I'm up to the section on Pythagoras and his eponymous theorem: in any right triangle in which the legs of the right angle are a and b, and the remaining side is c, then the square of c equals the sum of the squares of a and b. We all remember that one from school. Dantzig says that Pythagoras was so overwhelmed by the elegance of this that he went and sacrificed an ox to the gods.
But it turned out to lead to something worse: the incommensurability of the diagonal of a square with the sides. A square is just 2 right triangles slapped together, right? So given a unit square, that is, in which the length of the sides is 1, then, according to the Pythagorean theorem, the diagonal has the length of the square root of 2. And the square root of 2 is a very inelegant number indeed. This was very troubling to the Pythagoreans, who wanted everything to be beautiful and perfect. Legend has it that the one who discovered this problem was eventually assassinated.
Dantzig writes of what ensued:
Less than a century passed, and the Pythagorean secret became the property of all thinking men. The unutterable had been spoken, the unthinkable clothed in words, the unrevealable presented to the eyes of the uninitiated. Man had tasted of the forbidden fruit of knowledge and was condemned to be banished forever from the Pythagorean number paradise.
The beauty of spiritual realities is seductive. But if we just worship the beauty, and not the Spirit, the messiness of life and the complexities that are beyond us will always leave us frustrated.