Physicists of LW, would you care to weigh in on this? How well does Cochran's article describe your thought processes?
"And therefore the curves must cross" seems more like mathematical thinking to me. (Which has its uses in physics, obviously.) Certainly the curves must cross at some point, but it is not obvious (well, not to me) that they will do so within the range for which third-power decay and exponential decay are good approximations. (Obviously the electric field is nowhere infinite, so the x-inverse-cube relation cannot be intended as an exact description everywhere - it must break down near the zero.) To see that you'd have to put in the boundary condit...
A new interesting entry on Gregory Cochran's and Henry Harpending's well known blog (West Hunter). For me the information I gained from the LessWrong articles on inferential distances complemented it nicely. Link to source.