How does the quadratic equation help robots juggle?

Like it or not, over the coming decades robots will play an increasing role in our lives. They will clean our homes, mix our cocktails, even drive our cars. They may even become street entertainers, amazing us with their catching skills!

What has any of this got to do with the humble quadratic equation? The seemingly innocuous polynomial with the complicated “solution” that’s found in the front pages of exam papers, and is the bane of many high school mathematics students’ lives.

Read on to find out.

Imagine. You’re a fielder on a rounders’ pitch, standing out in the deep, the glare of the sun making your eyes squint. The opposite team’s big hitter has just come out, and is swinging her bat like she means business. Your pitcher tosses a lame throw, and — WHACK — the ball is struck far and high, and worst of all is arrowing in on your corner of the field.

No drama, though. You’re good. Somehow, by the magic of that wondrous computing device, your brain, in conjunction with your eagle eyes, you know where the ball is going to land. You get there. The ball comes down, hard and fast. You raise your hands, and–

OUT!

You might not be consciously aware of it, but the fact of the matter is that you’ve just solved the numerical/computational equivalent of a quadratic equation. How so? Well, the trajectories of objects under the sole influence of gravity are actually described by parabolas–the curves you get when you plot a quadratic equation. What this means is that if you can take a “measurement” of the ball’s position and velocity i.e. its speed and direction at any moment, then its future position at any later time in its flight is completely determined. Basically, you know pretty accurately where it’s going to land the moment it’s hit. And you can update your estimate on the fly, getting a more and more accurate prediction the longer the ball is into its flight.

Whether our brains actually “solve” a quadratic equation or use a numerical methods that lead to similar predictions is up for debate–the brain with its massively parallel and interconnected neuronal structure is unlike the simple algorithmic computing devices we build–but what’s certain is that the programmers and engineers who create juggling robots are getting their creations to solve quadratic equations in order to catch the balls.

So, next time you’re staring at a ax2 + bx + c = 0 and wondering what possible use solving this equation could bring, think about the next generation of robots whose very foundations might’ve been laid in the intimate knowledge of this piece of mathematica. From auto-laser weapon systems disintegrating enemy mortar shells, to car manufacturing plants where components are lobbed between the robotic construction workers, the quadratic equation could be key!

Tiger Woods look out, your golfing nemesis is coming.

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