God is a baker

Making dough is one of the most mathematical things you can do in the kitchen, far beyond measuring out ingredients. As you fold and compress dough you are carrying out topological deformations. The act of kneading constitutes an operation that has been canonized in chaos theory as the Baker’s Map, in which the mixing of a dynamical system arises from a map of that system onto itself and carried out many times over.

Mixing is a chaotic but not a random act. It occurs because of nonlinear self-interactions in a system that cause the system to reshape itself so completely that, over enough iterations, every possible configuration of the system’s matter will be reached. This is critical to an area of mathematical physics called ergodic theory —the theory that underlies much of statistical physics.

This is not without constraints of course. The atoms won’t experience nuclear fusion or spread out to distant lightyears unless that is part of how you defined the system. Yet, mixing will ensure that something like dough will not only reach its maximal entropy but the total huge collection of molecules in the dough will go through every possible permutation given enough time. And, even if not given enough time, they will statistically appear as if they were.

In our universe, mixing is one of the most fundamental operations, far more than randomness which, at its core, is the result of mixing at many different length scales. For example, the length scale of the size of the cut to be made as in this picture determines the largest scale. And the mixing is pushed down from the top length scale down to smaller ones by the squashing, so that all length scales are ultimately affected

What does that mean?

The basic idea is that a Baker’s map, carried out an infinite number of times in a chain (see Gaspard), has no predictability to it at all and all components are shuffled so completely as to be random.

Stochastic systems occur when you add a random process like this to a deterministic process, like an oscillating spring or a ball rolling down a hill. The deterministic process provides the overall motion, while the…

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