Why does gravity follow an inverse-square law?
Gravity weakens with the square of distance because space has three directions, and the exponent is the number of directions minus one. The world here is a network of small observers joined by seams, the links where neighbors compare readings. An influence whose total outflow is fixed by its source must cross seams on its way out, and that same total crosses every closed shell around the source, so the strength on one seam is the total divided by the seams in the shell. Twice as far out, a shell in three directions holds four times as many seams, so each carries a quarter. With four directions it would carry an eighth. Electric force obeys the same count, and a 1971 experiment at Wesleyan University pinned its exponent at two to fifteen decimal places.
Also in Chapter 26: Why Exactly These Forces?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 32: Why Does Anything Move?watch a universe make its own particles