## Motion Without Anything Moving?

This forum is dedicated to the student just starting out with the concepts of the Reciprocal System, or RS2. Questions and clarifications for the RS/RS2 concepts go here; please place new ideas and commentary in the appropriate RS2 fora.
bperet
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### Motion Without Anything Moving?

The #1 question from people starting out with the Reciprocal System is, "how can you have motion, without anything moving?"

Larson uses the term "motion" to represent a ratio of space to time. Just replace "motion" with "ratio" in your head, and you'll get the idea, as you can have a ratio, without any rationing.

In Larson's earlier works, like The Structure of the Physical Universe, he does not use the word "motion" at all, using "space-time" instead, because he was talking about a ratio of space to time. But that confused the conventional physicists and astronomers that he was trying to reach, as they would interpret space-time in Einstein's sense, and miss the point of a universe of motion.

The single, largest different between the Reciprocal System and conventional physics is that in the RS, everything is motion--that is, everything is a ratio of some amount of space, to some amount of time. You can't have one without the other. Larson liked to use the analogy of a box, where the outside was space, the inside was time, and the box, itself, was "motion." If you have an outside, then you've got an inside and a box. If you've got an inside, then you've got an outside and a box. If you have a box, then you have an inside and an outside--the concepts are linked together, just like the yin-yang of Chinese philosophy, and cannot be separated.

The underlying motion of the Reciprocal System is called the "progression of the natural reference system," which is a speed of one unit of space, to one unit of time, which we define as the speed of light. Conventional physics and astronomy differ in that their "stage" is static--it doesn't move, only the things on it move, which is where the misunderstanding sets in. That changes some of the concepts in the RS, since the floor of the "stage" is moving at the speed of light. Photons are just spots of paint on that stage, that aren't moving with respect to the stage floor... but if you happen to be in the audience (observer) and see those paint spots whiz by as the floor moves along, you may think you've just seen something moving at the speed of light. And from the observer perspective, you have. But the paint spot is still on the same place of the floor--that's an "absolute location."

So rather than think about "something moving," think about motion as "some amount of space, inversely proportional to some amount of time," and nothing more.
Every dogma has its day...

Coder
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### Photons are just spots of

Photons are just spots of paint on that stage, that aren't moving with respect to the stage floor... but if you happen to be in the audience (observer) and see those paint spots whiz by as the floor moves along, you may think you've just seen something moving at the speed of light. And from the observer perspective, you have. But the paint spot is still on the same place of the floor--that's an "absolute location."
I always had a difficulty with that analogy because two photons could never collide or superimpose in that scenario, yet they do!

"The case of two photons" essay makes this issue even murkier.

bperet
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### 3D shadows of scalar motion

I always had a difficulty with that analogy because two photons could never collide or superimpose in that scenario, yet they do!
Linearly polarized photons will never intersect absolute locations (in the natural reference system), because there is no relative movement between them. When a photon is circularly polarized (the E-beam from crystals, for example), they possess torque and are changing absolute locations, so they CAN intersect, and then the two, photon motions can merge, creating atomic structure.

When you are measuring photons from a 3D coordinate reference system, you are basically looking at the projective "shadows" of those photons, not the real, photon motion, itself. Under kinetic conditions, the shadows can intersect, giving the appearance that photons "superimpose," without the underlying motions ever coming into contact.

That is the difficulty when coming from a conventional, physics standpoint--you were taught "the geometry of shadows," not the underlying motions. Shadows don't behave like the objects casting them do (again, the "Plato's Cave" analogy).

I just typeset a paper by Nehru that discusses this to a degree: How Do We Meet the New Age Ushered By the Reciprocal System? (only 4 pages). Might find it helpful.
Every dogma has its day...

