Dimensions in the Reciprocal System

[bperet]

I noticed from some of the posts that there seems to be some confusion regarding dimensionality in the Reciprocal System. Let me attempt to clarify, because Larson's use of "dimensions of motion" do not match the conventional definition of a dimension being a single, scalar magnitude of measure.

In conventional parlance, a "dimension" is a measure of height, width or depth, in one of those directions. When it is applied to math or physics, a "dimension" is a magnitude attached to some unit of measure, which can be "3 inches," "5 seconds," "spin-1/2," etc. Multiple dimensions are just a list of numbers used to describe some structure or behavior.

For example, if you see Z³, it has a dimensionality of 3, because it is Z x Z x Z -- three "Z's" that happen to all have the same value. If Z=2, Z³ = 8 just as 2 x 2 x 2 = 8. A "dimensional power" is just the same magnitude, repeated. X.Y.Z is also 3-dimensional, but can have different magnitudes for X, Y and Z.

When it comes to the "dimensions of motion," or "scalar dimensions" (Larson tends to use the terms interchangeably), confusion sets in because in the RS, you cannot have space without time, nor time without space--the "dimensions" are actually ratios of s/t or t/s, composed of TWO magnitudes--not ONE.

Conventional thought would consider a "dimension of motion" to be 2-dimensional, because s/t = s¹t^-1. That's two variables, like X and Y on a graph and hence would be 2-dimensional.

The confusion with dimensionality in the RS stems from applying the rules of the conventional frame of reference (space only, with width, height and depth) to a universe based on the ratio of motion--three dimensions of speed, (s/t, s/t, s/t).

So when dealing with RS/RS2 concepts, remember that a "dimension of motion" is considered a single dimension, even though it is composed of two, scalar magnitudes, and that the datum of the system is UNIT SPEED -- a one-dimensional ratio.

In order to extract conventional dimensions from the RS dimensions of motion, three things are needed (described in detail elsewhere): an observer, something to observe and a second "something to observe" to act as a reference to define which way is "up." Once you have defined these absolute locations, a conventional coordinate system can be created from the scalar dimensions of motion as a projection, much like the sun casts a shadow of an object on the ground. Note that these coordinate dimensions have no independent existence--they are a shadow, only. If you remove the observer, observed or reference, coordinates can no longer be determined--and cease to exist.

The dimensions of motion are static, hence Larson's use of the term, "absolute location" to describe them. The coordinate dimensions (material sector s³/t or cosmic t³/s) are dynamic, in the sense that they are created by the observer.

If you are interested in a better understanding of how we create coordinate systems, study the learning process in infants--when a baby, new to the world, tries to figure out how to see what is going on around them, and reproduce it. The first things that show up are the line and circle... linear and angular velocity, tied to clock time to produce lengths and arcs. They see mom and dad as "stick figures" -- it takes a lot more to learn surfaces, colors, textures and the thousands of other factors that go into the properties of an object's projection. (If you've ever played around with face recognition software, it makes stick figures out of images--looking for the eye, mouth and nose "circles" at specific angles from each other.)

Larson's Reciprocal System is comprised of three dimensions of motion. It is the "projective stratum" of projective geometry, where the dimension of motion is actually a cross-ratio, with one of the ratios set to the unit speed datum. And the rules of projective geometry are followed, to produce the Euclidean projection by adding assumptions (affine, metric and Euclidean). There are two Euclidean projections in the RS, the material sector and the cosmic sector.

In RS2, there are technically four scalar dimensions, two forming a projective duality in space and two in time, making the system completely symmetric. However, because only a single dimension can be transmitted across the space-time boundary (again, a ratio--two magnitudes), we only observe three dimensions: the two in the aspect where our observer/observed is located and the net motion from the other two in the reciprocal aspect.

This projection of two dimensions into one is most noticeable in Larson's atomic displacement model of A-B-C, where A-B are the two, "magnetic" dimensions and C is the single, projected dimension from the other aspect, the "electric." In RS2, we have updated this to be A-B--C-D to define the full motion. (It turns out that C-D, when the electric motion is seen as 2-dimensional, defines the quantum energy levels--exactly.)

