Enzymind Labs

"A great vision of science — stretching from Pythagoras' credo "All things are number", to Kepler's ordering of the planets based on Platonic solids, to Wheeler's slogan "Its from bits" — has been that physical reality embodies ideally simple mathematical laws. As physics developed before the quantum revolutions of the twentieth century, the basic equations emphasized dynamics (how given systems evolve in time) as opposed to ontology (the science of what exists). Kepler's system was stillborn, but in the world of QCD and hadrons, the great vision lives and thrives." Frank Wilczek in Particle physics: Mass by numbers

Relationships between recursive sequences and physics

The essence of physics is finding simple patterns that occur naturally. These patterns are applied as broadly as possible and generalized as physical laws. So, for example, gravity under an apple tree (vertical acceleration is constant, no matter the object) is generalized to the moon "falling in its orbit", and further generalized to be universal (the acceleration between two bodies depends in a simple way on their mass and the distance separating them). [To Do: simple graphic illustration]

Are there physical systems that exhibit behavior indicative of simple recursive rules? We might expect to find correlations between spatio-temporal measurements and recurrent sequences like the Thue-Morse or Period-doubling sequences. While periodic patterns are ubiquitous and can be produced by recursive processes, aperiodic patterns are not as easily analyzed. That's not to say that aperiodic patterns and redundancy is not abundant; the most common patterns in nature are not periodic. Fourier analysis is a standard tool for recognizing periodic processes, but there are few analogous tools for discovering even the simplest recursive rules that generate aperiodic patterns.

While not as common as periodic patterns, aperiodicity occurs in several fundamental physical processes.

[To Do: Fibonacci sequences]

[To Do: Period Doubling and phase transitions]

[To Do: Fractal patterns in biology and physics, and analysis tools]

[To Do: Thue-Morse crystals and potentials]

[To Do: Engineered materials]

[To Do: Engineered structures] Using fractal structures for antenna design.

[To Do: QED and QCD calculations are performed on recursive systems of elementary particles.]

Particle physics: Mass by numbers

Frank Wilczek

Nature 456, 449-450 (27 November 2008) | doi:10.1038/456449a

A highly precise calculation of the masses of strongly interacting particles, based on fundamental theory, is testament to the age-old verity that physical reality embodies simple mathematical laws.

[Reference Science commentary, and original article. "Mass without mass" arising from calculation of virtual particle interactions in hadrons.]

References

J.-P. Allouche, Finite automata in 1-dimensional and 2-dimensional physics, Number theory and physics, J.-M. Luck, P. Moussa, M. Waldschmidt (Eds.), Proceedings in Physics, Springer, 47 (1990), 177{184.