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June 7th, 2014, 03:55 AM   #1
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4 color gravity and turning a sphere inside out

four color, or five if you count the ring you superposition along, gravity as multiverse of polygon mesh partially overlapping eachother.txt


Every planar graph has an integer perimeter. If that integer is odd, its a fermion. If its even, its a boson.

Any polygon (which may be triangulated or allow any size) can be rotated to the perimeter, its color removed, edges added where it hooks into other fourColoredGraphs it partially overlaps, and there are at least 4 factorial number of ways to color the combination, since you can always swap all of one color for another, a 4d rotation. I think this is the source of 4-vectors (hyperbolic geometry is negative distance in the time dimension, which is why time is -1 and x y z are 1 in the 4x4 identity matrix.

The purpose of this planned system based on this math explained here, is kind of like Windows Vista's "tilt bits" and also like Bitcoin's Proof Of work (which backs its economy with a free market of doing calculations that hold the network to one view of the shared data). Finding 4colorings, that align with the "block chain" (as they say in bitcoin) but in this case its a black hole, is my kind of proofOfWork. The 4colorings and choice of outer perimeter and choice of which colored graphs to assemble together, is at least practically a multiverse of polygon mesh that the global network will converge toward some kind of agreement in the most dense part, and I expect (but still have some kinds of math to fit together) it will match the black hole thermodynamics, hawking radiation, time dilation (by the block chain being harder to change the farther into the past you go, eventually time nearly stops as you have so few degrees of freedom in how the colored polygon meshes (spherical or planar graphs) can fit together.

Its an NP Complete problem how to fit them all together, Max Clique, but a good approximation will work enough to scale the network since its very high dimensional in all the ways the colored planar/sphere graphs can align on fermions (odd path length) and/or bosons (even path length).

No errors in the 4 coloring will be accepted, by those who choose to calculate that way and therefore hold eachother to also calculate that way by overlapping on extremely many unknown ways the most popular colored planar/sphere graphs fit together.

A boson can flow smoothly because 4color divides evenly into an even length path. It might alternate between 2 colors or use 3 or 4 as it has extra degrees of freedom (ways it can be 4colored without changing its shape).

A fermion must use at least 3 colors because its perimeter has odd length. We see this in the up+up+down and down+down+up quarks (protons and neutrons) each having 3 different colors.

The fourth color is here-and-now (lightcone, observe, point on the manifold of string theory).


The Four Color Theorem
"If we denote the number of vertices, edges, and faces (i.e., the bounded regions) of a planar graph by V, E, and F respectively, then Euler's formula for a plane (or a sphere) is V - E + F = 2."


"A graph is said to be n-colorable if it's possible to assign one of n colors to each vertex in such a way that no two connected vertices have the same color. Obviously the above graph is not 3-colorable, but it is 4-colorable. The Four Color Theorem asserts that every planar graph - and therefore every "map" on the plane or sphere - no matter how large or complex, is 4-colorable. Despite the seeming simplicity of this proposition, it was only proven in 1976, and then only with the aid of computers."


Some related info, some about AI research and longterm plans for the network, but for now its the best explanation of where pascals triangle fits into the angle quantization and hyperspheres.
...
Latest theoretical parts of my research:
Researching toward a shared Internet space where people use pattern matching (artificial intelligence) tools to represent thoughts as flows of colors, shapes, and patterns, and see how they fit together as a big puzzle.
Built many prototypes of parts of math, but still looking for ways to use them together to represent thoughts similar to how brains represent visual patterns and abstract ideas.
Rebuiding a foundation of math from statistics, circle/sphere/hypersphere and wave
Standard Deviation (stdDev) of sum of C^2 coin flips, counting each as -1 or 1, is C.
Do this with 2 groups of coins and you get circles, a 2d bell curve where density is spread evenly across all possible angles.
This extends to any number of dimensions as every n dimensional bell curve (hyperbell) has an n-1 dimensional hypersphere of constant density at each radius.
If you start anywhere in a 2d grid like an infinite chess board, move 1 square up, down, left, or right, and repeat C^2 times, you will be about C distance from where you started.
Fourier of a bell curve in 1d at any location in the circle input is another bell curve at a constant location, and its phase wraps around more times depending on original position,
and you can play with this in my open source Physicsmata 0.5.2 (not other versions).
In vision research a bellcurve windowed fourier is called the Gabor Transform.
Mountcastle's neocortex theory says it works the same way all over, levels of patterns made of the timing and sequences of other patterns, from low level visual, audio, and other details of senses, to high level abstract ideas, object made of other objects,
and the neuromodulation (short term memory) is similar to a boltzmann machine
which is a bidirectional neural net that works the same up and down.