So if that did not totally confuse you, I don't know what will!

[adam pogioli]

Like everything you write Bruce, this clarifies and confuses, excites and tortures my mind. It clarifies several things and opens up several more questions, most of which I am not sure how to ask. I am still trying to decipher Nehru's paper you suggested on the interdimensional ratio. He always tends to lose me in some of the mathematical detail, though I keep trying since I know he has addressed many of the important issues. I appreciate your attempts at plain conceptual explanations.

Can I make some comparisons and draw a general picture and you tell me where it goes wrong?

Dan Winter tends to often cite Bill Tilller's experiments that supposedly show that human attention compresses the "field". Dan claims that the phase conjugation that results from perception creates the spin path towards center that we call gravity. For Dan, everything seems to boil down to phase conjugation. I tend to understand that spiral path as describing a complex apparent motion caused by the coupling of the observer, the observed and the reference object. The shear stress caused by correlating what are inherently independent motions create the apparent motions that we observe through the reference frame. The rotation aspect creates periodicity from which we can judge progression, both of which are transmitted across the boundary as a net motion in the reciprocal dimension defining our imaginary/phase/reference motion, which along with the now normalized observer and observed make our three familiar dimensions?

What would your description be of how we get from a cross ratio where one ratio is unity, to the speed/energy dimension of Larson's two units of motion concept? What do you mean by a projective duality, two in space, two in time? Are the two in space between the observer, the observed, and unity, with the two in time as merely the inverse of the spatial motions balancing it all out to unity?

Why are space and time aspects named in the projective stratum? Aren't they pure ratios until the affine strata? Until there is some assumption added? I think it would help to see how you construct dimensions from the observer's perspective, starting with the a single reference point.

[sstivender]

BPERET

Thank you for the discussion on dimensions in the RS. In the spirit of gaining more insight I have a couple of questions.

How would you characterise the directions in a three dimensional frame of reference of speed? Would you even say a dimension of speed has direction?

Do these dimensions of speed follow a traditional definition such as a displacement in one dimension does not produce any displacement in the other two?

[jpkira]

I was attracted to RS because of its simplicity in describing reality but find now that it is anything but. I also believe the rule of speed of light made no sense as the top speed. Again another reason I find RS interesting. But the details as above seem to be tangled in words and concepts and leave me searching for something more. Perhaps our observation point makes RS so fuzzy. I don't think our reality is at all this complicated but our view [or our lack of truly understanding outside that view] makes it hard to describe and "fit" any theory.

[adam pogioli]

"Fuzzy" is what most of the quantum theory speculations make of reality. There is even a "fuzzy" logic to go along with it. RS theory is simple and coherent by comparison, at least in the sense that everything is analogically connected to everything else, rendering every phenomenon a reflection of every other since they are all built up of the same structures of motion. The universe obviously has some complex structures in it, but in RS they are still just aggregates of the simple fundamental motions that make up everything.

You are right to point to the oberver as a source of complication and complexity, but this isn't to say we are obfuscating some simple objective structure with the incoherence of our subjectivity. In order to collapse that complexity down to simple relationships, we would have to close off reality from novelty and difference. Absolute coherence depends on a completely deterministic structure. Any open system will have elements that seem random from within and which consequently prevent information from being compressed down to simpler algorithms. Any sophisticated formalism ends up being incoherent or incomplete. That is the nature of the mind and the world that is formed by it, which is the only world we know. The scalar domain or the absolute motion of the universe beyond our reference frames may be without the difficulties, conflicts and ambiguities of our relative worlds, but the coherence of unity is singular and without any structure to speak of. To get any perpsective on unity we have to build up symmetry through the murky waters of difference. We have to talk to each other and listen and think in different ways. We have to find and create a coherence that connects intuitively with that scalar motion, to the true motion and meaning of every process, which may be the complete opposite of the appearence in our organism-specific reference system. What is space and what is time? Where ends the meaning, where begins its context?

