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! :-)Forums:
I am working on updating the RS2 site and forum to Drupal 8. If you find the site or forum inaccessible or giving weird errors, please wait a day and try again. Even though this new version of Drupal has been out for a while, most of the contributed modules are missing or buggy... I won't know what the problems actually are, until I try the upgrade.
As I am sure you can tell, I am no physicist either, nor an engineer like many of those here. I find the crazy ideas here the most familiar, but struggle with the more mathematical aspects of the theory. I am in the alternative health field where I am always evaluating different theories and their corresponding technologies. My degree is in the social sciences and have spent most of my life studying the cultural context of ideas, which I find helps me evaluate any field or theory without necessarily understanding the details that those more involved are steeped in. Though unlike most scientists and engineers these days, many of the people involved with this website are pretty aware of other ways of thinking. I find the people and material here refreshingly comprehensive and open to this particular theory's connections with the culture at large.
Perhaps what you are experiencing as a circular explanation is bound to happen with such a comprehenisve theory. One weakness in this theory that might be holding it back is a natural product of its strength, or at least natural in this post-modern value climate. Larson conceived it at a time when grand theories had fallen dramatically out of fashion. Post-WW2 theory is characterized by the incredulity towards meta-narratives. One can mourn this loss of coherence, but it was an important turn away from the absolutist rhetoric that lead to the melodramatically violent clash of cultures, and which continued to lend ideological support to the cold war. The last major theorists of the Modernist era had many of the same intuitions of Larson; people like Whitehead and Gebser tried to see in relativity an opportunity to open up the somewhat closed grand systems of the previous era which took perspectival space for granted, into an open system that embraced time and creativity. But in the end it was people like Heidigger following Nietzsche that would influence future theory in his emphasis not just on openness to change and time but on a complete destruction(which becomes deconstruction with Derrida) of metaphysical absolutes. Parallel developments happend in physics as complementarity became the anti-metaphysical and anti-epsitemological doctrine of choice. Grand theories still are put forth of course but they are surrounded by an academic culture of pragmatic utilitarianism that renders them anything but theories of everything. We know enough now to know a complete theory in physics, even if it was possible, is hardly a complete theory of everything.
But another thread after the wars can be followed where the heterogeneous currents set loose by the post-modern turn were coming together in a general science. Emerging out of war time information theory, cybernetics had a lot of similar qualities to today's scientific underground in that it was developed mostly by engineers outside their professional discipline. They began what has become a thriving trans-disciplinary science culture. Unlike the the grand narratives of the Modernist era, what you have in the interdisciplinary sciences is an openness not just to time and other perspectives, but to a reflexive awareness of the model itself and, of course the modeller. This has had an effect on academic theory through cybernetic writers like Gregory Bateson who influenced the biggest transitional figure from post-modernism to the emerging complexity-science paradigm: Gilles Deleuze. Deleuze has been dead for decades now but he still is the biggest name in Theory, especially where it dovetails with science. The buzzword in Theory that is most relevant here is: virtual. Deleuze's ontology is materialist, but like RS there is an economy between the actual (material sector), virtual (cosmic sector), and intensive (scalar). But these trends in theory I think still struggle with the concepts of time they have inherited from Bergson. Bergson famously debated Einstein on time, and though his ideas are more radical than Einstein, they only anticipate dimensions of time that are fleshed out more coherently with rs2 and somewhat by others in the scientific underground. Suzie Vrobel's fractal time and the endophysics her group has developed is an interesting example, though they are more sucessful with observer systems. The fractal has been a particularly fruitful concept for understanding time, and it has leaked through from the controversial physics of el Nasschie and the scale relativity of Notalle down through to the biophysics community with people like Mae Wan Ho and the New Age with people like Dan Winter and Nassim Haramein.
