Relativity of "Direction"

Discussion of Larson Research Center work.

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Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

Relativity of "Direction"

Post by Horace » Sun Sep 25, 2016 3:00 pm

In the PA graph appearing in that post.
Image
The space and time axes are separated to emphasize that time has no direction in space and vice versa.
They are still both horizontal (and consequently parallel to each other) only to fit 3 axes on a 2D display and maintain the step-by-step progressional synchronization between them.

There are other (arguably better) schemes to depict the same relationships on a 2D display but I will stick with this one for now because it was the first one mentioned.

Anyway, that graph represents an infinite numerical series that can be written in the differential form that states how much each aspect of motion has grown or shrunk, compared to the previous unit in the progression. This series can be written like this:
+1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, +1Δs/+1Δt, -1Δs/+1Δt, ...

...or this series can be written in an absolute form ( where the numbers denote the absolute magnitude of space and time, as measured from the ORIGIN OF THE RELEVANT AXIS - marked in red color ) which can be written like this:
0s/0t, 1s/1t, 0s/2t, 1s/3t, 0s/4t, 1s/5t, 0s/6t, 1s/7t, 0s/8t, 1s/9t, 0s/10t, ...

Obviously we can transform the differential form into the absolute form by integrating it.

Now, that we have the basics behind us, we must ask ourselves:
"How can we be certain of the signs appearing in the numerators or denominators of the differential form ? "

The intuitive answer is that we can simply see it on the graph.
For example, we might assume that for the spatial aspect, an arrow pointing left means + (a positive, outward "direction" or growth of space) and an arrow pointing right means - (a negative, inward "direction" or shrinkage of space) and for time - vice versa, but that is only a feature of the graph.

But that answer is wrong in the context of RST because it relies on the directional relation of these arrows to the white background of the graph !!!
In RST there is no "white background" that a "direction" can be related to. The only relations are between motions (units of motions), and the "white background" does not represent any motion !

Do you see the inherent problem in such graphical representations of scalar motion in RST?

dbundy
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Re: Relativity of Direction

Post by dbundy » Sun Sep 25, 2016 8:53 pm

Yes, but the graph is only an aid to help us visualize the concept, within certain limitations. We are to take from it the idea of increase in radius over time (space), not a change in location along a diagonal. It is an abstraction of change in size.

The actual expansion/contraction represented by the alternating diagonals is effective in all directions simultaneously: The outward expansion is from a point to a ball of unit radius. The inward contraction is from the unit ball to a point.

There is no mistaking the "direction" of an increase from a point. It is outward by definition. Likewise for a contraction to a point. It is inward by definition.

Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

Re: Relativity of Direction

Post by Horace » Sun Sep 25, 2016 11:44 pm

dbundy wrote:Yes, but the graph is only an aid to help us visualize the concept, within certain limitations. We are to take from it the idea of increase in radius over time (space), not a change in location along a diagonal. It is an abstraction of change in size.
Yes, a graph is only an aid and an analogy. Change in location along a diagonal on the graph only symbolizes the expansion/shrinkage of space (or time) it is not that expansion/shrinkage itself.

However, just because that graph is not an ideal depiction of the motion, it tries to illustrate, it doesn't mean that it cannot uncover some of the underlying representation errors of the real thing. In fact, it makes a good analogy of the errors often made by RST researchers.

One of them is the fallacy of the "white background", which cannot be used to define either aspect's "direction".
In RST, motion can be only related to other motion, not to some arbitrary "white background".
The above is a very important point ! Mull it over...

Since the "white background" of the graph leads us down a garden path, so lets get rid of it.
If we do that, the graph almost falls apart, because the direction of these arrows relative to the "white" background stops having any sense. This is completely true when one unit of motion is considered. See below:
RST 1 unit ambiguity.PNG
RST 1 unit ambiguity.PNG (5.78 KiB) Viewed 14326 times
The 4 graphs above illustrate the ambiguity of both aspect's "direction" in one unit of motion. Considering that the the parallel space and time axes are allowed to be placed anywhere on the graph's plane and at any angle*, it doesn't take much imagination to realize that in the context of RST all of these graphs are equivalent.

