⬛ What is a Magic Square?
Magic Square
A magic square is a square grid of numbers in which all rows, all columns and both diagonals yield the same sum. This sum is called the magic constant (or magic sum). It is a mathematical object that has fascinated people for more than 4,000 years — and has been used throughout that time in magic, astrology, occultism and sacred mathematics.
The principle is elegant in its simplicity: take the numbers 1 through 9, arrange them in a 3×3 grid, and ensure that every row, column and diagonal adds up to 15. There is only one solution (apart from rotations and reflections) — and that solution has been known for thousands of years.
But the true depth unfolds when we discover that every classical planet possesses its own magic square, and that the numbers in those squares contain hidden cosmic patterns that magicians and alchemists used for centuries as keys to planetary forces.
Magical Amulets
In the Renaissance magic of Cornelius Agrippa (1486–1535), magic squares were engraved on metal plates as planetary talismans. Each square was crafted on the day and hour of the corresponding planet.
Mathematical Marvels
Mathematically, magic squares are a profound field of research. Euler, Ramanujan and many other great mathematicians have worked on them. The number of possible squares grows explosively with the size of the grid.
☀ The Seven Planetary Squares
In the Western esoteric tradition — codified by Cornelius Agrippa in his De Occulta Philosophia (1531) — each of the seven classical planets has its own magic square. The size of the square corresponds to the planet's position in the cosmic hierarchy:
| Planet | Square | Numbers | Magic Sum | Total Sum | Use |
|---|---|---|---|---|---|
| Saturn | 3×3 | 1–9 | 15 | 45 | Protective amulets |
| Jupiter | 4×4 | 1–16 | 34 | 136 | Prosperity and success |
| Mars | 5×5 | 1–25 | 65 | 325 | Strength and victory |
| Sun | 6×6 | 1–36 | 111 | 666 | The Solar square! |
| Venus | 7×7 | 1–49 | 175 | 1225 | Love and beauty |
| Mercury | 8×8 | 1–64 | 260 | 2080 | Magic and communication |
| Moon | 9×9 | 1–81 | 369 | 3321 | Intuition and dreams |
“The number 666 — the infamous ‘Number of the Beast’ — is simply the total sum of the Solar square: 1+2+3+...+36 = 666. It is not a diabolical number, but the number of the Sun — the source of all life and light.”
— After Cornelius Agrippa, De Occulta Philosophia, Book II (1531)Notice the fascinating pattern: Saturn, the slowest and most distant planet, has the smallest square (3×3), while the Moon, the fastest and closest celestial body, has the largest (9×9). The order of the squares reflects the Chaldean planetary sequence — the same sequence that determines the days of the week.
The Mystery of 666
The number 666, called the “Number of the Beast” in Revelation 13:18, is mathematically nothing other than the sum of all numbers in the 6×6 Solar square: 1+2+3+...+36 = 666. The magic sum of each row is 111, and 111 × 6 = 666. The Church Fathers who considered this number diabolical probably did not know its origin — it is a solar force, connected to the Sun as the source of life, consciousness and cosmic order.
🐢 The Lo Shu Square — The Oldest Magic Square
The oldest known magic square originates from China, circa 2800 BCE, and is known as the Lo Shu (Luo Shu). According to legend, the pattern appeared on the back of a divine turtle that rose from the Yellow River (Lo River) before Emperor Yu, the mythical founder of the Xia dynasty.
Check it yourself:
| Direction | Numbers | Sum |
|---|---|---|
| Row 1 | 4 + 9 + 2 | 15 |
| Row 2 | 3 + 5 + 7 | 15 |
| Row 3 | 8 + 1 + 6 | 15 |
| Column 1 | 4 + 3 + 8 | 15 |
| Column 2 | 9 + 5 + 1 | 15 |
| Column 3 | 2 + 7 + 6 | 15 |
| Diagonal ↘ | 4 + 5 + 6 | 15 |
| Diagonal ↙ | 2 + 5 + 8 | 15 |
Lo Shu = Saturn Square
The Chinese Lo Shu is identical to the Western Saturn square of Agrippa. Two traditions — separated by thousands of kilometres and centuries — independently discovered the same mathematical object and both assigned it cosmic significance. This is a striking example of the Hermetic principle: “As above, so below” — universal patterns manifest everywhere.