I think RS theory is remarkably coherent but it is in the process of shedding its original fundamentalism and applying its powerful logic of reciprocity to what quantum theory has been struggling with for generations: to move beyond an objectivist rendering of a complex indeterminate world and become a practical science of understanding the symmetries of transformation and applying them. Rather than breaking up the world trying to figure out some fundamental parts, ideas are emerging to show us how to perform transformations that create "quantum coherence", that create symmetries that can localize the non-local, condense and unify difference, and render the most complex system accessible to the simplest analogy or being.

[bperet]

The single, largest problem people face when trying to understand the Reciprocal System is not one of intelligence, but a lack of "prerequesites," namely a classic education in some very basic principles, stemming back to Plato. I was exposed to projective geometry back in Junior High. Today, most college graduates are totally unfamiliar with the concept.

Projective geometry is just the mechanical version of Calculus, where differentiation become the creation of shadows (dimensional reduction, as Nehru calls it) and integration is reconstructing an object from its shadows.

It all goes back to the allegory of Plato's Cave--we're talking 400 BC here, so nothing "new"--where people stuck in a cave with their backs to the door, try to understand the outside reality by the shadows cast on the wall. Science has become Plato's cave, because they are fixated on the shadows--the 3D spatial coordinate system--and rather than admit that there is something casting those shadows (scalar relationships) and they invent "devices" to explain away the interactions between shadows (quantum mechanics). That is where the RS came in--Larson looked behind him and saw what was casting those shadows, and spent 50 years of his life trying to explain what he saw to others, whom cannot see beyond the shadows cast.

Projective duality is one of the basics needed to understand the geometric reciprocal. To understand it, draw a triangle. Now, did you make the triangle by connecting three dots (vertices) with lines, or intersecting three lines to form the vertices? Does it make a difference? Yes, it does.

Connect-a-dot is constructive, one is associating locations into a filled shape. That comes from coloring-book days--connect the dots and look, it's a bunny.

Intersecting lines (actually edges of planes) is destructive, you are leaving a triangle-shaped hole. Place 3 sheets of paper on the table, so they leave a triangle-shaped hole.

Both define areas--but from different premises. If you don't understand the premise, then the answer does not make sense. So when the RS/RS2 does not make sense--a premise has been overlooked or misunderstood. And that is why the RS is difficult to learn--conventional premises that you were taught in school do not apply to the reciprocal relation--they only apply to the shadows on the wall, not what is casting the shadow.

Projective geometry is an attempt to define those premises (assumptions) that are ingrained in our consciousness, with the hope that by "knowing how you got there" (creating the shadow on the wall), one can reverse-engineer those premises and make an educated guess at what is actually casting the shadow.

When mathematics were applied to projective geometry principles, it was found that the only "invariant," the only concept that remained true to form, regardless of all the assumptions piled upon it, was the cross-ratio, a ratio of ratios, what Larson calls "motion" in the RS. The RS (moreso, RS2) is just the set of rules to transform between shadows (volulmes and structures) and the objects casting them (scalar motion).

In order to understand projection, I would recommend you download a program called POVray (http://povray.org) and go through the tutorial. POVray is a raytracing program, which allows you do define solid objects in a virtual world with a simple syntax (like a box by its corners), manipulate those objects, and insert a camera to render what the camera sees in this virtual reality. It will teach you all about coordinate space, transformations (key to projection) and the observer principle--the camera. But in the case of this virtual reality--ALL THE ASSUMPTIONS can be examined and altered, such as "which way is up," the kind of lens: perspective, orthographic, fisheye, etc., and you can SEE how those assumptions affect "what you see is what you get." And people can get really exotic with this program (see the Hall of Fame on the site), because it allows you to also put in pigments, textures, finishes--all the visual, sensory attributes, which are also assumptions. It can produce virtual images so real, it is difficult to distinguish them from a photograph.

