User:Bradley Klee/Physics Initiative

Overview

Physics is a subject like mathematics, where quantitative knowledge is easy to encode in a simple language of functions and numbers. The goal of the physics initiative is to give the OEIS functionality as a science reference, and to reach a new audience of science students who may have zero initial interest in number theory or integer sequences. We can accomplish this objective simply by finding more inspirational integer sequences and sharing them with as many people as possible.

Case Study: Hamiltonian Periods

The complete elliptic integral of the first kind is a good place to start. The [nice] sequence A002894 is the Hadamard product of [core] sequence A000984 with itself. Both A000984 and A002894 determine differentiably finite power series, but the later is more certainly a [phys] sequence. Since the days of Euler, we have known that the plane-pendulum period-energy function generates the integers of A002894.

As a follow-up to A002894, the OEIS also includes a few Ramanujan sequences: A006480, A113424, and A000897. These pages now list Hamiltonian generating functions, which help to explain hidden geometric dimensions and tangential connections to physics (see also: This Wolfram Demonstration).

Our main accomplishment so far has been the discovery (or at least re-discovery) of A318495 and related sequences (check cross refs if necessary). Years later, it seems no more references have been added to any of these pages disputing priority, but certainly many people past and present would have had the motivation and capabilities to do so (not to mention French or German language skills).

The general problem for plane and sphere curves, as far as I know, has not yet received an accessible description. We would like to see, in some computer language, a reference implementation explaining "how to", if such a general solution is even possible. Then it would be possible to continue the long term plan of designing an algorithm for approximating rotational spectra without reliance upon typical matrix methods.

The Future is always a Mystery

As Billy Ocean lyricised, "when the going gets tough, the tough get going". The same can be said about seemingly intractable problems. But if you have to give up, don't worry, there's plenty more physics questions to go after. More recently, we've become enamored with David Smith's hat tiling, and would like to do more along the lines of Josh Socolar's "Growing Perfect Quasicrystals". The best leads at OEIS so far seem to be A188068 and A275855 (see also: WFR`HatTrialityTrees).

Anyone with interesting physics ideas is welcome to contact me directly.