## The Universe as a Tree

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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### The Universe as a Tree

Recent experiments have led me to search for a non-mathematical approach to creating an RS2 universe, as math works for very simple structures but rapidly becomes overwhelming when even minor complexity is introduced. This led back to a study of how computers model an artificial reality. There are a number of approaches, but one, in particular, matches RS concepts closely: the octree (octal tree) structure.

Octrees (or any n-dimensional tree structure) have many of the same properties as the RS: they are discrete (units of "voxels", volumetric pixels), has a minimum quantity of "1," possess a concept of "void" where nothing can exist (unit speed), are based on displacement and decomposition (reverse of "compounding") structure. Anything can be represented, emptiness, solid or fields, as the contents of a "voxel" can contain any properties. It can model 1D, 2D, 3D, 4D... any number of dimensions, using the same algorithms (dimensionally invariant), so it is of "general applicability." Issues like the "n-body" problem do not exist, because you are getting results from a geometric solution--not a mathematical one. This concept shows a lot of promise for RS/RS2-based models, much better than anything else I've tried over the last 25 years.

I have attached Donald Meagher's 1981 paper on octree encoding, as it is one of the best at describing the model.

It is also curious that many philosophies and spirituality refer to the Universe as a great tree, such as the Norse Yggdrasil. Perhaps, in their own way, they were right!
Attachments
Geometric Modeling Using Octree Encoding (Meagher, Donald).pdf
Geometric Modeling Using Octree Encoding (Meagher, Donald), 1981.
Every dogma has its day...

blaine
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### Re: The Universe as a Tree

I like the idea of using a tree for the computer model because the issue with existing approaches in conventional physics is that they use a euclidean grid which is the "stage" upon which events are played out, whereas the RS deals with motions that are the stage. With a tree you are only simulating the existing motions and their possible transformations.

bperet
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### Re: The Universe as a Tree

Here is one of the original "quadtree" papers, done back in 1979. It discusses how to process trees for imaging, which is easily extended to the 3D octree.

Remember that back in 1979, a computer with 16KB of memory was a LOT! I find these old papers very useful, because they concentrate on efficiency and optimization--unlike modern programs that are massively bloated with "feature rich" nonsense.
Attachments
Operations on Images Using Quad Trees (Hunter, Gregory M; Steiglitz, Kenneth).pdf
Every dogma has its day...

bperet
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### Problems with tree structures

blaine wrote:
Sun May 20, 2018 3:28 pm
I like the idea of using a tree for the computer model because the issue with existing approaches in conventional physics is that they use a euclidean grid which is the "stage" upon which events are played out, whereas the RS deals with motions that are the stage. With a tree you are only simulating the existing motions and their possible transformations.
I was working with it last night... some interesting questions have come up:

Different dimensions: the papers indicate that all objects modeled in a tree have to have the same number of dimensions. This is NOT the case in the RS, however, since 1D "electric" and 2D "magnetic" exist in the same, 3D universe, at the same time. Larson addresses the problem by resorting to "random distribution" (such as the inter-regional ratio).

It is interesting because in order to "make it work," you basically have to "collapse a wave function." For example, take a 1D line on a 2D sheet of paper. How do you draw it? Using Larson's random distribution, you would have to draw ALL possible configurations, basically spinning the line into a circle. But in order to get a single line out of it, you must collapse that probability into a single solution by the observer adding a concept of "angle."

If I tell you to draw a line on a sheet of paper, it is "pot luck" if you draw it the way I intended you to draw it. BUT, if I tell you to "draw a line 30° to the horizontal axis, I will always get the line I was looking for. This takes the randomness out of it.

I think the same approach can be used for 1D and 2D objects in a 3D universe--the tree on lower-dimensional objects is just missing a dimension, so ALL possibilities exist--until something interacts with it, adding a value to that missing dimension, fixing the motion in place.

My conclusion from this is that "collapsing a wave function" is nothing more than "forcing an interaction" to supply the missing, dimensional component that converts a 1D/2D function into a static, 3D structure. It is not really "observer" based, because in order to observe it, we have to create some kind of physical interaction--and it is that INTERACTION that is collapsing the function.

Yin-Yang Aspects: these tree structures are based on linear, yang relationships (line, area, volume). In RS2, we also have angular, yin relationships (angle, solid angle, hyper angle). The yin relations are needed for "equivalent" space/time projections, but I have no idea on how to decompose the concept of "angles" into a tree structure. The key is probably in the use of counterspace, but as of yet, still alludes me.

Space-Time Aspects: conventional trees deal with areas (pixels) or volumes (voxels), so only the "space" aspect. To convert to speeds, time has to be included. It is more than just using s and t variables for each voxel to get a speed, because 3D time operates independently from 3D space--it is not a 1:1 correlation. Only the 1D projections of one sector influence the other sector, bring us back to the "different dimensions" problem--3D space is influenced by 1D temporal motion, and 3D time by 1D spatial motion, yet there is no way to fill in the missing data.

Boundaries: a concept introduced in the quadtree paper was that there are three pixel conditions for an object: external, internal and boundary. The RS has boundaries, as well, such as the "unit space" and "unit speed" boundary, but they are not tangible boundaries... there is no structure present. This is examined in detail in Larson's Liquid State papers where he discusses the concept of "surface tension," concluding that such a concept does not exist. Either you are "inside" or "outside" of an object--there is nothing special about where the two meet, other than a change of state or material.

