[F]iguring out where those pockets [of reducibility] are... is an essential thing... in science. ...If you just pick an arbitrary thing and say, "Wha… - Stephen Wolfram

Problem 9. What is the correspondence between cellular automata and continuous systems?
Cellular automatat are discrete in several respects. First, they consist of a discrete spatial lattice of sites. Second, they evolve in discrete steps. And finally, each site has only a finite discrete set of possible values.
The first two forms of discreteness are addressed in the numerical analysis of approximate solutions to, say, differential equations. ...
The third form of discreteness in cellular automata is not so familiar from numerical analysis. It is an extreme form of round-off, in which each "number" can have only a few possible values (rather than the usual 2¹⁶ or 2³²).

If we describe... heat... the air... it's this temperature, this pressure. That's as much as we can say... People [from the future] will say, "I just can't believe they didn't realize that there was this detail and all these molecules that were bouncing around, and that they could make use of that." ...One of the scenarios for the very long term history ...is the where everything... becomes thermodynamically boring... equilibrium. People say that's a really bad outcome, but actually... it's an outcome where there's all this computation going on... molecules bouncing around in very complicated ways, doing this very elaborate computation. It just happens to be a computation that right now, we haven't found ways to understand... [O]ur brains... and our mathematics and our science... haven't found ways to tell an interesting story about that. It just looks boring to us.

Can we use programs instead of equations to make models of the world? ...[I]n the beginning of the 1980s ...I did a bunch of computer experiments. ...It took me a few years to really say, "Wow, there's a big important phenomenon here that lets... complex things arise from very simple programs." ...[A] bunch of other years go by [and] I start of doing ...more systematic computer experiments ...and find ...that ...this phenomenon ...is actually something incredibly general... [T]hat led me to this... principle of computational equivalence... [A]s part of that process I said, "OK... simple programs can make models of complicated things. What about the whole universe?" ...and so I got to thinking, "Could we use these ideas to study fundamental physics?" ...I happened to know a lot about traditional fundamental physics. ...I had a bunch of ideas about how to do this in the early 1990s. I made... technical progress. ...I wrote about them back in 2002.