"Natural Mathematics"
Three points: political track, economic track, security track
Graphically:
The researchers suggest that a dog playing fetch chooses at each point in time the path that allows it to maximize its speed of approach to the ball.
Paths to the ball. Shoreline distance AC = z; perpendicular distance to target BC = x; DC = y; AB = w.
When running from A towards C, the ball at B appears closer and closer as the dog gets closer to C, but its speed of approach to B diminishes (reaching zero at C). At some moment of its run, its speed of approach while running on the beach equals its speed of approach when swimming directly to the ball. If the dog jumps into the water at this moment, the strategy yields the same y value as that provided by the travel-time minimization model (where r is the dog's running speed, and s is its swimming speed).
From, mathematics popularizer Keith Devlin, who wrote The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs
