## Relativity of "Direction"

Discussion of Larson Research Center work.

Moderator: dbundy

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

### Re: Relativity of "Direction"

Horace:
The signs are needed in the canonical scalar speed notation in order to avoid the "directional" ambiguity. How else would you distinguish inward from outward scalar speeds? This is manifested in that passage above, written by Larson, where he is analyzing only the attributes of scalar speed at unity - not any speed deviated from unity. He was the one to use the words "negative" and "positive" in reference to scalar speed that he was expressing in the canonical form of 1Δs/1Δt , as evidenced by his words "each unit of motion consists of one unit of space in association with one unit of time...".
You are missing my point. Larson uses the sense of polarity, but not in the sense you are want to use it. Although, I admit it could be used to indicate above and below unit speeds (in fact, I use it that way at times), but it's important to understand that unit speed is the datum which is referenced by him, not the "directions" of the deltas, as you are presenting them.

Each unit of motion that he refers to is an instance in a scalar time ordered, or a scalar space ordered sequence. This is easily understood with the help of the PAs. I cannot understand your reinterpretation of polarity in relation to a previous unit of motion only, To me, it's just bizarre. Sorry.
Horace:
Not according to Larson. In that passage above he was considering unit speed only (not any deviated speed). Exchanging the numerator with the denominator does not affect the unit speed, thus your distinction between (s/t) and (t/s) does not make sense for the unity speed that Larson was considering.
I don't think that's true, Horace. Here's the complete quote:
Since motion exists only in units, according to the postulates that define a universe of motion, and each unit of motion consists of one unit of space in association with one unit of time, all motion takes place at unit speed, from the standpoint of the individual units. This speed may, however, be either positive or negative, and by a sequence of reversals of the progression of either time or space, while the other component continues progressing unidirectionally, an effective scalar speed of 1/n, or n/1, is produced.
I understand from this that the negative speed is less-than unit speed, caused by the sequence of reversals of space, while the positive speed is greater-than unit speed, caused by the sequence of reversals of time. We can express the greater-than unit s/t speeds, as greater-than-one rational numbers, but they are the equivalents of the less-than-one rational numbers, when we invert the space/time terms to time/space terms.
Horace:

That might be true in general when using the operational notation of a fraction, but Larson was not using that notation and he was writing only about unity speed in that passage above.
I've just shown that he wasn't just referring to unity speed in that passage, but I don't quote Larson as an "authority," only to help clarify my own position, which differs from his at times.

With reference to the image of the timeline diagram you posted, it's important to realize that Larson didn't understand Hastenes' concept of an operational number, as most people don't. At least he never indicated he did. So, distinguishing the difference between the quantitative interpretation of number and the operational interpretation is crucial to the development of the LRC's RSt.

For instance, In the quantitative sense, the rational number 1/3 is one-third of the whole number 1, but the in the operational sense, 1/3 is -2, as you have shown. Yet, the question of how the 1/3 speed can arise from the unit progression, given that it's not an even number, was answered by Larson in a way that strains credulity and is really hard to follow. Namely, that the reversals occur in triplets - In-out-in, in-out-in, in-out-in, etc.

Nevertheless, given the less-than-unit, "unit," we can see that this bizarre conclusion is not necessary, because the value of the unit operational number 1/2, can be combined multiple times to produce any other operational number in the sequence of your diagram; That is to say,

1/2+1/2 = 2/4 = -2,
1/2+1/2+1/2 = 3/6 = -3,
1/2+1/2+1/2+1/2 = 4/8 = -4...

So, in this way, we can eliminate the confusion that dogged even Larson. Just sayin.
Horace
Posts: 276
Joined: Sat Apr 15, 2006 3:40 pm

### Re: Relativity of "Direction"

dbundy wrote: You are missing my point. Larson uses the sense of polarity, but not in the sense you are want to use it.
I disagree. I cannot read his mind nor ask him but I can read and analyze his words.
dbundy wrote: Although, I admit it could be used to indicate above and below unit speeds (in fact, I use it that way at times),
I know but it was not Larson's manner of expression.
dbundy wrote: ...it's important to understand that unit speed is the datum which is referenced by him, not the "directions" of the deltas, as you are presenting them.
I know that unit speed is his datum and so it is for me, but every speed is also a ratio of a chunk of space to a chunk of time - this is even stated in the Fundamental Postulate. These chunks are the deltas and every delta can always be either positive or negative by definition, representing expansion or shrinkage, respectively.
dbundy wrote: Each unit of motion that he refers to is an instance in a scalar time ordered, or a scalar space ordered sequence.
Instance?! Alas, instant is the temporal equivalent of a point. I thought you were a proponent of space growth or shrinkage in multiple dimensions as an aspect of motion...not points. What would be the ratio of points anyway ?!
dbundy wrote: I cannot understand your reinterpretation of polarity in relation to a previous unit of motion only,
I can see that. It is as if your mind cannot let go of the concept of a fixed background to relate directions to.
dbundy wrote: To me, it's just bizarre. Sorry.
"Bizzare" is an offensive word, especially to the proponent of the "bizzare" concept. Overuse of my name comes across as condescending, too.
dbundy wrote:
Horace wrote: In that passage above he was considering unit speed only (not any deviated speed).
I don't think that's true, Horace. Here's the complete quote:
DB Larson wrote:Since motion exists only in units, according to the postulates that define a universe of motion, and each unit of motion consists of one unit of space in association with one unit of time, all motion takes place at unit speed, from the standpoint of the individual units. This speed may, however, be either positive or negative, and by a sequence of reversals of the progression of either time or space, while the other component continues progressing unidirectionally, an effective scalar speed of 1/n, or n/1, is produced.
What he wrote after the word "and" (marked in red) is a subsequent logical development of his system leading to the concept of an "effective scalar speed" over multiple units, in contrast to the fundamental unit scalar speed of single units, he just described before it.
The words after the word "and" are not a description of the mechanism needed to create a "negative speed" through reversals over multiple units. Such grammatical analysis should be your forté.
dbundy wrote: I understand from this that the negative speed is less-than unit speed, caused by the sequence of reversals of space, while the positive speed is greater-than unit speed, caused by the sequence of reversals of time.
If by the words "positive or negative" he would have meant "the deviation from unit speed" then he would have skipped the words "and" and "effective" writing it as follows:
DB Larson would have wrote:This speed may, however, be either positive or negative by a sequence of reversals of the progression of either time or space, while the other component continues progressing unidirectionally, a scalar speed of 1/n, or n/1, is produced.
These two additional quotes below constitute more evidence that Larson meant unit speed, when he used the word "negative":
DB Larson in Universe of Motion pg.71 wrote: Here the net scalar speed reached is —1, which, by reason of the discrete unit limitation, is the maximum, in the negative direction.
DB Larson in Universe of Motion pg.70 wrote: Although scalar motion, by definition, has no direction, in the usual sense of that term, it can be either positive or negative.

dbundy wrote: I've just shown that he wasn't just referring to unity speed in that passage,
You only thought you did.
dbundy wrote: With reference to the image of the timeline diagram you posted, it's important to realize that Larson didn't understand Hastenes' concept of an operational number, as most people don't. At least he never indicated he did.
All the more reason not to expect him to refer to less-than-unity speeds, as negative speeds.
dbundy wrote: but I don't quote Larson as an "authority," only to help clarify my own position, which differs from his at times.
This is why I hate arguments based on "appeal to authority"...especially dead authority figures.
dbundy wrote: We can express the greater-than unit s/t speeds, as greater-than-one rational numbers, but they are the equivalents of the less-than-one rational numbers, when we invert the space/time terms to time/space terms.
Yes, but what about negative non-unity speeds ?
dbundy wrote: For instance, In the quantitative sense, the rational number 1/3 is one-third of the whole number 1, but the in the operational sense, 1/3 is -2, as you have shown. Yet, the question of how the 1/3 speed can arise from the unit progression, given that it's not an even number, was answered by Larson in a way that strains credulity and is really hard to follow. Namely, that the reversals occur in triplets - In-out-in, in-out-in, in-out-in, etc.

Nevertheless, given the less-than-unit, "unit," we can see that this bizarre conclusion is not necessary, because the value of the unit operational number 1/2, can be combined multiple times to produce any other operational number in the sequence of your diagram.
That is great news but it is also a different topic.
I will be happy to address it after we settle the relativity of "direction" issue, starting with the burning question whether both positive and negative unit scalar speeds exist in RST.
dbundy
Posts: 191
Joined: Mon Dec 17, 2012 9:14 pm

### Re: Relativity of "Direction"

1) No offense or condescension was intended.

2) The concept of unit scalar motion, and the possible positive (time) and negative (space) motion that "direction" reversals produce in it, is clear.

3) It is best that I disengage at this point.
Horace
Posts: 276
Joined: Sat Apr 15, 2006 3:40 pm

### Re: Relativity of "Direction"

dbundy wrote:The concept of unit scalar motion, and the possible positive (time) and negative (space) motion that "direction" reversals produce in it, is clear.
The latest burning question was whether both positive and negative unit scalar motion exists in RST.
"Direction" reversals cause deviation from unit scalar motion, thus they cannot be an answer to this question.