This (2006) is the 2nd time that I have read this marvelous little book. Numerous mathematical theorems are suggested and I thought I would see if I could prove or merely corroborate some of them.
On page 53 he says “the probability of an event is found by adding arrows for all the ways the event could happen”. This is in contrast to the preceding examples where he took only straight path segments between the events. The “all” in this claim needs elaboration as the history of geometry makes clear. The simplest case that it seems plausible to verify is to imagine a flat plane that separates a source S and detector D. We will consider paths that go from S to P which is some point on the plane, and thence to D. We pursue this further here.
This may be of interest. too