Dogs and the mathematics of calculus.
A remarkable story about two very clever men and an equally clever dog!
Five days ago, I received an email from a Richard Hake quite out of the blue! This is what it said,
Dear Paul Handover,
I’m taking the liberty of cc’ing this to Tim Pennings since he may be interested in your blog “Learning from Dogs.”
As founding author of the great blog “Learning from Dogs”, I thought you might be interested in the work of Tim Pennings.
Paraphrasing from the Hope College website:
Tim Pennings is a professor of mathematics at Hope College and owner of a famous Welsh Corgi dog, Elvis, who knows calculus. He has given over a hundred talks – including several speaking tours – based on his papers “Do Dogs Know Calculus?” [Pennings (2003)] and “Do Dogs Know Bifurcations?” [Minton & Pennings (2007)]. Articles about Elvis are easily found on Google and Youtube. For example:
1. “A Dog, a Ball, and Calculus” Ivars Peterson’s MathTrek,
2. “Calculating Dogs” Ivars Peterson’s MathTrek ,
3. “Dog Plays Fetch With Calculus” YouTube (see below)
4. “Elvis The Calculus Dog at Roanoke College” Vime0 Videos.
Richard Hake, Emeritus Professor of Physics, Indiana University
Honorary Member, Curmudgeon Lodge of Deventer, The Netherlands
President, PEdants for Definitive Academic References which Recognize the Invention of the Internet (PEDARRII)
Well what fun!
Let me start with that YouTube video mentioned above:
Tim Pennings of Hope College in Madison, Wisconsin takes a look at the mathematics his dog Elvis uses to play fetch.
And here are a number of wonderful pictures of Elvis from which comes this one:
More may be learnt about Tim Pennings from here, from which I quote:
I am a professor of mathematics at Hope College. My areas of research and writing include dynamical systems (the shadowing property in particular), mathematical modeling, and the infinite. I have directed the Mathematics REU Site since 1995 and have mentored research students almost every year since 1990. A complete list of published papers, talks, and other professional activity is included in my vitae.
My interest in infinity stems from my intrigue with the rich stuff that lies in the confluence of mathematics, physics, philosophy, and theology. My paper, “Infinity and the Absolute: Insights into Our World, Our Faith, and Ourselves” is the backbone of my senior seminar course, Pondering the Big Questions. Several other math-theology papers, published in Perspectives include “A Life Lesson from Calculus” and “Haggai, Mathematical Dynamics, and the Nature of Good and Evil”.
I have a famous Welsh Corgi dog, Elvis, who knows calculus. Here are some pictures of us. We have given over a hundred talks – including several speaking tours – based on our papers “Do Dogs Know Calculus?” and “Do Dogs Know Bifurcations?” (written with Roland Minton) both published in the The College Mathematics Journal of the MAA. Articles about Elvis are easily found on Google and Youtube.
Thanks, Richard, for getting in touch!