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Mark Farrugia

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3SAT==QBBR: Humans 'see' only a tiny slice of the known electromagnetic spectrum. Interestingly enough, this 'visible light' is centered around the peak of our Sun's 5800K blackbody curve.

Note here how random 3SAT cost curves look & behave exactly like quantum blackbody radiation (QBBR) curves, and that the most interesting & difficult 3SAT instances, which probably contain the most information, are also found centered around each curve's peak. 

I am guessing that there exists a quantum algorithm (using say, a QFT on superpositions of standing EM waves) that can solve any given 3SAT instance in O(n^3) time, since the total power radiated by a blackbody is proportional to O(T^4), with derivative O(T^3). QED. (c)
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(1) # of variables n == Temperature K
(2) Ratio m/n (clauses/variables) == Wavelength v/f (velocity/frequency)
(3) Peaks get sharper, and shift to lower X-axis values, as variables/temperature increase.
(4) Visible light is found centered around the peak of our Sun's ~5800K curve == location of the hardest problems in random 3SAT formulae.
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The Human Quantum Search Algorithm: Using photons (e.g. laser) to search for an object in an unlit circular room gives a quadratic speed-up over searching the room without photons, a result much like Lov Grover's quantum algorithm for searching an unsorted database.

Searching a dark circular room of radius n requires O(n^2) steps in the worst-case, where you must physically inspect all of the room's area. With a laser, though, you can sweep the entire room's perimeter from any static location (such as the center), and solve the search problem in O(n) steps. QED.
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Need to separate 3SAT hardness from 2SAT easiness for your P!=NP proof? Look no further than the Elementary Cellular Automata...
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BOOLEAN CONSTRAINTS ON 2 VARIABLES: For 2-cell neighbourhoods (r=1/2) with binary colours (k=2), there are 16 possible rules, and the most complicated pattern obtained is nested (like the rule 90 elementary CA). No wonder 2SAT is in P!

BOOLEAN CONSTRAINTS ON 3 VARIABLES: For 3-cell neighbourhoods (r=1) with binary colours (k=2), there are 256 possible rules, where we first encounter the onset of universality and intrinsic randomness (like the rule 110 and rule 30 elementary CA). No wonder 3SAT is in NP!  *QED.*
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3SAT Cost Graph: 5000 individual instances clearly showing the phase-transition of "under-constrained" SATISFIABLE formulae (blue) vs. "over-constrained" UNSATISFIABLE formulae (red). The hardest, most interesting, and ILLUMINATING instances are in-between, where the ratio of clauses to variables (m/n) is about 4.5 (experimentally determined w/ n=50 variables). Theoretically, it may be 3.0, as n goes to infinity.
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White Light + Triangular Prism => Sorted Poly-Chromatic Spectral Information.
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Angle of Incidence == Angle of Reflection? Well, not quite. But it is the most probable result of the quantum computation that Nature returns, as the genius of Richard Feynman shows below, without any mathematics. Remember children, things are not their names or symbols...
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Feynman replaces complex numbers with spinning arrows, which start at emission and ends at detection of a particle. The sum of all resulting arrows represents the total probability of the event. In this diagram, light emitted by the source S bounces off a few segments of the mirror (in blue) before reaching the detector at P. The sum of all paths must be taken into account. The graph below the mirror depicts the total time spent to traverse each of the paths above.
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Young's Double-Slit Experiment: Photons propagate out from a source spherically at speed c, covering an area of O(c^2) in 2-D. Clearly, the closed system 'device' is computing something analogous to the 'natural' function x^2 going forward, and sqrt(x^2) = +/- x in reverse:

x^2 = x*x = self-interference   <=>   sqrt(x^2) = +/- x = uncertainty

Nature also seems to return the quickest, most probable result of the computation, which is found at the expanding perimeter of the photon's 'propagation circle'. Note how the height of the 'peaks' of the probability distribution curve coincide with the fastest 'interception' time of said circle, minus the destructive interference.
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Young's Experiment, Squared Amplitudes, Complex Numbers:
If Nature computes, then presumably it also computes functions like x^2, which is not one-to-one, since (-2)^2 = 2^2 = 4, sth. its inverse is sqrt(4)= +/-2. So even knowing both the function being computed, as well as its result, it is still impossible to know from what initial value it came from. There exists a certain UNCERTAINTY...
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WWRFD? (Physics v Women v Bongos) => Just Do It.
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Stefan-Boltzmann Law: The energy radiated by an ideal blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature (T^4).
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dT/dY(T^4) == 4*T^3 == O(T^3)   What could this imply?
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High-energy 3-D EM standing-waves which oscillate FREQUENTLY between +/- values are very unlikely to be chosen as an occupying quantized mode within a blackbody cavity. They are often UNSATISFACTORY.
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