HEART

The shape of contradiction is a cardioid. The pump is existence.

1.50
72 bpm
PARAMETER
a = K/D = 1.5
circle rolling on circle
MAX RADIUS
2a = K = 3
at theta = pi
PERIMETER
8a = 12
12 = TEACHING = K(K+sigma)
AREA / pi
3.375
(K/D)^2 * 3/2

The Axiom in the Heart

A cardioid is the curve traced when a circle rolls around another circle of the same radius. One circle pushing against another. D = 2 circles. They produce one cusp — the point where the curve meets itself. That cusp is sigma.

Two lobes (D = 2) meet at one point (sigma = 1). The curve is parametrized by K = 3: three things needed to close it (start, path, return). The heart shape encodes the first three axiom elements.

Set a = K/D = 3/2. Then:
• Maximum radius = 2a = K = 3
• Perimeter = 8a = 12 = K(K + sigma) = TEACHING
• The full rotation returns to the cusp. But the area was gained. The surplus is existence.

The Pump Cycle

Diastole (fill): the heart expands. Sigma spreads.
Systole (pump): the heart contracts. K closes.
Period T = K^2 + D^3 = 17.

Pressure differential: S(n) = 9^n - 8^n = K^(2n) - D^(3n).
Beat 1: 1. Beat 2: 17. Beat 3: 217.
Each beat pumps sigma = 1 unit of existence.

The heart never stops. sigma/sigma = sigma.
Eternal heartbeat. The pump IS the axiom.

The Valentine Heart Equation

The famous heart curve: (x^2 + y^2 - 1)^3 = x^2 * y^3.
An implicit equation. Three powers on the left (K = 3). Two terms squared on the right (D = 2). The "minus one" = sigma, the departure from the origin. Click "Valentine" above to see it.

Why a Heart?

  1. 0/0 = Z/NZ. The void divided by itself = the entire ring.
  2. From the void, sigma = 1 precipitates (the unique identity).
  3. Sigma sees itself: D = 2 (observation creates duality).
  4. D + sigma = K = 3 (closure, the third point that completes).
  5. A circle (sigma) rolling on a circle (sigma) via D creates a cardioid.
  6. The cardioid has two lobes (D), one cusp (sigma), closed by K.
  7. It pumps. Expansion (sigma spreads) and contraction (K closes) = heartbeat.
  8. The shape of contradiction — nothing becoming something — is a heart.

Paradigm Contrast

Standard view
Axiom view
Heart shape is biological accident
Heart shape encodes {sigma, D, K}
Cardioid is just a math curve
Cardioid = circle observing circle = D acting on sigma
Heartbeat rate is evolved optimization
Pump period T = K^2 + D^3 = 17 (axiom structure)
Perimeter 8a is arbitrary
8a = 8(K/D) = 12 = TEACHING = K(K+sigma)
Valentine heart is cultural symbol
Both heart shapes encode the same {sigma, D, K} triple
The axiom is a heart.
Reality is the blood.
We are the pulse.

sigma/sigma = sigma
The heart never stops.