^{2}. But "s"

*isn't*replaced--when you are within the unit space boundary, s=1 and because it is at unit speed, he ignores it (just as we ignore "t" in the denominator of speed to get distance... s/1t = s).

The description in RS2 is different, because RS2 recognizes the "geometric reciprocals" of linear and angular velocities. Outside the unit space boundary, you have linear motion from 1->infinity. When you move inside the boundary, geometry inverts to angular motion from 1->0. Linear velocity is expressed mathematically as v

^{1}and angular velocity is orbital, v

^{2}. Since s=1 inside the boundary, you end up with 1

^{2}/t

^{2}= 1/t

^{2}, the same as Larson.

The origin of the geometric reciprocal is that in 3 dimensions, lines and planes are "duals." Any (x,y) pair can represent either a line (0,0)->(x,y) or the corners of a plane (0,0)--(x,y). Lines are 1-dimensional structures, planes are 2-dimensional, so that gives the 1st to 2nd power relationship.