Third page of notes
The ideas of this page of notes follow from the previous page. b(1) is the joining of two e’s. But then we can also rotate the intersecting loop of locations around so that the locations of the loop occupy the same placements, but the locations change placements. That is the loop of locations rotates around.
These loops can all be unfolded to each create a circle where we have the two e’s that create all of the different b’s.
Then we can think of this as happening continuously too. So that we instead of moving a small distance to get from b(1,1) to b(1,2), we move in a continuous way.
Then next, we can think of this circle of e’s folded over once to intersect itself. Here we have c(1,1) but c must be a different idea than e. Let c be the idea that we sum all of the e’s in one place, once around the loop. Then we can have another c, c(1,2) this will be another sum, in a slightly different order than c(1,1) but the sum will be the same. Move the different c’s around the loop, c’s being very near the outside.
Then if we unfold these and add, like we did previously we can obtain a circle of sums-all c’s. This one sum is seen everywhere on the circle.
