Whenever we talk of the expanding space, we do not have difficulty mentally imagining it. We naturally envisage a continuous increase of Cartesian distance in 3-space (that is, volume), starting from the zero or the 'origin.' Furthermore, we do not have difficulty imagining an un-ending, infinite, expansion.

Now Larson's crucial discovery that space, time, and motion are quantized demands a re-examination of our common sense (Cartesian) view of the expansion of space. Since there would be a MINIMUM quantity of space, Snat, we are not justified in envisioning the expansion of space as commencing from the Cartesian origin/zero---it rather commences from Snat. In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

There are two important consequences of this fact, namely, that the 'origin' of motion in the inside region is not zero but uniformly distributed over the inside surface of the sphere of radius Snat.

Firstly, all radial directions, from any point on the 'spherical origin' toward the center of the Cartesian frame are totally equivalent. They become scalar from the point of view of the Cartesian observer.

Secondly, the 'expansion'---that is, the contraction in the Cartesian reference frame---continues infinitely like it does in the outside region. The contraction, commencing from the distributed origin, progresses for ever inward toward the Cartesian origin, which is the INFINITY of the inside region, never eaching it. Some researchers called this the counter-space infinity, CSI.

Nehru, Bruce

## Part I - Re-examining Coordinate Systems

### Part I - Re-examining Coordinate Systems

Every dogma has its day...

### Re: Part I - Re-examining Coordinate Systems

A question of clarification - I understand the difference between using Cartesian zero point as origin and correcting it with the conceptualization of a spherical surface of radius Snat, but I'm a bit unclear on how the inside of that spherical surface (the 'distributed origin') appears as contraction to the Cartesian observer as the exterior expands. Can anyone help clarify this for me? As this conceptual sphere expands outwardly, does the interior have to contract in order to maintain the 'thickness' of the sphere as uniform? Does the 'thickness' of the sphere represent a unit speed boundary? Or am I mixing up concepts?bperet wrote: ↑Tue Aug 03, 2004 2:23 pm In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

### Re: Part I - Re-examining Coordinate Systems

I'm a bit confused as to why the inside of the sphere (the 'distributed origin') appears as a contraction; would it not stay the same size? Or must it appear as contraction as the exterior expands in order to keep the 'thickness' of the sphere uniform?bperet wrote: ↑Tue Aug 03, 2004 2:23 pm The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

I did attempt to post this question a few days ago, but the board would not allow me to. So, apologies if my question is not as thorough as it otherwise might have been. I am aware of Bruce's passing (RIP) and am asking at large as I know he cannot answer.

### Re: Part I - Re-examining Coordinate Systems

Mr. Kent wrote: ↑Wed Apr 22, 2020 1:39 pmbperet wrote: ↑Tue Aug 03, 2004 2:23 pm The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

The plane at infinity (space) and point at infinity (counterspace) exchange aspects of expression when moving across the unit speed boundary.

These are not structures but

*motions*(speed regions) and so there is no material thickness.

What was a point at the origin becomes a

*plane*-- the inside surface of a sphere -- becomes the origin (2D) and that motion is

*distributed*over an area in 3D coordinate space:

Continuous outward motion (towards a center point at infinity)

*appears*as a contraction as motion is distributed over increasingly greater temporal volume which must then normalized (scaled) to equivalent space for observation in extension space. This begets the concept of

*density*when projected into 3D coordinate space with resulting normalization to clock time. The

*farther outwards*in counterspace (inwards in space), the

*greater*the density.

There was a lapse in authorizing new-user registration. Welcome.

Infinite Rider on the Big Dogma

### Re: Part I - Re-examining Coordinate Systems

We are speaking of a sphere where s = 1 and all motion is in time (1/tMr. Kent wrote: ↑Mon Apr 20, 2020 8:15 amA question of clarification - I understand the difference between using Cartesian zero point as origin and correcting it with the conceptualization of a spherical surface of radius Snat, but I'm a bit unclear on how the inside of that spherical surface (the 'distributed origin') appears as contraction to the Cartesian observer as the exterior expands. Can anyone help clarify this for me? As this conceptual sphere expands outwardly, does the interior have to contract in order to maintain the 'thickness' of the sphere as uniform? Does the 'thickness' of the sphere represent a unit speed boundary? Or am I mixing up concepts?bperet wrote: ↑Tue Aug 03, 2004 2:23 pm In other words, the effective origin (of the expansion) is a spherical SURFACE of radius Snat---not the Cartesian zero POINT.

The next question is what happens when we cross this sphere of radius Snat and go inside! The effective (physical) origin of the 'expansion' is UNIFORMLY DISTRIBUTED on the entire inside of this spherical surface. Let us call this the "distributed origin." There is still expansion but this expansion appears as a radial contraction to us (the Cartesian observers).

^{2}). The spatial aspect is constant with motion in time only (energy).

The boundary can be considered as though speed-contours on a topographical map where s/t=1.

There is no "thickness" as these are motions (speeds or inverse speeds) not material structures. The boundary (for an individual motion, not necessarily an aggregate) is discrete. A line has zero "thickness" much as a "point" has no dimension.

You're thinking of the motion as spatial -- outward in space. Now go outward

*in time*-- inward in space.

Please don't get frustrated -- you can do it. It takes time and effort. Keep reading and if you haven't already Larson's publications are a necessary primer IMHO.

Infinite Rider on the Big Dogma

### Re: Part I - Re-examining Coordinate Systems

Thank you for the encouragement. I'm drawn to RS(2) and will continue in my attempts until I 'get it'. It's not easy, but everyone I've come across on the AQ forum has been exceedingly kind and helpful. Rare in today's world unfortunately. So, thanks again.

And I do have copies of Larson's books; which one do you recommend that I start with?

### Re: Part I - Re-examining Coordinate Systems

Nothing but Motion Volume I of a revised and enlarged edition of THE STRUCTURE OF THE PHYSICAL UNIVERSE

Keep in mind there will be some concepts that are revisited in RS2 which do provide a number of notable differences. Some of Larson's original concepts of RS lacked the primacy of rotational (Yin) motion in favor of a rather strictly linear (Yang) approach.

Infinite Rider on the Big Dogma