Hidden Markov model: There are some stopping points on the way to infinity

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

The best way to conceptualize Wilson’s renormalization group, said Paul Fendley, a condensed matter theorist at the University of Oxford, is as a “theory of theories” connecting the microscopic with the macroscopic.

Consider the magnetic grid. At the microscopic level, it’s easy to write an equation linking two neighboring arrows. But taking that simple formula and extrapolating it to trillions of particles is effectively impossible. You’re thinking at the wrong scale.

Wilson’s renormalization group describes a transformation from a theory of building blocks into a theory of structures. You start with a theory of small pieces, say the atoms in a billiard ball. Turn Wilson’s mathematical crank, and you get a related theory describing groups of those pieces — perhaps billiard ball molecules. As you keep cranking, you zoom out to increasingly larger groupings — clusters of billiard ball molecules, sectors of billiard balls, and so on. Eventually you’ll be able to calculate something interesting, such as the path of a whole billiard ball.

Quanta Magazine.  When doing particle physics the renormalization finds the stable scale. It sounds a whole lot like picking the proper node on the Markov 3-tuple tree.

In economics this is like finding the economies of scale, the depth of the value chain that can be supported by market size, a scale problem. Useful in studying water flow, avalanches and the immune system.  Botonists use it to scale trees and bushes. I look on the web now and there are a whole set of useful tricks with hidden Markov. It forms the center of the sandbox financial system, plays a key role in AI.

Best of all, the Markov solutions do it without the fake time and space variables. It is all based on Planck's 'actions'.