Space, Time and Motion

Larson considers space and time to both be "real" quantities, magnitudes as aspects of a ratio that define a speed (some distance in space to some amount of time), or in general terms, a motion. Motion comes in two flavors: speed, as space to time (s/t), and energy, as time to space (t/s). Larson also defines two, separate realms for these motions, the "Material sector", with a coordinate space system, and the "Cosmic sector", with a coordinate time system. Unfortunately, Larson never did get a clear connection between his scalar and coordinate systems and, indeed, the relationship of t/s could represent either "energy" or "cosmic speed".

When it became apparent through Prof. KVK Nehru's research into birotation that there was a polar geometry involved in many of the relationships of motion, RS2 moved to the natural consequence of the combination of linear and polar geometries into a single relation, that of the complex number. In RS2, motion is represented by a complex quantity, where the "real" component defines the rectilinear aspect, what is local, transient and observable, and the "imaginary" component defines the polar aspect, that which is nonlocal, periodic and unobservable (at least through direct measurement).

RS2 also defines two flavors and two "sectors", depending upon which aspect is associated with which geometry:

1. real space + imaginary time = Material speed
2. real time + imaginary space = Cosmic speed
3. imaginary time + real space = Material energy
4. imaginary space + real time = Cosmic energy

The difference between #1 and #2, compared to #3 and #4 is the geometric inversion. In the ratio of motion, the numberator and denominator can be either rectilinear or polar. #1 and #2 have a rectilinear numerator and a polar denominator, whereas #3 and #4 have a polar numerator and rectilinear denominator. This gives a clear distinction of what is material and what is cosmic; what is speed and what is energy.

RS2 treats motion as a cross-ratio, four points in the complex plane that can be either colinear (in a straight line) or concyclic (along the circumference of a circle). The colinear arrangement represents a rectilinear geometry, the concyclic arrangement represents a polar geometry.

There are 'technically', four possibilities, but the relations of space to space and time to time do not constitute neither speed nor energy, and hence are not "motion". Using the same analogy, rectilinear to rectilinear and polar to polar do not constitute geometric "motion", and are not considered to be naturally occurring in a reciprocal system.

What the RS2 interpretation of motion reduces to is a very old concept, that of the Tao of Motion... the ancient concepts of the yin-yang, or the feminine and masculine generative principles, bound together in the Tajitu--the ancient, philosophic idea of "motion".

Real versus Imaginary

What we can see and measure is that which we call "real". In the Material sector, the sector of our conventional experience, the "real" quantity is that of space, which we refer to as "local" and "observable". We see and measure rectilinear space ONLY! Remember this well!

Our "imaginary" quantity is what we call time. Being of a polar geometry, it has a natural periodicity to it, the clock.

Our measurement of space is modified by time. Clock time can be considered to be a scaling factor of space. 10 meters in 2 seconds can be reduced (scaled down) to 5 meters in 1 second, which maintains the same ratio (what is called a projective invariant). TIME SCALES SPACE. Notice the word in the middle--SCALE, as in "scalar motion."

Space versus Time

The only difference between space and time is "what we see" and "what we don't." This is a limitation of our physical sensory system, which evolved to measure space, scaled by time, to produce what we perceive as causality--an ordering of events. Without the cause-and-effect system created by our consciousness, the sensory world of space would just become jumble.

Since time has all the same attributes of space, beings of the Cosmic sector would have their locality in time--they see and observe "distances" in time, and it is the spatial aspect that becomes invisible. Our consciousness plays a large part in interpreting what we see and experience, though there is a lot more going on about us then we are normally aware of!

Additive Inverse, Multiplicative Inverse, Conjugate

By using the idea of "complex motion", based in the cross-ratio, in addition to Larson's basic, reciprocal relation, RS2 also introduces a third component, that of the conjugate. Prof. KVK Nehru noted some years ago that the mathematical relations concerning the Cosmic sector were conjugate relations, not reciprocal relations, and the Cosmic sector was not the "inverse" sector, but the Conjugate sector to the material. By using complex numbers, the complex conjugate becomes available for use in the relationships, which greatly helps to distinguish the material "energy" relations, which are inverses, from the cosmic "speed" relations, which are conjugates.

When you plot out the range of motion on the complex plane, 8 different regions appear; 4 outside the unit motion boundary, and 4 within. The outside regions define the coordinate relationships (Larson's "time-space" and "space-time" regions), the inside regions define the scalar ones (what Larson calls the "time region" and "space region"). It also defines regions of coordinate "energy", which account for the "field" concepts such as magnetism and gravity.