This system may be like randomMatrixTheory except with a recursive 4color constraint to extremely narrow down the possible states, leaving the degrees of freedom as superposition.

This system will be able to efficiently turn a sphere inside out as a variable precision continuous manifold, representing each point as the statistics of how the 4 colors push other colors in the same graph shape in opposite directions, since the blob of colored graphs they are trying to fit into will not fit with 2 different colorings. That will have to boson around (less dense, more degrees of freedom) and connect indirectly through a bunch of partially overlapping colored graphs (many of which are the same shape in some parts, and others being differently shaped where they hang off as lightweight dimensions. Pascals triangle defines dimensions continuously in the limit, zigzagging.

Any object in a 3d game can be represented by this system as a sparse network of overlapping polygon meshes (graphs).

Polygons are adjacent to other polygons, which is another view of the graph if you draw lines between their centers.

General computing can theoretically be represented using network of graphs.

The density of the 4 colors, if displayed on screen in any chosen location, defines proportions of black, red, green, and blue, so any color can be represented statistically, but if you look closer without increasing the detail recursively, you would see quanta (integer numbers of things). Pascals triangle jumps around by integer amounts, but if you count coins each as -1 or 1 and divide by squareRoot of number of coin flips you get the exact standard deviation.

Since the system should be able to continuously and in realtime raytrace a sphere turning inside out, it should be able to simulate a rotation between slower than light and faster than light, which is why there are theories about black holes being wormholes. I add to that theory that the set of all black holes is a clique of 3spheres which partially overlap as the statistics of colored graphs fitting together. This should allow us to mine gravity waves anywhere by pigeonholing more and more accuracy by using more partially overlapping colored graphs. Heisenberg is uncertain if you think there are only 3 quantum colors, but every planar graph or sphere is 4 colorable as in 4vectors.

It should also be able to simulate spherical harmonics as we see in the vibrations of atoms, and eventually we may be able to convert energy to mass with precision, which would be easiest to start with buckyballs. It may also simulate protein folding in a faster complexity class than existing methods. We may be using the word gigaqubit if we can align the exploration of how the colored graphs fit together in many permutations, align it to a market force to drive the network toward tighter fits, less number of possible colorings, because the many overlapping puzzle pieces each pull it a little tighter even if they dont exactly align on every node and edge or have the same number of them. Those who believe things stay the same integer quantity as themself will have a serious problem with double slit.

I need this for a very important kind of game, one that can only be won by large scale cooperation of the players.

Last edited by BenFRayfield; June 7th, 2014 at 04:04 AM.
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June 7th, 2014, 06:56 AM   #2
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power sources and complexity classes

Also, cold fusion is putting fermions closer together, combining 2 odd length paths and adjusting the 4coloring to align everywhere which would require changes recursively outward very deep (as deep as there are quanta in the atoms and their pascalstriangle-like bellcurve of possible positions in each degree of freedom, which is the bits that the complex numbers are made of). I dont know how to practically get cold fusion to work at large sizes (accuracy is experimented with and simulated over time) but I do know cold fusion is interchangible with NP Complete (clique, subset sum, etc) which is the difficulty when you have planck-size (somewhere around that, or is it planck squared?) graph size to find clique in. Cold fusion at just above 0 kelvin (the 3 degrees of background radiation is like small water waves, preventing you from touching anything with precision, so that temperature would be a problem) is fitting the odd length paths between the 4colorings of graphs together as a big puzzle, finding the clique of how the most of them align. If you could solve clique more accurately and efficiently, you could use grids of piezoelectric molecules to touch the graph from a sphere surrounding 2 atoms to be cold fused so accurately that it would slide outward similar to the smoothness of sigmoid instead of throwing energy around randomly. Instead, would probably be easier to use such a grid (to access the 4colored graphs fitting together like a puzzle) to change some of the frequency and split or merge directions of sunlight so solar panels could get the frequencies we cant normally touch, or even more extreme whatever the nuclear reactions at the suns center are throwing at us around its burning surface (we're not 3d, I wish people would move on already). Energy from the center of the sun does not have to move through the sun to get to us because theres lots of dimensions to go around.

