One more thing: Before thinking about all this, I always thought that
since a high gain antenna has a narrower beam than a lower gain
antenna, the high gain antenna "sees" a smaller part of the incoming
field. I now believe this is wrong. The higher gain antenna sees a
larger field area. But as the antenna is rotated the sum of all the
rays decreases faster than if there were fewer of them. This is
probably due to the rays from the outer edge of the field causing a
faster decrease in the coherent summation of all rays than the closer
in rays. Of course, as the rotation is continued, many (but not as
many) of the rays add coherently again, giving rise to the side lobes.

Ron, W4TQT

Ron wrote:
This was only a mental exercise to help me visualize the concept of
gain. No resemblance to a real antenna or RF field was intended.
Thinking about it has helped me understand what antenna gain is
(assuming my conclusions are correct). And that's all it was supposed to
do. I hope it has helped someone else to do the same.

Ron