The Tetractys is a triangular figure of ten points arranged in four rows, equivalent to the fourth triangular number. It was considered sacred by the ancient Pythagoreans of yore.
- "The Tetractys symbolized the four elements—earth, air, fire, and water.
- The first four numbers also symbolized the harmony of the spheres and the Cosmos.
- The four rows added up to ten, which was unity of a higher order (in decimal).
- The Tetractys represented the organization of space:
- The first row represented zero-dimensions (a point)
- The second row represented one-dimension (a line of two points)
- The third row represented two-dimensions (a plane defined by a triangle of three points)
- The fourth row represented three-dimensions (a tetrahedron defined by four points)"
An unfortunate consequence of the ubiquity of this figure in certain esoteric traditions is that it has served—along with a nebulous collection of other symbolic associations with the decad—to justify modern society's ill-conceived decimal notation systemt. I cannot think of a single reason why these two issues should be related, given the fundamentally practical nature of positional notation and the self-evident unsuitability of base ten for this purpose. However interesting and pertinent the Tetractys may be to certain archetypal affairs, it does not seem to have any relevance to the issues that make an effective and practical positional notation radix—factorability, et cetera. Nonetheless, the fact that when one "counts to ten" one "goes back to one" is often cited as pertinent to the cosmic significance of the Tetractys. This is of course patently absurd.
The lines are added to highlight the hexagonal nature of the arrangement—the figure itself consists only of the ten points.