The oldest stars in the Milky Way may give us an insight into the formation of our galaxy
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?
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.
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:
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