Now when addressing a concept like the gravitational limit, a boundary, you now have to have some kind of "internal" structure to represent the region where gravity has effect, not just its limit. The same situation exists for electric and magnetic fields. Since you cannot include multiple "materials" in a single node of a tree, because each material has a different speed for a particular voxel, it seems to be necessary to use multiple tree structures to represent these features, like "layers." But this does not seem to be efficient, because you've moved off of the single tree structure representing all motion, to a number of trees representing layers of motion. This might be the case, but not certain.

Every dogma has its day...

Horace
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### Re: The Universe as a Tree

It would seem to me that such trees would take up more memory for an object consisting of two atoms 1 inch apart than 1 mile apart., which would be wasteful unless distances are computed through some kind of a temporal indirection that embodies the reciprocal relation between time and space.

bperet
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### Re: The Universe as a Tree

Horace wrote:
Mon May 21, 2018 2:25 pm
It would seem to me that such trees would take up more memory for an object consisting of two atoms 1 inch apart than 1 mile apart., which would be wasteful unless distances are computed through some kind of a temporal indirection that embodies the reciprocal relation between time and space.
Not really, as the distance between is just a null node. The spatial "size" of the node is determined by the tree depth, each level is 1/2 the distance as the parent node. So you get a binary decomposition, 1, 1/2, 1/4, 1/8, 1/16 ... by the time you get to 32 nodes, you are at 1/4294967296 (one 4 billionth) of the original size -- your mile has been reduced to 0.375 microns.

Doug should like this structure... the 2nd node is a 2x2x2 cube (his "Larson's Cube") and it acts a bit like a scaled version of his SUDR/TUDR system (recursion vs stacking).
Every dogma has its day...

blaine
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### Re: The Universe as a Tree

In regards to the dimension problem, perhaps 1D and 2D motions are 3D motions, its just that 2 or 1 of the dimensions consists of motion at unit speed?

In regards to the yin aspect of the tree, would it be possible to just have two trees, one for the angle (yin) and the other for the magnitude (yang) aspect?

bperet
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### Re: The Universe as a Tree

blaine wrote:
Wed May 23, 2018 8:04 pm
In regards to the dimension problem, perhaps 1D and 2D motions are 3D motions, its just that 2 or 1 of the dimensions consists of motion at unit speed?
Yes, it is true that the missing dimensions would be unit speed, but that does not solve the problem as unit speed is scalar--no direction--so it does not provide any information to give an orientation in a 3D environment.

The only solution is that the missing dimensions get "filled in" with another motion, to bring the structure up to 3D. Last night, it occurred to me that the most likely motion to do this is a charge (vibration).

Consider the uncharged electron, a "rotating unit of space." It can be expressed by an imaginary number, which is 1D (angular velocity only). We cannot observe an uncharged electron--shows up as a "hole," something missing in a conductor, UNTIL it acquires a charge--then it becomes a particle. A particle is a 3D structure that is observable... a 1D rotation and a 2D birotation combining to make a 3D object.

Same situation with magnetic charges, taking a 2D rotation with the charge bringing it to 3D. This is why conventional physics, which is based on "observation," only recognizes charged particles (resolved to 3D) and ignores the uncharged state, interpreted as a "wave function."

In a tree structure, the 3D system is an octree--8 "leafs" hanging off any branch. A 1D system is a complex number, 2 "leafs," and a 2D system is a quadtree, 4 "leafs." You can add a 2 or 4-leaf node to an 8-node branch without any issue--but you just cannot "image" it (insufficient data)--but it is STILL THERE and interacts with other nodes and the environment. You get interaction without any observable "particle" expression.

What are fields? A dielectric field is 1D--it interacts but cannot be seen. A magnetic field is 2D--it interacts but cannot be seen. See a pattern developing here? Fields are already a vibration, so they cannot acquire a vibration to become a "particle."

All these invisible forces are just non-3D motions. Not to forget that only the net magnitude of a motion can be transmitted across the unit speed boundary, so ALL cosmic motions are perceived as a 1D, complex, 2-leaf system, influencing things invisibly.
blaine wrote:
Wed May 23, 2018 8:04 pm
In regards to the yin aspect of the tree, would it be possible to just have two trees, one for the angle (yin) and the other for the magnitude (yang) aspect?
Yes; experimenting with that idea now. (Actually 4 trees... yin and yang for normal and "equivalent" space and time.)
Every dogma has its day...

blaine
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### Re: The Universe as a Tree

I see, its tautological: we are 3D so we see 3D motion. We can only directly observe charged motion (all particle detection involves a number of electrons creating a voltage), because the "missing dimensions" from their rotation must be the charge. It explains why we only observed the charged versions.

bperet
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### Charge of Consciousness

blaine wrote:
Sun May 27, 2018 11:07 pm
I see, its tautological: we are 3D so we see 3D motion. We can only directly observe charged motion (all particle detection involves a number of electrons creating a voltage), because the "missing dimensions" from their rotation must be the charge. It explains why we only observed the charged versions.
You got it. Since we design our test equipment to amplify and extend our physical senses, they are all constructed around the 3D premise. Anything that isn't 3D becomes "probability" -- wave functions and the like.

From this analysis, I must also conclude that "consciousness" (the conscious act of observation) can impose a charge on a motion, converting it to 3D. Now think about that... this may explain that "feeling" you get when someone is staring at you--that act of observation is imposing a charge on "wave functions" in the brain, converting them into charged particles that affect neurons.

This concept alone opens the door to a huge number of metaphysical principles, along with understanding the physics behind it. This may be how the "feeling" function actually works--which means it can be trained. With good training, one should be able to detect emotions of others (empathy) and even transmit: telepathy.
Every dogma has its day...