SIMIODE Director's Blog - Biking into Trees
Biking into Trees
A few years back we got news from SIMIODE member, Tim Pennings. He is the author of a way cool and famous, indeed iconic, article, “Do dogs know calculus?” about his little dog Elvis which was published in the College Mathematics Journal in 2003 (34(3): 178-182). Here is the abstract, “In all calculus books appears the problem of minimizing the time to get to a point on the other side of a river, running part of the way and swimming the rest. Isomorphic to this, if you are a dog, is the problem of minimizing the time to get to a ball that your master has thrown into a lake. The author has made measurements of how his dog retrieves the ball and finds that he indeed seems to choose the optimal path.”
If you have never read this paper you owe it to yourself and to your students to do so.
Tim has contributed a Modeling Scenario to SIMIODE, called 1-050-BargingAhead which he describes as, “As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy. Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if traveling too slow, it will almost take an infinite amount of time to arrive, which is also inefficient. How fast then should you go? We find an answer to this question, and to the related question of minimizing cost of travel, where the cost is a linear combination of the energy and the time.”
So, there you have a man who is interested in studying motion and motion continues to interest him, indeed distract him. We got this email from him today, “I was thinking about you this past Sunday - while lying in the ER with 4 broken ribs and collarbone. I ran into a low hanging branch while on a bike ride. They had to cut my shirts off me - including my favorite - the lightweight cotton (rather sheer) but surprisingly warm SIMIODE T-shirt that I got from you a year or so ago.” He says he was not reading a differential equations book at the time of the incident, but if he had stayed home that day and done so he would not be in the predicament he was in! We sent the patient a replacement SIMIODE T-shirt to keep him comfortable while he mends.
BTW his dog, Elvis, was a small corkie and was featured on the cover of The College Mathematics Journal. I suspect Elvis never ran into a tree, for it would not be an optimal thing to do.
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