The Lo Shu in the Chinese Tradition
In Chinese cosmology, the Lo Shu is the foundation of three fundamental systems:
Feng Shui
The Lo Shu grid is placed over the floor plan of a house to determine the energetic quality of each sector. Each cell corresponds to a life domain: wealth, relationships, career, health, etc.
Ba Gua (8 Trigrams)
The eight outer cells of the Lo Shu correspond to the 8 trigrams of the I Ching — the eight fundamental cosmic principles. The number 5 in the centre represents the earth, the centre, equilibrium.
It is remarkable that the magic sum 15 corresponds to the number of days of the waxing moon (from new moon to full moon) in the Chinese lunar calendar. The number 5 in the centre corresponds to the fifth element in Chinese philosophy: earth, the centre that connects the four other elements (water, wood, fire, metal).
🔬 Prime Numbers — The Irreducible Building Blocks
Besides magic squares, there is another category of numbers that has fascinated magicians and mathematicians for millennia: prime numbers. A prime number is a number greater than 1 that is divisible only by 1 and itself:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...
Prime numbers are the atoms of mathematics: every integer can be decomposed into a unique product of primes (the Fundamental Theorem of Arithmetic). Just as all matter is built from atoms, all numbers are built from primes.
The Mystery of Distribution
Prime numbers follow no predictable pattern. The Riemann Hypothesis (1859) — the most important unsolved problem in mathematics — concerns precisely the question of how primes are distributed. There is a $1 million reward for the solution.
Hermetic Significance
Prime numbers are the irreducible building blocks of creation. They cannot be “broken down” into smaller parts — they are archetypal, indivisible, pure. In the Pythagorean tradition they are the most “masculine” numbers: unbreakable and generative.
“Prime numbers are to mathematics what atoms are to chemistry: the indivisible units from which all complexity is built.”
— Marcus du Sautoy, The Music of the Primes (2003)Notice that the first four primes — 2, 3, 5, 7 — are precisely the numbers most often considered sacred in the Hermetic tradition. Two (duality), three (synthesis), five (the human/Phi) and seven (cosmic completion). These are the irreducible building blocks of cosmic order.
Fill in the Lo Shu Square Yourself & Reflection
- Lo Shu puzzle: Draw a 3×3 grid on paper. Fill in the numbers 1 through 9 so that every row, column and diagonal adds up to 15. Hint: start with the number 5 in the centre. The even numbers go in the corners, the odd numbers on the sides.
- Discovering connections: Compare the Lo Shu square with the Ba Gua diagram of the I Ching. What similarities do you see? How do the 8 outer cells relate to the 8 trigrams?
- Reflection question: The Lo Shu appeared in both China (2800 BCE) and Western magic (Agrippa, 1531). The Saturn square is identical to the Lo Shu. What does this say about the universality of mathematical patterns? How does this relate to the Hermetic Principle of Correspondence?
📋 Summary: What You Have Learned
Magic Squares as cosmic keys
Every classical planet possesses its own magic square — from the 3×3 Saturn square to the 9×9 Moon square. For over 4,000 years they have been used as instruments of magic and meditation.
Lo Shu — universal pattern
The oldest magic square (China, 2800 BCE) is identical to the Western Saturn square — proof that universal mathematical patterns are independently discovered in different cultures.
Prime numbers — atoms of number
Prime numbers are the irreducible building blocks of all numbers, just as atoms are the building blocks of matter. Their distribution remains one of the greatest mysteries of mathematics.
Module 2 of 14