Alice laughed. ‘There’s no use trying,’ she said. ‘One can’t believe impossible things.’
I daresay you haven’t had much practice,′ said the Queen. ’When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast. There goes the shawl again!
― Lewis Carroll
See also this article discussing the usefulness of believing impossible things.
I can imagine it. You just have to embed it in a non-Euclidean geometry. A great circle can be constructed from 4 straight lines, and thus is a square, and it still has every point at a fixed distance from a common center (okay, 2 common centers), and thus is a circle.
I am now imagining a square circle. That’s interesting.
Can you describe it?
It’s circular, and square.
That’s literally all there is. I can’t imagine it visually, the way I usually would. Wonder why. :P
― Lewis Carroll
See also this article discussing the usefulness of believing impossible things.
I can imagine it. You just have to embed it in a non-Euclidean geometry. A great circle can be constructed from 4 straight lines, and thus is a square, and it still has every point at a fixed distance from a common center (okay, 2 common centers), and thus is a circle.
The four straight lines in your construction don’t meet at right angles.