The Larson Research Center

A discussion in the ISUS General discussion forum (see: http://forum.rstheory.com/viewtopic.php?p=4117&sid=b3f59c952b141b923c0a433791fc21f1#4117) entitled, "FP-1 What is Wrong, What is Right," has turned to the discussion of scalar dimensions, a never ending story among students of the RST. The problem is in understanding what the idea of scalar dimensions can mean. In a Reciprocity article entitled "Dimensions in the Universe of Motion," Larson spoke of mathematical dimensions as opposed to geometric dimensions:

"When I refer to dimensions in my works, this term has no geometrical connotations, except where so specified. Dimensions are scalar magnitudes, just numbers. Different phenomena involve different numbers of independent magnitudes. It follows that the number of dimensions with which we are concerned depends on the particular phenomenon with which we are dealing."

Take for instance the dimensions of the unit progression ratio (UPR), where ds/dt = 1/1. Here, (1/1)^0 = (1/1)^1 = (1/1)^2 = (1/1)^3 = (1/1)^n, because a quantity of one raised to any power is still equal to one, mathematically. However, geometrically, (1/1)^1 is different than (1/1)^2, which is different than (1/1)^3, as linear dimensions are distinct from the dimensions of area, and they both are distinct from the dimensions of volume.

Unless this distinction is kept in mind, scalar motion concepts can get awfully confusing, as is readily apparent in the current ISUS discussion:

Peret writes:
"There is a lot of confusion regarding dimensionality in the RS, but I think Ron stated it clearly: s/t. Motion, as speed, is a 1-dimensional relationship between space and time, as indicated by the implied exponents of "1" in the ratio, s/t = s^1/t^1. We know from Larson's dimensional analysis that s^3/t^3 is "gravity", the inverse of mass. If this were the default, his books would be called 'Nothing but Gravity' and 'Universe of Gravity'."

This is a totally confused statement. First of all, when Larson uses dimensions as the dimensions of units, such as units of mass, s^3/t^3, he doesn't mean to imply that the inherent motion of mass has three geometric dimensions. He makes this clear in the quote above, but very explicitly in the following text from the same article:

"The dimensional situation is complicated by the fact that I necessarily have to use the term in its broadest sense, whereas it is more generally used with a very restricted meaning. From the general standpoint, “dimension” is a mathematical term that may be, but is not necessarily, capable of being represented in geometric form. An n-dimensional quantity is simply one that requires n independent numbers for definition. As one dictionary says, by way of illustration, “a²b²c is a term of five dimensions.”

Similarly, the dimensions of mass, given in the dimensional analysis of physical units in Larson's RSt, requires a term of three dimensions, or numbers, to completely define it: a combination of a one-dimensional vibration, with dimensions s^1/t^1, and a two-dimensional rotation of the vibration, with dimensions s^2/t^2. Symbolically, this term would be written, ab^2, a term of three-dimensions.

However, there's a problem here too, because the rotational motion is simply combined with the linear motion, it is not a product of it; that is, in the initial combination, the linear vibration in Larson's theory is a positive value relative to unity, while the rotation is a negative value, and the magnitude of both is unit speed-displacement, resulting in the net zero motion of the rotational base.

If these dimensions were geometric dimensions, mathematically speaking, we would be trying to combine the dimensions of length with the dimensions of area, something we wouldn't want to try to do. We can't add units of different geometric dimensions, though we can multiply them. Clearly, however, in Larson's theory, these discrete units must be algebraically added together, which means that they must be scalar values of different powers, not vectorial values of different dimensions.

With scalar units, this is no problem, because 1^1 = 1 and 1^2 = 1, and the combination, 1+1= 2, would make sense, but given the opposite polarity of the two speed-displacements, the sum is actually 1+(-1) = 0, nothing at all, a seemingly meaningless result.

