Invisible wrote:
> If you could prove not that one particular "simple" system is 
> Turing-complete, but that huge classes of simple systems are, *that* 
> would be an interesting result.

Um, we already have that. It's called "A Turing Machine." :-)  I mean, that 
was the whole point of defining Turing machines, then coding a universal 
turing machine, then proving that all kinds of multi-tape multi-this 
multi-that all reduce down to the same single-tape single-program 
UTM-capable machine.

> (Presumably such a result would include deciding exactly when a simple 
> system is or isn't Turing-complete.)

We already have that too.

> I still wouldn't describe it as a "new kind of science". Indeed, from 
> what I can gather, NKS isn't some sweeping new paradigm. It's just a new 
> and unusual way of looking at and thinking about things. That's not to 
> say there aren't interesting things to be learned from this point of 
> view, but it hardly rocked my world.

No.  I think he was asserting that science should look at computational 
systems as the basis of science, rather than (say) the closed form fomulas 
of how the world works that science uses now. However, since he didn't do 
what you're talking about, namely being able to point at the attributes of a 
system and determine how computationally complex it is, he failed at that task.

> Fractal geometry already tells us that simple rules can generate complex 
> behaviour. Chaos theory already tells us that deterministic, simple 
> systems can still be highly unpredictable. NKS doesn't seem to add very 
> much. There's a few small, specific things which are interesting, but 
> it's not nearly as radical as people are saying.

I don't think anyone but Wolfram are saying it's radical. :-)

> But then again, isn't this the same Mr Wolfram who claims that 
> Mathematica fundamentally transforms the way computer mathematics 
> happens? Or that Wolfram Alpha is going to revolutionise the human race?
> 
> Sure, Mathematica is a great piece of software, but I guess we should 
> take anything Mr Wolfram says with a pinch of salt...

Yep.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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