From 5076caa470a200ab4fa66bb4656e63d0a559af69 Mon Sep 17 00:00:00 2001 From: teahubxyz Date: Tue, 27 Oct 2026 23:53:55 +0000 Subject: [PATCH] wick: narration script (sphere, plane, sphere: the four Wick turns) Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_01FAqjv3n4yABxvJPJHFRhVA --- src/wick/script.json | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 src/wick/script.json diff --git a/src/wick/script.json b/src/wick/script.json new file mode 100644 index 0000000..81fdd1e --- /dev/null +++ b/src/wick/script.json @@ -0,0 +1,9 @@ +[ +"Every unit quaternion is a point on a three dimensional sphere. We can't see four dimensions, so we project, from the point minus one, into our space. The pure imaginary quaternions, i, j, k and everything in between, land on an ordinary sphere. This is the sphere we'll watch.", +"Multiply on both sides, q times p times q inverse, and the sphere rotates. Lock the two factors together and that is all it can ever do: spin in place. The sphere never leaves itself.", +"Now multiply on one side only. p goes to q times p, with q turning, e to the i theta. Watch. The sphere drifts, swells, and passes through the very point we project from. At the quarter turn it is a plane. Not a different object. The same sphere, with one point sent to infinity.", +"Keep turning. At the half turn it is a sphere again, but inside out: every point has gone to its opposite. At three quarters, a plane again, facing the other way. At the full turn, home. Four quarter turns: sphere, plane, sphere, plane, sphere. That is the Wick cycle.", +"A plane is a chart: a picture of the sphere with one point missing. The sphere is the whole thing. So passing from the plane phase to the sphere phase means putting the missing point back: making an affine picture projective. That is exactly what analytic continuation does.", +"Now draw latitude and longitude on the sphere about the j axis, and go to the plane phase. The grid becomes circles nested around minus one and one, with arcs swinging between them. Shrink it by a half and slide it by a half, and that is the picture zeta draws: poles on zero and one, the equator on the critical line.", +"One more piece. Zeta's far hemisphere is not quite the mirror of the near one. It is the mirror, dressed by a gamma factor. Fold that factor in and you get xi, which lives on the sphere cleanly, with the half turn as its symmetry. Sphere to plane is continuation. The gamma factor is the fare for the trip." +]