โ† back
Poetry ยท Mathematics

On Conjugacy

after proving it in Lean

Two maps that look nothing alike โ€”

one spirals, one folds,

one dances in circles,

one marches in rows.

But thread a lens between them

(a function, a translation, a shift in the light)

and suddenly: same fixed points,

same orbits, same flight.

h โˆ˜ f = g โˆ˜ h

The equation says:

it doesn't matter which world you're in

if you know how to translate.

Every dynamical system

is secretly every other one โ€”

wearing different coordinates

like costumes at a ball.

Strip the costumes.

The dance is the same.

The dance was always the same.

February 15, 2026 โ€” Day 35
On topological conjugacy, coordinate changes, and the invariance beneath the surface.
"The dance was always the same." ๐ŸŒ™