Animals that solve Feynman's quiz intelligently without using mathematics

A famous physicistRichard P. FeynmanIt seems that there are animals that intuitively solve the mathematical puzzle "Feynman's Quiz" that was issued.

To Save Drowning People, Ask Yourself "What Would Light Do?"
http://nautil.us//blog/-to-save-drowning-people-ask-yourself-what-would-light-do

The figure below is a quiz called "Which route should the lifeguard take?" Issued by Feynman. To get to people who drown in the sea and ask for help as soon as possible, Lifeguard is a question asking which route of A, B or C to choose.


Route A connecting the life guard and the drowning person with a straight line is the shortest distance, but the swimming distance is the longest among the three routes. Given that running on a beach is faster than swimming, you can see that route A is not shortest in time distance. On the other hand, the route B that connects the drowning man and the beach at right angles is the shortest distance to swim, but the distance to run on the sand beach is the longest and it seems not to be the shortest route if it is considered in total time. So, the correct answer is route C somewhere between routes A and B.

These quizzes are mathematical problems in which the shortest path is calculated by calculus, and in terms of physical historyPierre de FermatIs the problem of the same kind of principle as "Fermat's theorem" in the refraction of light thought "Choose a route that light can reach in the shortest time".


However, the interesting part of Feynman's quiz is that many animals including human lifeguards can intuitively make judgment regardless of mathematical knowledge, he says he engages in engineering education at Princeton UniversityArtis-battiaHas pointed out.

Professor Tim Pennings, a mathematician taught at Roanoke University, had a Corgi named "Elvis". Professor Pennings and Elvis said that he threw a tennis ball at the shore of Lake Michigan and was playing.


As Professor Pennings throws the tennis ball to the lake from the beach, Elvis will take pleasure and throw the received ball into the water ... ... while playing as playing, Professor Pennings goes straight to Elvis to the ball It seems he noticed heading to the ball after running a wave at a certain distance rather than to the ball.


Professor Pennings who thought "Is Elvis intuitively seeing the shortest path at the time distance?", Measured the position where the ball was thrown and the distance the Elvis traveled the coastline, 35 points The data was gathered and plotted, and it was confirmed that Elvis chose the fastest route ideally rather than the shortest route. Professor Pennings admired Elvis, the result(PDF file)"Do Dogs Know Calculus?"It is announcing as a paper.


Not only in Elvis but also in Anti, the same ability has been confirmed in Anti that I could intuitively find the shortest path at a time distance rather than the shortest distance. The research team of Dr. Jean Oteller of Regensburg University prepared glass and felt as sandy beach and sea, respectively, and conducted an experiment to search for the shortest route at a time distance among them in an experiment, it was found that the ideal route To chooseDiscoverydoing.


The fact that animals that do not know mathematics intuitively solve Feynman's quizz is mysterious, but it is said that how to solve the problem has not been elucidated yet.