Interatomic Distance

Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
bperet
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Interatomic Distance

I have found a conceptual difficulty with Larson's interatomic distance, where he uses the function:

$s=ln(t) = \int \frac{1}{t} dt$

Namely, that in the time region, the quantity 1/t cannot exist!

According to Larson, in the equations of motion, the spatial component (s) of speed (s/t) is replaced by its temporal equivalent (1/t), resulting in (1/t)/t = 1/t2. In the "time only" region, the three dimensions are 1/t2, 1/t3 and 1/t4. The quantity 1/t can only exist at the unit boundary--not inside the region. Needless to say that all of Larson's work on interatomic distances are based on this conceptual error, which surprises me.

The actual relations would have to be based on integration and differentiation, as Larson uses to determine the time-space region to time-region relationships:

Differential, moving from time-space to time region, where s=1: $\frac{s}{t} dt = -1/t^2$

Integral, moving from time region back into time-space: $\int \frac{1}{t^2} dt = \frac{-1}{t}$

This gives the same, 2nd power relation in the time region that Larson uses, except without the need to substitute 1/t for s. Plus the added bonus of reversing the direction of the motion, as we know that "outward in time" = "inward in space." But it also says that the natural logarithm is not involved in the interatomic distance calculation.
Every dogma has its day...

user737
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Re: Interatomic Distance

Integral of 1/x dx to be ln(x) + C is a lie as we know.
That would imply that inter-atomic distance is indeed not logarithmic.

The question then becomes how precisely do you integrate without the dreaded infinity.
This further implies we are dealing with counterspace.
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bperet
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Re: Interatomic Distance

user737 wrote:
Mon Sep 02, 2019 1:08 pm
The question then becomes how precisely do you integrate without the dreaded infinity.
The further implies we are dealing with counterspace.
Larson's "equivalent space" is basically counterspace, as it is a polar region that is a spatial projection of motion in time. The log gives very accurate results when compared to observation, but there may be a polar function that does something equivalent. Unfortunately, I do not know what it is... perhaps Gopi does.
Every dogma has its day...

user737
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Joined: Wed Oct 24, 2018 7:39 pm

Re: Interatomic Distance

Please to allow me to attempt a try.

Remember this? (see diagram below)

Of course you do, it's from the RS2 Tutorial Series; RS2-105: Quantum π, to be precise.

The first line represents in its truest current form the discarded 'rotational base' but is still the default outward progression with regard to yin motion (spin). That's rotational +1. And rotational being temporal (yin) is an equivalent space motion and so may be more appropriate to consider relations with regard to planes (areas).

r = 2 then becomes 1 displacement unit
r = 3 is 2 displacement units

Up until this point we note that the radial-to-square area changes with radius, the perimeter does not, even if when following the
jagged path around the clipped boxes. The perimeter is always 8r, or 2πr, where π=4.

Clipping first appears at r = 4 or 3 displacement units just like ln(3) = 1.1 ... which we are now calling shenanigans on, yes? If not altogether another reason to discard the log natural approach, this may lend further evidence as we could perhaps create a more complete understanding of why this effect is first encountered at 3 displacement units...

Yin-yang (temporal-spacial) balance in total area (area + polar area = 1) up until 3 displacement units wherein clipping (gravitational motion outside the unit boundary) first occurs. The circle is the very geometric embodiment of equivalent space (temporal motion). This in comparison/contrast to the ridged edges of the yang quantization of discrete space.