Sublime
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The real answer is that it’s a space-filling curve, which is the natural consequence of any surface of dimension n growing within a topological space of higher dimension.
This, specifically, occurs because a 2-manifold (the cortex or cabbage sheaves) begins to grow within a 2-sphere (empty “ball”, either skull or outer... See more
Matthew Pirkowskix.comFormation precludes equilibrium, and it’s about how structures or patterns form from simpler or earlier elements. That’s what complexity is about, par excellence, and complexity opens the door to rigorous study of all these questions of formation.
W. Brian Arthur • Complexity Economics: Proceedings of the Santa Fe Institute's 2019 Fall Symposium
but from the study of logic and mathematics. It’s a very weird framework that doesn’t come out of empiricism, but of a certain kind of armchair philosophizing that turned out to be very useful. So the minimality expectations can be dropped. You could have a very, very cumbersome computational system that produces the correct output. So that’s
... See moreW. Brian Arthur • Complexity Economics: Proceedings of the Santa Fe Institute's 2019 Fall Symposium
In his early 20s, in his small college notebook, Newton developed infinite series, the binomial theorem, differential and integral calculus, music theory, and more. Today I showed my Math History students an *exact* copy of that notebook. Exact—down to the last smudge! https://t.co/JjaLt1OqpM
Oldies but goldies: S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, 1988. Lays out the foundations of the level set method for curve and surface evolutions. https://t.co/ntkCUD9yUG https://t.co/NnWDwQPbXb
the exponential increase that occurs when you combine even a small number of possibilities.