I think Horace's objections may be related to the lack of "postulates" for the Bi-radial matrix system. The observer/observation perspective is not stated clearly, so the reader is left to whatever assumptions they currently have about what you are looking at, and how it is being transformed. It would be probably be very helpful to include some introductory material stating that this is done from a material-sector observer viewing the coordinate realm of extension space.

For example, when I look at the diagrams, I see the equally-angled radial lines not as a measurement of a bounded angle, but a representation of constant, angular speed. If the angular separation increased or decreased going around the point, then it would indicate an acceleration or deceleration. (Assumptions made because I use projective geometry

*pencils*a lot. May not be at all what Russell intended!) By treating it as the projection of angular speed, you don't run in to the problems of trying to represented an

*unbounded*angle in a linear reference system, since angular velocity is always finite (whereas the turn angle, itself, isn't).

That is a very interesting observation. TheThis re-cycling after 360 degrees is the "wave" function integral with the physical universe and the human reference system is a vvalid reference system.

*turn*is an unbounded, 1D angle in time, analogous to its distance counterpart. Projection requires integration, or as Nehru puts it, dimensional expansion: 1D time becomes 2D space, just as when moving 1D space into the time region, you get 2D time and hence the t

^{2}relationship in the time region. When a

*turn*shows up as an

*angle*, it is 2D--a circle--but like any integration, there must also be a

*constant of integration*, which is the number of times that 2D circle occurs in the

*same*space: frequency.