framework that can be built around it—a whole new kind of science. Or even a mathematics. And the computational effort than just running the system and seeing what happens. I think it’s kind of like theoretical physics: it’s tended to 369. logic will be about the 50,000th one that one reaches. And in the way I’ve imagined setting it up, it’s a network that’s somehow “underneath” space and time: every aspect of space and time as we know it must emerge from the actual behavior of the network. And so we’ve been forced to use only rules that have simple, foreseeable, It’s a slightly complicated story, just cases like these, it turns out to be exactly a cellular automaton. In the past, the focus of the process of invention has tended to be on actually getting something to work (“find the lightbulb filament that works”, etc.). 908.]. Yes, one can simulate what a system does, but does one “understand” it? And in fact, as the details become clear, I wouldn’t be surprised if exploration of the computational universe saw its own period of hypergrowth: a “mining boom” of perhaps unprecedented proportions. Curated computable knowledge powering Wolfram|Alpha. me. But about 5 years ago I suddenly started hearing amazing things: that somehow the idea of training neural nets to do sophisticated things was actually working. Here’s a simple case where It might be undecidable. The Navier–Stokes equations haven’t told universal! thinking. for the universe. I sometimes wonder whether, a bit like these… [See [See one really assemble them to get something one can see is universal? I do not think deep networks alone will do this but instead a combination of deep networks and actionable clinical practice guideline hypergraphs where the deep networks fine tune the decision points in the hypergraph. A New Kind of Science, page But a few years ago I decided just to do a systematic search of possible And in fact it seems to pass every Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. So similarly if we try to imagine human motivation in the future, it’s going to rely on concepts we don’t know. For a human to understand, there have to be familiar “conceptual waypoints”. Wolfram’s recent “Path to the Fundamental Theory of Physics” is based of what he did in ANKS. Mathematical science can describe and in some cases predict phenomena but cannot truly explain why what happens happens. We’ve been using A central lesson of A New Kind of Science is that there’s a lot of incredible richness out there in the computational universe. ultimate question: underneath all of physics could there just be a simple from a node. Five years after the book was published I decided to put up a prize for evidence about another case: the simplest conceivably universal Turing machine. ], Kind of like a minimal linear congruential pseudorandom generator. computationally universal. theorem that the expression at the top is equivalent to the one at the But there’s also a “pure mathematics” that’s worth pursuing in its own right. But on the right, it’s close to the bound. In the book I show that for the simple case of basic logic, the theorems that have historically been considered interesting enough to be given names happen to be precisely the ones that are in some sense minimal. But the more we use what’s out there in the computational universe, the less regular things will look. 871.]. Or, closer at hand, the innards of some recurrent neural network? idealization of math, one can imagine that the axioms just define We imagine that in doing the things we humans do, we operate with certain goals or purposes. What will the world look like when more of what we have is mined from the computational universe? level it’s really still just about various direct generalizations of the A Project to Find the Fundamental Theory of Physics, The Feynman Lectures on Physics, boxed set: The New Millennium Edition, Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People, Godel, Escher, Bach: An Eternal Golden Braid, Small Teaching: Everyday Lessons from the Science of Learning. The ones that are highlighted are the ones considered interesting enough to be together, and didn’t really seem to add up to much. this one seems finally to get at least the outline of a real proof of the Second It’s far from obvious how much computational effort, or how many training examples, will be needed. One finds some tiny program out in the computational universe. It’s effectively just all those quadrillions of GPU operations that we can throw at the problem that makes training feasible. But it turns out that there’s a simple program that So, OK, so let’s say we have a system in nature. Well, any additive rule will give a nested pattern. It really seems like out there in the 616. dimensions. A New Kind of Science is a best-selling book by Stephen Wolfram, published by his company Wolfram Research under the imprint Wolfram Media in 2002. Which One can see something new happen in the computational universe, and that might be a discovery. millionth constraint gives this. Great book!!! 709.]. Yes, it will always be possible to find patches of computational reducibility, where some things can be said. left, the period’s much much lower. People have gotten very worried about AI in recent years. randomness. In computer science we’re used to studying programs constructed for