Excitedly, he climbed down from the rock and headed for a patch of bare sand at the river's edge.
In every framework of thought which man had ever devised, the circle was prominent, vital. It played its part in every creed of every race, of every time. It was as essential to the ancient arts of magic as to the current methods of science. It played its part in the movement of planets, the shape of stars, perhaps the essence of the total universe.
Man might be too didactic in requiring that awareness develop a physical science comparable to his own, but surely awareness, whatever form it took, would know the circle.
He sank down on his haunches beside the smooth sand, and with the tip of his finger he quickly drew a circle.
The furrow, scratched in the sand, did not close or smooth out!
He sat back and waited. Nothing happened. It was almost as if the invisible intelligence were saying, "All right. You are aware of a circle. That was obvious to us from your artifacts. What else do you know?"
He leaned forward, and as nearly as he could estimate, he dotted the center of the circle with a finger, then scratched a radius to the perimeter. It stayed. To one side he drew another line, approximating the radius and in parenthesis he drew a small 2. Beside this he wrote R². He drew an equals sign. He scratched the pi sign.
Then he drew another circle and with the palm of his hand he smoothed all its interior. That should be plain enough. The symbols stayed. They understood his mathematics, then. The equation seemed undisturbed, yet there was something wrong with it. He had to look closely at the sand before he saw what it was.
The = had changed to : !
Why had they changed the meaning by substituting "proportionate to" for "equals"? He felt a flash of exasperation. Well sure, without tools he could not draw a perfect circle, nor two of them entirely equal. It was pedantic of them to split hairs over that? He must practice, without tools, to draw a perfect circle?