Re: Discrete theories of space

[Philip Thrift]

On Saturday, January 19, 2019 at 5:22:25 PM UTC-6, Philip Thrift wrote:
>
>
>
> On Saturday, January 19, 2019 at 11:20:16 AM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, agrays...@gmail.com 
>> wrote:
>>>
>>> Since it seems conceptually impossible to model a theory with DISJOINT 
>>> discrete spatial units, thus requiring the units to be juxtaposed, do such 
>>> theories acknowledge difficulty of motion between the units, which might or 
>>> might not have boundaries? TIA, AG
>>>
>>
>>
>> In quantum space or quantum spacetime approaches (like loop quantum 
>> gravity, casual dynamical triangulation), space or spacetime is in really a 
>> collection of 3D or 4D *cells *(tetrahedra or pentahedra) that are 
>> "glued" together somehow.
>>
>   
>   > or 5-cells here [ https://en.wikipedia.org/wiki/5-cell ] 
>
>>
>> There is no "space"  in the conventional Euclidean of Riemannian  
>> geometrical/metrical sense, so these cells aren't *in* space (there is 
>> no space inside of them or between them). The cells collectively *are* 
>> space.
>>
>> - pt
>>
>>
>>
> One could have cellular space (leaving time as it is) or cellular 
> spacetime (LQG).
>
> - pt
>


This by Carlo Rovelli:

https://arxiv.org/abs/1802.02382

Space and Time in Loop Quantum Gravity
Carlo Rovelli 

(Submitted on 7 Feb 2018)

Quantum gravity is expected to require modifications of the notions of 
space and time. I discuss and clarify how this happens in Loop Quantum 
Gravity.


concludes

*Notice that nowhere in the basic equations of the theory a time coordinate 
t or a space coordinate x show up.*

- pt


 

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Discrete theories of space

[Philip Thrift]

On Saturday, January 19, 2019 at 11:20:16 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, agrays...@gmail.com 
> wrote:
>>
>> Since it seems conceptually impossible to model a theory with DISJOINT 
>> discrete spatial units, thus requiring the units to be juxtaposed, do such 
>> theories acknowledge difficulty of motion between the units, which might or 
>> might not have boundaries? TIA, AG
>>
>
>
> In quantum space or quantum spacetime approaches (like loop quantum 
> gravity, casual dynamical triangulation), space or spacetime is in really a 
> collection of 3D or 4D *cells *(tetrahedra or pentahedra) that are 
> "glued" together somehow.
>

> or 5-cells here [ https://en.wikipedia.org/wiki/5-cell ] 

>
> There is no "space"  in the conventional Euclidean of Riemannian  
> geometrical/metrical sense, so these cells aren't *in* space (there is no 
> space inside of them or between them). The cells collectively *are* space.
>
> - pt
>
>
>
One could have cellular space (leaving time as it is) or cellular spacetime 
(LQG).

- pt

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Discrete theories of space

[Philip Thrift]

On Saturday, January 19, 2019 at 5:42:12 AM UTC-6, agrays...@gmail.com 
wrote:
>
> Since it seems conceptually impossible to model a theory with DISJOINT 
> discrete spatial units, thus requiring the units to be juxtaposed, do such 
> theories acknowledge difficulty of motion between the units, which might or 
> might not have boundaries? TIA, AG
>


In quantum space or quantum spacetime approaches (like loop quantum 
gravity, casual dynamical triangulation), space or spacetime is in really a 
collection of 3D or 4D *cells *(tetrahedra or pentahedra) that are "glued" 
together somehow.

There is no "space"  in the conventional Euclidean of Riemannian  
geometrical/metrical sense, so these cells aren't *in* space (there is no 
space inside of them or between them). The cells collectively *are* space.

- pt


-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Discrete theories of space

[agrayson2000]

Since it seems conceptually impossible to model a theory with DISJOINT 
discrete spatial units, thus requiring the units to be juxtaposed, do such 
theories acknowledge difficulty of motion between the units, which might or 
might not have boundaries? TIA, AG

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Re: Planck Length

[Philip Thrift]

On Saturday, January 19, 2019 at 2:36:23 AM UTC-6, Bruno Marchal wrote:
>
>
> On 18 Jan 2019, at 15:44, Philip Thrift > 
> 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  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
>>
>> 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
>
>

The key to the higher-type computing approach

from *Infinite sets that admit fast exhaustive search*
 http://www.cs.bham.ac.uk/~mhe/papers/exhaustive.pdf


is to relate a certain kind of computing to topology

   *exhaustible sets are to compact sets as *
*   computable functions are to continuous maps*

There is one example in the above paper [code below]  (I haven't run any of 
his code).


It should be really be called something like  *topological computing*: 

Programs that are like continuous maps have the property that even though 
they apparently deal with infinite objects, because these objects are (in a 
computationally-defined way) topological compact, their computing time is 
finite (and maybe even efficient).



[code from paper]
type Cantor = N -> Bit
foreveryC :: (Cantor -> Bool) -> Bool
equalC :: (Cantor -> N) -> (Cantor -> N) -> Bool
equalC f g = foreveryC(\a -> f a == g a)

f,g,h :: Cantor -> N
f a = a(10*a(3ˆ80)+100*a(4ˆ80)+1000*a(5ˆ80))
g a = a(10*a(3ˆ80)+100*a(4ˆ80)+1000*a(6ˆ80))
h a = if a(4ˆ80) == 0 then a j else a(100+j)
where i = if a(5ˆ80) == 0 then 0 else 1000
   j = if a(3ˆ80) == 1 then 10+i else i


The queries “equalC f g” and “equalC f h” answer
False and 

Re: Planck Length

[Bruno Marchal]

> On 18 Jan 2019, at 15:44, Philip Thrift  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 > 
>> 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
>>  
>> 
>> 
>> 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





> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com 
> .
> To post to this group, send email to everything-list@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list 
> .
> For more options, visit https://groups.google.com/d/optout 
> .

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.