Is the world made of numbers?

That time, that place

Croton was a Greek colony in southern Italy. What Pythagoras founded was as much a religious community as a school: vegetarian, disciplined, sworn to secrecy. To them, number was not a tool but something sacred.

Why this question

It began, they say, with music. Stop a taut string exactly halfway and it sounds an octave higher. Divide it two to three and another pleasing interval appears. Behind what the ear calls beautiful sat a simple ratio of whole numbers.

What was found

Then perhaps the whole world is made of number — this became the school's creed. The constant relation among the sides of a right triangle was studied inside that creed. Egypt and Babylon had used the relation already; what this group asked was why it must always hold.

And then they dug up a problem with their own hands. The diagonal of a square with sides of one cannot be written as any fraction at all. They believed the world was made of number, and had found a length no number could write.

Terms on this card

Irrational number