A new kind of science

A new kind of science - Stephen Wolfram

  (This is the first of a series of posts related to next week’s tenth anniversary of A New Kind of Science. The second covers what’s happened since it was published, and the third its future.)   On May 14, 2012, it’ll be 10 years since A New Kind of Science (“the NKS book”) was published. After 20 years of research, and nearly 11 years writing the book, I’d taken most things about as far as I could at that time. And so when the book was finished, I mainly launched myself back into technology development. And inspired by my work on the NKS book, I’m happy to say that I’ve had a very fruitful decade (Mathematica reinvented, CDF, Wolfram|Alpha, etc.). I’ve been doing little bits of NKS-oriented science here and there (notably at our annual Summer School). But mostly I’ve been busy with other things. And so it’s been other people who’ve been having the fun of moving the science of NKS forward. But almost every day I’ll hear about something that’s been being done with NKS. And as we approach the 10-year mark, I’ve been very curious to try to get at least a slightly more systematic view of what’s been going on. A place to start is the academic literature, where there’s now an average of slightly over one new paper per day published citing the NKS book—with that number steadily increasing. The papers span all kinds of areas (here identified by journal fields): And looking through the list of papers my main response is “Wow—so much stuff”. Some of the early papers seem a bit questionable, but as the decade has gone on, my impression from skimming through papers is that people are really “getting it”—understanding the ideas in the NKS book, and making good and interesting use of them. There are typically three broad categories of NKS work: pure NKS, applied NKS, and the NKS way of thinking. Pure NKS is about studying the computational universe as basic science for its own sake—investigating simple programs like cellular automata, seeing what they do, and gradually abstracting general principles. Applied NKS is about taking what one finds in the computational universe, and using it as raw material to create models, technology and other things. And the NKS way of thinking is about taking ideas and principles from NKS—like computational irreducibilityor the Principle of Computational Equivalence—and using them as a conceptual framework for thinking about things. And with these categories, here’s how the academic papers published in different types of journals break down: So what are all these papers actually about? Let’s start with the largest group: applied NKS. And among these, a striking feature is the development of models for a dizzying array of systems and phenomena. In traditional science, new models are fairly rare. But in just a decade of applied NKS academic literature, there are already hundreds of new models. Hair patterns in mice. Shapes of human molars. Collective butterfly motion. Evolution of soil thicknesses. Interactions of trading strategies. Clustering of red blood cells in capillaries. Patterns of worm appendages. Shapes of galaxies. Effects of fires on ecosystems. Structure of stromatolites. Patterns of leaf stomata operation. Spatial spread of influenza in hospitals. Pedestrian traffic flow. Skin cancer development. Size distributions of companies. Microscopic origins of friction. And many, many more. One of the key lessons of NKS is that even when a phenomenon appears complex, there may still be a simple underlying model for it. And to me one of the most interesting features of the applied NKS literature is that over the course of the decade typical successful models have been getting simpler and simpler—presumably as people get more confident in using the methods and ideas of NKS. Of NKS-based models now in use, the vast majority are still based on cellular automata—the very first simple programs I studied back in the early 1980s. There’s been some use of substitution systems, mobile automata and various graph-based systems. But cellular automata are still definitely the leaders. And beginning with my work on them in the early 1980s, there’s been steady growth in their use for nearly 30 years. (Notably, the numbers of papers about them firmly overtook the number of papers about Turing machines around 1995.)