Re: Relativity of "Direction"
Posted: Mon Sep 26, 2016 3:44 pm
Since comparing the properties of entire ratios (units of motion) is the only operation that makes sense in the scalar realm, then comparing their aspects individually does not make sense there. Because over the span of one ratio, the speed is always the same, the only property that can vary between ratios are their delta signs. Thus the only difference that two units of motion can have, are their signs and their order in the progression. Two consecutive identical signs tell us that the ratio is the same as the previous ratio in the progression order.
These observations allow for certain homotopic transformations to be performed on the graphs, namely they allow us to flip BOTH signs in any row of the PA graph and do not change anything from the scalar standpoint, because the resulting sign of the entire ratio does not change under such transformation. Flipping the sign of just one aspect, does change the sign of the ratio though, so it is disallowed, ...unless you are considering only one ratio in complete isolation, where the sign of this ratio is not related to the sign of another ratio so nobody cares about it and it just doesn't matter. The only use of the latter case, that I can see, is in teaching activities or in formulation of the Fundamental Postulate.
Flipping both the numerator and denominator sings in a ratio, changes nothing in the scalar realm, but it does affect the integration of multiple units. The latter is where the most of the variability is.
The animation below shows the result of such homotopic transformation at row 4. Note that the ratio of the last row is 6/8 before the transformation and 4/9 after the transformation. That last row represents the result of an integration over 9 stages of progression.
I could make these transformations on any rows of the PA graph and did not change anything from the scalar standpoint, but it would change the result of the integration.
Below is a different motion (series of ratios) that is being gradually normalized to uniform unit time, from top to bottom, using the same signs-flipping transformations. Q:Who does such normalization in nature ?
A: The observer does (that's why c-Krypton is our material Muon)
These observations allow for certain homotopic transformations to be performed on the graphs, namely they allow us to flip BOTH signs in any row of the PA graph and do not change anything from the scalar standpoint, because the resulting sign of the entire ratio does not change under such transformation. Flipping the sign of just one aspect, does change the sign of the ratio though, so it is disallowed, ...unless you are considering only one ratio in complete isolation, where the sign of this ratio is not related to the sign of another ratio so nobody cares about it and it just doesn't matter. The only use of the latter case, that I can see, is in teaching activities or in formulation of the Fundamental Postulate.
Flipping both the numerator and denominator sings in a ratio, changes nothing in the scalar realm, but it does affect the integration of multiple units. The latter is where the most of the variability is.
The animation below shows the result of such homotopic transformation at row 4. Note that the ratio of the last row is 6/8 before the transformation and 4/9 after the transformation. That last row represents the result of an integration over 9 stages of progression.
I could make these transformations on any rows of the PA graph and did not change anything from the scalar standpoint, but it would change the result of the integration.
Below is a different motion (series of ratios) that is being gradually normalized to uniform unit time, from top to bottom, using the same signs-flipping transformations. Q:Who does such normalization in nature ?
A: The observer does (that's why c-Krypton is our material Muon)