The question
Why would a triangle of ten dots be sacred?
The short answer
The tetractys packed the Pythagoreans’ favourite ideas into one figure: the numbers 1 to 4, their sum 10, and the ratios of musical harmony. Later writers read even more into it.
What science knows
Historical FactLater sources, including Sextus Empiricus and Iamblichus, report a Pythagorean oath “by him who gave our soul the tetractys”, a reference to Pythagoras himself.
For the Pythagoreans, 10 was a perfect number, the completion of counting.
The pattern
Established MathematicsThe tetractys is the fourth triangular number: 1 + 2 + 3 + 4 = 10. Its rows give the ratios 2:1, 3:2 and 4:3, the octave, fifth and fourth of music.
What is still uncertain
Mixed EvidenceBecause the evidence comes from centuries after Pythagoras, what the earliest Pythagoreans meant by it is uncertain. The reading of its rows as point, line, surface and solid appears in later writers.
Why humans find it interesting
Cultural TraditionThe figure was later adopted in other traditions; some Christian Kabbalists arranged the letters of the divine name in a tetractys.
CUE perspective
CUE PerspectiveThe tetractys shows the ancient habit CUE shares: seeing a few small numbers as a key to order.
CUE’s framework is modern and its own, but the instinct is very old.