View source for Symmetry

Symmetry (an often should be presented in its plural form [[symmetries]], as a [[namespace]] or [[wikipedia:Configuration space (mathematics)|configuration space]]) is a term connected to the ideas of [[Invariance]], [[Equivalence]], [[Reversible logic]], and [[Conservation]]. On Page 180 of Lawvere's book<ref>{{:Book/Conceptual Mathematics/OnSymmetries}}</ref>, Felix Klein of Klein bottle suggested a way to study objects using symmetries. Sir William Hamilton also had a one-pager memo that relates [[wikipedia:Quaternion|quaternion]] with the subject of [[symmetry]]<ref>{{:Paper/Memorandum respecting a new System of Roots of Unity}}</ref>. This idea was later discussed in the paper on [[Paper/General Theory of Natural Equivalence|General Theory of Natural Equivalence]] as the foundational paper<ref>{{:Paper/General Theory of Natural Equivalence}}</ref> of [[Category Theory]].

{{:Meta-Rule/Composition}}

Given the [[Meta-Rule|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. 

<noinclude>
=A few excellent tutorial videos on Symmetry so far=
{{:Video/Symmetries, groups and actions}}
{{:Video/Galois theory explained simply}}

=References=
<references/>
[[Category:Invariance]]

==Related Pages==
{{#ask: [[Category:Symmetry]]
|format=ul
}}

[[Category:Symmetry breaking]]
</noinclude>