The Worst People in the World
I really, really hate those guys.
Buford Lister, personal communication
I have a list of the worst people I have ever known; it is not a written list. I have it committed to memory; I will never forget who they are. I don’t dwell on it, but I use it as inspiration for many of the things I write. A few of those people could not help themselves; they simply didn’t know better. Some of them were victims of circumstance; others were too self-centered to think of anyone other than themselves. One of the people was a mean-spirited drunk, and he was always drunk. Oddly, most of them are (or were) near Youngstown, Ohio.
This isn’t a post about those people; I don’t know what purpose such an essay would serve. It is enough to see that they show up in one form or another in the stories I write.
This post is about a group of people, a loosely connected consortium, who share a love for one math problem. These people are known as The Trisectors, and count yourself lucky if you have never met one. They are often referred to as cranks, crackpots, and naïve ignoramuses. And those remarks are among the kinder things said about them.
The story begins in 1837. Pierre Wantzel, a French mathematician, published a complicated proof showing that the trisection of an arbitrary angle with just an unmarked straightedge and a compass is not possible. No matter how hard you try or how smart you think you are, all attempts are doomed to spectacular failure. Of course, The Trisectors ignore this nasty little fact.
This trisection problem dates back to ancient Greek mathematics. You may have even heard about it in school. Uninformed math teachers often tell their students that no one has ever been smart enough to trisect an arbitrary angle. Ignorant of Wantzel’s proof, they send some unlucky students down a path of despair. Not only is it impossible, but it is a tremendous waste of everyone’s time to make any attempt at all. There is nothing to be gleaned from failed trisections.
Think of it this way, if I were to send you off with the task of finding two even numbers, any two, that when added together give you an odd number, what would you do? Would you spend decades trying to find the elusive answer? Perhaps you would realize what a terrific waste of time the question is, and you would quickly move on to something else.
What if I asked you to think really hard about finding a power of 2 that is evenly divisible by 3? It is not possible; there is no such number. In very simplified terms, this is why the type of trisection we are talking about is impossible.
Underwood Dudley, a mathematician with a great name, collects as many of these attempts at trisection that he can find. He has written a book about The Trisectors, including advice about what to do when you run across one. The book is called Mathematical Cranks, and I hope he is writing part two as I write this post. The world deserves nothing less. By the way, the best advice seems to be to run as fast as you can in any direction when confronted by a Trisector.
It has been a while since I have come across a true Trisector. They are probably laying in wait, polishing up their “proofs,” binding them in leather, preparing for the opportunity to spring them on me. The next time I meet one, I will tell them that what they are trying to do is impossible. After they argue for a bit, I will tell them about Wantzel’s proof. The bottom line is, if they want any chance for their “proof” to be considered, they must first find a mistake in Wantzel’s work. Try as they might, they won’t find one.
So, we have a mathematical proof that it can’t be done, but that does not stop The Trisectors. They waste vast amounts of time writing and then rewriting their “proofs.” It is an embarrassment. One thing they are fond of doing is sending their indecipherable work to math departments all over the world. After all, who else could possibly recognize their genius?
I will end this post on a positive note. I hope everyone smiles when they hear what math departments do with the goofy, impossible “proofs” they receive on a weekly basis. Let’s say that Fred Gorman sends in a 150 page “proof” of his brilliant trisection to the math department at Reederstock University in Iroquois County. A couple of days later, Laszlo Crump sends in a “proof” of his brilliant approach to the trisection problem. Now that the stage is set, consider the following letters that the department secretary sends out a few days later…
Dear Mr. Gorman,
Thank you for your proof. As our department does not have anyone expert enough to vet your mathematics, we would like to put you in touch with an expert in your field. Laszlo Crump can be reached at…
Dear Mr. Crump,
Thank you for your proof. As our department does not have anyone expert enough to vet your mathematics, we would like to put you in touch with an expert in your field. Fred Gorman can be reached at…
Odds are that both men will report back to the math department that the other guy is crazy and talked nothing but nonsense. What is certain is that as long as Underwood Dudley is alive, he will be receiving recycled, unintelligible “proofs” from naïve ignoramuses. The Trisectors and their band of slack-jawed yokels are going to die hard.