However, in Larson's RSt, it's not a meaningless magnitude of motion, but just an ineffective magnitude of motion. By adding a second unit of two-dimensional motion to this net zero combination, the first physical entity of matter is formed. Thus, we have 1^1 linear vibration plus (-2^2) negative rotation (or vice-versa, which gives us a (-1^2) net 2D rotation, if we now regard the 2^2 term as two units of 2D scalar motion, one of which is offset, not 4 units of 1D scalar motion. In other words, since the 1D linear vibration is still present, just offset by one unit of the two-unit 2D rotation, we can think of the operation as adding a unit of rotation to the 0^3, ineffective, rotational base,

Therefore, we can now add either a positive or a negative unit of 2D rotation to this base. Adding a negative unit of rotation, 0^3 + (-1^2) = -1^2, but adding a positive unit of rotation, 0^3 + 1^2 = 1^2. The negative combo is identified by Larson as the physical electron, and the positive as the positron.

However, since the net, or effective, 2D rotation is two-dimensional, these two entities are massless. To have mass, the combos need to have effective inward motion in all three dimensions. This happens when an optional unit of 1D motion is added to the electron, or positron, which is identified as an electrical charge, in the form of a rotational vibration. In the case of the electron,

-1^2 + -1^1 = -2^1, and in the case of the positron,

1^2 + 1^1 = 2^1,

or does it? Actually, it doesn't. From Larson's perspective these are 3D combos, where

-1^2 + -1^1 = -2^3 = -8, and

1^2 + 1^1 = 2^3 = 8


Seem confusing? Well, it is confusing, and the confusion comes precisely from mixing up the scalar idea of dimension with the geometric idea of dimension.The trouble is that the concept of rotation is a vectorial concept; It can't be defined as a scalar value, except as an increase/decrease of angle, and angle is defined as a change of direction, a property that scalars don't have.

However, Larson seems to want his scalar cake and eat it too. He does this by regarding 1D linear vibrations as units of discrete scalar motion, and 2D rotational, and 1D rotational vibration units, as independent scalar units of speed-displacement. Thus, if a 1D portion of the cake is eaten up by a linear unit, there remains two units of cake, regardless of the dimensions of these portions. Of course, he uses the concept of a rotating vibration, not a cake, to visualize this:

1) First, the 1D rotation eats up a third of the cake.
2) Second, the 2D rotation of the vibration eats up the second third.
3) Third, the 1D rotational vibration eats up the final third of the cake.

It makes sense, when looked at that way, but looking at it that way requires us to regard 1^1 + ((-1^2)+(-1^2)), not as 1-2 = -1, but as 1 1D + (-2 2D) = -1 2D, something very difficult to explain to mathematicians, unless they understand the independent linear spaces of Hestenes Geometric Algebra (GA). The concepts of GA fit beautifully with Larson's concept of scalar rotation. There is only one problem; They are vectorial concepts not scalar concepts.

At the LRC, we think we've identified the scalar way to work with units of scalar motion, and we are trying to work it out, but the proof will be in the pudding, as they say. Right now, many members of ISUS disagree with our tentative conclusions, which has become the topic of the discussion over there, but whether they agree or not, they at least have to demonstrate that they understand the problem. So far, it doesn't appear that they do. At least, that's how we see it.

Firstly I don't understand how you can get anything not 3D out of combinations of 3D UPRs and 3D (S)TUDRs

Horace,

The best way to understand how a scalar increase or a scalar decrease can be three dimensional is to look at the worldline chart. I can't reproduce it with the software of this forum, but it's not hard to imagine.

With the time progression plotted vertically, and space progression plotted horizontally, when the reversals occur in the space aspect, the space aspect stops increasing. At that point it's possible to pinpoint the space location on the upper side of the unit line that is at 45 degrees to the two orthogonals; that is, it is stationary in space, while time continues to progress vertically.

Let's designate the stationary (actually oscillating over one unit) space location, as q, which is a point with coordinates x, y, z. Now, at point q time is increasing scalarly, but this doesn't affect the spatial extent of point q. It is still a one unit location at x, y, and z, but it's vibrating between point q, at x, y, and z and point q', at x', y', and z', one scalar unit removed. This means that point q is either one scalar unit smaller than, or one scalar unit larger than point q', depending on which point is at the beginning of the increase, and which point is at the beginning of the decrease.

Let's say that point q is at the end of the decrease, and the beginning of the increase, and that point q' is at the other end. The difference between them is the volume x'- x, y'- y, and z'- z, a 3D magnitude.

