## A squirrel in the glade

It was raining…We had just sat down for lunch at our holiday home when one of the guests asked us whether we would like to hear what had happened to him in the morning.

Everyone assented and he began.

“I had quite a bit of fun playing hide-and-seek with a squirrel,” he said. “You know that little round glade with a lone birch in the centre? It was on this tree that a squirrel was hiding from me. As I emerged from a thicket, I saw its spout and two bright little eyes peeping from behind the trunk. I wanted to see the little animal, so I started circling round along the edge of the glade, mindful of keeping the distance in order not to scare it. I did four rounds, but the little cheat kept backing away from me, eyeing me suspiciously from behind the tree. Try as I did, I just could not see its back.”

“But, you have just said yourself that you circled round the tree four times,” one of the listeners interjected.

“Round the tree, yes, but not round the squirrel.”

“But, the squirrel was on the tree, wasn’t it?”

“So, it was.”

“Well, that means you circled round the squirrel too.”

“Call that circling round the squirrel when I didn’t see its back?”

“What has its back to do with the whole thing? The squirrel was on the tree in the centre of the glade and you circled round the tree. In other words, you circled round the squirrel.”

“Oh no, I didn’t. Let us assume that I am circling round you and you keep turning, showing me just your face. Call that circling around you?”

“Of course, what else can you call it?”

“You mean I’m circling round you though I’m never behind you and see your back?”

“Forget the back! You are circling round me and that’s what counts. What has the back to do with it?”

“Well, tell me, what’s circling round anything? The way I understand it, it’s moving in such a manner so as to see the object I’m moving around from all sides. Am I right, professor? He turned to an old man at our table.”

“Your whole argument is essentially one about a word,” the professor replied. “What you should do first is agree on the definition of “circling”. How do you understand the words ‘circle round an object”? There are two ways of understanding that. Firstly, it is moving round an object that is in the centre of a circle. Secondly, it’s moving round an object in such a way as to see all its sides. If you insist on the first meaning, then you walked round the squirrel four times. If it’s the second that you hold to, then you did not walk round it at all. There’s really no ground for an argument here, that is, if you two speak the same language and understand words in the same way.”

“All right. I grant there are two meanings. But, which is the correct one?”

“That’s not the way to put the question. You can agree about anything. The question is which of the two meanings is the more generally accepted? In my opinion, it’s the first and here’s why. The sun, as you know does a complete circuit in 26 days…”

“Does the sun revolve?”

“Of course, it does, like the earth. Just imagine, for instance, that it would take not 26 days but $365\frac{1}{4}$ days, that is, a whole year, to do so. If this were the case, the earth would see only one side of the sun, that is, only its “face”. And yet, can anyone claim that the earth does not revolve round the sun?”

“Yes, now it’s clear that I circled round the squirrel after all.”

“I have a suggestion, comrades!” one of the company shouted. “It’s raining now, no one is going out, so let’s play riddles. The squirrel riddle was a good beginning. Let each think of some brain-teaser.”

‘I give up if they have anything to do with algebra or geometry,” a young woman said.

“Me too,” another joined in.

‘No, we must all play, but we’ll promise to refrain from any algebraic or geometric formulae, except, perhaps, the most elementary ones. Any objections?”

“None!” the others chorussed. “Let’s go.”

“One more thing. Let professor be our judge.”

More brain-teasers will be served…

Nalin Pithwa

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