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"This remarkable equation is why people move to the big city," West says. "Because you can take the same person, and if you just move them to a city that's twice as big, then all of a sudden they'll do 15 percent more of everything that we can measure." While Jacobs could only speculate on the value of our urban interactions, West insists that he has found a way to "scientifically confirm" her conjectures. "One of my favorite compliments is when people come up to me and say, 'You have done what Jane Jacobs would have done, if only she could do mathematics,' " West says. "What the data clearly shows, and what she was clever enough to anticipate, is that when people come together, they become much more productive."

OK, this post is already way too long, but one final thing. Physicists, I think, become even more drawn to economics when we look into economics and see broad resistance to research pursuing this "complexity" perspective. It seems instead that most of mainstream research tries to get around system complexity with mathematical tricks, rather than facing up to it. I'm thinking about ideas like representative agents, or rational expectations. The assumptions make it possible to build models without having to deal with the complexity of interactions and the emergent structures they create; but the resulting models, naturally, look very pale and questionable as models of anything real. When physicists see that a small minority of ("heterodox") economists also find the standard approach hugely limiting, they feel an urge to help out. And they believe that some of their ideas can help.

This site is designed for people interested in complex systems and complex dynamical processes. Complexity Explorables hosts different collections of interactive illustrations of models for complex systems in physics, mathematics, biology, chemistry, social sciences, neuroscience, epidemiology, network science and ecology. Topics include pattern formation, synchronization, critical phenomena, chaotic dynamics, evolutionary dynamics, fractals, collective behavior, reaction-diffusion systems and more.

This blog is part of the economics project of the London Mathematical Laboratory. We're re-deriving formal economics without making the ergodicity assumption. That means questioning 350 years of scientific history, and of course much it is quite technical. But beyond the technical side, we've found that this generates a broad perspective, a culture maybe, that seems worth sharing.

Feeding The World--With Math http://ift.tt/2aQVpxH