Reciprocal System Research Society

How do you talk about a theory without defining what you mean by its basic tenets?

What is time?

What is space?

Then define motion.

And finally dimensions of space and time.

What is time?

The label for one aspect of a ratio.

What is space?

The label for the other aspect of a ratio.

Then define motion.

The ratio.

And finally dimensions of space and time.

The dimensions are of motion (ratio).

If I understand RS2 correctly I can offer a more complex answer:

space time and motion are defined by their properties in RS:

(1) space is always orthogonal to time

to represent it we can use a complex number composed of two scalar parts (scalar time and scalar space; let time be real part and space the imaginary)

(2) the ratio between space and time (the two parts) is the scalar motion

now we can couple two orthogonal motions in the same way we coupled space and time

(3) the ratio between two scalar motions (crossratio) spawns the equivalent space (or equivalent time)

now we have a quaternion - a pair of complex numbers (see Cayley-Dixon construction) - wich has 3 imaginary parts - the equivalent space - and one real part - the clock time. So far only the clock time could be related to our experience: it is what we normaly call time. Note that now you have three independent motions instead of just two.

(4) one of the motions can be represented in three-dimensional framework

Coupling the space-like crossratio with the time-like crossratio one gets the the extension space which is the space we live in: the octonion contains three threedimensional subspaces connected by one axis. We can choose one of them to be the spatial framework we are in. So now we have an octonionic-valued field representing this space-time which is not unique but is subject to some gauge transformations. These are souch that the crossratio is always conserved.

In other words motion - which is fundamental and unique provides a nonunique mapping from threedimensional (equivalent) space to threedimensional (equivalent) time. There is one further constraint: the motion is quantized but that is for a longer talk.

PS: please give me some feedback on whether it was understandable and/or correct

Thanks in advance

(1) space is always orthogonal to time

Even though correct, the statement can be confusing because people will think of time as an orthogonal, spatial axis, like X-Y on a graph. I prefer to think of space and time being "out of phase" by 90 degrees, like sine and cosine waves are (when one is at the min/max, the other is at zero).

In a 3D coordinate system, you can visualize it by the center of a spatial cube being a corner of a temporal cube. (Technically, it is a 4D system, since points and volumes are being dualized.)

to represent it we can use a complex number composed of two scalar parts (scalar time and scalar space; let time be real part and space the imaginary)

Originally that is what I thought, but since discovering how the "rotational operator" (imaginary number) was misprepresented by treating it as a vector, I have come to a different conclusion where the imaginary portion represents the "equivalent" space or time, or the yin aspect. Therefore, the complex quantity is (yang + yin) or (speed + energy) or (linear + angular).

When trying to express scalar motion in a coordinate system, the "real" part is the clock (scale factor), because you use homogeneous coordinates (x y z w) and it is all linear velocity. Homogeneous coordinates are backwards from the normal vector system. Normally, the w would be the first entry as it is in a quaternion (and I do flip it around in my computer simulations).

(2) the ratio between space and time (the two parts) is the scalar motion

now we can couple two orthogonal motions in the same way we coupled space and time

I think the confusing bit here is that we are accustomed to a dimension being a single variable, not a ratio. Like yin-yang, you cannot separate space-time. In the RS, you are dealing with dimesions of speed, not distance or duration, and our system of math requires us to use two, independent variables to express a single dimension of speed. You cannot "couple" space and time to get a ratio, as they are not independent aspects.

(3) the ratio between two scalar motions (crossratio) spawns the equivalent space (or equivalent time)

Equivalent space (or time) is just how Larson expresses the yin (angular) aspect of motion since he assumed everything was linear (which is why he had to create a "line" with a photon, in order to have something to rotate). RS2 integrated the yin aspect with imaginary numbers.

You have the right idea, though, with complex numbers. But consider:

Parallel: (1,i) (1,-i) = birotation, cosine wave function

Orthogonal: (1,i) (1,j) = quaternion (since i.j = k)

The cross-ratio is hidden in the RS by the concept of "displacements," which are offsets from unit speed. The cross-ratio would be (1:1)/(s:t)

time is a label? So the fundamental parts of RS are labels? ratio of labels? is that the best we can do?

time is a label? So the fundamental parts of RS are labels? ratio of labels? is that the best we can do?

I think that's pretty good. Science can't answer what are ultimately philsophical questions. What you really want is utility in the conventions used for modeling the behavior of what we experience. In my view "space" and "time" are fundamentally one in the same thing and only made distinct in their mutual identity by labels. Define any spatial or temporal attribute and its exact complement must also coexist as the same "motion'".

I think the confusing bit here is that we are accustomed to a dimension being a single variable, not a ratio.

These words should be framed and hung on a wall.

IMO they should be in your next book/tutorial, too.