Do Dogs Know Calculus? Bifurcations at the Beach

Timothy J Pennings from Calvin University spoke to a group of students and faculty on October 20, 2023.  He showed that dogs – at least his dog, Elvis – knew calculus. That is, Elvis could find the optimal – fastest – route to a ball thrown into the water some distance down the beach. But what happened when Elvis is positioned in the water and retrieved a ball that is also in the water? When should he swim straight to the ball, and when should he swim in to the shore, run along the shore, and then swim back out to the ball? What is the bifurcation point for the change in optimal strategy? Did Elvis bifurcate? There were many affirmative answers as students reviewed some of the mathematics learned in their courses.