I am far from an expert on this subject, but it might be illuminating to consider what happens when a dog catches a ball. Neglecting air resistance and other secondary effects, the ball follows a predictable trajectory that is shaped by gravity, and math allows us to predict where it will land. Astonishingly, a dog can _also_ predict where the ball will land almost immediately after the throw, and some dogs can even run and leap to catch the ball before it touches the ground. When you consider that the dog has far less visual acuity than we do and that it is estimating the three-dimensional geometry of the world and position of the ball in real time from imperfect two-dimensional signals bouncing on its retinas as it runs, you might be tempted to award the dog a degree in Applied Mathematics!

So does the dog that successfully locks the ball in its jaws in mid-air invent math, discover it, or neither?

.:quora.com->