Code: Select all

 1st Unit
-----------
+Δ1s/+1Δt 
+Δ1s/-1Δt 
-Δ1s/+1Δt 
-Δ1s/-1Δt 
ALL OF THE ABOVE ARE EQUIVALENT

However, not all sense of orientation is lost when more than one unit of motion is considered, because that other unit of motion can serve as a reference for the "direction" of the first. Of course, 2 units of motions can be represented in 16 (24) different ways on the graph, but some of these representations will be equivalent to each other.

Can you see where I am going with this? Can you join the equivalent representations on a list of 16 possible representations, below?

Code: Select all

1st Unit      2nd Unit
-------------------------
+Δ1s/+1Δt     +Δ1s/+1Δt 
+Δ1s/+1Δt     +Δ1s/-1Δt 
+Δ1s/+1Δt     -Δ1s/+1Δt 
+Δ1s/+1Δt     -Δ1s/-1Δt 
+Δ1s/-1Δt     +Δ1s/+1Δt 
+Δ1s/-1Δt     +Δ1s/-1Δt 
+Δ1s/-1Δt     -Δ1s/+1Δt 
+Δ1s/-1Δt     -Δ1s/-1Δt 
-Δ1s/+1Δt     +Δ1s/+1Δt 
-Δ1s/+1Δt     +Δ1s/-1Δt 
-Δ1s/+1Δt     -Δ1s/+1Δt 
-Δ1s/+1Δt     -Δ1s/-1Δt 
-Δ1s/-1Δt     +Δ1s/+1Δt 
-Δ1s/-1Δt     +Δ1s/-1Δt 
-Δ1s/-1Δt     -Δ1s/+1Δt 
-Δ1s/-1Δt     -Δ1s/-1Δt 
+Δ1s/+1Δt     +Δ1s/+1Δt 
How many equivalency groups do you get?


* As long as some auxiliary graphical device maintains the step-by-step correlation between the two axes, to maintain the depiction of the progression

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

Re: Relativity of Direction

Post by dbundy » Mon Sep 26, 2016 5:39 am

Ok, I must be really dense. I'm having difficulty understanding you, Horace.
You wrote:

One of [the errors of the PA] is the fallacy of the "white background", which cannot be used to define the direction of either aspect's "direction".
In RST, motion can be only related to other motion, not to some arbitrary "white background".
The above is a very important point ! Mull it over...
I'm not sure what the "white background" is exactly, but I know that I don't feel much like defending the PA's representation of scalar motion. It was a starting point, but that's all. When you make the space and time halves independent of position and orientation, I'm not sure what that accomplishes.

On the space half, time would be increasing in the top-to-bottom "direction" of the grid, while on the time half, space would be increasing, regardless of the two grids' relative positions or orientations. To show this more clearly, the horizontal arrows could be replaced with diagonal arrows running from less space (time) over time (space) to more space (time) over time (space), and vice versa.

I know this must be missing your point, but for the life of me, I can't see it yet.

Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

Re: Relativity of Direction

Post by Horace » Mon Sep 26, 2016 6:51 am

dbundy wrote: I'm having difficulty understanding you, Horace.
Sorry, must be the remnants of my hurried editing. I corrected the quote below to get rid of the redundant phrasing.
You reply in a very narrow window of time and that makes me hurry to finish before that window closes.
Horace wrote: One of [the errors of the PA] is the fallacy of the "white background", which cannot be used to define either aspect's "direction".
dbundy wrote: I'm not sure what the "white background" is exactly,
Well, the white background is yellow now :)
1-0ST sep Y.PNG
1-0ST sep Y.PNG (3.1 KiB) Viewed 14327 times
dbundy wrote: ...but I know that I don't feel much like defending the PA's representation of scalar motion. It was a starting point, but that's all.
...and I don't expect you to. Their real value is in studying their failings to correctly represent scalar motion. The wrong assumptions they make, the wrong directional references they imply...
dbundy wrote: When you make the space and time halves independent of position and orientation, I'm not sure what that accomplishes.
It illustrates that space does not have direction in time. I also wrote about positioning the axes at an angle to emphasize that independence - Do you want me to draw it ?
dbundy wrote: On the space half, time would be increasing in the top-to-bottom "direction" of the grid, while on the time half, ???? would be increasing, regardless of the two grids' relative positions or orientations.
No, the top-to-bottom vertical direction on the PA graph represents the progression, which describes the order of units (which unit comes after which). Without it I could mix up the rows at will, in any order.
The horizontal direction on that graph carries the information about the magnitudes of time and space (growth or shrinkage) between consecutive rows (steps of progression).

