> On 10 Mar 2021, at 22:43, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> wrote: > > > > On 3/10/2021 7:15 AM, Bruno Marchal wrote: >> >>> On 10 Mar 2021, at 00:19, 'Brent Meeker' via Everything List >>> <everything-list@googlegroups.com >>> <mailto:everything-list@googlegroups.com>> wrote: >>> >>> >>> >>> On 3/9/2021 2:00 PM, Bruce Kellett wrote: >>>> On Wed, Mar 10, 2021 at 6:00 AM Jason Resch <jasonre...@gmail.com >>>> <mailto:jasonre...@gmail.com>> wrote: >>>> On Tue, Mar 9, 2021 at 9:41 AM Lawrence Crowell >>>> <goldenfieldquaterni...@gmail.com >>>> <mailto:goldenfieldquaterni...@gmail.com>> wrote: >>>> Nothingness is a paradoxical thing. Does nothingness exist? If so, then by >>>> having existential properties it is not pure nothingness. If nothingness >>>> does not exist then there must exist something. In a sense God is the >>>> antithesis of nothingness and in a sense shares the same paradoxical issue. >>>> >>>> There is a strange and paradoxical sort of identity between nothing and >>>> everything, particularly as it relates to information theory. Insofar as >>>> the total set of all possibilities has zero information content. >>> >>> Even if it tells us what is not possible? I think you're getting in over >>> your head. What kind of "possible" to you mean? Simple not >>> self-contradictory? Nomological? Or what? >>> >>>> >>>> >>>> A random message string can contain zero information, but still exist -- >>>> written on a piece of paper, for example. >>> >>> I agree with your basic point, but a random string carries maximum >>> information, per Shannon. That's why maximally compressed string looks >>> random; although you can't really define random in the information >>> theoretic sense for finite strings. >> >> >> You can define randomness for finite strings, up to a constant. > > What does it mean "up to a constant”?
It means that the notion of algorithmic randomness is the same for all universal machine, except for the (finite) sequence which are small compared to the length of the (finite) code of the universal machine in use. The precision are lengthy to describe, as you need a language with prefixed (self-delimiting) programs, but the idea is basically the idea of Kologorov complexity, and use some theorem by Chaitin. Then there are many variants, obtained by Martin Löff, and also Solovay. Basically, a finite sequence is random is the program to generate it is as long as the sequence itself. But it is obvious that the length will depend on the universal machine use to run the programs, so different machine might get different result, and then it can be shown that the difference can be bounded by a constant, depending natural of the code of the universal machine in use. Maybe you will find an answer to your question in this pdf: https://math.uchicago.edu/~may/REU2013/REUPapers/Steinitz.pdf <https://math.uchicago.edu/~may/REU2013/REUPapers/Steinitz.pdf> (I should find some time to (re)read it). > >> Most universal machine will agree on some large string being random, but can >> differ on strings shorter than themselves, say. See the book by Calllude on >> the randomness of finite string. >> This is usually defined first, and then an infinite sequence is said to be >> random if almost all his initial segments are. > > Even with only two "l"s in his name, I find no reference to him. If you have > a finite string you can just adopt a notation in which it has a short name, > "Bob", and then it's Kolomogorov complexity is that of "Bob". So I don't > see by what definition you can prove a finite string to be random. The name of a program is not the program itself. The program is supposed to be written in the computer language. Its name is only a local macro, and if you use macro, you need to compile it first. The wiki is not bad on this: https://en.wikipedia.org/wiki/Kolmogorov_complexity <https://en.wikipedia.org/wiki/Kolmogorov_complexity> Bruno > > Brent > >> >> Bruno >> >> >> >> >>> >>> Brent >>> >>>> This idea that zero information equates to 'nothing' is just an elementary >>>> confusion of categories. >>>> >>>> This is the main subject of Russell Standish's book: Theory of Nothing: >>>> https://www.hpcoders.com.au/nothing.html >>>> <https://www.hpcoders.com.au/nothing.html> >>>> >>>> >>>> That is why Russell got so many things wrong in this book. >>>> >>>> Bruce >>>> -- >>>> 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 >>>> <mailto:everything-list+unsubscr...@googlegroups.com>. >>>> To view this discussion on the web visit >>>> https://groups.google.com/d/msgid/everything-list/CAFxXSLTXSHt%3DASkdBiA%2Bh_-4d3FCAHMX7puXWq9_1tG%3DnjbXSg%40mail.gmail.com >>>> >>>> <https://groups.google.com/d/msgid/everything-list/CAFxXSLTXSHt%3DASkdBiA%2Bh_-4d3FCAHMX7puXWq9_1tG%3DnjbXSg%40mail.gmail.com?utm_medium=email&utm_source=footer>. >>> >>> >>> -- >>> 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 >>> <mailto:everything-list+unsubscr...@googlegroups.com>. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/everything-list/60facf25-7c8b-1cd6-a1fc-f20d80406479%40verizon.net >>> >>> <https://groups.google.com/d/msgid/everything-list/60facf25-7c8b-1cd6-a1fc-f20d80406479%40verizon.net?utm_medium=email&utm_source=footer>. >> >> -- >> 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 >> <mailto:everything-list+unsubscr...@googlegroups.com>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/386FCCCB-5232-4ED9-87DB-8A6C4EFD2E0A%40ulb.ac.be >> >> <https://groups.google.com/d/msgid/everything-list/386FCCCB-5232-4ED9-87DB-8A6C4EFD2E0A%40ulb.ac.be?utm_medium=email&utm_source=footer>. > > > -- > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/ad09055f-874c-59d3-bf91-868b8bc962b2%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/ad09055f-874c-59d3-bf91-868b8bc962b2%40verizon.net?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3A236481-394F-4C2A-BF94-75D82015C8CA%40ulb.ac.be.