Ardavarz
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I was thinking much about the "Plato's Cave" analogy these days and I was wondering whether we can consider our conventional "coordinate" space and time as "shadows", i.e. projections of motion (actually in ancient Greek geometry the word used for " projection" was indeed "shadow"). My reason was that we can visualize the scaling factor (that is the radical expression from the Lorentz transformations) as cathetus in a right-angled triangle where the other one represents the speed while the hypotenuse is 1 (= unit of motion). Thus the displacements from unity could be visualized as angles under which the unit of motion is projected as "unit" (scale factor) of coordinate "space" or "time" seen from different perspectives, but I still haven't figured out where to put this analogy in the context of the Reciprocal System.

bperet
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### Coordinate Caves

Plato's Cave is a good analogy for thinking of a 3D reference system. When it comes to transforming motion, you have to remember that all motion is a displacement from unit speed, the progression of the natural reference system, and it is the progression that forms the "clock," the rate of change of which we measure change.

So there are actually two "Caves," the exterior (yang) cave that forms the time-space region of 3D space and clock time, and the interior (yin) cave that forms the time region of 3D time and clock space. If you consider the cave to be made of clear crystal, one perspective is sitting outside it, watching the shadows of those moving within the cave (atomic rotation) and the other is sitting inside, watching the outside world (spatial relationships).

I am using a similar triangle-based concept with my RS2 artificial reality; it became essential to create a tetrahedron as an "observer" to create a 3D coordinate reference system from scalar motion; 4 points for the observer and 1 point to be observed. Otherwise, you do not have enough data to generate 3D coordinates (works like a GPS).

If you extend your triangle concept into 4D, 3 dimensions of space and clock time, you end up with the concept of homogeneous coordinates, or their rotational analog, the quaternion (3 rotational axes + clock space). The clocks are the progression; the "dimensions" become the displacements to measure change from the clock.
Every dogma has its day...

Ardavarz
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### RS and Aristotelian physics

I contemplate lately that some notions of the Aristotelian physics could be re-interpreted to fit the Reciprocal System. Thus the “prime mover” which is immovable, but moves everything could correspond to the scalar motion. It was thought to exist beyond the sphere of the fixed stars from where all motion begins through gradual retardation toward the center – the Earth or the world of the ordinary matter (the four elements). An interesting detail is that this primary motion was considered rotational because – as they thought - since the cosmos is “everything” it has no other place to move save to rotate in itself. The difference from Reciprocal System is that Aristotle thought that this rotation exists in the extremely large (the celestial spheres) and not in the extremely small (the time region). Or maybe we should consider the celestial spheres - the realm of the ether or the fifth element - to correspond to the cosmic sector (then maybe “etherial sector” as opposed to “material” could be a better name for it?). The material sector would correspond to the Earth where two of the elements (earth and water) are “heavy”, i.e. naturally move toward the center thus corresponding to the gravitational motion, while the other two (air and fire) are “light” – moving upward which would correspond to the radiation. From the other hand the progression of the natural reference system would correspond to the rotation of the sphere of the fixed stars (here the photons would be an analogue of the stars). But of course this analogy is not perfect. Then Aristotle was continualist and substantionalist and so he rejected the notion about the atoms and his idea of "motion" is of course not the same as Larson's - it was only measured by time which was "number of the motion" as Aristotle defined it. But still these similarities seem very curious.

Recently while studying the Pythagorean theory about the “music of the spheres” and its Babylonian and Sumerian predecessors I was constantly reminding to myself the notions of the Recirpocal Systems since Larson’s space and time displacements while forming arithmetic and harmonic progressions would constitute the same proportions as those of the musical scale. Thus maybe we could speak by analogy about a “music of the atomic rotations” for instance. And again its more like the Aristotelian notion that numbers are rather measures of the ratios and not the other way around (i.e. self-existing entities from which the ratios are formed as Pythagoreans thought). Or as in the first verse of John’s gospel (if translated literally): “In the principle there was the ratio (logos)”…

dave432
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### the 12D life unit

I am a beginning, non-scientist student of the Reciprocal System and have been working with daniel's papers, the tutorial RS material, the Conscious Hugs forum, and Bruce's Reevaluation book on this site. I also study music and in the last few years have discovered the ratio system for tuning musical scales known as "just intonation." One of the things that initially attracted me to the RS was its use of ratios because I had already been familiarizing myself with them in a musical context

Learning this new approach to scales was revolutionary for me because I discovered that the ratio system is "in tune" with nature, one example being the study of phyllotaxis. Our current system of musical tuning, equal temperament, is not in sync with nature because it does not use ratios. Equal temperament solves the many tuning problems musicians can have with their instruments but at a biological cost. This is due to the musical distance between each consecutive note in the12-note chromatic scale being based on an irrational number - the twelfth root of 2. There is a 24-note equal temperament chromatic scale in the East, but the concept is the same - equal irrational number distance between consecutive notes.