Only this diagram below (and one other) depicts the unity increase of both the space and time (undeviated/undisplaced motion at unity), in the "top-to-bottom direction" of the graph, like you wrote.
Unity Progression.PNG
Unity Progression.PNG (3.96 KiB) Viewed 14327 times
dbundy wrote: To show this more clearly, the horizontal arrows could be replaced with diagonal arrows running from less space (time) over time (space) to more space (time) over time (space), and vice versa.
I was trying to show you such advanced visualization scheme in this thread, but you did not seem to like it, so I thought this scheme would be more familiar.


BTW: You did not indicate any equivalencies in the set of 16 ways to represent two units of motion (two rows) on the PA graph. :(
I asked you about it in the previous post.

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

Re: Relativity of Direction

Post by dbundy » Mon Sep 26, 2016 8:57 am

BTW: You did not indicate any equivalencies in the set of 16 ways to represent two units of motion (two rows) on the PA graph. :(
That's because I don't understand how to do it.

I know I'm dense sometimes, but please bear with me, until I can grasp what you are saying.

I see now that you literally meant the "white" background. Thanks for making that clear, but I still fail to see the relation you want me to "mull over." The white background is irrelevant to the "direction" of the increase of space or time the PA depicts. I agree that the ORDER of progression is from top to bottom, but that order is a "direction." It's the "direction" of increasing time (space) in the respective grids, regardless of relative position or orientation.

Taking the space grid for example, the 2D grid indicates increasing space to the left, relative to the red line and decreasing space to the right. As time increases in the downward "direction," space increases in the leftward "direction" and decreases in the rightward "direction," independently of the background (replacing the horizontal arrows with diagonal ones makes this more clear.)
But then you wrote:

No, the top-to-bottom vertical direction on the PA graph represents the progression, which describes the order of units (which unit comes after which). Without it I could mix up the rows at will, in any order.
The horizontal direction on that graph carries the information about the magnitudes of time and space (growth or shrinkage) between consecutive rows (steps of progression).

Only this diagram below (and one other) depicts the unity increase of both the space and time (undeviated/undisplaced motion at unity), in the "top-to-bottom direction" of the graph, like you wrote.
I think I understand the order for the space grid as order in time and the time grid as order in space. Space has no direction in time and time has no direction in space, but "directional" changes (i.e. increases/decreases) of space magnitudes have to take place over increases in directionless time, and "directional" changes (i.e. increases/decreases) of time magnitudes have to take place over increases in directionless space.

No cycle of space (time) oscillation can be completed, except it "consumes," as it were, two units of time (space). Is this where our disconnect is?

Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

Re: Relativity of Direction

Post by Horace » Mon Sep 26, 2016 10:01 am

dbundy wrote:The white background is irrelevant to the "direction" of the increase of space or time the PA depicts.
Ah!, but it is!
The equivalency of these 4 graphs did not seem to sink in, so let's reconsider them.