Once you understand what goes into a computer program producing a "reality," you can learn quite a bit about how your consciousness does it--since the program is just an externalization of those functions of consciousness. And remember--the ONLY input to POVray is numbers in a machine... yet from these numbers, a reality is created. The same process as the RS "reality."

[bperet]

For Dan, everything seems to boil down to phase conjugation.

As you've noticed, my diagrams include an inverse, opposite and conjugate. Each is applicable to a specific domain, and phase conjugation demonstrates the relations between the material and cosmic sectors. It can be seen numerically as conjugate units of measure: force in the material sector is t/s². Force in the cosmic sector is s/t². Notice that this is NOT the reciprocal, which would be s²/t, but its conjugate (numerator and denominator flip, but the dimensional magnitudes keep their place).

So "phase conjugation" plays a big part in "how time changes space" at a macroscopic level.

What would your description be of how we get from a cross ratio where one ratio is unity, to the speed/energy dimension of Larson's two units of motion concept?

A cross-ratio of 1:1::1:1 doesn't do much... you have to create a displacement (a non-unit speed in relation to the unit speed of the progression). A displacement is a "delta," a change from the datum which is what gives rise to a "dimension," because you now need one magnitude to express it. (Unit speed is dimensionless, because it is the datum of measurement.) Remember, dimensions are how many numbers (or variables) we need to describe something, and a displacement needs ONE, so it is 1D. Once you have a dimension, you've got 2 possible "units of motion" as Larson describes in his books, speed or energy. Inherently, it is neither because we don't know how to observe it without making some assumptions as to whether the displacement is in space or time, and where we are observing from (space or time).

In his books, Larson assumes the "conventional reference system" of 3D space and clock time, the material sector, and starts with the "speed" assumption of s/t being the 1st unit of motion.

What do you mean by a projective duality, two in space, two in time? Are the two in space between the observer, the observed, and unity, with the two in time as merely the inverse of the spatial motions balancing it all out to unity?

When one rotation encounters another, there are two possible outcomes: first, the interaction is "orthogonal" and a dimensional increase is the result. Take one circle and intersect it with another, to produce a sphere. In math, multiply two complex quantities to get a quaternion. The other possibility is what Nehru calls "birotation," after Euler's formula--the rotations are coplanar and dimensional reduction occurs, producing a wave. In math, two complex numbers merge through the Epsilon function (duality--still independent rotations, but the net result is dimensionally reduced).

The maximum expression of duality is two, which Larson refers to as "principle" and "subordinate." Because everything that exists in space also exists in time, and vice-versa, that same situation must occur in the reciprocal aspect--even if we cannot directly observe it. That is why the C-D duality only shows up as C in Larson's notation. (Even though Larson realized the symmetry between space and time, he did miss a few things, like this.)

Why are space and time aspects named in the projective stratum? Aren't they pure ratios until the affine strata? Until there is some assumption added?

It is just a convention, as ratio is motion and motion is conceptualized as speed and speed has the aspects of space and time. You could as easily call them "numerator" and "denominator," but IMHO it just makes it more confusing.

I think it would help to see how you construct dimensions from the observer's perspective, starting with the a single reference point.

This was discussed in the programming forum, between Zuoqian and myself trying to figure out how to transform scalar motion into a coordinate system.

[bperet]

How would you characterise the directions in a three dimensional frame of reference of speed?

Since we normalize time (reduce it to unity) in a 3D reference system, they would be the conventional directions, with the first axis being up/down and the other two orthogonal to that. All 3D frames are gravitational (an assumption missed by conventional science), so there is always an up/down along that line of force. The other two are aribitrary, but tend to follow the rotation of equivalent space in the 2nd unit of motion, like north-south / east-west.

Would you even say a dimension of speed has direction?

It depends on the reference system in question. Speed in a scalar sense DOES have a direction--inward or outward. As Adam pointed out, it doesn't at the projective layer--an assumption as to which values are numerator/denominator (or space/time) in the ratio needs to be introduced to determine which way is "in"/"out". (Most of Larson's "scalar" stuff is in the affine layer of projective geometry).

