What if I told you math is dangerous?  No, not in the sense that the numbers might jump off the page and attack you—but rather, because math is often thought to be the world of absolutes, no exceptions.

The Pythagoreans were a group of ancient Greek mystics, who wore white robes and spent their days studying and measuring the cosmos.  They were masters of geometry and knew more about numbers and shapes than anyone.  One of the foundations of their mathematical knowledge was the idea that any number can be written as a ratio of two other numbers: 6 is 12/2; 2.333 is 7/3; and so forth.

But their greatest discovery, the Pythagorean Theorem, created a problem.  Hippasus of Metapontum discovered that the length of the hypotenuse of a right triangle is a number that cannot be written as a fixed ratio.

Okay, so what?  How’s that dangerous?  Well, Hippasus made his discovery while on a ship…and when the other Pythagoreans saw that he had proven an exception to one of their basic beliefs, they threw him overboard!

People throughout history have faced danger for new discoveries.  Math is no different.  In fact, because it deals in numbers and proofs—the stuff of absolute certainty—it might be even more dangerous. 

Don’t get me wrong—this doesn’t mean that human knowledge is impossible.  It just means that our knowing—in math, or in anything—still should come with a bit of humility.  Otherwise, man overboard!

And now, for the Friday funnies

An MIT linguistics professor was lecturing his class the other day. “In English,” he said, “A double negative forms a positive. Example: I won’t not go to the store, means I will go.  However, in some languages, such as Russian, that double negative still expresses a negative—I won’t not go can still mean, I won’t go. But there isn’t a single language, not one, in which a double positive can express something in the negative.” And a voice from the back of the classroom said, “Yeah, right.”

Have a wonderful day.