duane wrote: ↑Sun Feb 05, 2017 1:56 pm

so the space coordinate system and the time coordinate system ..coordinate

when you spin up a bunch of stuff, you also spin up a bunch of time

and there is no time in the natural progression

am I getting close?

If you want to understand it, you need to understand some basics of projective geometry. Now if you look up Projective Geometry on the Wikipedia, you'll go, "I'll never understand this!!!" -- I know I didn't -- because it is treated as mathematical abstractions. But the useful concepts originate from the military--taking high-altitude photos of enemy bases and trying to reconstruct 3D models from those flat photographs at some undetermined distance. If you are looking at a 8x10 glossy of a new, enemy aircraft next to a hanger, take out your ruler and measure it, it might be 1/2 inch long--which you know isn't the actual size of the plane. So they had to learn how to scale things up from other objects in the photo that had known sizes, like the door on the hanger being 100 feet across. But due to perspective (the further something is, the smaller it appears), you had to constantly adjust for things by making various assumptions about the photo.

When you start with scalar motion, you have basically the same thing--objects, like atoms or stars, that you know are there but cannot determine the actual size, because we cannot put a tape measure on them. So you do the same thing, start making assumptions about how to get from what you see to an actual model.

To go from a ratio (motion) to a coordinate system, a bunch of assumptions need to be piled on to the ratio, which are called "geometry strata." There are basically 4: projective (what we call "scalar"), affine, metric and Euclidean (coordinate system). Our senses on work with the lowest layer, Euclidean, and that is probably why the study of projective geometry stopped there. All the other layers look like Picasso drew them.

My early models of the RS were based on matrices, and I had found this link quite useful:

http://www.cs.unc.edu/~marc/tutorial/node8.html
Summary of strata:

http://www.cs.unc.edu/~marc/tutorial/node32.html
It shows how you have to develop a "transformation matrix" to take random locations and ratios, and get a recognizable image out of it. Most of the terms I use regarding projective geometry with RS2 come from this author (Marc Pollefeys, University of North Carolina - Chapel Hill, USA).

I recommend you browse through his projective geometry pages, even if you don't understand matrix algebra. The descriptions give you an idea of what the math is trying to do, so you can see the assumptions going in. Once you have that, you can see that the progression is right at the top of the projective pyramid of assumptions, and what we call the "clock" -- a ratio of distance(s) : duration (t) -- is what we measure everything from.

You can go back to Larson's "direction reversal" concept... if you have a direction reversal in space, you get a single location in space and a structure in time (a displacement). If you have a reversal in time, you get a location in time and a structure in space. Our senses and instruments measure how "locations in space" change with respect to the temporal structures connected to them--but in order to make sense of more than one location, we have to make sure the denominator is the same for all the ratios--so we scale space appropriately (10 space to 2 time is the same as 5 space to 1 time). Once all the denominators are the same (which is the metric to Euclidean assumption), we get something we can understand.

and there is no time in the natural progression

If by "time" you mean "clock time," then yes--since the progression IS the clock, the clock cannot change relative to itself.

Every dogma has its day...