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FuzzyNAND

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A node is a Godel like statement that the Dot Product between 2 specific nodes is a certain number. NAND is Turing Complete because all digital technology can be described as combinations of NANDs. A node that represents the statement that 2 nodes are perpendicular is a NAND because other nodes can be parallel to one, the other, but not both. This is a new branch of math that most naturally represents the Max Clique view of the P vs NP math problem (and its million dollar millenium prize for proving P equals or does not equal NP) this way: Node pairs without edges have a dot products of 0, and with edges its 1. A dot product of -1 means parallel and opposite directions. By using spring-like forces (in specific softwares using FuzzyNAND) the Max Clique math problem can be represented in a possibly hill climbable way. This is a minimalist language where statements can refer to eachother in terms of dot product. Its similar to Fast Fourier Transform as a Base Pi math system.

A set of n nodes can be referred to together by choosing any order and creating n-1 nodes to refer to pairs of them, then n-2 nodes to refer to pairs of those n-1 nodes, and so on as a triangle-array until you get a root node that refers to the AND of that set of n nodes. This root node can be defined as parallel to 1 of the n nodes to align the definition of "true" between them so they can be used together. All the nodes in that tree would refer to dot product as 1 of their child nodes. This can be optimized with objects that represent known cliques, without the need to explicitly calculate the triangle array to represent AND of a large set of nodes. Its simply an existence proof. This will eventually be a practical system for a complete global infrastructure with seamless integration between digital and quantum grid computing and variable bit length addresses into this high dimensional space, so theoretically we can display and play with on screen the universal wave we call reality., It may be better to define only the squared dot product between nodes (as quantum physics says can measure squared magnitude but not directly) so -x and x dot product are equal in the view of constraints. I have found this wave behavior is more chaos-theory than when sign is part of the calculation, so that implies its closer to Turing Complete that way. More importantly, not considering the sign aligns with polarized glass, which only lets light through when parallel to a certain vector and you can take 2 perpendicular and you cant see through them but put one in the middle and it lets you see between them or not depending on its angle and gradually between those angles depending on how much you turn the middle quantum polarizing glass. You can buy it in some sunglasses., Bell curves can be derived as cellular automata where each cell becomes the average of its ajacent cells, and after n steps you get a bell curve of squareRoot(n) standard deviation. Similarly, bell curves naturally form in a space of all possible relative dot products, and specific dimensions observing bells when that is constrained to less than unity., The relative dot products between each pair of nodes with springs of various strengths will work as a turing machine just fine, but I'm running into a problem when I try to define those dot products and springs as nodes to close the NAND loop... To set a dot product to 1 or -1 is to quantum observe it into a specific state. Everything has to sum to 1 so only points on hypersphere surface are possible. NAND is defined as 1 when 2 inputs are not both 1, so in vectors NAND means the other 2 are perpendicular. That's balanced because perpendicular leaves most other vectors free to move around the 2. Everything can be perpendicular to everything else, and no problem in the statistics, but when something is constrained to be closer to something else (a dot product closer to -1 or 1 than 0), I don't know how to answer the question: What is the dot product of the observer with the constraint node? If the 2 constrained nodes are near the target dot product, the observer should see the constraint node as near 1, but if they are constrained to be a dot product of .9 then there is only .1 more to go one direction and 1.9 to go the other direction (more accurately viewed as perimeter of circle specified by dot product but that's not the point). Even if its mirrored so it allows .1 more one way (both sides of circle) and .9 more the other way (both sides of circle toward perpendicular middle), that is still an unbalance of .1 to .9 that the dot product between observer and constraint node will be unbalanced by. Therefore there must be an extra parameter, or area of possibilities, that becomes more filled when vectors are aligned to eachother more. When a dot product is constrained to be .64, this other area of possibilities must be constrained to be .36, so on hypersphere surface you get 2 dimensions of .8^2=.64 and .6^2=.36 summing to a hypotenuse of 1. I don't know where this extra area of possibilities goes. Maybe its why they use complex numbers in quantum physics, why each variable has 2 dimensions that are perpendicular to eachother (the real and imaginary parts of a complex number). I think I just derived Heisenberg Uncertainty from the need for the output of NAND to have the same statistical distribution as each of its inputs, in the generalized form of NAND (FuzzyNAND) where it can be about any dot product instead of just perpendicular. A constraint on 2 nodes to be closer together reduces their "amount of dimension" as they are constrained closer, because it is less of a free parameter, and the remaining amount of the 1.0 magnitude state of the universe vector must be more defined in terms of other nodes and constraints on them. To observe any vector into a specific state, or continuously closer to it, is to redefine the thing you're observing to have less and less effect on your observation. Its not just a property of physics. Its a property of all Turing Complete vectors. Still, I expect it will be useful to put subtle influence on vectors and observe them statistically.

FuzzyNAND License - Public Domain

Free download from Shareware Connection - A node is a Godel like statement that the Dot Product between 2 specific nodes is a certain number.

Publisher: Fuzzynand | License: Freeware | Price: 0.00
Version: 1.0 | Platform: WinOther
Released Date: | Rating: 0 | Title: FuzzyNAND

Author Url: http://sourceforge.net/projects/fuzzynand
Program Info Url: http://sourceforge.net/projects/fuzzynand
Download Url: http://sourceforge.net/projects/fuzzynand

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