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April 7th, 2015, 03:15 PM   #1
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Eulers Identity: e^(i*pi) = -1 vs bellCurve: sqrt( e^(i*x)^(i*x) / circle ) ?

Eulers identity:
e^(i*pi) = -1

Bell curve:
e^(-x*x/2)/sqrt(2*pi)

(x^y)^z = (x^z)^y = x^(y*z)

e^(-x*x/2) = sqrt( e^(-x*x) ) = sqrt( e^((i*x)*(i*x)) ) = sqrt( (e^(i*x))^(i*x) )

Divide by circumference of a circle (which I left off to simplify until now):

bell curve height = sqrt( (e^(i*x))^(i*x) / (2*pi) )

Looks alot like e^(i*pi) = -1, doesnt it?
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April 8th, 2015, 07:43 AM   #2
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Explaining the basic idea of wavefunction gradient when squared as mass/bellcurve instead of wave:
Energy can be mined from beach waves or any vibration with a system of heavy (or microscopic and fast) balls rolling on a curved 2d surface, like 2 vars of sigmoid but curved however you need it and so it doesnt roll out, where many such balls in energy mazes (multiple local minimum) pull on eachother with strong ropes, using the force of some balls rolling down while others roll up, depending on which part of the curved surface each ball is on, effectively entangling 2 dimensions if the corners differ in height gradually. A basic computer could be designed to calculate any logic statistically using 2 dimensions at a time as 2 vars, like boltzmann or neural vars using sigmoid, but more basic using gravity like the ancient mechanical computers. If the balls roll smarter than randomly, as the ocean waves push and pull in partially predictable patterns, as would be defined in the program of such mechanical computer, then it could power the movement of water, maybe using buckets pulled on a hanging rope on gears or pulleys like ski lifts, which the balls would turn such gears, and other balls would be attached to the intersection of such bucket pull lines to pour from some into others or lift... Mining entropy is only hard if your strategy is random. Computers are good at statistics and waves.


Eulers identity:
e^(i*pi) = -1

Bell curve:
e^(-x*x/2)/sqrt(2*pi)

(x^y)^z = (x^z)^y = x^(y*z)

e^(-x*x/2) = sqrt( e^(-x*x) ) = sqrt( e^((i*x)*(i*x)) ) = sqrt( (e^(i*x))^(i*x) )

Divide by circumference of a circle (which I left off to simplify until now):

bell curve height = sqrt( (e^(i*x))^(i*x) / (2*pi) )

Looks alot like e^(i*pi) = -1, doesnt it?

---

Restricted/layered boltzmann machines, a symmetric kind of neural net using sigmoid (which is related to bell curves) flow information only on paths of even length. Fully connected boltzmann/hopfield has both odd and even length paths and is much harder to use as statistical learning tool (on pairs of scalar or bit vars being on together). The difficulty of including odd length paths is the big mystery of npcomplete. Its counterpart in quantum complexity theory is BQP, which is statistical and parallel and in theory in polynomial time could merge those parallel calculations into something useful about a large part of the whole at an observation.

Position and speed are 2 views of the same thing, as seen in a spring's acceleration being negative proportional to its position difference from average length. Energy is the squared magnitude (or just the magnitude?) of that complex number or view it as position and speed, with acceleration being a view of position.


Lightspeed appears to be a limit because you stretch yourself as a spring and reach ever higher energy levels of spring stretched. Mass cant go that fast because mass's position is spread across a bellcurve of some number of dimensions. Every n dimensional bell curve has an n-1 dimensional hypersphere surface of constant density at each radius, or the bellcurves can be different sizes and positions lik we see in zeta function, the sum of all positive integers exponent negative of complex number parameter, but I'm not sure exactly where that fits in other than the complex numbers and every smooth unitary map of complex to complex is approximated infinitely well in that part of zeta near 1/2 real. Its a bunch of bell curves made of bell curves or waves whichever you want to view it as.

bell curve height = sqrt( (e^(i*x))^(i*x) / (2*pi) )

Hopfield network, where all nodes are -1 or 1 and all weights are 1, has *nodes choose nodes/2) minimum energy, since xor is true a little more often between the 1s and -1s (nodes with that state at the time) than between 1s and other 1s or -1 and other -1s, because I'm excluding a node's weight to itself. That looks like a bell curve, 2 of the same thing. All reals, bell curve height.

X exponent y means do x y times, each time on what you got the last step. (x^y)^z = (x^z)^y, so permutation number of possible orders of the supersuperexponents.. the exponential map I think they call it or something like it.

e^(i*x))^(i*x) means wave x, then when you get there do wave x again, and you're back to bell curve which is how mass moves and how double slit hits the back wall, in either of 2 bell curves if distubed much or wave if disturbed gradually less.

Gradually. Since wave and particle are just even/odd recursions and permutations of Eulers Identity and bell curve, quanta is practically useful but technically only an approximation of Bloch sphere - Wikipedia, the free encyclopedia which has that exponent and superexponent as its 2 dimensions, and they can be mixed somehow.

A 3d lcd is simply 2 normal lcd filters which already twist as quantum phase glass in the spiral molecules some of them are made of. One lcd for controlling brightness at each pixel, and the other to rotate the phase of whatever comes out, so for example if it rotates 1/8 turn you would see it equally with each eye of normal 3d movie glasses. 1/4 turn is perpendicular and only 1 eye can see, if your head is turned that angle. Solar panels probably work something like getting the light to push on the liquid crystals between 2 differently angled quantum phase glass which should work like a light resistor and resist less, lower energy, when the crystals twist to maximize light going through. I'd like to see how that combines with ring laser gyroscope with 4 mirrors or optical internet wire, which detects rotation by difference in distance light travels clockwise vs counterclockwise, same loop same distance from newtonian perspective, but different distance the light travels in opposite loop directions, as viewed from outside the loop, so it would measure differently to different observers but probably gravity pulls it together a little like copenhagen... but copenhagen is wrong, and manyworlds technically true but practically we are not adjacent to all those variations they are closer to other permtuations, same way mass blobs together while it has a slight chance of being anywhere and everywhere.

Wavesim java applet 1d schrodinger equation simulates soliton in alternating even/odd odd/even pairs of complex numbers, and I was able to branch it recursively by multiplying by a hill with a sharp point but smooth hills it just lengthens and crosses or turns around if too high.

lattice boltzmann, a cellular automata in 2d grid where each 3x3 squares has total velocity normalized so all squares sum to 1.

I'm thinking massively multiplayer paint program and music tools, using the statistical ai and wave math, would be a good way to demonstrate.
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April 8th, 2015, 08:01 AM   #3
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