In a coordinate system, speed + direction is referred to as a velocity.

Do these dimensions of speed follow a traditional definition such as a displacement in one dimension does not produce any displacement in the other two?

Correct, they are independent dimensions of motion--one cannot influence the other, but the shadows cast by them into a coordinate system DO affect what the resulting shadow looks like. Larson projects a single dimension into a 3D system, and the shadows from the other two dimensions then modify that initial projection, making the shadow behave differently--no effect on the dimensions casting the shadows. (This is what Nehru's paper on the Interregional Ratio is talking about.)

[sstivender]

“ How would you characterise the directions in a three dimensional frame of reference of speed? ”

"Since we normalize time (reduce it to unity) in a 3D reference system, they would be the conventional directions, with the first axis being up/down and the other two orthogonal to that."

I get that when time is normalized the result is the conventional directions, but what if we think in terms of the natural reference frame of speed? If the three dimensions of speed (s/t, s/t, s/t) must be independent of one another, then it seems to me that we will need to have three independent units of space (say s₁, s₂, and s₃) as well as three independent units of time (such as t₁, t₂, t₃). The three speed dimensions are then (s₁/t₁, s₂/t₂, s₃/t₃). Without independent space and time units, the three dimensions of speed cannot be independent.

Normalizing time then is making t₁=t₂=t₃ and t=(t₁² + t₂² + t₃²)^1/2. This is my interpretation of the shadow casting process.

[bperet]

If the three dimensions of speed (s/t, s/t, s/t) must be independent of one another, then it seems to me that we will need to have three independent units of space (say s₁, s₂, and s₃) as well as three independent units of time (such as t₁, t₂, t₃). The three speed dimensions are then (s₁/t₁, s₂/t₂, s₃/t₃). Without independent space and time units, the three dimensions of speed cannot be independent.

OK, you're not ripping the numerators off to form space, inverting it, and repeating for time. In Larson's system, only ONE scalar dimension produces the 3D coordinate system. A scalar dimension is speed. Speed means something is changing with respect to a fixed clock. The s/t scalar dimension is then seen as a vector, with a start, a passage of time, and an end. It requires 3 spatial coordinates to express that to our consciousness (two locations, start and end of the vector), with time running at unit velocity. The result is still speed... (xx/1t, ys/1t, zs/1t, 1). Because motion is discrete (quantized), we don't see the middle bit where the point slides along the vector, we can only observe the unit boundaries.

Try thinking of it this way... the spatial location of that scalar motion that is coincident with the reference system was HERE, then it was THERE, so we now have the endpoints of a vector of motion--speed + direction. That is how consciousness becomes aware of change. But since the clock is 1t, and the denominators of that vector are all 1t, we (as people, not Nature) just ignore that component and see (x,y,z) and label them points and distances.

The other two scalar dimensions (the ones not coincident with the reference system) just modify how that initial scalar dimension moves in its vectorial shadow--they are not casting any 3D shadow as a velocity vector, themselves.

Larson does not distinguish which scalar dimension is coincident with the reference system. Research has shown that, because the dimensions are independent and indistinguishable, it depends on the environment. In the material sector, is is usually the dimension with the largest spatial displacement, which is why we tend to see everything as an "electric universe" (the C dimension), rather than a magnetic one.

Normalizing time then is making t₁=t₂=t₃ and t=(t₁² + t₂² + t₃²)^1/2. This is my interpretation of the shadow casting process.

That is a process of normalizing a vector to unit length. To cast a shadow, you normalize to the unit plane, the projective plane, where w=1. For example, if I normalize (2,2,2,2) to unit length, I get (.5, .5, .5, .5) -- the 4th coordinate, "w" the projective plane, is not unity--so you shadow is underground (.5), not on the surface (1). To normalize to the projective plane, (2,2,2,2) becomes (1,1,1,1), where the 4th coordinate is unity--which is how we interpret clock time, (x/t,y/t,z/t,t/t).

In a 3D coordinate system, you do the same projection to a unit volume, instead of a unit plane.