I read one of daniel's replies in a Conscious Hugs forum post entitled "the 13 steps" and combined that concept with bruce's Reevaluation book concept from "note 3" in the chapter entitled "Opposites."

Here is daniel's partial forum reply from "the 13 steps" post: 'A life unit is a stable combination of material and cosmic atoms (Beyond Space and Time), so it has two, 6D systems involved, which give the life unit a total of 12 independent variables, or is 12D. 12D gives rise to 13 "speed ranges", so to transition from a 3D, spatial body in the low speed range, all the way over to the 3D, temporal body in the inverse-low speed range, requires a total of 13 steps.'

Here is Bruce's note "3" in the Reevaluation book: 'A “displacement” is used as a notation to represent atoms and particles, being the displacement (or offset) from unity. Hence a speed of ¼ has a temporal displacement of 3 (1/4-1/1=0/3; numerators (1-1=0) and denominators (4-1=3) are treated independently, not as normal fractions). Spatial displacements are put in parenthesis, so that a speed of 4/1 has a spatial displacement of (3).'

So I set out to calculate the speeds for the 13D biological life unit:

1D, 12s, 0t, 13/1 speed, 13/8 musical ratio (major sixth)

2D, 11s, 1t, 12/2 speed, 3/2 musical ratio (perfect fifth)

3D, 10s, 2t, 11/3 speed, 11/6 musical ratio (major seventh)

4D, 9s, 3t, 10/4 speed. 5/4 musical ratio (major third)

5D, 8s, 4t, 9/5 speed, 9/5 musical ratio (minor seventh)

6D, 7s, 5t, 8/6 speed, 4/3 musical ratio (perfect fourth)

7D, 6s, 6t, 7/7 speed, 1/1 musical ratio (unison)

8D, 5s, 7t, 6/8 speed, 3/2 musical ratio (perfect fifth)

9D, 4s, 8t, 5/9 speed, 10/9 musical ratio (major second)

10D, 3s, 9t, 4/10 speed, 8/5 musical ratio (minor sixth)

11D, 2s, 10t, 3/11 speed, 12/11 musical ratio (minor second)

12D, 1s, 11t, 2/12 speed, 4/3 musical ratio (perfect fourth)

13D 0s,12t, 1/13 speed, 16/13 musical ratio (minor third)

The reciprocal speeds are also reciprocal musical relationships. For example, 2D is a 3/2 perfect fifth and 12D is a 4/3 perfect fourth . A fifth (5) and a fourth (4) add up to 9. All musical reciprocals add up to 9. The musical ratios I used are expressed in an octave where the decimal equivalent is between 1.0 and 2.0.

Another example, 1D is a 13/8 major sixth and 13D is a 16/13 minor third. A sixth (6) and a third (3) add up to 9. Also, the reciprocals of major ratios become minor and vice versa. Perfect ratios remain perfect when in a reciprocal relationship.

I noticed, though, that the diminished fifth tritone was missing and that there were two perfect fifths and two perfect fourths instead of one each.

When looking for frequencies to plug in to the these ratios, I followed some advice from daniel that I might try using frequencies based on 8, because he said light starts at multiples of 8 which are then multiplied by 9 -- based on the 9 degrees of freedom of the photon.

8X9X1 = 72

8X9X2 = 144

8X9X3 = 216

etc.

I noticed that 72 Hz can be thought of as a 1/1 unison, then 144/72 = 2/1.

Then I noticed that 216/144 = 3/2.

