January 17, 2019 at 12:45:31 PM UTC-6, Brent wrote:
>> 
>> 
>> On 1/17/2019 12:22 AM, agrays...@gmail.com <> 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
>>  
>> <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


That is the constructive move. With mechanism, this is given by S4Grz1, and/or 
typing the combinators. It corresponds to the first person. Tegmark seems 
oscillate between third and first person views, but when taking mechanism 
seriously *in the cognitive science* (and not in physics), we have to take both 
points of view, and derive their relations from self-reference. As I said, the 
1p/3p relation is more subtle than the bird/frog change of scale.

You might try to explain Haskell monad for infinite search in finite time. 
Mechanism explains this from the first person point of view, but is not seen as 
being something algorithmic.

Bruno





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