(Pythagorean tetractys of addition, as interpreted by Robert Fludd, 1626)

The tetractys is a symbol composed of ten dots in an upward-pointing triangular formation. It was a sacred pattern for the school of philosophers who followed the teachings of the Greek sage Pythagoras (lived 6th century BC). They used the tetractys to swear their oaths upon, in much the same way that modern Christians swear oaths upon the Bible.

The Pythagorean oath, as quoted by the Renaissance magician Cornelius Agrippa, is as follows:

"I with pure mind by the number four do swear;
That's holy, and the fountain of nature
Eternal, parent of the mind..."

Some authorities claim that the oath was sworn to the "one who bestowed the tetractys to the coming generations," which might be interpreted to mean the Monad, or the teacher Pythagoras. Probably all three -- God, Pythagoras, and the tetrad -- were in the mind of the individual taking the oath. However, I believe that the oath was primarily focused upon the tetractys itself, as the symbolic blueprint of creation.

Pythagoreans possessed two tetractys, the tetractys of addition (1 + 2 + 3 + 4 = 10) and the tetractys of multiplication (1 + 2 + 3 + [2x2] + [2x2x2] + [3x3] = [3x3x3]). It is easier to understand the tetractys of multiplication by means of a simple diagram.

(Pythagorean tetractys of multiplication)

The 1 at the highest level of the tetractys of multiplication is the Monad, symbolic of perfect unity. According to Theon of Smyrna, it contains the principles of "ratio, of limit and of point." The 2 and 3 on the second level are "prime, incomposite numbers, and measured only by the unit, and are consequently linear numbers." The third level contains the numbers 4 (2 x 2) and 9 (3 x 3), which are the first square numbers (numbers created by the multiplication of a number with itself). They represent the geometric surface or plane. The fourth level contains the numbers 8 (2 x 2 x 2) and 27 (3 x 3 x 3), which are the first cubic numbers (numbers created by the multiplication of a number with itself, then with the number again). Cubic numbers represent the geometric solid. It was held to be of the highest significance that all of the numbers that compose the tetractys of multiplication sum 27, the final number of the symbol (1 + 2 + 3 + 4 + 8 + 9 = 27). Theon remarked that it was with these numbers that Plato constituted the human soul.

Usually when the tetractys is written about, the tetractys of addition is intended. In order to understand why the tetractys was held to be so sacred, you must know that the Pythagoreans believed the entire universe to be composed of numbers, specifically the numbers from one to ten, upon which all higher numbers are based in our familiar decimal system. For Pythagoreans, numbers were not merely indicators of aggregate amounts of things, but living deities, each with its own unique personality and occult powers.

For example, the number five was held to represent the sacred principle of justice, because it occurs in the exact center of the tetractys of addition, as well as in the middle of the single-digit numbers from one to nine, and therefore symbolizes balance and equality. But to the Pythagoreans, five was not merely a symbol but a living being, a spiritual intelligence embodying the active principle of justice wherever it found expression on earth or in heaven. The number five was regarded in a way somewhat similar to the way we look upon the graphic symbol of the scales held in the hand of the goddess Justice, except that five was the goddess herself, not merely a symbol for the goddess.

The number six was looked upon as the principle of holy marriage, since it contained within itself the mathematical formula 2 x 3 = 6. Two was considered the first feminine number, and three the first masculine number. Their sexual union was expressed by the process of multiplication, since by multiplying more is brought forth than the original amount, just as in sexual union, children exceed the natures and abilities of their parents.

The first true number in the Pythagorean system is the number three. Pythagoreans referred to the number one as the monad, and to the number two as the duad. The monad signified perfect unity of all, the duad was the root of all diversity throughout the universe:

"The all-perfect multitude of forms, therefore, they obscurely signified through the duad; but they indicated the first formal principles by the monad and duad, as not being numbers; and also by the first triad and tetrad, as being the first numbers, the one being odd, the other even..." (Thomas Taylor, Theoretical Arithmetic).

Thus the tetractys of addition contains within itself the monad, the duad, the first odd true number, and the first even true number. Odd numbers were held by Pythagoreans to be masculine, and even numbers to be feminine, for reasons which should be obvious upon consideration (evenness was represented by the two legs, oddness by the two legs plus the male penis). The number four, or tetrad, contained within itself all of the principles of the tetractys (1, 2, 3, 4). It is the smallest number that embodies all parts necessary for manifest existence, and for this reason four is the number of the material world.

Musical theory played an extremely important role in the philosophy of the Pythagoreans. The tetractys symbolizes all of the classical tonal divisions of music. "The importance of the quartenary obtained by addition (that is to say 1, + 2, + 3, + 4) is great in music because all the consonances are found in it" (Theon of Smyrna).

When the tetractys of addition was considered in company with the tetractys of multiplication, both combined were held to represent the musical, geometric and arithmetic ratios upon which the entire universe was structured. Man was viewed by Pythagoreans as a full musical chord in the harmony of the music of the spheres. For the benefit of any musicians who may be reading, the chord of man is a fundamental or tonic, its major third, its just fifth, and its octave.

Jewish Kabbalists were strongly influenced by Greek philosophy. They created their own version of the tetractys using the Hebrew letters of Tetragrammaton (IHVH), the divine name of four letters. When these letters on the tetractys are written out in a line and added together, they number ten, and compose a Ten-letter name of God that Agrippa called "the name of Jehovah with ten letters collected" (Three Books of Occult Philosophy, Book II, Ch. 13).

(Kabbalistic tetractys of the letters of Tetragrammaton)

The meaning of Tetragrammaton in the Kabbalah is similar in many respects to the meaning of the tetractys. The Hebrew letters in the name were linked to the four elements -- together, they express manifest existence. The letters are both three and four in number, three distinct letters, yet four letters numerically. In this way they express the first two true numbers of the Pythagoreans. The tetractys is also three and four, in that it has three sides, yet four levels.

The numbers of Tetragrammaton also represented the ten Sephiroth, the emanations of God by which the universe was created. Each Sephirah has its own divine name of power. In a mystical sense, the ten-letter name of God embodies the powers of all those names. When counted together, the letters of the Kabbalistic tetractys total 10, yet when the numerical values of the Hebrew letters are added, they total 72 (10 + [10+5] + [10+5+6] + [10+5+6+5]), an extremely significant number in the Kabbalah. There are 72 divine names in the Shemhamphoresch, and 72 demons were imprisoned by Solomon in a vessel of brass. The 360 degrees of a circle, when divided by 5 yield divisions of 72 degrees.

At first consideration, the tetractys of the Kabbalah appears more complex than that of the Greeks. This is an illusion caused by the modern tendency to regard numbers as all more or less the same, apart from their numerical values. To the Pythagoreans, each number had its unique identity, just as to Kabbalists each Hebrew letter has its unique vital energy and nature. Since both tetrads express the same fundamentals of the process of emanation, there is naturally a great deal of correspondence between the two. Indeed, I have found that the study of the Kabbalah leads to a much deeper understanding of Pythagorean number mysticism, and I recommend the Kabbalah to anyone seeking to learn Pythagorean philosophy.