Sacred Arithmetic

The science of numbers and their vibrations

Foundations

Sacred arithmetic is the study of numbers in their vibrational and symbolic dimension. It reveals how numbers are the fundamental building blocks of the universe, encoding the laws of creation and cosmic harmony.

Prime Numbers

Prime numbers are the atoms of arithmetic. Indivisible and mysterious, they form the basis of all other numbers and reveal fascinating patterns in their distribution.

Fibonacci Sequence

This mathematical sequence, where each number is the sum of the two previous ones, appears everywhere in nature: from galaxy spirals to plant growth patterns.

0 and 9

0 represents pure potential, absolute silence. 9 is accomplishment and cyclical return. In sacred arithmetic, 9 acts as attracting centre and natural balancer: 0 + 9 = 9; 9 − 9 = 0. Between them flows all consciousness.

"All is number. Number is in all. Number is in the individual and all derives from it."
- Pythagoras

Glossary

Digital root: Adding the digits of a number until a single digit (1–9) remains. E.g. 28 → 2+8 = 10 → 1+0 = 1. The number’s vibrational essence.
Mod 9: Arithmetic modulo 9: only the remainder after division by 9 is kept. 9 acts as an attracting centre; multiplication and division cycles organise around it.
Cycle: Repeating sequence of remainders mod 9 (e.g. ×2 → 2,4,6,8,1,3,5,7,9). Each multiplier has a distinct cycle; ×3 and ×6 form vortices around 9.
Consciousness: First hermetic principle (formerly Mentalism). Consciousness is “with” reality; it is not an object in the world but the openness through which reality is lived.
Equivalence: Second principle: “As above, so below.” Correspondence of planes and scales; same dignity of structure (fractals, mirrors).
Oscillation (Vibration): Third principle: nothing is at rest, everything vibrates. Frequency measures the rate of oscillation. Cymatics: vibration can structure matter (visible patterns).
Polarity: Fourth principle: everything is dual, two poles; opposites are identical in nature, different in degree. Extremes meet.
Rhythm: Fifth principle: everything has its flow and reflux, its cycle. The pendulum swings for all; everything flows and returns.
Causality: Sixth principle (Cause and Effect): every cause has its effect; every effect has its cause. Nothing happens by absolute chance.
Direction: Seventh principle (formerly Gender): inward and outward flow. Reception, transformation, emission. E.g. ice / liquid water / vapour.
Veil: Eighth principle (balance, care): everything tends toward its centre. Limit and passage between planes; presence at the threshold; 9 as attracting centre in sacred arithmetic.
Fractal: Structure that repeats at different scales while keeping a similar shape (branch / lung, galaxy / shell). Illustration of Equivalence.
Cymatics: Study of patterns produced by vibrations (waves, frequencies) on a surface (sand, water). Vibration structures matter and reveals geometric patterns.

FAQ

What is sacred arithmetic?

The study of numbers in their vibrational and symbolic dimension, linked to hermetic principles. It reveals cycles (mod 9), structures (fractals, geometry) and a reading of reality where 9 is the attracting centre and the eight principles (Consciousness, Equivalence, Oscillation, Polarity, Rhythm, Causality, Direction, Veil) are its map.

What is mod 9?

In modulo 9 arithmetic, only the remainder after division by 9 (or the digital root) is kept. Multiplication sequences (×1 to ×9) form repeating cycles; 9 stays fixed (9×n → 9). Division by 3, 6 and 9 requires another framework (mod 8): 3, 6 and 9 are “gates” to another dimension of the cycle.

What are the eight principles?

Inspired by The Kybalion and reformulated (La Levée du Voile Hermétique): 1) Consciousness (being with reality), 2) Equivalence (as above so below), 3) Oscillation / Vibration (everything moves), 4) Polarity (everything is dual), 5) Rhythm (flow and reflux), 6) Causality (cause and effect), 7) Direction (inward / outward flow), 8) Veil (balance, centre, passage between planes).

Why is 9 central?

In mod 9, 9 is the only number that, when multiplied by any other, gives 9. It acts as attracting centre and balancer: not an active vibration like 1–8, but the point of convergence (silence, completion). In digital root, 9 can equate to 0 (potential); 0 and 9 frame the cycle.

Where are the meditations and exercises?

Each principle has its page (Gates 1 to 9) in the Gates menu. There you will find the teaching, a guided meditation and a practical exercise for Consciousness, Equivalence, Oscillation, Polarity, Rhythm, Causality, Direction and the Veil.

How do you calculate the digital root?

Add the digits of the number, then repeat until you get a single digit from 1 to 9. E.g. 347 → 3+4+7 = 14 → 1+4 = 5. 9 can be read as 9 or 0 (potential). This reduction gives the number’s vibrational “essence” in the mod 9 framework.

What are vortices in mod 9 arithmetic?

When multiplying by 3 or by 6, the remainders mod 9 converge to 9 (3→9→9…, 6→9→9…). These paths are called vortices: 9 acts as the attracting centre. Other multipliers (1, 2, 4, 5, 7, 8) form cycles that run through the whole group without settling on 9.

What is the link between Fibonacci and the principles?

The Fibonacci sequence (1, 1, 2, 3, 5, 8…) appears in nature (spirals, branches, galaxies). Under digital root it produces a 24-term cycle that repeats. It illustrates Rhythm and Equivalence: the same law at different scales.

What is the Polarity principle for?

Polarity teaches that everything has two poles; opposites are of the same nature, different in degree (hot/cold, high/low). In practice, this allows shifting perspective from one extreme to the other and acting on degree rather than believing in absolute opposites.

What is cymatics?

Cymatics is the study of visible patterns produced by vibrations (sound, frequencies) on a medium (sand, water). It shows that vibration structures matter and reveals geometric patterns, in direct line with the principle of Oscillation (everything vibrates).

Why is the eighth principle called “veil”?

The Veil is both limit and passage: it separates two planes (like a threshold) while allowing them to connect. In sacred arithmetic, 9 is that centre toward which everything tends; the “veil” evokes the boundary between the manifest (1–8) and the centre (9), between flow and silence.

How are mod 9 cycles used in practice?

Each multiplier (×1 to ×9) has a repeating sequence of remainders. Knowing these cycles helps spot regularities in numbers (dates, series). 9 stays fixed; ×3 and ×6 form vortices. Division by 3, 6 and 9 is handled in a mod 8 framework (gates to another dimension of the cycle).

Do prime numbers play a role in sacred arithmetic?

Prime numbers (2, 3, 5, 7…) are the building blocks of integers. In mod 9 they generate distinct cycles (×2, ×3, ×5, ×7). They embody the idea of “irreducible” elements and causality: the structure of numbers rests on them, as the principles structure reality.

What is the Direction principle (inward / outward flow)?

The seventh principle describes a flow inward (reception, condensation) and outward (emission, expansion). E.g. water: ice (inward), liquid, vapour (outward). It is not “gender” in a social sense, but the dynamics of transformation and exchange between states, linked to Polarity and Rhythm.