> On 17 Jan 2019, at 21:02, Philip Thrift <cloudver...@gmail.com> 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 <javascript:> 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



> 
> - pt
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