Pressing Toward the Prize

Archive for the ‘Blogs’ Category

After having a really rough week, I decided to search some blog sites for a little humor. Thankfully, I found a couple that fit the bill. In his blog Division by Zero, Dave Richeson offers pumpkin pi, a limerick, exceptional math reviews, and some fun with the concept of infinity. The definition of infinite he shares from “The Hitchhiker’s Guide to the Galaxy” is rivaled only by this sentence in John D. Cook’s blog about a googol: “Inconceivably large numbers pop up in intermediate steps on the way to moderate-sized results.”

For humor of a different sort, Tanya Khovanova shares how mathematics helped her learn to say, “No.” Okay, except for the last couple of sentences, it really has nothing to do with math, unless you want to start adding up the number of  marriage proposals she has received over the years. (Hint: You might need a calculator!!) But like I said, I was looking for something humorous. And if riddles are your cup of tea, Tanya also offers some interesting puzzles. Who says math isn’t fun?

While perusing the website Teaching College Math, I came upon a blog entitled Mathematics of Coercion. I was immediately intrigued, and discovered it was actually a review of a video on TED Talk called “Bruce Bueno de Mesquita Predicts Iran’s Future.” Apparently Mr. Bueno de Mesquita has created a model using mathematical analysis to make predictions about complicated issues involving negotiations, such as war and politics.

After watching the video, I was a bit disappointed that even though there are a couple of references to mathematics, nothing of substance is offered. He mentions game theory, and that the factorial is used in determining the number of interactions of n people influencing an issue, but he never explains how he quantifies the various characteristics of the “influencers,” or how math is used in his simulation computer program. He does state that his predictions are based on estimations of future behavior, not statistics of past behavior. So even though we don’t really know what he does use, he makes it clear what he doesn’t, and no statistics are needed!

On Tanya Khovanova’s Math Blog I encountered a couple of interesting probability puzzles involving a truel. In one, the three men have an infinite number of bullets and they shoot in order until only one man is left alive, and in the other, each truelist has only one bullet. Ms. Khovanova gives the solution for the second one, based on probabilities and basic survival instincts, but leaves the first one to the reader. These puzzles remind me of a problem we were given in Professor Edgar’s M317 Proofs class:

“The five Dukes of Earl are scheduled to arrive at the royal palace on each of the first five days of May. Duke One is scheduled to arrive on the first day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king’s place, becomes the new king, and awaits the next Duke’s arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke’s first priority is to remain alive, and his second priority is to become king. Who is king on May 6?”

We all tried to solve this, and there was some interesting logic involved in our attempts, but even with the hint that working backwards would help, only one young lady in our class was able to solve it. She also solved it for six Dukes, and discovered a pattern that followed for even and odd numbers of Dukes. I have given a few hints, but I am not going to give the solution in case others might like to try it.

I have noticed that in order to solve any of these three puzzles, not only must probabilities for each action be considered, but one must have a good understanding of human nature as well. These are not merely about numbers, but also involve a fair amount of psychology. Two things I take away from this: 1) sometimes it is necessary to work backwards to find a solution, and 2) math does not exist in a vacuum!

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  • gramsonjanessa: I can't wait to listen to your capstone presentation in the spring! Your proposal was really interesting and I'm interested to see how the linear alge
  • dewittda: This is impressive! I thought I was good because I solved a rubik’s cube once in an hour. I served with a guy in the Air Force who could solve a r
  • ZeroSum Ruler: The Euclidean algorithm should me the mainstream way we teach students how to find the GCF. Why isn't it? A mystery.