The symbolism of the first four numbers of the arithmetic series, [i.e., 1,2,3,4], has an ancient and venerable origin. It goes back to the Pythagorean tetractys, a sacred symbol represented thus: four rows of pebbles, four, three, two, and one:
The geometric form of the symbol is shown below:
ML p.277THE PYTHAGOREAN
TETRAKTYS
Here are some things Walter Burkert has to say about the ancient tetractys:
ML p.277PYTHAGOREAN WISDOM
The kernel of Pythagorean wisdom is the “tetractys,” or “four-group,” made up of the numbers, 1, 2, 3, 4, which add up to 10. They are represented in a pebble figure, in the form of the “perfect triangle”;these four numbers contain not only the basic intervalsfourth, fifth, octave, and double octavebut alsopoint, line, plane, and solid ( Walter Burkert, Love and Science in Ancient Pythagoreanism, p. 72 and pp. 187f. )
ML p.277TETRACTYS CONTAINS THE
SECRET OF THE WORLD
The tetractys, a “tetrad” made up of unequal numbers, is a cryptic formula, only comprehensible to the initiated. The word inevitably reminds us of the trictus, the “triad” of different sacrificial animals. Is the sacrificial art of the seer involving the shedding of blood, superseded by a “higher” bloodless secret? [There is perhaps a hint toward an explanation in the text that says:] “What is the oracle of Delphi?” “The tetractys, that is, the harmony in which the Sirens sing.” The later tradition is more explicit: The “tetrad” of the numbers 1, 2, 3, and 4, which add up to 10 (the “perfect triangle”), contains within itself at the same time the harmonic ratios of fourth, fifth, and octave. The Sirens produced the music of the spheres, the whole universe is harmony and number.The tetractys has within it the secret of the world; and in this matter we can also understand the connection with Delphi, the seat of the highest and most secret wisdom.Later sources speak of[the] mysterious ringing [of the bronze tripod of Apollo] ( Walter Burkert, Love and Science in Ancient Pythagoreanism, p. 72 and pp. 187f. )
ML p.277SECRET OF THE WORLD
FOUND IN NUMBER
The meaning of the shibboleth or symbolon “tetractys” can only be explained in a tentative fashion. In place of that which was connected with it from the beginning, in the form of belief or experience, the later sources give us more and more rationalizations. Some way or other the secret of the world is to be found in number ( Walter Burkert, Love and Science in Ancient Pythagoreanism, p. 72 and pp. 187f. )
ML p.277Well, that gives you just a little sense of the sacred numinosity the ancients attached to the symbol of the tetractys
ML p.278