Dogs can use mathematical algorithms

I’ve always suspected that Fitzroy might be a mathematician or some kind of a computing wizard… who doesn’t necessarily go out of his way to boast about his talents.

A fascinating article on the theory of so-called shepherding has just appeared in the Interface journal of Britain’s Royal Society.

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Researchers succeeded in building a model that simulates correctly the way in which a dog herds up sheep. Click here to access the article. To understand the article, which is quite readable, you need to replace the term “shepherd” by “dog”, and the term “agent” by “sheep”.

Most of us (at least in Australia and the UK) have seen demonstrations of smart dogs herding sheep. Here at Gamone, in the past, I’ve tried to herd a dozen or so sheep with the help of my two children, but without a smart dog. It turns out to be difficult, if not impossible, for the simple reason that humans can’t possibly run after stray sheep at the speed of a dog. But what exactly takes place in a dog’s brain when it succeeds in moving a flock of sheep from one place to another?

A basic assumption made by the researchers is that a stray sheep, located beyond the main outside perimeter of the flock, sees the dog as a would-be predator, and it “escapes” from this “predator” by moving back into the midst of the flock. In the model imagined by the researchers, a dog is thought of as engaging, at any particular moment, in one or other of two operations:

— A collecting operation takes place when the dog rushes out beyond the perimeter of the flock to round up the sheep that has strayed the furthest distance from the flock.

— A driving operation takes place whenever there is momentarily no immediate need for collecting, enabling the dog to get behind the flock and drive it towards the destination, which we can call the pen.

The following graph shows the way in which phases of collecting and driving take place, one after the other, until the flock has assembled, as desired by the dog, down in the lowest left-hand corner.

Now, once the theoretical model was created, the researchers were able to validate it by calling upon a genuine sheep dog and a flock of genuine sheep, down in Australia. The dog they chose for the experiment was an Australian Kelpie, which has the extraordinary habit of jumping up onto the backs of the sheep in order to obtain a bird’s-eye view of the global situation, so that it can locate the most distant stray sheep. The following excellent photo (by Martin Pot) illustrates this behavior:

In fact, the algorithm used by the dog to carry out its herding assignment is relatively simple, and it should be an easy matter to create a robot capable of performing this task. I can hear Fitzroy laughing. Like me, he’s trying to imagine a robot capable of racing through the weeds on the slopes of Gamone, jumping over fallen tree trunks, and biting the hind legs of recalcitrant ewes to get them moving in the right direction…

POST SCRIPTUM
I'm amused by the idea of an Australian Kelpie strutting across the backs of the sheep as if they were a nice soft pathway. I'm wondering whether the dog developed this technique on its own (unlikely in my opinion) or whether the grazier trained the dog to do so. I'm reminded of the experimental situation known as the monkey & bananas problem, which used to be a favorite with artificial-intelligence theorists. If you were to put a hungry monkey in a room where a bunch of bananas was hanging, but just out of reach, would the monkey be smart enough to drag a box-like object beneath the bananas so that he could climb up and attain the bananas? I introduced a variant in which there were two monkeys. Would one of them be smart enough to climb up onto the back of the other monkey in order to be able to reach the bananas? I believe that the answer to these questions is no... unless you train the monkeys to behave like the Kelpie.