Change, Order, Randomness

Fascinating, technical.  Implications?

Proof Finds That All Change Is a Mix of Order and Randomness

All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.”

Kevin Hartnett  Senior Writer in QuantaMagazine

Dynamical Systems Mathematics Random Numbers

Imagine a garden filled with every variety of flower in the world — delicate orchids, towering sunflowers, the waxy blossoms of the saguaro cactus and the corpse flower’s putrid eruptions. Now imagine that all that floral diversity reduced to just two varieties, and that by crossbreeding those two you could produce all the rest.

That is the nature of one of the most sweeping results in mathematics in recent years. It’s a proof by Tim Austin, a mathematician at the University of California, Los Angeles. Instead of flowers, Austin’s work has to do with some of the most-studied objects in mathematics: the mathematical descriptions of change.

These descriptions, known as dynamical systems, apply to everything from the motion of the planets to fluctuations of the stock market. Wherever dynamical systems occur, mathematicians want to understand basic facts about them. And one of the most basic facts of all is whether dynamical systems, no matter how complex, can be broken up into random and deterministic elements.

This question is the subject of the “weak Pinsker conjecture,” which was first posed in the 1970s. Austin’s proof of the conjecture provides an elegantly intuitive lens through which to think about all manner of bewildering phenomena. He showed that at their heart, each of these dynamical systems is its own blend of chance and determinism. .... "