THE PARITY OPERATOR space, mirror-flipped — an involution that physics almost obeys
Parity is the operation that mirror-flips space: P: x → −x (here, reversing a list). It is an involution — P·P = identity — so its eigenvalues are ±1: functions are even (parity +1, unchanged) or odd (parity −1, negated). For decades physics was assumed parity-symmetric — the laws the same in a mirror — until Wu's 1956 experiment showed the weak force violates parity: the mirror world is not quite our own. It is the deepest fact in the batch: a symmetry everyone believed was exact turned out to be broken, and the breaking is why there is a difference between left and right at all.
THE TECHNIQUE P: x → reverse(x); P·P = identity (an involution); eigenvalues ±1
The demo applies parity (reversal) twice and recovers the original — an involution, P·P = id: live demo
HISTORY & CREDIT Lee & Yang · Wu 1956
“The laws of physics are the same in a mirror.” — not the weak force: Wu's 1956 experiment found parity violation. The mirror world is subtly not ours. cited
the operator · P: x→−x; P²=1 — an involution, eigenvalues ±1 (even/odd). 1956 · Lee & Yang proposed, Chien-Shiung Wu demonstrated — the weak force violates parity (Nobel to Lee & Yang, 1957). the batch · parity is reflection (dart 399) as a physical operator; a self-inverse.
Mirror space, mirror it again, and you are home — an involution physics almost, but not quite, obeys. The symmetry that broke. Wu 1956
RECOMMEND FOR I-13 the involution, on the compiler
On the canonical compiler, applying parity (reversal) twice returns the original (involution=1):
$ i13 run sy_parityoperator.i13 # P(P(x)) == x ?
RUN OK · 269 step(s) · peak stack 6 · call depth 4
involution = 1 -- P.P = identity ; eigenvalues +-1 (even / odd)
Recommend: the parity operator is reflection made physical — an involution (P²=1) splitting the world into even and odd — and i13 confirms P·P=id. Not a keeper (it is the self-inverse axis, CRC/Verlet, as an operator). But the batch's deepest dart: the symmetry everyone assumed exact, broken by the weak force (Wu, 1956) — which is why left and right are genuinely different, not just labels.