How do you know, whether the space or time grows or shrinks on these graphs?
The origins marked in red might imply something, but these origins are merely graphical artifacts designed to keep the graph centered on the screen and they imply no physical information.
The leftmost graph appears to depict an increasing space and time magnitudes, but that's only an illusion because the directions of the axes are not defined. The "white background" and "red origin" appear to define the direction of these axes on the graph, but in RST there is no "white background" and "red origin" to define these directions, thus physically these directions remain undefined and we cannot tell whether an aspect of motion is increasing or decreasing on these graphs. Thus all 4 graphs are equivalent.
dbundy wrote: I agree that the ORDER of progression is from top to bottom, but that order is a "direction." It's the "direction" of increasing time (space) in the respective grids,
Not always. For example on this graph, space and time are always increasing in the progression order and on this graph one aspect is growing and shrinking (not always increasing) in the progression order.
dbundy wrote: Taking the space grid for example, the 2D grid indicates increasing space to the left, relative to the red line and decreasing space to the right.
The red line is the origin (which is a graphing artifact design to keep the graph centered on the screen) and that origin does not imply a direction, so it is false to write that it "indicates increasing space to the left" and "decreasing space to the right". To do so would imply that this increase or decrease is defined by the origin which is a part of the "white background".


Do you want me to keep analyzing the rest of your post?

dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

Re: Relativity of Direction

Post by dbundy » Mon Sep 26, 2016 10:46 am

I think I'm beginning to see what you're getting at, but it seems to me to be confusing the PA as an imperfect abstraction used to communicate a more complex and nuanced concept, with a complaint against that concept, if that makes any sense.

It is true that the arrows indicating the "movement" need the white background and the red origin to communicate the idea of the scalar change concept, but the actual concept of scalar change doesn't need them.

Another abstraction we can use is two electronic counters, one counting the increase of space and the other the increase of time. When they are in sync, the unit progression is represented, but if one or the other counts backwards every other count, it will fall behind the count at a ratio of 1:2, no?

There is no really foolproof way to deal with the RST concept. We have to do the best we can, with what our minds can conceive. So far, I've been able to develop some useful consequences, by starting with the PAs, where one side shows a progression of s/t and the other a progression of t/s. Will your point throw a monkey wrench in all of that, or will it improve it?

Horace
Posts: 275
Joined: Sat Apr 15, 2006 3:40 pm

Re: Relativity of Direction

Post by Horace » Mon Sep 26, 2016 1:07 pm

dbundy wrote:I think I'm beginning to see what you're getting at, but it seems to me to be confusing the PA as an imperfect abstraction used to communicate a more complex and nuanced concept, with a complaint against that concept, if that makes any sense.
Actually, the problem with the PAs is that they are communicating more nuances than the RST concept can provide at this stage of complication.
Chiefly, they imply direction where there is none.
dbundy wrote: It is true that the arrows indicating the "movement" need the white background and the red origin to communicate the idea of the scalar change concept, but the actual concept of scalar change doesn't need them.
The catch is in the concept of change. What changes? What two things do you compare to determine the sign of that change?
Space to space, time to time or a ratio to a ratio. Space to space does not constitute motion so it is ruled out. Time to time is also, for the same reason.
dbundy wrote: Another abstraction we can use is two electronic counters, one counting the increase of space and the other the increase of time. When they are in sync, the unit progression is represented, but if one or the other counts backwards every other count, it will fall behind the count at a ratio of 1:2, no?
Yes, but not completely because these two counters are synced by the progression, so if one starts counting backwards then the other will too but from scalar standpoint there is no difference because +/+ = -/-

One again, you cannot have a lone space counter (or lone time counter) because you cannot measure one aspect without relating it to another, so the idea of an advancing lone space counter is fundamentally wrong, because it cannot even be determined whether that counter is counting forward or backwards - that depends which way the time counter counts (and vice versa). On a scalar level you can only compare the signs of the ratios between ratios, not the change in their individual aspects.
dbundy wrote: There is no really foolproof way to deal with the RST concept.
I refuse to believe that.
dbundy wrote: So far, I've been able to develop some useful consequences, by starting with the PAs, where one side shows a progression of s/t and the other a progression of t/s. Will your point throw a monkey wrench in all of that, or will it improve it?
It will improve it dramatically because it will allow you to do homotopic transformations on the PAs or orthogonal ST graphs or other visualization and analytical devices. This transformation forms the beginning of scalar motion calculus.

dbundy
Posts: 191
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Re: Relativity of Direction

Post by dbundy » Mon Sep 26, 2016 2:46 pm

Ok, it sounds good, Horace, but, honestly, I can't see it. At least not yet. Lead on brother,

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