Sep 26, 2022 09:33 PM
https://www.discovermagazine.com/the-sci...-followers
EXCERPT: . . . The basic tenet of Pythagoreanism was that numbers are the essence of everything, as declared in their motto: “All Is Number.” They had some good reasons for looking at things this way. They were the ones who worked out that musical intervals corresponded to the lengths of the strings on a stringed instrument, and they had derived the golden mean, or golden ratio, from examining patterns in nature, such as nautilus shells and the petals of flowers.
As David Foster Wallace explains in Everything and More: A Compact History of Infinity, the Pythagoreans’ “attempts to articulate the connections between mathematical reality and the physical world were part of the larger project of pre-Socratic philosophy, which was basically to give a rational, nonmythopoeic account of what was real and where it came from.” They wanted to figure out how things worked — absent gods with thunderbolts — and everywhere they looked, they found numbers.
Prior to the discovery of the Pythagorean Theorem, the Greeks thought all numbers could be expressed as either a whole number or a fraction — a ratio of two whole numbers. But the Pythagorean theorem blew a big hole in that notion. Hiding in plain sight in the theorem was something very disturbing. If, for example, you look at a right triangle with two sides of 1 inch (or foot, or some such), the hypotenuse is a number the square of which is 2.
So what’s the square root of 2? Something the Pythagoreans couldn’t deal with: an irrational number; that is, a number that can’t be written as a fraction (or ratio). To us, this just means that the math is a bit more challenging (OK, maybe a lot more challenging). To the Pythagoreans, it was a challenge to their entire worldview, which was built on the supremacy, even divinity, of numbers that did not do such weird things.
Of course, now we have all kinds of weird numbers: imaginary numbers, transcendental numbers, the truly disruptive zero, plus quantum mechanics. And we muddle along more or less fine — even managing to make airplanes fly and invent computers... (MORE - missing details)
EXCERPT: . . . The basic tenet of Pythagoreanism was that numbers are the essence of everything, as declared in their motto: “All Is Number.” They had some good reasons for looking at things this way. They were the ones who worked out that musical intervals corresponded to the lengths of the strings on a stringed instrument, and they had derived the golden mean, or golden ratio, from examining patterns in nature, such as nautilus shells and the petals of flowers.
As David Foster Wallace explains in Everything and More: A Compact History of Infinity, the Pythagoreans’ “attempts to articulate the connections between mathematical reality and the physical world were part of the larger project of pre-Socratic philosophy, which was basically to give a rational, nonmythopoeic account of what was real and where it came from.” They wanted to figure out how things worked — absent gods with thunderbolts — and everywhere they looked, they found numbers.
Prior to the discovery of the Pythagorean Theorem, the Greeks thought all numbers could be expressed as either a whole number or a fraction — a ratio of two whole numbers. But the Pythagorean theorem blew a big hole in that notion. Hiding in plain sight in the theorem was something very disturbing. If, for example, you look at a right triangle with two sides of 1 inch (or foot, or some such), the hypotenuse is a number the square of which is 2.
So what’s the square root of 2? Something the Pythagoreans couldn’t deal with: an irrational number; that is, a number that can’t be written as a fraction (or ratio). To us, this just means that the math is a bit more challenging (OK, maybe a lot more challenging). To the Pythagoreans, it was a challenge to their entire worldview, which was built on the supremacy, even divinity, of numbers that did not do such weird things.
Of course, now we have all kinds of weird numbers: imaginary numbers, transcendental numbers, the truly disruptive zero, plus quantum mechanics. And we muddle along more or less fine — even managing to make airplanes fly and invent computers... (MORE - missing details)