If you think about things that happen, as being computations... a comp — Stephen Wolfram

"Thats... the big discovery of this principle of computational equivalence of mine. ...This is something which is kind of a follow-on to Gödels theorem, to Turings work on the ... that there is this fundamental limitation built into science, this idea of computational irreducibility that says that even though you may know the rules by which something operates, that does not mean that you can readily... be smarter that it and jump ahead and figure out what its going to do."

"Its 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. Its just sampling whats out there in the computational universe."

"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."

"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."

"[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."

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

"The absolute requisites for the study of this work... are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry. ...A. De Morgan. London July 1, 1836"

"A free people will always refuse to put up with preventable poverty. If freedom is to be saved and enlarged, poverty must be ended. There is no other solution. The problem of how to prevent these three forces from coming into head-on collision is the principal study of the more politically conscious Conservative leaders. How can wealth persuade poverty to use its political freedom to keep wealth in power? Here lies the whole art of Conservative politics in the twentieth century."

"A clear prediction in an area undergoing vigorous study permits doctrines to be subject to disproof. The last posture a bureaucratic religion wishes to find itself in is vulnerability to disproof, where an experiment can be performed on which the religion stands or falls."

"Spencer argued in a very articulate way for the communality of these processes of self-organization, and used his ideas to make a theory of sociology. However, he was not able to put these ideas into mathematical form or argue them from first principles. And no one else has, either — doing so is perhaps the central problem in the study of complex systems."

"The commercial exploitation of the web has become a growing facet of the world economy, particularly in the last several years. In June 1999 NUA Internet Surveys estimated that 179 million people are connected to the Internet worldwide. A recent study by the sponsored by estimated that the "Internet Economy" generated $300 billion in revenue in the United States alone."

"In biology the Cartesian view of living organisms as machines, constructed from separate parts, still provides the dominant conceptual framework. Although Descartes simple mechanistic biology could not be carried very far and had to be modified considerably during the subsequent three hundred years, the belief that all aspects of living organisms can be understood by reducing them to their smallest constituents, and by studying the mechanisms through which these interact, lies at the very basis of most contemporary biological thinking. This passage from a current textbook on modern biology is a clear expression of the reductionist credo: One of the acid tests of understanding an object is the ability to put it together from its component parts. Ultimately, molecular biologists will attempt to subject their understanding of cell structure and function to this sort of test by trying to synthesize a cell."