Gate 134: חע — SYMMETRY

חע

Pillar 5: NUMBER AND PATTERN

[134:1] "Symmetry is what we see at a glance."

[134:2] --- Blaise Pascal

[134:3] "The mathematical sciences particularly exhibit order,

symmetry,

[134:4] and limitation; and these are the greatest forms of the

beautiful."

[134:5] --- Aristotle

[134:6] "God is a mathematician of a very high order."

[134:7] --- Paul Dirac

[134:8] [134:1] The Hebrew חמ (Cham) means "warm"---and

symmetry is the warmth of order, the satisfying balance that makes

structures beautiful.

[134:9] [134:2] Symmetry is what remains the same under

transformation. Rotate a circle, and it looks unchanged: rotational

symmetry. Reflect a face across its midline, and it roughly matches:

bilateral symmetry. Symmetry is invariance---the property that survives

when everything else shifts.

[134:10] [134:3] "Symmetry is what we see at a glance." Pascal

identifies the perceptual power of symmetry. Symmetric patterns are

easily processed; the brain grasps them quickly. Beauty often correlates

with symmetry; we find symmetric faces, symmetric structures, symmetric

arguments more pleasing.

[134:11] [134:4] "These are the greatest forms of the

beautiful." Aristotle links symmetry to beauty. The beautiful is not

arbitrary; it has structure; symmetry is that structure's signature.

The aesthetics of mathematics, of music, of architecture rest upon

symmetries explicit or hidden.

[134:12] [FIGURE 134.1: A snowflake---six-fold rotational

symmetry, each arm mirroring the others, infinite variations within

invariant structure.] [134:5] "God is a mathematician of a very high

order." Dirac found the fundamental laws of physics to be expressions

of mathematical symmetry. The Standard Model is built on symmetry

groups; the forces of nature emerge from symmetry principles; the

universe at its foundations is symmetric.

[134:13] [134:6] Conservation laws derive from symmetries.

Noether's theorem (Emmy Noether): every symmetry implies a conservation

law. Time symmetry gives conservation of energy; spatial symmetry gives

conservation of momentum; rotational symmetry gives conservation of

angular momentum. The deepest physics is the study of symmetries.

[134:14] [134:7] Symmetry in nature: starfish, flowers,

crystals, galaxies. Nature repeatedly produces symmetric forms---not

perfectly (nature is approximate) but recognizably. Evolution favors

certain symmetries (bilateral symmetry in animals); physics favors

others (spherical symmetry in stars). Symmetry is selected.

[134:15] [134:8] Symmetry in art: patterns, repetitions, rhymes,

correspondences. The sonnet has symmetries of structure; the fugue has

symmetries of melody; the mandala has symmetries of form. Art without

symmetry is rare; art is often the creative play with and against

symmetric expectation.

[134:16] [134:9] Hidden symmetry: some symmetries are not

obvious. Supersymmetry (hypothetical) posits a deep symmetry between

fermions and bosons. Broken symmetry (actual) means that the laws are

symmetric but the solutions are not---the universe is messier than its

equations.

[134:17] [134:10] See symmetry. Train your eye to notice

invariance, balance, correspondence. The world is full of symmetries

waiting to be recognized. And when you find asymmetry, ask: what

symmetry was broken? The asymmetric tells the story of the symmetric

that was its origin.

[134:18] See Also: • Gate 121: זל (Zal, "Flow") --- The Gate of

Sacred Geometry (geometric symmetry) • Gate 133: חל (Chal, "Profane")

--- The Gate of Chaos and Order (symmetry as order) • Gate 135: ×—×  ---

The Gate of Asymmetry (symmetry's complement) • Gate 216: מס --- The

Gate of Harmony (symmetry experienced)