The Legend of Hippasus
There was once an ancient Greek geometer named Hippasus who belonged to the Pythagorean Brotherhood. The Pythagoreans were a school of philosophers who held a special reverence for numbers and proportion. To these men, mathematics was more than just a method for quantifying and describing the world around them. The Pythagoreans held that numbers, themselves, were divine things, worthy of awe and worship. Relationships between these numbers– what we would now think of as a “proportion” or “ratio” of numbers– were intensely studied, as these proportions were thought to hold the secrets of the cosmos. If one were to divide a string according to some specific ratios, he could produce beautiful music. If one compared the proportions of two legs of a triangle, he could come to understand the remaining leg. Nothing in existence was more beautiful to the Pythagoreans than the discovery of these proportions and the properties they endowed.
Occasionally in their calculations, the Pythagoreans would happen upon a proportion that was mysterious, to them. Discovering the exact ratio of numbers between these mysterious proportions was a delight and a treasure for members of the Brotherhood. Such finds were celebrated and lauded, and therefore these mysteries were pursued with diligent hearts. Hippasus was working on just such a problem. The particular case that Hippasus was attempting to resolve was actually a very common proportion, but its exact calculation had stumped many great minds for quite a long time. If he could discover the ratio behind this proportion, he would be guaranteed fame and glory amongst his brethren. So, Hippasus dedicated himself entirely to this pursuit, not even resting from his work while he travelled. And it just so happened that, while sailing across the Mediterranean, Hippasus discovered his answer.
But, it was not the answer he had expected.
Hippasus had been trying to find a ratio between two numbers which would describe his problematic proportion; but the answer that he discovered was that no such ratio could possibly exist. The number was, quite literally, irrational. This discovery was revolutionary. One of the principle tenets of the Pythagorean philosophy was the fundamental universality of these ratios. According to their beliefs, everything in the universe should be able to be described as a ratio between two numbers. And here, Hippasus had proven that there existed certain proportions which could not possibly be described rationally. Excited and thrilled at his discovery, Hippasus sprinted across the deck of the ship, yelling to his brothers about his breakthrough. But when they heard his claim, the Pythagoreans were appalled. In their eyes, Hippasus was not only preaching heresy, he had definitively PROVEN his heretical claim. Where Hippasus had expected to be met with praise and celebration, he instead found fear and denial and anger. The other Pythagoreans soon built into a murderous rage, and their curious brother became the target of their ire.
For the transgression of discovering the truth, Hippasus was thrown overboard and drowned in the waters of the Mediterranean Sea.
Now, this legend likely never actually happened, historically. The tale I’ve told expands quite a bit above and beyond what can be pieced together from ancient historians, and even those bits which I’ve accurately retold remain dubious, at best. But, as in any parable, the truth to be found in this story has nothing at all to do with whether or not it actually occurred, as written. There is a moral– a meaning to be discovered– in the text of the tale. And in the case of poor Hippasus, I have attempted to illustrate the dangers of constructing dogmatic views of reality based upon unjustified beliefs.
Throughout history, such dogmatism has often found itself in harsh opposition to evident reality. When Galileo Galilei showed the validity of the heliocentric model, he was arrested and threatened by men who believed, without ample justification, that the Earth must be the center of the universe. When Charles Darwin formulated his theory of Evolution by Natural Selection, he was harried and bullied by men who believed, without ample justification, that all life had been specially created. When Monseigneur Georges Lemaître showed that our universe likely began in an event later dubbed “the Big Bang,” he was belittled and ostracized by men who believed, without ample justification, that the universe was static and eternal.
When we attempt to assert how the universe must be structured, rather than attempting to learn how it truly is, we might as well be drowning Hippasus ourselves.