Though most people seem to still struggle to eschew conventional notions of time. One cybernetic theorist that seems closest to the RS system is a particularly esoteric one named Charles Muses. He has a particularly strange and interesting book called "Destiny and Control in Human Systems: Studies in the Interactive Connectedness of Time(chronotopology)" One of his students is a friend of mine here in Oregon who has developed his work in what he called "hypernumbers" into a whole sophisticated algebra of ontological transformation. Quaternions are just the first level in a dialectical progression. It is interesting as far as I can understand it, but so many of these developments launch off from shaky fundamentals. RS theory I think has got the core principles right that can bring other things into focus. Larson was writing from the perspective of a classical scientist and like other heroes of the scientific underground, because he was reacting to the direction post-classical science was taking, he often is described and understood in reactionary terms. If we are going to take these ideas out of the basement they have to shed neo-classical language that most theorist use. There are many good ideas out there, but with the RS theory and in particular the culture of RS2 here, the retro ether theories of post-tesla people like Dollard and much of the New Age scene with its probelmatic reification of "consciousness" can be put on the same ground as other general systems science theory. The key theme that I see in this context would be that Larson was seeing an advanced reciprocal relation between objective and subjective dimensions, but putting it in the language of classical physics that he knew--with some modifications. Everyone here has done a great job of teasing out the radical ideas and making them explicit. Projective Geometry has long been an obsession of the esoteric science community without a whole lot of understanding as to its concrete meaning beyond the sensed need to integrate the oberver and the modeller into the model. Now we can perhaps see how to do this and can begin to integrate other perspectives with that in mind. But by integrate, I mean connect to, reflect and illuminate, not co-opt and consume. There have been other attempts at integration in the alternative contemporary theory world --like Ken Wilber, Spiral Dynamics, and other New Age spins on systems theory. They become cults and I think people are becoming sensitive to and distrustful of anything resembling an insular system or theory. And if some of what is discussed in the alternative research community is correct, the groups that have developed this science well beyond us are very much cults and totalitarian break away societies. We don't just need to figure out how free energy works, we need a sophisticated and heterogeneous society that can handle it. Thankfully the ideas here are ripe with potential for bringing coherence without closure. Its all about the nature of the reference frame, and how it structures and interfaces with the universe.
Rather than discuss how many dimensions the universe has, which is a pretty absolutist metaphysical framing, I think it more appropriate to say how do a certain number of dimensions structure the universe? In that way the relative and absolute aspects of nature are both put in context. I think what RS concepts are showing, which is, again, echoed by others, is that there at most three spatially objective dimensions. When we objectify the universe we deform it and reduce it down. If we want to see more of the picture we have to add internal dimensions, interiority, virtuality, vitality, mentality, etc... we store memory of time, -- we add temproal dimensions.
What is the nature of a reference frame that objectifies the very parts of the universe that we have chosen to bracket and internalize? I tend to turn to occult literature here, though the RS concepts shed much light on it. I don't think the two sectors are the same. Actually I was implying they were more different than RS theory suggests. But yes I think they are part of one world, which I am sure most would agree with.
Adam, I had to chime in here because I hear from you some of the same thoughts I have been digging into. To looks to me the phase of a probability wave is very much like what I would expect rotations in 3d time to look like.
Interference patterns can produce locations where there is a zero chance of an object showing up, how can this be? Can time somehow progress normal to our time in this location?
There seems to be a conclusion in the RS that you can only have 3 dimensions in either space or time. Multiple spatial dimensions seem to only be compatible with a scalar time, while multiple temporal dimensions only seem to be compatible with scalar space. Something to do with the direction reversals if I remember correctly. But I don't buy into that. We should be able to incorporate 3 dimensions of space coincidentally with 3 dimensions of time.
My thought is that three dimensional time is all around us but we only see it as a scalar because it is moving so fast. A small displacement at a right angle has an incredibly small impact. However, at the quantum level, or natural unit level, the ratios of space to time are closer to unity and the addition of just one unit of time has a measurable impact.
The cosmic sector is also just as real and present in our universe as the material sector. There is no parallel universe that we can only reach by passing through some magic gate. The material and cosmic sectors are really one in the same: only one universe. Our everyday experiences are so accustomed to accounting for displacements in space that we are not skilled in speaking about vectorial temporal displacements.
As you can probably tell I am not a well trained physicist and my thoughts are not well developed, but the way I see it, this forum is for people that have new thoughts about our physical universe. I see the post from the member asking what is motion in 3d time and the answers posted by the regular members. There is a feeling of circular explanations that I have run into in the past. I applaud your attempt at an alternate approach to an explanation.
I don't know if this is any help to RS theory but......
Simple Set Game Proof Stuns Mathematicians this is the part that caught my eye
could this help with your projective geometry?
Game, Set, Match
To find an upper bound on the size of cap sets, mathematicians translate the game into geometry. For the traditional Set game, each card can be encoded as a point with four coordinates, where each coordinate can take one of three values (traditionally written as 0, 1 and 2). For instance, the card with two striped red ovals might correspond to the point (0, 2, 1, 0), where the 0 in the first spot tells us that the design is red, the 2 in the second spot tells us that the shape is oval, and so on. There are similar encodings for versions of Set with n attributes, in which the points have n coordinates instead of four.
The rules of the Set game translate neatly into the geometry of the resultingn-dimensional space: Every line in the space contains exactly three points, and three points form a set precisely when they lie on the same line. A cap set, therefore, is a collection of points that contains no complete lines.