My Jack Russells are pretty smart sometimes.
Yup.. and the boys of summer make physics calculations while standing in the batter's box.
They do calculus and urinate on the rug. They are geniuses all right..
Ping!
Yep, this is fabulous science. I would have never known that dogs know how to fetch a thrown ball with accuracy. I'll bet flying birds use thermals with a precision similar to mathematical models showing how to best soar through the air; dolphins cut through the water in a manner reducable to numbers that demonstrate that they use the least amount of muscular power for the amount of forward motion; and wolves run down prey reflecting a near-perfect relationship between energy used to maintain the chase and finally killing the quarry. Wow.
I suspect it's the same with the dog. The fallacy in the writer's theory is that calculus came first and the behavior follows. In truth, calculus is simply a tool used to describe the behavior that already existed.
Very funny topic, I must say. I wouldn't be at all surprised if there is, indeed, some mathematical process going on in the dog's brain. But then, we'll never know for sure, will we? If I could venture a guess, I would have to say that it is some sort of successive approximation process.
duh, the idiot has it the wrong way around...the mathematical formula closely matches the optimal way the dog, Elvis performs this particular task!
The dog is doing this intuitively. There is no "dV/dT" calculation going on, the dog is simply estimating (based on experience) where the ball (or Frisby, or stick) is going to be at a particular time, and speeds up, slows, or turns to meet the object at that particular point. As the dog has its eye on the object, it continues to adjust the estimate to meet the anticipated contact point at the optimal time.
Human beings do the same thing when trying to beat out a red light.
They told me blue heelers were smart, but mine is almost 4 and barely reads.
Must be a different kind of calculus than my dog used; the one who did not know how to use the doggie door until after I got on my hands and knees and modeled it for him a few times and finally pushed him through it.
Unfortunately for Atlas (and fortunately for the squirrels), the rodents can vary their speed in a nanosecond; frequently, they will slam on the brakes, and Atlas will overshoot. Good planning, but poor execution when it comes to adapting to rapidly changing circumstances. A Weimaraner chasing a squirrel looks like a Mercedes S-Class trying to run down a skilled skateboarder: it ain't gonna happen. Atlas is zero-for-several hundred with respect to squirrels. Plenty of speed (he has dispatched a couple of rabbits, whose lack of tree-climbing ability proved fatal), but a bit lacking in mobility.
Wow, who would of thought that a dog having the ability to fetch something using the least amount of effort would be news worthy.
Wow, the same principle that explains refraction.
You'll not that for a fixed running to swimming speed ratio, the optimal entry point occurs when the stick location makes a fixed angle to the perpendicular, so the problem is the same every time, regardless of where the stick is thrown.
If the dog always cues on this angle, and the angle is anywhere near optimal, it would be easy to draw these conclusions.
Some dogs are smarter than others. Mine is smart enough to stay on the sofa and avoid chasing pointlessly after balls.