The Principle of Computational Equivalents

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Computational reuceability is the ability to reduce the computational effort necessary to find the answer. Lots of systems that are computationally irreducible, in the sense the only way to find out what they'll do is just to run every step and observe them. The system youare trying to predict will seem to you sort of irreducibly complicated. You will be exactly computational equivalent to the system you are trying to predict.

It’s not easy, figuring out the fundamental laws of physics. It’s even harder when your chosen methodology is to essentially start from scratch, positing a simple underlying system and a simple set of rules for it, and hope that everything we know about the world somehow pops out. That’s the project being undertaken by Stephen Wolfram and his collaborators, who are working with a kind of discrete system called “hypergraphs.” We talk about what the basic ideas are, why one would choose this particular angle of attack on fundamental physics, and how ideas like quantum mechanics and general relativity might emerge from this simple framework.

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Stephen Wolfram received his Ph.D. in physics from Caltech. He is the founder and CEO of Wolfram Research, and the creator of Mathematica, Wolfram|Alpha, and the Wolfram Language. Among his awards are a MacArthur Fellowship. Among his books is A New Kind of Science. He recently launched the Wolfram Physics Project.

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