To heck with work! A couple of beers makes it all ok. (Note to employer: I am only kidding about that of course.) As I said, I think the definition of randomness within a constrained system makes a lot more sense then the alternative. However, a definition must then be relative. Perhaps Matt meant for his claim (his definition of randomness) to be within the context that he had in mind. But I have no way of knowing that. If a definition does not lead to an analytically computable or analytical mathematical algorithm (to detect an entity of the definition for instance) then it is not provable by logical constructivist reasoning (I think - I am on the edge of my knowledge here). The hypothesis stands as a hypothesis and not a theorem. You might suggest that we can have a specialized domain for the theorem and say that it can be verified ad hoc for some problem within a given subdomain of mathematics. So now, any knowledge that we have about some relations within a system can then be verified (by whatever analysis Matt was thinking of? If my memory is correct, you guys are 'prediction' mongers. Here you - or Matt - seem(s) to be saying that an abstract hypothesis that can not lead to prediction but which can be used in post-diction or an ad-hoc application of analysis can stand as a superlative theorem that might even stand as a foundation of AGI. (Maybe I am stretching a little here but I do know enough about you guys to at least put the statement out there.) But my challenge is this: Doesn't the strength of this constructivist-like argument call the absolutism of Matt's (and John's) point of view (about this) into question? I can try to make this a little clearer if anyone is interested. Jim Bromer On Thu, Oct 11, 2018 at 1:44 PM Jim Bromer <[email protected]> wrote: > > I think Matt's last post is wrong about the idea of the randomness of > a string but I am really supposed to be working. > I think John's abstract example would constitute an example of what I > was thinking about but there are also other exemplars, both abstract > and explicit. > Jim Bromer > > On Thu, Oct 11, 2018 at 1:37 PM Matt Mahoney via AGI > <[email protected]> wrote: > > > > On Thu, Oct 11, 2018 at 12:38 PM John Rose <[email protected]> wrote: > > > OK, what then is between a compression agents perspective (or any agent > > > for that matter) and randomness? Including shades of randomness to > > > relatively "pure" randomness. > > > > A string is random if there is no shorter description of the string. > > Obviously this depends on which language you use to write > > descriptions. Formally, a description is a program that outputs the > > string. There are no "shades" of randomness. A string is random or > > not, but there is no general algorithm to distinguish them in any > > language. If there were, then AIXI and thus general intelligence would > > be computable. > > > > > From an information theoretic (and thermodynamic) viewpoint in your mind > > > what happens when you see the symbol for infinity? Semi-quantitatively > > > describe the thought processes? > > > > The same thing that happens when you see any other symbols like "2" or > > "+". Mathematics is the art of discovering rules for manipulating > > symbols that help us make real world predictions. > > > > -- > > -- Matt Mahoney, [email protected]
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