I think you will also agree that we cannot have space without time, nor time without space. Yet you insist on considering only one aspect in separation from the other, which is evident in your quote below:

dbundy wrote:

We only need refer to numbers to see that no other reference is necessary than that which preceded the increase or decrease. One way to put is the way the ancients understood it: If we have two numbers (magnitudes,) one greater than the other, there will always be another number (magnitude) greater than them both.

The ancients were correct and also there will always be another number smaller than them both.

Note that In these examples three numbers are compared (that comparison requires time to determine whether the numbers got bigger or smaller). If you had just one number you would have nothing to compare it to and you could not even begin to tell if it grew or shrunk.

Horace, Larson's assumption that "direction" reversals, were the only way to introduce variation into the uniform progression of space and time was challenged by Nehru and Peret, who came up with their alternative assumption based on the concept of bi-rotation.

On the other hand, I maintained that the objections to Larson's idea of "direction" reversals could be overcome, if the reversals were considered as 3D reversals instead of 1D reversals, since that would eliminate the "saw tooth" waveform, which was the main objection to the reversal assumption.

But a 3D reversal has its own challenges, one of which leads us to the consideration of the profound concept of a "point" which so plagues philosophers to this day.

But now, you raise another one of those challenges: If space and time can only be regarded together as motion, how then can there ever be what Larson called a "displacement" between them? My answer to that question is found in the nature of numbers. We think of the integers as separate from the rationals, but in reality, they are not. The set of integers that we call natural numbers, or counting numbers, are in reality rational numbers, partially represented.

The unit denominator of these numbers is ignored for convenience of expression, but the truth is, they are always part of the number. What we choose to call negative numbers, which are so troublesome philosophically, are actually inverse integers, with unit numerators.

These inverse integers can also be regarded as fractions of a whole, but not without introducing an element of confusion into the discussion of ratios. The ratio of time over space is the inverse of the ratio of space over time, but when we consider the number line as a whole, we have to realize that there is another sense, a second sense in which we can perceive the reciprocity of numbers and that is a reciprocal number line.

The best analogy I can think of to illustrate this is to picture a "teeter-toter," or "see-saw." The lever is balanced upon a fulcrum in the center. When it is unbalanced, say with a man on one end and a woman on the other, the view from one side, where the lower end is on the left say, and the higher end on the right, the view from the opposite side, which is looking in the opposite direction, shows the lower end is on the right, and the higher end on the left, the reciprocal of the first view.

This analogy is very useful for understanding the two senses of reciprocity in the RST. The view of the unit progression from the MS point of view is the reciprocal of the same unit progression from the CS point of view. This is important to keep in mind, when we consider variations from the unit progression, because if we don't we can easily lose track of what the numbers mean.

The number s/t = 1/2 is the inverse of the number s/t = 2/1 in the MS, where s/t = 1/2 is normally represented on the number line to the left of the unit progression, s/t = 1/1, and s/t = 2/1 is to the right. To be consistent, the CS representation of the number line, should have t/s = 2/1 on the left of the unit datum, and t/s = 1/2 on the right, if we were to extend our investigation into the CS. Just sayin.

Now this exact correspondence of our number system of ratios to the fundamental scalar motion ratios of the theoretical universe is just uncanny, in my opinion, because it permits us to quantify an RST-based theory (RSt), something students of the RST have long called for.

Remember, that in any given RSt, everything is a motion, combination of motions, or a relation between motions and combinations of motions, so the ability to quantify these motions and combinations and relations is invaluable to the theoretical development.

So, with this much understood, we come to the question of absolute magnitudes. Does Larson's postulate hold that posits these? I think so, precisely because an increase or decrease in magnitude of space over time, or time over space, can be quantified as just discussed. We cannot know what causes the increase or decrease to occur, but because it can exist, it does exist.

Representing tne cycle of expansion/contraction for every two units of time (space) is completely analogous to the analysis of a rolling wheel, or a swinging pendulum or a propagating water wave, sound wave or light wave. It's well understood in all but the 3D case, which seems physically impossible, but mathematically feasible, nevertheless.

That's all I can say at this point, Horace. I can understand and work with these numbers, but I can neither understand nor work with the concept you are presenting here, at least so far.