04/28/2025
When weāre working in class on teaching Stay, and the dog changes position or moves away from where you left her, Iāll insist (and repeat as often as necessary): Do NOT warn the dog from a distance; you must return to the dog and correct.
Again: _Do NOT warn the dog from a distance; you must return to the dog and correct._
And hereās why:
In 2005, Stanford mathematician Keith Devlin wrote a book called "The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)" and when we work on stays in class, youāve heard me quote from that book. A lot.
Devlin argues that basic forms of mathematical reasoning, such as estimation, pattern recognition, and spatial navigation are hardwired into the brains of living creatures because these skills are essential for survival. So when we see animals like birds navigating thousands of miles, spiders spinning intricate webs, or dogs catching frisbees weāre witnessing forms of mathematical intuition.
Humans developed formal mathematics to explain or account for everyday activities like cooking, shopping, and driving, things that involve estimation, measurement, and logic. Thatās in part because humans, unlike dogs, think in language, and also because language makes possible the understanding of abstractions such as the notion of linear time.
Anyway, how is all this this relevant to teaching a dog to hold a Stay? Because if you warn your dog from a distance, you are providing your dog with what Devlin calls an āoptimizationā challenge.
In fact, Devlin spends a whole chapter on how dogs solve optimization problems. His example: when a dog catches a frisbee, it must figure out the best path to intercept it. Mathematically, this is an optimization problem: finding the quickest or most efficient path to meet a moving target.
If you warn your dog from a distance on stays, youāre providing your dog an optimization problem that is the inverse of catching the flying frisbee. Instead of finding the quickest or most efficient path to meet a moving target, you are actively teaching your dog to recognize a pattern that allows him to find the quickest or most efficient path to EVADE a moving target (where that target is you) by doing calculus.
In human-created technical terms, solving such a problem would involve differential calculus ā finding the trajectory that minimizes time or distance. A human would need to model the motion of the frisbee, apply Newtonian physics, set up equations, differentiate, and solve. But a dog does calculus too -- instinctively and instantly.
How does a dog do calculus? Youāre in the park. You tell the dog SIT, then STAY and walk thirty feet away. Dog sees a squirrel on the ground. Dog stands up. You warn him. Dog stares at you. You warn him again. Dog takes off. Instinctively heās quite aware of how quickly he can go from zero to forty mph and correspondingly, how long itās going to take you to 1) realize heās in motion and 2) get in motion yourselfā¦and from there, exactly how far he can travel in the time heās allocated.
This isnāt calculation in the human sense. Instead, dogs rely on perceptual feedback loops that we create for them: they continuously adjust their speed and direction based on how the frisbee, the squirrel and/or the chasing, shouting human looks to be moving in their field of vision.
These are dynamic adjustments and now that we know how they work, we can also adjust accordingly and teach a proper Stay. :)
Happy training!
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