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The Pythagoreans’ most profound discovery was a link between numbers and the real world: things could be described by numbers, and numbers described by things. Unfortunately, they made the mistake of believing in something a little more extreme: that numbers are things and that things are numbers. And while this seemed to make sense in most cases, they eventually found that some numbers simply didn’t add up.

Making use of their ever-so-famous Pythagorean Theorem, the Pythagoreans found that if the two legs of a right triangle were both 1, then the hypotenuse must be the square-root of two.

What the hell?” they said.

The square-root of two is 1.41421356… It continues indefinitely. It cannot be defined outside of the statement “the square-root of two” and is completely and utterly irrational. This was a problem, because if such a number did exist, then something in the real world must exist that is equivalent to it. And if the basis of human reason, rationality, is broken (or, if something in the world is irrational), then there must be some irrationality to man in correspondence with irrationality in nature.

In other words, who are we when we cannot be defined? And what can something undefined really know about itself, or anything for that matter?

Well, even though the Pythagoreans suspected the numbers might not exist in the real world, they feared where the numbers did exist. What if these irrational numbers were maybe some door into chaos and oblivion, or signs of some malevolent god? In essence, it scared the shit out of them, and so they simply stopped thinking about them. They didn’t deny irrational numbers, but they wouldn’t touch them with a ten foot pole.

This check in knowledge has been commonplace throughout history. We constantly come to lines that we aren’t sure whether to cross or not. The reason for this? Pandorra’s Box. When you discover something, it doesn’t just go away. This happened in the early 20th century with nuclear weaponry, and it’s happening now with the human genome and nanotechnology. Will we become genetically selective, conditioning our children and oblitering the less-perfect humans? Will nanodust be released and destroy life on earth?

What the future holds is hard to predict. What we stare in the face now is not so different from what the Pythagoreans faced 25 centuries ago. The difference is: they drew a line. And though we no longer fear irrational numbers, some wonder: should we worry about this Brave New World, or these little robots of death?

A slightly less well-known bit of Pythagorean goofiness was their elitism about the dodecahedron. The dodecahedron is probably the least intuitive of the five Platonic solids, and when the Pythagoreans figured out that it can exist, they got a little goofy about it. They were already sort of mystical about their numbers, and they assigned elements to each of the five aforementioned solids. The thing was, they didn't tell anybody outside of the cult about it, you only learned about it if you reached the Pythagorean Thirty-Third Degree or something. Apparently they thought that all hell would break loose if the great unwashed knew that you could build a twelve-sided polyhedron out of regular pentagons.

Carl Sagan said that one guy tried to publish the existence of the dodecahedron - however that was done in a paper-minimal society - but was suppressed and thrown out of the Pythagorean cult. Later, the guy died in a shipwreck, and people in the cult said that he only got what was coming to him. The similarity of this story to legbagede's seems to indicate that either people drowned at sea regularly, or that the Pythagorean cult has reached mythical status.

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