Now, the inverse of this point, on the other side of unity is a 3D magnitude in the same manner, but it's a 3D magnitude of time, not space. Relative to one another, the "distance" separating them across the unit boundary is two octaves of frequency (the frequency of the SUDR measured in the material sector is (1/2)c, and the frequency of the TUDR is (2/1)c), which can be specified with one number. That's what makes the relation between SUDR and TUDR 1D. It's a mathematical relation of 1 dimenison of magnitude, not a geometric relation of 1 dimension of space.

Having said that much, when the SUDR and TUDR actually combine, the combination DOES constitute an entity of more than one dimension, because the S|T combo obviously must have three numbers to specify it, but we're still investigating the full implications of this. In the meantime, the idea of the VECTORIAL analog, as a line with two end points relative to the middle, works very well, in some respects.

Thus, the short answer, Horace, is that your observation is correct, but for other than geometric reasons.

I hope this helps.

Perhaps the word "anything" had too broad of a meaning.

I wanted to know how in your system you can get a non-3D relation in THE SAME aspect, eg.: 1D relation in space between two motions.


BTW, I hate your forum.
Can't you install something better like the free software at http://www.phpbb.com

To me the "spatial extent" of a point is: a line, area, volume or some of the higher dimensional constructs.

When you state that its extent is not affected, do you mean that point q does not "swell" and still has zero-volume ?

This always bothered me in your 3D SUDR idea, that it is incompatible with the concept of a simple point.

When a volume of a SUDR grows and shrinks, and the points within that volume do not increase with that volume, then the density of points in that volume must decrease.
The alternative are "growing points" and constant density - an even more apalling idea.


Horace

> Doug wrote:
> but this doesn't affect the spatial extent of point q

What is a one "unit location" ?!
Is "location" a one unit sphere or a point ?



> Doug wrote:
> It is still a one unit location at x, y, and z

Horace wrote:

"When you state that its extent is not affected, do you mean that point q does not "swell" and still has zero-volume ?"

I mean that the passage of time does not affect its size in a direct way. I realized when I wrote that statement that it might be problematic, because, of course, the size changes over time, but I meant that we are talking about the change in size due to the space progression's "direction" reversals.

Horace wrote:

"This always bothered me in your 3D SUDR idea, that it is incompatible with the concept of a simple point."

In a universe of nothing but motion, a point too must be motion.

Horace wrote:

"When a volume of a SUDR grows and shrinks, and the points within that volume do not increase with that volume, then the density of points in that volume must decrease.
The alternative are "growing points" and constant density - an even more apalling idea."

In a universe of nothing but motion, there is nothing that can be construed as points within points. Think of two electronic counters. One is a space counter, and the other is a time counter. When you are sitting at your desk, both are running. While you have no trouble imagining the steady increase in time marked by the time counter, when you think of the space counter you try to imagine that the increase marked by its counter as separating everything in the room, but that doesn't happen. Why?

It is because things are made up of matter and the space of matter doesn't increase, it increases and decreases, or oscillates. Therefore, the relative positions of everything in the room is actually a history of the vectorial motions that place them in their positions.

Start at a more fundamental level. The size of the "locations" of the two counters are increasing in sync in the beginning. Therefore, when one reaches size n in the count, the other does too. Hence, spatial size n+100, corresponds to temporal size n+100, but if the spatial counter begins to oscillate between size n+100 and n+99, while the temporal counter continues to increase, when the temporal count reaches n+150, the spatial counter will still be at n+100 or n+99. But the total space progression, or ticks of the counter, will still be the same as the temporal progression count, except that half of them will be counts that went from n+99 to n+100, and half of them will be counts that went from n+100 to n+99.

The PAs show this very clearly, don't you agree?

Horace wrote:

"What is a one "unit location" ?!
Is "location" a one unit sphere or a point ?"

In the above analogy, the one unit location is between n+99 and n+100. From the perspective of n+99, n+100 is a 3D increase, or 1 unit volume. From the perspective of n+100, n+99 is a point. From the perspective of n+98, both n+99 and n+100 are volumes: 99 is a one unit volume, and 100 is a two unit volume.