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Cosmic

~10^22+. Observable universe, cosmic web, dark energy.

Galactic

~10^15 to 10^22. Galaxies, clusters, filaments.

Stellar

~10^10 to 10^15. Stars, solar systems, nebulae.

Planetary

~10^7 to 10^10. Moons, planets, orbits.

Geographic

~10^2 to 10^7. Mountains, oceans, continents.

Human

~10^-2 to 10^2. Body, senses, tools, buildings.

Cellular

~10^-5 to 10^-2. Cells, organelles, microorganisms.

Molecular

~10^-8 to 10^-5. Molecules, compounds, proteins.

Atomic

~10^-10 to 10^-8. Elements, ions, electron shells.

Nuclear

~10^-15 to 10^-10. Protons, neutrons, nuclei.

Subatomic

~10^-30 to 10^-15. Quarks, leptons, force carriers.

Planck

~10^-35 to 10^-30. The quantum foam. Planck length, Planck time.

Continuum of Scales

The master die. 12 faces spanning Planck to Cosmic. Roll to select a magnitude band — dice of that scale emerge from the field.

Octahedron {3,4}

8 triangular faces, 12 edges, 6 vertices. Dual of cube. Air element. Two pyramids base-to-base. 16 card slots, 160 gem capacity.

Icosahedron {3,5}

20 triangular faces, 30 edges, 12 vertices. Dual of dodecahedron. Water element. The roundest Platonic solid — closest to a sphere. 40 card slots, 400 gem capacity.

Cube {4,3}

6 square faces, 12 edges, 8 vertices. Dual of octahedron. Earth element. The most familiar solid — the die, the building block. 12 card slots, 120 gem capacity.

Tetrahedron {3,3}

4 triangular faces, 6 edges, 4 vertices. Self-dual. The simplest Platonic solid — fire element. 8 card slots (4 faces × 2 sides), 80 gem capacity.

Dodecahedron {5,3}

12 pentagonal faces, 30 edges, 20 vertices. Dual of icosahedron. Cosmos/aether element. Plato said the gods used it to arrange the universe. 24 card slots, 240 gem capacity.

Sacred Number Translation

Every number exists in all three systems simultaneously. Auto-detection by glyph type — unambiguous because each system uses unique characters. SacredNumber.parse() handles decimal, binary, ternary.

Ritual Glyph Interface

Numpad as sacred input device. Vertical axis (2/5/8) = Ternary: ▼△▲. Horizontal axis (4/6) = Binary: ○●. Center (5) = Air/equilibrium. Buffer accumulates glyphs into numbers.

▲△▼ Balanced Ternary

Three digits: Fire(▲/+1), Air(△/0), Earth(▼/-1). Balanced ternary — no sign bit needed, negation flips all digits. 13 = ▲▲▲. Force analysis counts element distribution. The deepest numeral form.

○● Sacred Binary

Two families: Open (□○) and Filled (■●). Shape is value (square=0, circle=1), fill is family. Symbolic reading: grounded/structural vs fluid/cyclical vs balanced.

ℙ Prime Numbers

2, 3, 5, 7, 11, ... Divisible only by 1 and themselves. The atoms of multiplication. Infinite (Euclid). Distributed by π(x) ~ x/ln(x). The fundamental theorem.

Sacred Units

Sacred measurement units — facets, stones, trits. Portal-native units that map to but transcend metric/imperial. The language of sacred quantity.

0 Zero

Additive identity. Multiplicative absorber. Neither positive nor negative. The void from which number emerges. Placeholder, origin, nothing.

ℤ Integers

..., -2, -1, 0, 1, 2, ... Naturals extended with negatives. Closed under addition, subtraction, multiplication. Ring structure.

π Pi

Ratio of circumference to diameter. Transcendental, irrational. Appears in circles, waves, probability, number theory. The most sacred ratio.

φ Golden Ratio

(1+√5)/2. Algebraic irrational. The ratio where whole:large = large:small. Fibonacci limit, phyllotaxis, sacred geometry.

∞ Infinity

Not a number — a concept. Limit behavior, unboundedness. Countable (ℵ₀) vs uncountable (c). Division by zero approaches it. The horizon of number.

- Subtraction

Binary operator. Non-commutative. Identity: 0 (right). Precedence: 1. Also serves as unary negation. The inverse of addition.

1 One

Multiplicative identity. The unit. Neither prime nor composite. Generator of naturals by succession. Unity, individuality, the monad.

* Multiplication

Binary operator. Commutative, associative. Identity: 1. Absorbing: 0. Precedence: 3. Repeated addition. Distributes over addition.

/ Division

Binary operator. Non-commutative. Identity: 1 (right). Precedence: 3. Undefined at divisor 0. The inverse of multiplication.

ℕ Natural Numbers

0, 1, 2, 3, ... The counting numbers. Closed under addition and multiplication. Foundation of arithmetic. Peano axioms. The first infinity.

+ Addition

Binary operator. Commutative, associative. Identity: 0. Precedence: 1 (low). a + b = b + a. The most fundamental combining operation.

ℚ Rational Numbers

p/q where p,q ∈ ℤ, q ≠ 0. Dense in the reals but measure zero. Countable. Field structure. Every ratio of whole numbers.

i Imaginary Unit

√(-1). Extends reals to complex plane. i² = -1. Rotation by 90°. Euler: e^(iπ) + 1 = 0. The orthogonal dimension of number.

^ Exponentiation

Binary operator. Right-associative (2^3^2 = 2^9 = 512). Non-commutative. Precedence: 5 (highest). Repeated multiplication. Growth and decay.

ℝ Real Numbers

The continuum. Rationals plus irrationals. Complete ordered field. Uncountable. The number line. Where analysis lives.

Sacred Number Lattice

Numbers as coordinates — every integer maps to a position in the family lattice. Triads, quads, pentads, hexads. The geometry beneath arithmetic.