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

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