I'm reading this book by Charles Seife called Zero: The Biography of a Dangerous Idea, and it should be mandatory reading for every adult who's in a position to 1) lock someone away, 2) impose a death sentence, or 3) inflict any kind of punishment, because it demonstrates just what kind of clowns we can be when we find an idea threatening to our settled way of thinking. Humans are capable of some pretty terrifying acts of violence when something threatens their worldview. Last night I went to go see "The Imitation Game" with my parents, a movie about how Allan Turing invented the computer during World War II under massive pressure. His job was to decode the German's encrypted messages that got radioed to their warships every day. After successfully decoding their messages, the war ended, and he went home, only to be convicted of being a homosexual. He had to take hormonal therapy to reverse his preferences, which led to his committing suicide. We sure have perfect vision in hindsight, but at the time, we feel like we're being completely rational.
Speaking of being rational, in studying the Enneagram, I've come across Pythagoras a few times, and I just assumed he was this wise old man with a long beard who did math and geometry all day and taught his students about the spiritual quality of numbers. It turns out he did a lot more than sit around and stoke his beard and think about numbers- there was an ugly side to him, and I don't mean his hypotenuse side. He sentenced one of his own students, Hippassus of Metapontum to death by drowning (so the legend goes) for revealing to "the outside world" that irrational numbers were a mathematical possibility.
It was a discovery completely at odds with the spirituality of the brotherhood- their entire worldview-- not to mention their understanding of their own role in the world-- was based on being able to make sense mathematically of their universe.
For everything in the universe to be govered by ratios, as the Pythagoreans hoped, everything that made sense in the universe had to be related to a nice, neat proportion. It literally had to be rational. (pg. 35).
As Greek scholars tended to be interested in mathematics-- having learned their math from the Egyptians who were also leaders in science, but moreso in geometry-- many of them studied ratios and "the interchangeability of math, music, and nature". To them, perfect ratios were a way to connect to divinity. Even the planets, in their minds, made music in perfect fifths- the most harmonious ratio in music- as they rotated around the earth (that's where the music of the spheres comes from). So when Hippassus got out a really tiny ruler and realized that the diagonal line connecting two inner corners of a perfect square can't exactly be plugged into an a/b ratio where a and b are commensurable (able to be meaured by a comon yardstick), it didn't make sense.
Irrationality was dangerous to Pythagoras as it threatened the basis of his ratio-universe. To add insult to injury, the Pythagoreans soon discovered that the Golden Ratio, the ultimate Pythagorean symbol of beauty and rationality, was an irrational number. To keep these horrible numbers from ruining the Pythagorean doctrine, the irrationals were kept secret. Everyone in the Pythagorean brotherhood was already tight-lipped - nobody was allowed even to take notes - and the incommensurability of the square root of two became the deepest, darkest secret of the Pythagorean order.." (pg. 37).
Let this be a lesson to everyone in power, or who has any measure of power over anyone- to sure, be bold about our opinions, but to hold them loosely. We might end up being the next judge who sentences the next Allen Turing to hormonal therapy, or Pythagoras who makes a massive mistake in discounting irrational numbers.