I was beside myself when my 8-year-old grandson Ganesh asked, “I love curves! Do you thatha?” I looked around, ensured no one was around, and gently asked, “What curves?” With a booming voice, he clarified, “The curves you see on the top of a cup of milk, they are so nice’. ‘Oh that!’ I was greatly relieved, if not mildly disappointed, that he was bringing me down to earth at my age. My mother used to say it was the bottom of the holy cow. But Ganesh deserved better, and I attempted an explanation: “It’s called a Caustic curve and is formed by the reflection of light on milk from the surface of the remaining cup.”
After a brief silence, he asked, “What if the cup is full?” Without waiting for an answer, he ran to the kitchen and returned with a cup filled to the brim: “Thatha, there is no curve now.” Drink a little bit; the cow will return, I wanted to say. But I knew the humour would be lost on him. Instead, I went on: Nature is full of beautiful curves. If you hang a string between two points, it forms a beautiful curve called a catenary, the same as a garland or chain on your mother’s neck. Now, whatever the weight of the chain, the shape is the same if the length is the same, hung from the same points.
The most beautiful curve is what a cricket ball takes when one hits a sixer. However fast you may hit the ball, it comes down sooner or later after taking a magnificent curve, a parabola. Why does it take that shape? The speed with which you bat at an angle is not lost horizontally but suffers much more vertically on account of gravitation, hence the compelling downward motion. If you catch the ball, your hand will feel the downward gravitational push but also the severe backward thrust, depending on how fast the batsman hits it. If you are standing still to catch the ball, you’ll fall backward.
While all these are school topics, Richard Feynman brings a new significance to the whole business. Nature spends the least energy moving a particle from one place to another, and he proves quite easily that a parabola is the curve to follow on a free throw. The man who catches the ball would just absorb the energy given out by the batsman.
Now, all these—the caustic curve, catenary, and parabola—are just names, but what’s important is to know how nature forms them. Feynman quotes, ‘I learned very early the difference between knowing the name of something and knowing something’. His dad influenced him. That’s another story.
Now back to curves. Before he grows older and gets distracted, I want Ganesh not to fritter his mind on testing his memory like the good old Bournvita quizzes in the seventies but to focus on the how and why of things.