Rob and Chris, (01)
Don't attribute claims to Wolfram that come from Wikipedia: (02)
RF> Or you could look at Stephen Wolfram's idea of "computational
irreducibility". It appears to me to be saying the same thing:
>>
>> "The empirical fact is that the world of simple programs contains a
>> great diversity of behavior, but, because of undecidability, it is
>> impossible to predict what they will do before essentially running
>> them. The idea demonstrates that there are occurrences where theory's
>> predictions are effectively not possible."
>>
>> http://en.wikipedia.org/wiki/Computational_irreducibility (03)
CM> Yes, although he appears to be citing undecidability to illustrate
> a more general claim about the predictive limitations of theories. (04)
I agree that statement is confused. But it comes from Wikipedia.
Wolfram himself is more nuanced. See (05)
http://www.wolframscience.com/nksonline/page-737 (06)
For example, Wolfram says (p. 741) (07)
SW> [Computational irreducibility implies] that for many systems
> no systematic prediction can be done, so that there is no
> general way to shortcut their process of evolution, and as
> a result their behavior must be considered computationally
> irreducible. (08)
In other words, Wolfram is saying that the amount of computation
needed to predict what the system will do may be extremely large,
but finite. The technical term for that is 'intractable'. (09)
Undecidability implies that *no* finite amount of computation
can make the prediction. (010)
John (011)
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