On Sunday, December 23, 2018 at 11:49:59 PM UTC-6, Jason wrote:
>
>
>
> On Sun, Dec 23, 2018 at 11:49 PM Bruce Kellett <bhkel...@gmail.com 
> <javascript:>> wrote:
>
>> On Mon, Dec 24, 2018 at 3:45 PM Jason Resch <jason...@gmail.com 
>> <javascript:>> wrote:
>>
>>> On Sat, Dec 22, 2018 at 9:33 PM Brent Meeker <meek...@verizon.net 
>>> <javascript:>> wrote:
>>>
>>>> On 12/22/2018 12:04 PM, Philip Thrift wrote
>>>>
>>>>
>>>> https://www.eurekalert.org/pub_releases/2018-12/lsu-be122018.php
>>>>
>>>> Theoretical physicists developed a theory called loop quantum gravity 
>>>> in the 1990s that marries the laws of microscopic physics, or quantum 
>>>> mechanics, with gravity, which explains the dynamics of space and time. 
>>>> Ashtekar, Olmedos and Singh's new equations describe black holes in loop 
>>>> quantum gravity and showed that black hole singularity does not exist.
>>>>
>>>>
>>>> "In Einstein's theory, space-time is a fabric that can be divided as 
>>>> small as we want. This is essentially the cause of the singularity where 
>>>> the gravitational field becomes infinite. In loop quantum gravity, the 
>>>> fabric of space-time has a *tile-like structure*, which cannot be 
>>>> divided beyond the smallest tile. My colleagues and I have shown that this 
>>>> is the case inside black holes and therefore there is no singularity," 
>>>> Singh said.
>>>>
>>>> "These tile-like units of geometry--called 'quantum excitations'-- 
>>>> which resolve the singularity problem are orders of magnitude smaller than 
>>>> we can detect with today's technology, but we have precise mathematical 
>>>> equations that predict their behavior," said Ashtekar, who is one of the 
>>>> founding fathers of loop quantum gravity.
>>>>
>>>>
>>>> But is this consistent with https://arxiv.org/abs/1109.5191v2 which 
>>>> showed spacetime to be smooth down to 1/525 of the Planck length?
>>>>
>>>
>>> Brent,
>>>
>>> Wouldn't this be a successful prediction of Bruno's theory?  In another 
>>> thread you said it had only made retrodictions, but wasn't one of Bruno's 
>>> predictions that space and time would be continuous (not discrete), 
>>> therefore it would predict LQG is false, and then 
>>> https://arxiv.org/abs/1109.5191v2 would be a confirmation of that.
>>>
>>
>> How did Bruno predict that from a digital (integral) model)? 
>>
>
> https://groups.google.com/d/msg/everything-list/zq6LVIjhrn0/kVZao94IeGkJ 
> (A post from 2007, citing his work from 2004)
>
> The essential idea is that the first person experience of a physical 
> world, and of making predictions or measurements involves infinite numbers 
> of competing programs going through and realizing the state of the 
> observer's mind at one point in time. Predicting what happens next, the 
> outcome of an experiment, a measurement of a particle's location, etc. 
> involves the statistics concerning the infinity of these programs. It means 
> the physical appearances/physical universe is itself not computable (not 
> without infinite time and resources), and this implies a continuum 
> somewhere in physics. (i.e. eechanism is incompatible with digital physics)
>  
>
>> And where did he make such a prediction?
>>  
>>
>
> https://groups.google.com/d/msg/everything-list/2numMVaxsJ0/QePUwROUln4J 
> (post from 2007, explaining the continuum)
>
> https://groups.google.com/d/msg/everything-list/yKiXo8jB7VY/VxqraVyz5c4J 
> (post from 2009, describing that physics cannot be entirely computational 
> if "I am a machine")
>
> https://groups.google.com/d/msg/everything-list/QuedsKrpW4g/C6pAbJItvfMJ 
> (post from 2009, pointing out that if digital physics is true, then 
> mechanism would be refuted)
>
> Jason
>



One can still get a "computable continuum" from *higher-type* computing.



*Exhaustible sets in higher-type computation*
Martin Escardo
[ https://arxiv.org/abs/0808.0441 ]

*We say that a set is exhaustible if it admits algorithmic universal 
quantification for continuous predicates in finite time, and searchable if 
there is an algorithm that, given any continuous predicate, either selects 
an element for which the predicate holds or else tells there is no example. 
The Cantor space of infinite sequences of binary digits is known to be 
searchable. Searchable sets are exhaustible, and we show that the converse 
also holds for sets of hereditarily total elements in the hierarchy of 
continuous functionals; moreover, a selection functional can be constructed 
uniformly from a quantification functional. We prove that searchable sets 
are closed under intersections with decidable sets, and under the formation 
of computable images and of finite and countably infinite products. This is 
related to the fact, established here, that exhaustible sets are 
topologically compact. We obtain a complete description of exhaustible 
total sets by developing a computational version of a topological 
Arzela--Ascoli type characterization of compact subsets of function spaces. 
We also show that, in the non-empty case, they are precisely the computable 
images of the Cantor space. The emphasis of this paper is on the theory of 
exhaustible and searchable sets, but we also briefly sketch applications.*


*Robust computability notions for higher types arising in classical 
analysis*
John Longley
[ https://andrejbauer.github.io/domains-floc-2018/slides/Longley.pdf ]

etc.

- pt

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