Why does space have three dimensions?
Space has three directions because three is the width of the one pattern that lasts long enough to hold a position. Each piece of the world has twelve readings, and the repair that settles disagreements between them splits into bands that fade at fixed rates per pass: three directions keep 0.9539 of their content, five keep 0.9, and three keep 0.8794. The wiring allows no other rates. The quickest question an observer can put to the far side and get answered takes six repairs, longer than the fast band's half-life, so fast content has drained before anyone can confirm it. A position has to be something two observers can compare and both get. Only the slowest band survives that, like the lowest note left ringing after a struck bell, and it is three wide.
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 15: Why Does Space Have Three Directions?watch a universe make its own particles