Stephen Wolfram quotes

It's always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex. Well, I think we found its secret. It's just sampling what's out there in the computational universe. (Stephen Wolfram)
I had a very selfish reason for building Mathematica. I wanted to use it myself, a bit like Galileo got to use his telescope four hundred years ago. But I wanted to look, not at the astronomical universe, but at the computational universe.
Stephen Wolfram
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, we'd never be able to... know what's going to happen.
Stephen Wolfram
The thing that got me started on the science that I've been building now for about 20 years or so was the question of okay, if mathematical equations can't make progress in understanding complex phenomena in the natural world, how might we make progress?
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.
Stephen Wolfram
Could it be that some place out there in the computational universe, we might find our physical universe?
Stephen Wolfram
I think Computation is destined to be the defining idea of our future.
Stephen Wolfram
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.
Stephen Wolfram
There's a tradition of scientists approaching senility to come up with grand, improbable theories. Wolfram is unusual in that he's doing this in his 40s.
Stephen Wolfram
[In] Ancient Babylon... they were trying to predict three kinds of things.... where the planets would be, what the weather would be like, and who would win or lose a certain battle; and they had no idea which of these things would be more predictable than the other.
Stephen Wolfram
[S]cience has become used to... using the little... pockets of computational reducibility ([A]n inevitable consequence of computational irreducibility... There have to be these pockets ...scattered around.) to be able to find those cases where you can jump ahead. (Stephen Wolfram)
So the thing I realized rather gradually - I must say starting about 20 years ago now that we know about computers and things - there's a possibility of a more general basis for rules to describe nature.
Stephen Wolfram
I'm committed to seeing this project done. To see if within this decade we can finally hold in our hands the rule for our universe, and know where our universe lies in the space of all possible universes.
Stephen Wolfram
Stephen has gone out on a limb. He is proposing a paradigm shift. A new twist on everything.
Stephen Wolfram
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."
Stephen Wolfram
The most important precedents deal with the whole idea of symbolic programming - the notion of setting up symbolic expressions that can represent anything one wants, and then having functions that operate on both their structure and content.
Stephen Wolfram
There are a few very small incompatible changes - I really doubt most people will ever run into them.
Stephen Wolfram
You kind of alluded to it in your introduction. I mean, for the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
Stephen Wolfram
Problem 9. What is the correspondence between cellular automata and continuous systems?
Stephen Wolfram
The fact that the same symbolic programming primitives work for those as work for math kinds of things, I think, really validates the idea of symbolic programming being something pretty general.
Stephen Wolfram
[W]e live... in the pockets of reducibility. ...I should have realized [that] very many years ago, but didn't... [I]t could very well be that everything about the world is computationally irreducible and completely unpredictable, but... in our experience of the world there is at least some amount of prediction we can make. ...[T]hat's because we have ...chosen a slice of ...how to think about the universe, in which we can... sample a certain amount of computational reducibility, and that's... where we exist. ...It may not be the whole story about how the universe is, but it is that part of the universe that we care about and ...operate in. ...In science, that's been ...a very special case ...science has chosen to talk a lot about places where there is this computational reducibility... The motion of the planets can be ...predicted. The... weather is much harder to predict. ...[S]cience has tended to concentrate itself on places where its methods have allowed successful prediction. (Stephen Wolfram)
Well, the first thing to say is that we've worked hard to maintain compatibility, so that any program written with an earlier version of Mathematica can run without change in 3.0, and any notebook can be converted.
Stephen Wolfram
It's clear that we can go further than the quantum mechanics that I've known for the last fifty years.
Stephen Wolfram
What's happened is, for 300 years people basically said, "If you want to make a model of things in the world, mathematical equations are the best place to go. In the last 15 years: it doesn't happen. New models... most often are made with programs, not with equations. ...Was that ...going to happen anyway? Was that a consequence of my particular work and my particular book? It's hard to know for sure. ...Was there a chain of academic references? Probably not.
Stephen Wolfram
[F]iguring out where those pockets [of reducibility] are... is an essential thing... in science. ...If you just pick an arbitrary thing and say, "What's the answer to this question?" That question may not be one that has a computationally reducible answer. ...If you ...walk along the series of questions... you can go down this chain of reducible, answerable things, but if you just... pick a question at random... most likely it will be irreducible. ...When we engineer things, we tend to ...keep in this zone of reducibility. When we're thrown things by the natural world... [we're] not at all certain that we will be kept in this... zone...
Stephen Wolfram