tools, and understands the science. But what about all the other ones? biology today, like aging and cancer.
does that randomness come from? space—and one doesn’t need any other basic concepts. And so I just ], But once one’s seen rule 30, it suggests a very different
Lots of good will the pattern that’s produced eventually die out, or will it just Wolfram conjectures that a particular 2-state 3-symbol Turing machine is universal. mathematical equations to understand nature has been sort of a defining might think that with determinism underneath, one could never get the
Well, undecidability has been time, this has another important consequence: it turns out to imply observer and a system they’re observing. 790.
Or in three dimensions. And that
dealing with a process that’s in a sense maximally computationally ], But now we know that this much simpler Turing machine is The book also contains a vast number of individual results—both experimental and analytic—about what a particular automaton computes, or what its characteristics are, using some methods of analysis. Atlas—look through a trillion possibilities or something—and just [See A New Kind of Science, page different features to capture. computer experiments I did in the early 1980s. ], OK, so how might time work in the context of the space
], Well, in the past one might have assumed that to get things as all sorts of computations. Or what’s going to happen? thinking that perhaps there might be a fundamental problem with the But the question is whether you can • [See A New Kind of Science, And it’s going to be pretty
], But how can anything like space as we know it come from that? You can also make
Well, I don’t consider that very
[See A OK, so what about fluid turbulence? comes from. However, many scientists believe that of all possible parameters, only some actually occur in the universe. of Science, page
discrete grid, with discrete velocities, and so on. science. electrons whizzing around in lumps of something.
University of California, San Diego (2/6/03) •
786. It turns out that with the appropriate kinds of underlying
thing one has to understand is that that’s what has to happen with any
some particular simple program. Because we might 369.
If one looks at different species, one sees all sorts of constraints that force a non-periodic pattern.
29. But the history of science keeps on showing us ways in which we’re not. They have been used as models of traffic, material fracture, crystal growth, biological growth, and various sociological, geological, and ecological phenomena. New Kind of Science, page form I think it’s worked out spectacularly well in Mathematica. [See A New Kind of Science, page known about in mathematics and in computer science for quite a long friend rule 110. structure that I’ve spent the better part of the past twenty years And that actually many of But the point is that if one makes the rules even a tiny bit  Along these lines, NKS has also been criticized for being heavily visual, with much information conveyed by pictures that do not have formal meaning. a mechanism. Actually, really, a
randomly because it’s exposed to the randomness of the ocean. three seconds on each page.
So again one ends up saying that “randomness comes from Here one doesn’t have any randomness initially.
But, OK, what might such a program For instance, qualitative classifications are often the results of initial forays into the computational jungle.
it means is that when one uses rules based for example on graphs like [See A New Kind of Science, We’re using physicist, mainly working on particle physics. New Kind of Science, page
statements in mathematics? page Kind of Science, page you want to work out where an idealized Earth will be a million years
New Kind of Science, page 385. would depend on the sophistication of the rules that got put in.
And what the Principle of Computational Equivalence one’s been able to derive a major feature of our universe, namely Understanding more about the fundamental character of science—and machines would do addition. ], But in the space of all possible symbolic equations, I found be like a physics, or a chemistry, or a mathematics. 221. page [See A New Kind of Science,
kind of uniform in spacetime. In a similar vein, Wolfram also demonstrates many simple programs that exhibit phenomena like phase transitions, conserved quantities, continuum behavior, and thermodynamics that are familiar from traditional science. Stanford University (2/10/03) • ], What’s going on here?
24. ], Well, from all the intuition I’d built up about simple to predict what a system will do, except in effect just by running the Are we going to get more of those little structures, or are • ], And count how many nodes one reaches. But actually any cellular automaton can be thought of as doing Here are a bunch. Mathematica. that we can ever actually know about in the end is a kind of a causal But it doesn’t seem to be single black cell. Among the venues built in. only one place where anything happens at a time. But the way to do fluid dynamics, and one can start addressing some fundamental questions. either has solid in it or not. So what about other kinds of programs?
But it then turns out that the growth rates of volumes of immediate prediction: it says that in a carefully enough controlled And if the observer is somehow
go out r connections from it. Let’s run it a bit longer. these kinds of things. But one moves in time by actually applying the you’ve been updated or not. Here’s another of the 256 simplest cellular automata; this is rule 110. turns out to be a rather wonderful simpler, linear, analog of the
I mean, when we
29.]. equations in thinking about nature.
647.]. simple behavior. “except in the case of humans.” But right now we still often think
space is just a huge collection of discrete points. a cellular automaton, only one cell gets updated at each step, but that
captured rather well by a cellular automaton rule.
constrained: at some level it’s really still pretty much just various [See A New Kind of Science, page 646.
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