Stephen Paul King wrote: > >Dear Jesse, > > Hasn't Stephen Wolfram proven that it is impossible to "shortcut" >predictions for arbitrary behaviours of sufficienty complex systems? > >http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/ > > >Stephen
The paper itself doesn't seem to prove it--he uses a lot of tentative language about how certain problems "may" be computational irreducible or are "expected" to be, as in this paragraph: "Many complex or chaotic dynamical systems are expected to be computationally irreducible, and their behavior effectively found only by explicit simulation. Just as it is undecidable whether a particular initial state in a CA leads to unbounded growth, to self-replication, or has some other outcome, so it may be undecidable whether a particular solution to a differential equation (studied say with symbolic dynamics) even enters a certain region of phase space, and whether, say, a certain -body system is ultimately stable. Similarly, the existence of an attractor, say, with a dimension above some value, may be undecidable." Still, I think it's plausible that he's correct, and that there are indeed computations for which there is no "shortcut" to finding the program's state after N steps except actually running it for N steps. Jesse _________________________________________________________________ Catch suspicious messages before you open them--with Windows Live Hotmail. http://imagine-windowslive.com/hotmail/?locale=en-us&ocid=TXT_TAGHM_migration_HM_mini_protection_0507 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