Or my favorite... In yiour bathtub the drain turns a certain way, powered by curved space. If you spin it the opposite direction and same speed, it is resisting that. If you hold it the same volume, it must get slightly hotter. If you hold a compass needle still when its trying to spin, it must get slightly hotter than the surrounding liquid or air. Difference in temperature is energy for the taking, especially when it can be done smoothly and consistently since its the same curl everywhere at the same height.
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June 7th, 2014, 08:44 AM   #3
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some ideas how to test it - a new kind of double slit

Based on the, unusual and not accepted by a majority of experts, research of Claude Swanson, specificly the experiment where a laser shined on DNA in a calm near empty closed box with mirrors on all its sides for hours then it was removed then the laser shined much lower power and surprisingly the shape of the DNA still reflected the laser as if it was many places in that empty space but by copenhagen standards its collapsed somewhere far away... Based on that observation of physics, I propose a more advanced experiment, to use a box containing pieces of DNA that could be assembled into half as many total pieces of the same length and molecule types, and conserving momentum by putting them at the right average positions, I predict that if you vibrate the box (maybe with a speaker bolted to each side with precision at least 1/44100 second (really big and inaccurate compared to light but manyworlds doesnt care how big you branch as long as you dont unbalance it), and if the mirrors are really shiny and have absorbed as much energy as they can so it all reflects back and forth, then I predict that for the same reason the "browser cache was not cleared" leaving the many shapes of DNA floating around, that these pieces of DNA will superposition and assemble into the lowest energy state, which is closer to eachother, and then the 2 times as many DNA pieces as we have mass for will choose half of those locations at random and, as if a replicator or transporter beam on star trek, be assembled by the vibrating-mirror-box-recursive-superposition-and-imprint-on-space. It may also need other angles of the lasers and tuning of the wavelength difference in the light resulting from playing a certain frequency on the speaker vibrating the mirror, and I'm sure it will have to be explored many variations, but if Claude Swanson did his experiment and observed what he wrote that he did, I don't see how it could be any other way. Each unique frequency of light stores a pattern and imprints its 4coloring of graphs fitting together in a puzzle onto many permutations of the space. Check the fractional fourier transform for the rotating between of time vs frequency. I dont know exactly how to calculate that frequency, but there must be some configuration of the vibrating-mirror-box-recursive-superposition-and-imprint-on-space which allows the molecules to slide into a lower energy state. If we define what is a lower energy state by how we set up the experiment, we tell it what to go toward. This probably happens in water all the time and we don't notice it since we cant see individual atoms except when we're unbalancing them with the observation device. I expect the right wavelength and maybe adjustments to it would cause water molecules to align like magnetism but instead because of being superpositioned on eachother by that distance, if its the right distance and angle. You could test this by if it happens in a straight line and if others to the side move randomly or fall into the grid. Dentists shine a blue light to harden advanced materials filled in a tooth in just 1 minute, and growing yogurt is accelerated by certain frequencies/colors of light (organic chem fine tuning), so we're at the nanotech level. I see a frequency as a blob of 4colored graphs approximating a shape, near any smooth shape not just a simple sine wave. A person is a frequency like a molecule is, just made of more curves, but until we can tell the difference between blood and skin in terms of fitting shapes together, we should be careful to keep them on the outside and inside in the combination they already are, because fluids have lower energy states all around the room not just where your skin may land. If an evenly spread blob of all the right proportions of your up and down quarks electrons energy etc were ahead by the right wavelength then you might easily find yourself in those atoms like changing clothes, or you might find yourself spread evenly to match it.

I dont think in terms of what time the laser shined forward and reflected back and forth, because time is things getting randomized (increase entropy, energy moves where its harder to use) like its harder to unmix 2 liquids than to mix them as they do on their own just sitting there. The back and forth, while branching various amounts from the vibration of the mirrors, movements of the laser are just a direction sitting still in space, a shape, a quarter rotation so it knows where to align the wave forward instead of backward, but forward in time then mirror then mirror again and back here is still here and forward, and branched and blurred and sliding around somehow differently than eachother. If I believed in time in that way, I'd say it was looping around and falling into its past which happen to be at the same place in the box. The imprint of the past is still there ("browser cache wasnt cleared", shapes of DNA still reflect the laser even when copenhagen says its not there). Instead of calling it time, we have a word for a loop that pulls things together as it floats around unknown dimensions without sticking to our preferred dimensions, a graviton, but I'm not sure if they mean it in quanta form (path of length 2 back the same direction) or manifold form (4coloring of graphs fitting together into multiverse of nspheres or 3spheres easier to see). The past may be blurred and less probability amplitude (complex numbers are closer to 0 as multiplied by the bayesian-like ket_vectors), but if we are careful not to unbalance very cold or very calm and still things then it has no reason to move. Shining a laser between 2 mirrors back and forth is like pulling electricity through a wire. It doesnt have the electrons in just 1 place in the wire. They all move together especially when it loops around in coils. Maybe an optical coil would work better, which has voltage of spacetime flowing through it since light is the shape of spacetime (bosons have more degrees of freedom than fermions since they can be colored more ways, at least on average).
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