|
![](/i/fill.gif) |
>> 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.
Sure. But a UTM is carefully *designed* to be universal. Wolfram asserts
that many kinds of things "just happen to be" universal. Now if he had
offered a proof rather than an assertion (i.e., a theorum stating
exactly which kinds of things are Turing-complete), that might have been
interesting. As it is, he just goes through a collection of CAs and
demonstrates that just one of them is definitely Turing-complete.
>> (Presumably such a result would include deciding exactly when a simple
>> system is or isn't Turing-complete.)
>
> We already have that too.
Really? So you can tell me exactly which CAs are or aren't
Turing-complete then?
(Actually, I have a sinking feeling the general question might be
undecidable, but anyway...)
> 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.
Yeah, even after reading NKS, I'm still not *exactly* sure what he was
getting at. Maybe he isn't either...
Post a reply to this message
|
![](/i/fill.gif) |