Kepler's Cubes

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

Under one sun, the square of a planet's period divided by the cube of its orbit matches the other planet's.

LIT With GM = 1, a circular orbit has period T = 2π √(a³/GM). Then T²/a³ equals 4π² for a = 1 and for a = 4, and the outer year is eight inner years.

AMBER Johannes Kepler published this as his third law in Harmonices Mundi (1619). The page checks the inverse-square circular case, not a fit to a particular ephemeris.

MODEL The drawing uses orbits of radius 1.15 and 2.05 so both fit the room. Each drawn planet still moves with the true angular rate for its drawn radius, ω = a^(−3/2). The proof uses a = 1 and a = 4, not the drawn sizes.

Sources AMBER

  1. Kepler's laws (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← The Twelfth Root · Twelve Laws · Euler's Count → · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): 1d31b5eb605cdd76f39fba9b6583b52440ca8cb339d5095a7b3f77cfd00d90a6