Nearly 40 years ago, we were asked this question at school:
Imagine a string tied around the middle of an orange, in effect forming a circumference. Now imagine another string, this time tied around the middle of the earth, at the equator.Okay? Now increase the length of each of these strings by a foot. Imagine each string now suspended around its sphere as an annulus. Tell me, which string will be further away from the sphere it contains?
And we all answered “the one around the orange, of course”. Or words to that effect. And we wondered why someone would ask such a silly question.
And then we did the math.
- C=2pi r
- C+1=2pi R
- R-r=(C+1)/2pi -C/2pi
- Or (cancelling out the Cs), R-r=1/2pi
What?!?! How can this be? How can the change in radius be independent of the circumference of the sphere (or for that matter the radius)? You mean that both strings will be the same distance away from “their” sphere? Im-possible.
It didn’t matter how many times we invoked Sam Goldwyn (he was still alive at the time), the answer did not change. No hidden tricks. No small print. No scams involving oranges and geoids. Just the facts. When you increase circumference by X, the radius increases by X/2pi. Regardless of what the original radius was. Regardless of what the original sphere was. One string round a table tennis ball, the other round the sun, same answer.
I tell you, it kept me up nights as a boy, it just didn’t make any sense to me. I had to drill the answer into my head, drag it there kicking and screaming. It took time, but the pain subsided in the end.
And went through all that pain again. From “does not compute” to “im-possible” to “I don’t believe it”. So if you’ve got a similar penchant for mind-masochism, go out and buy the books. Both of them. You won’t regret it.
I need to keep challenging my biases and prejudices, the anchors and frames I cannot see. And books like these help me exercise my mind, they ensure that I don’t reject ideas just because they’re counterintuitive.