On Saturday, January 19, 2019 at 2:36:23 AM UTC-6, Bruno Marchal wrote: > > > On 18 Jan 2019, at 15:44, Philip Thrift <cloud...@gmail.com <javascript:>> > 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> 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 True respectively, in less than 3s - 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.