I notice that "erasure of information" on a goto instruction occurs only for goto instructions which send the Turing machine to an instruction already executed. Thus the self-reference is a reference to the *past* self of the Turing machine, which in a sense is the only self the Turing machine knows.
Tom Tom Caylor wrote: > Bruno Marchal wrote: > > Le 25-avr.-06, à 17:37, Tom Caylor a écrit : > > > > > > > > In fact, "closed system" and "meta element" seem to be contradictory. > > > > Not necessarily. It could depend of what you mean exactly by "closed". > > Closure for the diagonalization procedure is the key. Diagonalization > > is the key of the "heart of the matter". I will come back on this > > later. > > > > Closed system (Principia Cybernetica): An isolated system having no > interaction with an environment. A system whose behavior is entirely > explainable from within, a system without input... > > Mathematically, a closed system contains its boundary, or it contains > its limit points. In other words, anything expressable with the given > axioms/language is itself a member the system. > > > > > > And, back to the original question, "closed system" and "erasing > > > information" seem to be contradictory. > > > > Why? > > > > I'm at an impasse with myself in trying to explain my intuition > further. Meanwhile I'm studying up on diagonalization, waiting for > your "heart of the matter" (which I take as just a pun and not > referring to physical matter, heaven forbid). > > Speaking of "impasse with myself" and diagonalization, a thought > occurred to me that an instruction that "erases information", like a > Turing machine "goto" statement (e.g. Wei Dai's "go to the beginning of > the tape" instruction) seems to be a *self-referential* instruction. > Maybe this has something to do with the original question and (I > maintain) the need for a meta viewpoint, or an open system, to > understand it. > > Tom --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---