Symmetry

Symmetry is a term connected to the ideas of Invariance, Equivalence, Reversible logic, and Conservation.

Symmetries as the first Meta-Rule

According to Mathemaniac, symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are:

1. Closure: Symmetrical operations on symmetries always create symmetries
2. Associativity: Symmetries composition with symmetries are symmetries Associative
3. Identity/Unit: Doing nothing is a symmetrical operation
4. Inverse Exists: Symmetrical operations can be undone, and returns to the original symmetry.

A mathematical treatment of this subject was explained by Norm Wilberger in a video.

Given the meta-rule about symmetry, one may consider applying these properties to the manipulation of functions. More specifically, one may utilize some functional programming language to automate the transformation operations to manipulate functions.

Functions as symmetrical objects

This can be implemented using a combination of JavaScript, Cascading Style Sheets, and HTML as a combination of functional programming language, declarative rule engine, and a display mark-up rendering formatting specification language. It would be particularly convenient to manage the interactions of these three kinds of languages using MediaWiki's existing infrastructure.

The two most excellent tutorial videos on Symmetry so far

{{#ev:youtube|EsBn7G2yhB8}} Galois Theory provides a computational framework for studying symmetry. |Ct2fyigNgPY}}