If I recall correctly, that generic probability, say P(L) is, in principle, related to Chaitin's Omega using J as a, Turing complete, programming language :
Omega = sum (over L= 0,1,2,...) of P(L) According to Chaitin, Omega is a well defined real number and it is not only non-computable but, in some sense, it is the hardest kind of numbers to compute. It packs information about the halting problem so efficiently that is digits very quickly become randomly (uniformly) distributed. Yet, it is claimed, knowing just few thousands of its digits would resolve many current outstanding conjectures in number theory (those that can be posed as, relatively simple, hating problems). Chaitin's literature on Algorithmic Information Theory can be found in his home page: http://www.cs.auckland.ac.nz/~chaitin/ > [EMAIL PROTECTED] On Behalf Of Stuart Baker > Sent: Tuesday, September 25, 2007 5:30 AM > To: General forum > Subject: Re: [Jgeneral] :[[(- .]]:!*: +()! *)[(:[ ! )+!*-! > > I wonder what is the probability that a randomly selected string of a > given length (maybe with an agreed proportion of non-alpha characters) > is actually executable in J? What kind of probability distribution > over increasing string length would you get? Overall it must be a lot > higher than with most of the other languages - I have occasionally > slumped over the keyboard late at night and accidentally entered > gibberish - no Shakespeare yet, but occasionally something happens > other than just getting an error... > > (another Stuart - Baker) > > On 9/23/07, Stuart Bruff <[EMAIL PROTECTED]> wrote: > > Out of curiosity, how many of you would automatically try (as I did) > to > > interpret the following nonsense that appeared as the header from a > piece of > > spam I received? > > > > :[[(- .]]:!*: +()! *)[(:[ ! )+!*-! > > > > I initially thought it was a misplaced J Forum email. I can't decide > whether > > it's sadder that I tried to interpret it, or that it took me about 3 > seconds to > > realize it what it actually was :-( > > > > Stuart > > --------------------------------------------------------------------- > - > > For information about J forums see > http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
