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 everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
