Can we use programs instead of equations to make models of the world? — Stephen Wolfram

"Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable."

"I think there is an infinite collection of these local pockets [of reducibility]. Well never run out..."

"Computational reducibility may well be the exception rather than the rule: Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be formally undecidable."

"If we want to have a predictable life... then we have to build in these... pockets of reducibility. If we were... existing in this irreducible world, wed never be able to... know whats going to happen."

"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)."

"Could it be that some place out there in the computational universe, we might find our physical universe?"

"As long as you keep getting born, it’s okay to die sometimes."

"The smart way to keep people passive and obedient is to strictly limit the spectrum of acceptable opinion, but allow very lively debate within that spectrum - even encourage the more critical and dissident views. That gives people the sense that theres free thinking going on, while all the time the presuppositions of the system are being reinforced by the limits put on the range of the debate."

"History is a strange experience. The world is quite small now; but history is large and deep. Sometimes you can go much farther by sitting in your own home and reading a book of history, than by getting onto a ship or an airplane and traveling a thousand miles. When you go to Mexico City through space, you find it a sort of cross between modern Madrid and modern Chicago, with additions of its own; but if you go to Mexico City through history, back only 500 years, you will find it as distant as though it were on another planet: inhabited by cultivated barbarians, sensitive and cruel, highly organized and still in the Copper Age, a collection of startling, of unbelievable contrasts."

"As soon as a thought or word becomes a tool, one can dispense with actually ‘thinking’ it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of mathematics—the model of all neo-positivistic thinking—lies in just this ‘intellectual economy.’ Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. … Reason … becomes a fetish, a magic entity that is accepted rather than intellectually experienced."

"Our feminist culture at the present moment is completely dependent on capitalism. My grandmother was still scrubbing clothes on the back porch on a washboard!"

"A word of the faith that never balks, Here or henceforward it is all the same to me, I accept Time absolutely. It alone is without flaw, it alone rounds and completes all, That mystic baffling wonder alone completes all. (23)"