I kept going and realized that the harmonic series was developing with the frequencies increasing by factors of 72 Hz. daniel also mentioned that the speed of light (unit speed) can be interpreted as 1 Hz, so I decided to use octaves of 1 Hz to be the unisons 1/1, 2/1, 4/1, 8/1, etc. instead of octaves of 72 Hz. All the harmonic series ratios stayed intact when I made the conversion to octaves of 1 Hz.

Here are frequencies I came up with for a 16-ratio harmonic series scale . I used 256 Hz as one of many possible octaves of 1 Hz to be the 16/1 unison:

16/1, C, 256 Hz (unison) - or think of this as another octave of 1/1

17/16, C#/Db, 272 Hz (minor second)

9/8, D, 288 Hz (major second)

19/16, D#/Eb, 304 Hz (minor third)

5/4, E, 320 Hz (major third)

21/16, F, 336 Hz (major fourth) - a perfect fourth would be 4/3

11/8, F#, 352 Hz (augmented fourth)

23/16, Gb, 368 Hz (diminished fifth) - with the ratio system, an augmented fourth can be a different pitch than a diminished fifth; in equal temperament they are identical

3/2, G, 384 Hz (perfect fifth)

25/16, G#, 400 Hz (augmented fifth)

13/8, Ab, 416 Hz (minor sixth) - same idea as augmented fourth/diminished fifth

27/16, A, 432 Hz (major sixth)

7/4, Bb, 448 Hz (minor seventh)

29/16, Bb, 464 Hz (minor seventh) - or diminished minor seventh

15/8, B, 480 Hz (major seventh)

31/16, B, 496 Hz (major seventh) - or diminished major seventh

32/1, C, 512 Hz (unison) - next octave, which will contain 32 ratios

All the frequencies are 16 Hz apart.

These ratios of the harmonic series, though, are not matching the speeds I came up with earlier, so maybe someone has some suggestions as to a next step.
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bperet
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### Musical ratios

This is very interesting, as I've always wondered about the correlation between RS ratios and the musical scale, particularly in application to John W. Keely's work--where he represented atoms as chords of music, leading to the discovery of methods to dissociate matter or fuse material together, with nothing more than vibration of those chords in discord or sympathy.

The photon "scale" is in groups of 256 natural units, which is 28, or 8 octaves in music. There are 8 of these groups above and below unit speed, so a total of 16 groups of 8 octaves, giving a total of 128 octaves on the keyboard of electromagnetic radiation. (A regular piano has 7.25 octaves, so that's a lot of keys!)

Using my EM Spectrum table as a reference, visible light stands in the 4th octave above unit space, spanning sx8 to sx16, about the same place you'd find middle-C. It is interesting that the 8 octaves in that group containing visible light spread from uV to iR, being about the same size as a piano keyboard.

Miles Mathis came up with an interesting idea that the spectrum was only composed of two colors on opposite ends, and the harmonic breakdown gave us the impression of the intermediate colors. You seem to be using a similar approach with the life unit speed scale, approaching the middle from both sides. What if you were to modify the range from 13 to another number, and see how the ratios progressed? It may not be the speed range that is the contributing factor, as it may be more analogous to light.
Every dogma has its day...

dave432
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### musical ratios and color associations

I made an argument for and against the harmonic series ratios being related to or even the same as the speed ranges but am wanting them to be related because both the harmonic series and the natural life units begin with a ratio of 1/1 and then progress by continually doubling the amount of ratios or natural life units per octave. For the harmonic series, 1/1 is the fundamantal frequency and the unit space ratio is also 1/1. In each case, the ratio of 1/1 exists by itself in its own octave with no other ratios present.

One idea I needed to sink in is that 1/1 is not part of the next group of 256 harmonics or natural life units. The 256th harmonic begins the next octave of the series which contains 512 ratios. The 256th natural life unit of the photon group seems to be the first natural life unit of the next group, "Larson's Unit Frequency."

