I believe Chaitin has a definition of randomness that works for finite strings. If I remember correctly it has to do with the length of the shortest program that outputs the string being longer than the string itself.
Jason On Wed, Mar 10, 2021, 3:43 PM 'Brent Meeker' via Everything List < [email protected]> wrote: > > > On 3/10/2021 7:15 AM, Bruno Marchal wrote: > > > On 10 Mar 2021, at 00:19, 'Brent Meeker' via Everything List < > [email protected]> wrote: > > > > On 3/9/2021 2:00 PM, Bruce Kellett wrote: > > On Wed, Mar 10, 2021 at 6:00 AM Jason Resch <[email protected]> wrote: > >> On Tue, Mar 9, 2021 at 9:41 AM Lawrence Crowell < >> [email protected]> 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"? > > 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. > > 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 >> > > > 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 [email protected]. > 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 [email protected]. > 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 [email protected]. > 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 [email protected]. > 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. 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