For thousands of years, people thought numbers were mildly amusing… and occasionally useful for counting apples, perhaps, or for setting the correct number of plates around the dinner table, or for telling jokes the begin with, “Two guys walk into a bar…”
Then the mathematicians got hold of our poor, innocent numbers, and things went to hell in a handbasket.
One of the early mathematical mischief-makers was a Greek named Euclid, who came up with a whole system of silly ideas which he then published in a book called Elements. The book was eagerly embraced, we are told, by the mathematical smart alecks who hung around the Alexandria library in Egypt. There’s not a single “Two guys walk into a bar” joke in the whole book… which certainly provides ancient evidence (as if we needed any) that a mathematician is a clever person with no sense of humor.
We now call this system “Euclidean geometry” although Euclid himself probably called it by some kind of Greek name. And we really shouldn’t blame Euclid for how poorly things have turned out. Originally, his book described a bunch of charming parlor games that can be played with a compass and a ruler and a few sheet of papyrus, and as we noted, it was pretty popular until the Romans, or Arabs, or somebody, burned down the library. Various stories have the Romans destroying the library “by accident,” and other stories have the Arabs burning it down “on purpose.” I tend to believe the second version.
At any rate, whoever it was didn’t do a very complete job of destroying Euclid’s little parlor book, because somehow, 1800 years later, some clever European Protestants somehow got hold of it and proceeded to completely misinterpret it, thinking it was a true story about how the God had designed the world according to mathematical principles. A poignant lesson in how seemingly innocent parlor games can turn bad.
Once the European number crunchers deluded themselves into believing God had something to do with mathematics and geometry, the stage was set for mathematicians to become high priests. Which brings us to modern America, where even Kindergarten teachers are under pressure to teach basic algebra to 5-year-olds who haven’t yet learned to tie their shoes or brush their teeth.
A sad situation indeed… but all the more tragic because mathematics is — basically — defective.
Allow me to illustrate.
Several of Euclid’s geometry-based parlor games involved the drawing of straight lines with a ruler. We can do that ourselves:
Thus far, we have a pretty simple art project. But the object of the game is to make it confusing. So Euclid would suggest that we establish two “points” on the line:
We’ve marked the two points “A” and “B” which together define “Line Segment AB“. Some wise-ass will probably ask, “Why A and B? Why not something else?” Good question. The reason we have chosen “A” and “B” is because this game involves mathematics. Point A is intended to represent the position of an “Airedale Terrier” — a hungry Airedale Terrier — and Point B represents a “Bone”.
The line we drew with our ruler now represents (theoretically at least) the shortest distance between the Airedale and the Bone.
Now we’re going to screw everything up by adding mathematics. Halfway between Point A and Point B we add Point X. (Don’t ask why it’s called Point X. It’s math. It doesn’t have to make sense.)
Point X is exactly halfway between Point A and Point B. Now sharpen your pencils, and we’ll discover why mathematics is so misleading.
The Problem: Our Airedale (whose name is Sparky) is running towards the Bone at a gallop. It has taken him exactly 15 seconds to cover the distance between Point A and the halfway mark, at Point X. Now, using mathematics, calculate how many total seconds it will take Sparky to run from Point A (his canine starting point) to Point B (his calcium-rich reward.)
With any luck, you remember a smattering of math from your tedious 12-years of experience in public (or Catholic) school, and you have calculated the obvious mathematical answer: 30 seconds. You may have calculated this answer using a quadratic equation… but maybe not?
Anyway, however you got your answer, it’s dead wrong. What Euclid and the rest of the math rascals (including your Kindergarten teacher) forgot to tell you about is: Point C.
They forgot to tell you about Point C, because mathematics utterly ignores reality in favor of silly parlor games. Point C represents the neighbor’s Cat, who has just stepped out from behind a sycamore tree.
Point C exists in the real world — the real world in which you and I forget to pay our bills on time and watch poorly-produced Reality TV shows. But Point C does not exist in mathematics, because it’s simply too inconvenient.
When reality appears from behind a tree, Line Segment AB means diddly squat. Now, suddenly but understandably, the important Line Segment is Line Segment XC.
In real life, our noble Airedale, Sparky, never arrives at Point B at all. While he’s chasing the cat through the neighborhood, a shaggy little mutt named Roger comes upon the Bone and carries it off, to chew it contentedly under a Willow Tree down by the river. (Point W. We will not be able to draw Line Segment BW because our paper is not big enough. Sorry. Even more proof that mathematics is worthless when you try to apply it to real life.)
All of which brings is to the biggest sham of all. Statistics.