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--- geopro:pedro:books:wolfram [2008/04/23 12:57] – pedro
+++ geopro:pedro:books:wolfram [2008/04/23 15:06] (atual) – pedro
@@ Linha 1: / Linha 1: @@
 ====== A New Kind of Science ======
-|Stephen Wolfram| [[http://www.wolframscience.com/nksonline/register.cgi?page=25&access=515235:786bfd76b8bb2d72|html]]|
+|Stephen Wolfram| [[http://www.wolframscience.com/nksonline/register.cgi?page=10&access=515232:b363182ea5ec4ad0|html]]|
 {{ http://www.leg.ufpr.br/~pedro/figures/wolfram.jpg}}
+{{http://www.leg.ufpr.br/~pedro/figures/rule90.jpg  }}
 One might have thought that if the rules of a program were simple then this would mean that its behaviour must also be correspondingly simple. For our everyday experience in building things tends to give us the intuition that creating complexity is somehow difficult, and requires rules or plans  that are themselves complex. But the pivotal discovery that I made some eighteen years ago is that in the world of programs such intuition is not close to correct.
@@ Linha 21: / Linha 23: @@
 to a new level of complexity (see, for instance, [[http://wiki.dpi.inpe.br/doku.php?id=geopro:pedro:complexity|More is Different]], or [[http://wiki.dpi.inpe.br/doku.php?id=geopro:pedro:books:gol|Games of Life]]).
+{{http://www.leg.ufpr.br/~pedro/figures/rule30.jpg  }}
 **Programs based on simple rules do not always produce simple behaviour.**
+In my study of simple programs I have seen [...] that even when programs have quite different underlying rules, their
+overall behavior can be remarkably similar. So this suggests that a kind of universality exists in the types of
+behavior that can occur, independent of the details of underlying rules.
+BORING: But the discoveries about simple programs in this book finally allow new progress to be made.
+Randomness can occur independently of the initial state being random or not.
+{{http://www.leg.ufpr.br/~pedro/figures/wolfram-perturbation.jpg  }}
+[...] when the perturbations are sufficiently large, the sequence of colors of the center cell does indeed
+change. But the crucial point is that for perturbations below a certain critical size, the sequence always
+remains essentially unchanged. [...] and the reason this is important is that in any real experiment,
+there are inevitably perturbations on the system one is looking at [p. 324]
+{{http://www.leg.ufpr.br/~pedro/figures/wolfram-randomwalk.jpg  }}
+almost any rule whose behaviour is not obviously simple should ultimately be capable to
+achieving the same level of computational sophistication and should thus in effect
+be universal.
+Without the Principle of Computational Equivalende one might assume that different
+systems would always be able to perform completely different computations, and that
+in particular there would be no upper limit on the sophistication of computations
+that systems with sufficiently complicated structures would be able to perform.
+-oTuring Machines ARE UNIVERSAL, and it was proven decades before this book.
+:?: The point is that, as most simple a universal machine is, most complicated is to codify a program for it.