The Irrational

This story is not reliably founded in history, but serves well as a moral lesson, or myth, as per the myths of the Greeks and Hebrews and others. All that follows must be read with this in mind.

Hippasus was a Pythagorean philosopher, who, so the story goes, discovered irrational numbers, and was murdered by being thrown off a boat and left to drown because of it.

The Pythagoreans, a school of philosophy and mathematics founded by the renowned Greek thinker Pythagoras, believed that the world was governed by whole numbers, 1, 2, 3, 4, 5..., and their ratios, (the rational numbers), 1/2, 1/3, 2/5, 3/7 etc. Harmonious musical chords, for example, were governed by simple rational ratios of the basic frequency of a given note, and the universe was governed by this "music of the spheres".

Such was the compelling nature of this conception of nature, that any spanner in the works, any mote in God's eye, was regarded as a sort of heresy.

Hippasus, so the story goes, was the one to discover that this conception was indeed based on a false assumption.

The proof that not everything in nature, when described by mathematics, is "rational" in the Pythagorean sense, is given below. But the point I am making here was prompted by news that in Ohio, legislation has been passed that students should not be penalised by handing in work that is utter garbage, if that garbage has a religious motivation behind it.

Here is a proof that irrational numbers exist. No amount of religious excuses can touch this. A student who denies this should not necessarily be drowned (unless they are excessively persistent ;) )  but should not be awarded any grades.