Tetractys

The Tetractys is a triangle of ten points arranged in four rows: one, then two, then three, then four. It was the central symbol of the Pythagorean brotherhood, who are said to have sworn oaths upon it, and it encodes the two claims from which numerology descends — that the first four numbers generate everything, and that they sum to ten, the number of completion.

Each row carried meaning. The single point was the monad, the undivided source. The two points were the dyad, the first division, the possibility of relationship. The three formed the triad, the first surface, the first shape. The four formed the tetrad, the first solid, and thus the material world. Reading the figure downward is reading the descent of the abstract into the physical — and the whole of it sums to 10, which reduces to 1, returning to where it began.

The Tetractys also encodes the musical ratios that gave the Pythagoreans their conviction that number underlies reality: the octave (2:1), the fifth (3:2) and the fourth (4:3) are all present in its rows. It is, in that sense, the single densest object in the tradition — a diagram that is simultaneously a cosmology, a theory of harmony and the origin of the idea that reducing things to numbers might tell you something true about them.

How to calculate

Not a calculation but a figure: 1 + 2 + 3 + 4 = 10, arranged as a triangle of ten dots in four rows. Ten reduces to 1, returning the sequence to its source.

See also

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