Part III - Implications of rotational space

This forum is dedicated to the student just starting out with the concepts of the Reciprocal System, or RS2. Questions and clarifications for the RS/RS2 concepts go here; please place new ideas and commentary in the appropriate RS2 fora.
Post Reply
User avatar
bperet
Posts: 1501
Joined: Thu Jul 22, 2004 1:43 am
Location: 7.5.3.84.70.24.606
Contact:

Part III - Implications of rotational space

Post by bperet » Tue Aug 03, 2004 2:34 pm

1. There is another implication of the maximum rotational space (angle) being infinite in the Inside Region, coupled with the inversion that takes place at the unit boundary. Within the circle of radius 1 Lnat, representing the Inside Region, the increase in angle follows an inverse pattern. That is to say, instead of the series 1, 2, 3, 4,... , it would be:

1, (1 + 1/2), (1 + 1/2 + 1/3), (1 + 1/2 + 1/3 + 1/4), ...

The physical effect of this diminishing nature of the angular increment in the Inside Region is to pack infinite angle in the finite Cartesian circle of 2π radians. Once again, an implication not foreseen by common sense!

2. There is also a dimensional implication. In the Outside Region multiplying two orthogonal lines (m * m) produces an area (m2). Further multiplying the area by an orthogonal line produces volume (m3). In the Inside Region, an angle (θ) sweeps an area (A = 0.5 * θ * r2), and a two-dimensional angle (θ2) sweeps a four-dimensional hypervolume (H = 0.25 * θ2 * r4).

Bruce, Nehru
Every dogma has its day...

Post Reply