Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
Stephen Wolfram’s four classes of computation.
When I first met Stephen Wolfram, I was an unemployed cyberpunk writer. I found
his work so interesting that, half an hour after I’d met him, I’d decided to dive back into
academia and become a computer scientist.
As the years went by, I ran into Stephen a number of times around Silicon Valley.
Somehow he and I always remained friends.
To me, one of the most interesting things about his work is that he is pushing so hard
int two diametrically opposite directions. In creating and promoting his Mathematica
software for symbolic computation, Stephen has perfected the old style of formula-based
science. But his theoretical work in A New Kind of Science explicitly denies the ultimate
validity of the formula-based approach that Mathematica makes possible.
If a large part of physical and mental reality can be built up from computations, it’s
instructive to look at what kinds of computation can occur.
Now we might think that the computations that simulate reality are very carefully
constructed. But the same generic behaviors occur in all kinds of computation.
It’s instructive to look at what computations do if we simply pick them at random
rather than looking at ones specifically designed to do something.
Restate Wolfram’s taxonomy in terms of chaos.
Intrinsic Randomness
There’s a popular belief that chaos is “about” excavating digits from initial
conditions. In reality, nothing can be measured to more than at most thirty decimal places —
all of which get used up in the first few minutes of a chaotic process. As Wolfram points out,
seeming randomness stems neither from initial conditions nor from jostling by the
environment. Complex computational processes create their own randomness. What’s really
significant about chaos is not the sensitive dependence on initial conditions enthroned as the
mythical “butterfly effect,” but rather the fact that events cluster upon strange attractors —
which usually are fractals.
Even though the steps are deterministic, it can be hard to see very far into the future
when watching such a process. Turing’s work on this subject; the Halting Problem.
Randomness, chaos, and computational universality.
Used a scientific instrument in this fashion, the computer is a bit like a microscope, a
device that lets the user peer into unknown new worlds — albeit a microscope must needs on
some object in the external world, while a computer can be fruitfully focused on its own self.
The Principle of Computational Equivalence.
Further distinctions prove significant. Many kinds of computational devices are
“universal” in the sense that, given the appropriate software, they can simulate any other
computation. It turns out that universality is in fact very common among all sorts of
computing devices. Many physical systems — such as the patterns on a seashell or the
ripples in a brook — are themselves universal. This in turn implies that the world is harder
to predict than we may have imagined.
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