A new kind of science is one of my favorite books, I read the entirety of the book during a dreadful vacation when I was 19 or 20 on an iPod touch.
It goes much beyond just cellular automata, the thousand pages or so all seem to drive down the same few points:
- "I, Stephen Wolfram, am an unprecedented genius" (not my favorite part of the book)
- Simple rules lead to complexity when iterated upon
- The invention of field of computation is as big and important of an invention as the field of mathematics
The last one is less explicit, but it's what I took away from it. Computation is of course part of mathematics, but it is a kind of "live" mathematics. Executable mathematics.
Super cool book and absolutely worth reading if you're into this kind of thing.
I would give the same review, without seeing any of this as a positive. NKS was bloviating, grandiose, repetitive, and shallow. The fact that Wolfram himself didn’t show that CA were Turing complete when most theoretical computer scientists would say “it’s obvious, and not that interesting” kinda disproves his whole point about him being an under appreciated genius. Shrug.
That CA in general were Turing complete is 'obvious'. What was novel is that Wolfram's employee proved something like Turing completeness for a 1d CA with two states and only three cells total in the neighbourhood.
I say something-like-Turing completeness, because it requires a very specially prepared tape to work that makes it a bit borderline. (But please look it up properly, this is all from memory.)
Having said all that, the result is a nice optimisation / upper bound on how little you need in terms of CA to get Turing completeness, but I agree that philosophically nothing much changes compared to having to use a slightly more complicated CA to get to Turing completeness.
It goes much beyond just cellular automata, the thousand pages or so all seem to drive down the same few points:
- "I, Stephen Wolfram, am an unprecedented genius" (not my favorite part of the book) - Simple rules lead to complexity when iterated upon - The invention of field of computation is as big and important of an invention as the field of mathematics
The last one is less explicit, but it's what I took away from it. Computation is of course part of mathematics, but it is a kind of "live" mathematics. Executable mathematics.
Super cool book and absolutely worth reading if you're into this kind of thing.