Stand a line on end, you have a point.
Stand a 2-dimensional figure on end, align 2 pairs of points, you have a line.
Turn a four-dimensional object on end, align 4 pairs of points, you have 2-dimensional object.
The conjectures carry this out to any N. The third conjecture is clearly false; perform a mega-alignment of two four-dimensional objects (or one object separated in space over time), you have a 2-dimensional object. But it will be interesting to see at higher dimensions where the conjecture might hold true.
Credit to BLW for the relation P = 2^(P-1) implied here.