Can a ratio of 1:1 exist?

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.
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bperet
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Can a ratio of 1:1 exist?

Post by bperet »

In the RS, the natural datum is unity, the speed of light, numerically "1". But can a ratio, speed, energy or motion of 1/1 exist, indicating 1 unit of space per 1 unit of time?

When you have a cross-ratio where the two ratios are identical, the cross-ratio "degenerates" and becomes a simple ratio, since one component cannot be distinguished from the other.

It would be logical to assume that when you have a ratio, where both aspects are identical, it would also degenerate into a single magnitude. It appears to be another type of "dimensional reduction", as Nehru documented in the case of bi-rotation.

This would indicate that the ratio 1s/1t would degenerate into simple unity, where the aspects and concepts of space and time no longer existed and its corollary, that space and time can only exist in non-unit motion.

It makes for some interesting programming problems, because if you use alter a ratio within a cross-ratio class instance so that the ratios become identical, you actually have to alter the instance, itself, from cross-ratio class to a 'ratio' class. And should the ratio become uniform, reduce that back to a pure integer! Not something programming languages like to do... It appears that the class of the motion actually needs to be soft-coded as a variable.

Anyone with programming experience, some ideas could be helpful here.
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Can a ratio of 1:1 exist?

Post by Horace »

What language?
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bperet
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Can a ratio of 1:1 exist?

Post by bperet »

Horace wrote:
What language?
Right now I am using PHP 5, because it is fast and easy. I would like to use a strong-typed language for the final product, which will work at least on Windows, Mac and *nix.
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Horace
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Can a ratio of 1:1 exist?

Post by Horace »

Bruce,

The problem with OOP is that the virtual function tables are fixed at compilation time, and the type checking is done by the compilator according to static function/procedure definitions. This means that you cannot change the class definitions at runtime, because by that time the compiler is out of the picture (RTTI or not)

I suggest that you make one universal class with a bitmapped variable (eg. named ClassType), which will determine what class functions are accessible according to the bits in it. Storing the pointers to the instances of this class in an array, would also be a good idea.

In my opinion, the most interesting will be the interaction between the instances of different types e.g how can the photon class modify a neutrino class, and whether any variables external to them can influence their interaction (e.g. their separation).

Also, will you implement the motion conservation constraint ? (the amount of motion/displacement cannot vary in a closed universe - it can only be shuffled around).

Regards,

Horace

P.S.

With VMware freeware you can write your program in anything (even IA32 assembler), and have it running on Wintel, Mac and *nix, just as well.
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Re: Can a ratio of 1:1 exist?

Post by Horace »

DB Larson in NBM pg.97 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
, ...

In your opinion: Did Larson mean negative unit speed when he used the word "negative" in that quote above or did he mean speed less than unity by it?

Do both positive and negative unit speeds exist in Larson's RST ?
Are you aware of similar Larson's statements that would help to clarify this ?

P.S.
I know that a single unit of motion (a ratio) is not oriented and it is impossible to determine only from it, whether space (or time) is expanding or contracting. But it is possible with multiple units...
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Re: Can a ratio of 1:1 exist?

Post by bperet »

Horace wrote:In your opinion: Did Larson mean negative unit speed when he used the word "negative" in that quote above or did he mean speed less than unity by it?
He is referring to his concept of "scalar direction" (outward = +, inward = -). He needs the negative unit (inward) to create the direction reversal. You end up with this sequence: +++/+-+ = 3/1 (one +- pair cancels out in the denominator, leaving a single "unit of motion.")
Horace wrote:Do both positive and negative unit speeds exist in Larson's RST ?
Are you aware of similar Larson's statements that would help to clarify this ?
Understand that +/- is a property of the zero-datum additive inverse (not the unity-based multiplicative inverse) so negative speed does not exist in the natural reference system--it can only exist as a displacement.

As a displacement, the progression is +1, the "direction reversal" (inward or negative unit) results in 0 (+1 -1 = 0), and the "inward rotation" of the photon created by the direction reversal creates another negative displacement, resulting in gravitation:

+1 (progression) + -1 (direction reversal) + -1 (inward rotation) = -1 (gravity)

This situation does not arise with RS2, because of the inclusion of the yin/angular velocity as a primary motion: Real(i0) = +1, Real(i1) = 0, Real(i2) = -1 (in one dimension). For the material sector, Real = spatial displacement.

Nehru explained this in a Reciprocity article, though I don't recall which one offhand. I think it was a in a reply to one of Tom Kirk's. Though you could look through Chapter VI of New Light on Space and Time, concerning "Progression vs. Gravitation." He goes into more detail there.
Horace wrote:P.S. I know that a single unit of motion (a ratio) is not oriented and it is impossible to determine only from it, whether space (or time) is expanding or contracting. But it is possible with multiple units...
That is why we use a cross-ratio--to get that comparison.
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Re: Can a ratio of 1:1 exist?

Post by Horace »

bperet wrote: He is referring to his concept of "scalar direction" (outward = +, inward = -). He needs the negative unit (inward) to create the direction reversal.
... +/- is a property of the zero-datum additive inverse (not the unity-based multiplicative inverse) so negative speed does not exist in the natural reference system
So in that Larson's quote, he invokes an additive inverse when he uses the word "negative" to refer to negative direction of scalar speed, which does not really exist and cannot cause his reversals, which are needed to cause non-unit speeds? :shock:
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Re: Can a ratio of 1:1 exist?

Post by Horace »

bperet wrote:So when dealing with RS/RS2 concepts, remember that a "dimension of motion" is considered a single dimension, even though it is composed of two, scalar magnitudes, and that the datum of the system is UNIT SPEED -- a one-dimensional ratio
The scalar direction of a series of 1-dimensional ratios (1Δa/1Δb) cannot gradually change its direction. That change has to be an abrupt reversal at the unit boundary, because there is no other choice in 1D.

For example the series:
1Δ/1Δ, 1Δ/1Δ, 1Δ/1Δ, 1Δ/1Δ, 1Δ/1Δ ...can only make an abrupt change to: -1Δ/1Δ or 1Δ/-1Δ

Seems, that in order to have any resemblance of rotation (including birotation) at least two dimensions are needed.

P.S.
Of course: 1Δ/1Δ = -1Δ/-1Δ (they are isomorphic), so we need another ratio for a reference to determine its orientation.
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