In the harmonic series, 1/1 is followed by 2/1, the biggest leap it will make, a doubling. Then for the rest of the series, the harmonic ratios continually decrease, doubling the amount of ratios per octave as they attempt to return to 1/1 while the frequencies continually increase. Like the harmonic series, the natural life units continually double in each successive octave but the frequencies continually decrease instead of increase. This is my strongest argument against the harmonic ratios and the speed ratios being related.

I thought of the possibility of subharmonics fitting in with your electromagnetic spectrum chart, where there is an initial halving from 1/1 to 1/2, a doubling down. Then the subharmonics continually increase back up to 1/1 as the frequencies decrease -- like you said, "approaching the middle from both sides." Using subharmonics doesn't seem to work in this case because even though the frequencies of the subharmonics and the natural life units are both decreasing, the destination of the subharmonics is 1/1 and the eventual destination of the natural life units is the "maximun wavelenth/minimum frequency boundary." So I am kind of stuck on this issue for the moment.

Regarding the visible spectrum being in the range of middle C, the fourth musical octave on the piano, I used the frequencies of the colors in proportion to Thz octaves of 1 Hz, which I am using to represent the note of C. The infrared, dark red, light red, orange and yellow seem to first appear toward the higher frequency end of the fourth octave, but I am counting up from the lowest frequencies not the other way around.

Here again is where I might have my concept backwards because I am used to the octaves of the harmonic series containing less ratios having the lowest fequencies and the octaves with more ratios having the highest frequencies. In your chart, the octave with two natural life units contains the highest frequencies of the vacuum ultraviolet rather than the lowest frequencies.

Then in the fifth octave, green, blue, indigo and violet appear toward the lower frequency end of that octave. I adjusted the octaves of all the colors in order to place them in an octave together and added what could be the musical value.

1/1, 281.475 Thz, C, yellow-green, unison

17/16, 299.067 Thz, C#/Db, green, minor second

9/8, 316.659 Thz, D, green-blue, major second

19/16, 334.251 Thz, D#/Eb, blue, minor third

5/4, 351.844 Thz, E, blue-indigo, major third

21/16, 369.436 Thz, F, indigo, major fourth (not a 4/3 perfect fourth)

11/8, 387.028 Thz, F#/Gb, indigo-violet, augmented fourth

23/16, 404.620 Thz, F#/Gb, violet, diminished fifth tritone (Earlier and later octaves are infrared and ultraviolet and also unit speed - this may be my missing tritone from my last post which showed up as a unison. This is exciting if correct because the unison means a beginning/end and unit speed is also a beginning/end.)

3/2, 422.212 Thz, G, black?, perfect fifth

25/16, 439.805 Thz, G#/Ab, dark red, augmented fifth

13/8, 457.397 Thz, G#/Ab, less dark red, minor sixth

27/16 474.989 Thz, A, light red, major sixth

7/4, 492.581 Thz, A#/Bb, red-orange, minor seventh

29/16, 510.173 Thz, A#/Bb, orange, minor seventh

15/8, 527.766 Thz, B, orange-yellow, major seventh

31/16, 545.358 Thz, B, yellow, major seventh

2/1, 562.950 Thz, yellow-green, C (next octave of unison which will contain 32 ratios/colors/notes)

My frequencies are close to yours but not exact. I want to try other phyllotaxis "scales" as well, such as 1/3, to see how close they match your chart. The ratios I used here are increases of 1/2.

Musically speaking, from the vantage point of the Key of C, I find it interesting that Eb, 19/16 minor third, shows up as the blue note because the "blue note" in jazz and blues is basically the interplay of a minor third/major third "sweet spot" note played over a major chord. The Gb, 23/16 dimininished fifth tritone, is sometimes referred to as a blue note as well but the "ultraviolet note" might work better, the note that sends you out of space and into time. The Ab, 25/16 augmented fifth or 13/8 minor sixth, is a muddy red and the minor sixth is often referred to as the interval giving the natural minor scale its "dark" quality.
"just down the road a little way, turn left, cross the drawbridge, and you will be my guest tonight."
-- directions to the grail castle. We'll have some toast.