> On 19 Jan 2019, at 11:36, Philip Thrift <[email protected]> wrote: > > > > On Saturday, January 19, 2019 at 2:36:23 AM UTC-6, Bruno Marchal wrote: > >> On 18 Jan 2019, at 15:44, Philip Thrift <[email protected] <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 <[email protected] <>> wrote: >>> >>> >>> >>> On Thursday, January 17, 2019 at 12:45:31 PM UTC-6, Brent wrote: >>> >>> >>> On 1/17/2019 12:22 AM, [email protected] <> 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 <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/ >> >> <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/ <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).
As I said, a sort of topological intuition arise from the modes []p & p (p sigma_1), and quantum topologies appears there too, but also in []p & <>t & p ([] = Gödel’s bewesibar, <> = ~[]~). Bruno > > > > [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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
