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June 22, 2009

All hail Leibniz

srikanth @ 9:30 pm, GMT +0000 ( 1245706206 ) Play

The mathematician and the canine did some interesting experiments and arrived at a very interesting theory. Who’s the prof (1) and what’s the  experiment (rest)?

  1. A is the dog, B is the ball, BC is the  perpendicular distance to the ball.

Cracked (in some cases with slight mixups) by udupendra , krudebox , Jean Valjean , emrohit , Dibyo , Raghuvansh , p vs np , Johny Walker , shenoyvarun86 , Rogi , lordmaldy , akhi , Logik , varuns88 , madhur , Ananth , BASAB , dheeraj , Deepthi JS , Mo , superbrat , byslexia and foobar.


Prof Timothy Pennings and his dog Elvis. After some experiments with a ball and a beach he realized that dogs intinctively perform rudeimentary calculus to figure out the shortes path to a ball, even across multiple mediums of travel.

The answer leaked out on Twitter, too :-)

23 Responses to “All hail Leibniz”

  1. udupendra

    Tim Pennings, and his dog Elvis. By playing fetch on the beach, Pennings proved that dogs are essentially lazy and do better math than most high school kids.

  2. krudebox

    1. Prof. Timothy J Pennings
    2. Elvis, a Welsh corgi.

    The experiment:
    Referring to (3),Standing on the water’s
    edge at A, he throws a ball into the water to B. Depending on the angle at which Pennings tosses the ball relative to the shoreline, his dog can run along the beach until he is directly opposite the ball, then swim out to get it. Or Elvis can plunge into the water immediately, swimming all the way to the ball. What happens most of the time, however, is that Elvis runs part of the way, then swims out to the ball.
    This behavior reminded Pennings of a standard problem found in just about any calculus textbook—one that involves minimizing the time of travel to a target when the available paths require traversing different mediums at different speeds.

    There’s an equation too, which gives the optimal path. But its kind of hard to depict square roots in here.

    (Answer flicked from )

  3. Prof. Tim Penning and his dog who became famous for being calculus-literate.

  4. emrohit

    The mathematician is Prof. Timothy J Pennings. He found out that his dog Elvis was following the quickest possible path to fetch a ball thrown in the lake. This kind of indicates that dogs are capable of doing the basic calculus needed for this activity although they or their masters may not be aware of the fact that they are actually using calculus ;)
    Full story here:;page=1

  5. Dibyo

    Timothy Pennings, Elvis the Corgi, Optimal Path calculations when two mediums need to be traversed (land and water, e.g.), y = 0.144x, and so on.

    Elvis doesn’t actually do calculus. Nonetheless, Pennings remarked, “Elvis’ behavior is an example of the uncanny way in which nature . . . often finds optimal solutions.”
    “I’d guess that most dogs have the same problem-solving software built in from the factory,” he says. My article is just “drawing attention to something that has been in front of us all the while.”

  6. Raghuvansh

    Thanks to Udupendra’s Twitter feed today, I happen to know that this gentleman’s dog seems to calculate the quickest path to the ball using rudimentary calculus-type instinct. Uncle’s name is Tim Pennings.

  7. p vs np

    This is Prof. Timothy Penning’s finding that dogs are somehow able to calculate the optimum path to a ball thrown in the water while playing fetch, thereby considering the possibility that dogs have an innate knowledge of calculus :)

  8. Tim Pennings and optimal ball fetching by his dog Elvis

  9. As a mark of respect to Twitter and Udupendra I shall retweet the answer instead of commenting…

    RT @udupendra – Dogs can do better math than most of us

  10. Rogi

    Tim Pennings found that his dog would naturally find the most efficient path, within a foot, based on total retrieval time required for the running and swimming parts, to fetch a tennis ball, thrown from a beach out on to the water at various angles, consistently choosing a point along the beach to enter the water that minimizes the swimming distance.

  11. Timothy J. Pennings of Hope College, Michigan. The theory’s that dogs can do calculus out-of-the-box.

    I think that’s an over-generalization. Now everybody knows Welsh Corgis can do graduate level math with impunity, but lets see a dumb poodle try to figure out how much is arf + arf

  12. akhi

    Elvis the calculus dog and Tim Pennings

  13. Logik

    1.Prof. Tim Pennings,
    and his dog,Elvis.
    Apparently the dog finds optimal routes, and is hence solving a basic problem in calculus.

  14. varuns88

    Tim Pennings found that dogs are able to calculate the optimal path to a ball thrown in the water.

  15. madhur

    1. Tim Pennings

    2. From his experiments, he revealed to the world that his Welsh corgi, Elvis, appears to be solving a calculus problem when finding the optimal path (minimizing travel time) to fetch a ball

  16. Ananth

    Tim Pennings
    His publication ‘Do Dogs Know Calculus’. He used to throw a ball into Lake Michigan. His dog would run down the beach and then jump into the water, rather than diving into the water immediately.

  17. Dr Tim Pennings and his dog Elvis, who knows Calculus. Pennings proved that dogs chose the optimal mix of running and swimming to get to the ball in the water in the shortest time

  18. dheeraj

    timothy J.penning and his dog elvis.
    elvis follows the path that takes the least time.The path more or less matched the theoretical solution(got using calculus)

  19. Deepthi JS

    Prof.Tim Pennings and his experiment with his dog Elvis.His work involved the optimisation of path dogs use in fetching a ball.

  20. Mo

    Dr. Roland Minton, professor of math, physics and computer science at Roanoke, found an article in The College Mathematics Journal by Pennings, a professor at Hope College in Holland, Michigan, about the dog whom Pennings claimed could do calculus. Elvis is a 6-year-old Welsh-Corgie mix and has been the inspiration for much of Pennings’ calculus observations.

    The article stemmed from a trip to Lake Michigan when Pennings tossed a tennis ball into the water and watched as Elvis raced to grab it. Pennings noticed that Elvis’ process of retrieving the ball could be transferred into a mathematical equation. He set up an experiment with his students to determine whether Elvis would instinctively choose the optimal path – that is, the most efficient route to the ball. The optimal path allows the person (or dog) to minimize its time of travel over different rates of speed and different mediums. Pennings found that if he threw the ball a certain distance, Elvis would swim directly to the ball if it was close to the shore. However, if the ball was further out in the lake, Elvis would run along the beach until he reached the burification point, or the point in time when he changed his mind about when to leap into the lake, and then scamper into the water.

  21. superbrat

    Time Pennings with his dog Elvis. He took his dog out on the shores of Lake Michigan to play ‘fetch’. And he found his dog appears to be solving a calculus problem to find the fastest way to get to the ball.

  22. byslexia

    Edward Pennings measured that his dog, Elvis, used the optimal path when fetching balls thrown out to sea.

  23. foobar

    1) Dr. Tim Penning
    2) His dog “Elvis”
    3) Their theory based on experiments “Do dogs know bifurcations?”

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