Danehy

Evariste Galois may have turned out to be the greatest mathematician of all time had he not died at the tender age of 20 after fighting a duel over a teenage girl who really didn’t even like him all that much. Just another all-too-common intersection of genius and stupidity.

His was a sad and tortured life. His father was briefly the mayor of a small town outside of Paris, but he committed suicide after a feud with an unscrupulous and dishonest village priest. When Galois tried to get into the best school, the École polytechnique, it wasn’t so much his deficiencies in other areas that hurt him as much as the fact that his math was so advanced that the instructors who were testing him didn’t have a clue and turned him down.

A couple decades after his death, the New Annals of Mathematics would note, “A candidate of superior intelligence is lost with an examiner of inferior intelligence.”

Things actually got worse for him. His work kept getting lost by mentors and examiners. One time, he entered the equivalent of a prestigious math contest. The judging committee’s secretary took the paper home with him and then died. The original paper was never found. Galois later re-did the paper; it is considered one of the most inspiring works in the history of mathematics.

While much of his stuff is out there, there are a couple semi-practical applications thereof. One may find its way into the American political process if some people get their way. It involves using probability to select the best candidate from an extremely large field. It has long been known as The Dating Problem, but the website Numberphile2 recently hilariously updated it as The Glastonbury Toilet Problem.

Imagine you’re at the Glastonbury Music Festival and nature calls. There are 100 Port-a-Potties from which to choose. How can you use math to give yourself the best chance of using the least-disgusting toilet?

Using probability theory, you construct a nice bell-shaped curve along the x-axis (while holding in your pee). To find the (optimum) value of the curve’s peak, you take the derivative of the curve’s equation and arrive at – ln (natural log) of x minus 1 = 0. That solves to 1/e, which, believe me, will make a nerd all tingly. One over e is about .37, so 37 percent becomes key here.

According to probability, you would have to inspect the first 37 (of the 100) toilets, keeping a mental note of the conditions of that which was the least disgusting. You then select the first one after No. 37 that is superior to all of those you inspected. (You can’t go back.) Mathematically speaking, this will give you the best chance of finding the least disgusting toilet. Obviously, there was a 1/100 chance that the very first one was the best, and an equal chance that the second, third or fourth (and so on) was the best. But the Galois method gives you the highest probability.

Keep all this in mind if the raging Independents and others try to install the Top Two method to election results in Arizona.

I have to detour briefly here. A couple weeks ago, I used the phrase “mythical Independent voter.” I probably could have used a better word. The second definition of “mythical” is “idealized,” which, at the time, I thought was better than “stereotypical.” Well, some guy who goes by “Harry Red Dog” got all butt-hurt. (Why can’t people use their real names in online posts?)

Anyway, Harry (…) or Mr. Dog, if you prefer, I understand that a lot of people are fed up with both parties. The last time I poked fun at Independents, my long-time friend and colleague, Jim Nintzel, took me to task and sent me an absolute treatise on the emergence and evolution of the non-party-affiliated voter. My instinct is to stay and fight (perchance to effect positive change from within) rather than stepping outside and uttering, “A pox on both their houses!,” but (…) different strokes.

The top two method, which is the crackpot scheme du jour of many Independents, is simple (and simply awful). You throw everybody in one big primary and the top two vote-getters square off in the general election. Leaving Galois out of it for now, in even simple mathematical terms, it’s a recipe for disaster. We’ll say you have an open seat in a district that’s heavily (say 56 percent) Republican. Four Republicans see an opportunity and jump in the race, while two Democrats also run. The four Republican newcomers split the vote pretty evenly, with each winning between 12 percent and 16 percent of the total vote. Meanwhile, the two Democrats grab 24 percent and 20 percent of the total vote, respectively, and will square off in the general election. That would seem to subvert the will of the people in that district. And the more candidates in the primary, the more likely that Galois will rear its ugly head.

Oregon rejected a move to top two, but California used it in last month’s primary election, with predictably chaotic results. So, while we welcome our Independent brethren to the voting process, we must reject the absolutely ridiculous Top Two. And if this turns out to have been a false alarm, at least we all learned a little bit about Galois Theory.

Math is our friend.

This article appears in Jul 10-16, 2014.