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February 15th, 2014, 02:55 PM   #1
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Cardinality of integers equals cardinality of reals

pi squared is an integer because its last digit in base 2 is 0. The surface hypervolumes (or hyperareas/hypervolumes on alternating indexs) are an integer multiple of eachother while having sometimes different and sometimes same exponent of pi.

So theres really no important difference between a volume and a surface. area = pi*radius^2. Around the circle = 2*pi*radius. It continues with higher exponents of pi and combinations of integers, especially factorials (which should be calculated using the simple "add the 2 numbers above" cellular automata of pascals triangle. Fortunately its partially symmetric, 2 cells above and 2 below. Heat spreads like bell curve mostly, and you can always get more accurate with better curves in your view of the world, but newton wasn't wrong, just one level of recursion lower, and very necessary for thinking in the strategy of Occams Razor (keep it simple, and a statement about which things are more likely to be true and how much as you can recursively calculate using Bayes Rule, 3SAT, or Boltzmann Machines). The physicists will be happy to know, if they dont already, that there is, not even in principle or thought experiment no difference between a surface and a volume, a rediculous idea anyways since the universe would have loose ends which are not implied by either nonexistence or the set of all things, which is a good example of a surface being a volume since they are both the same shape, one being made of "something" and the other made of "nothing" but something and nothing are only labels which cant change what it is.

http://en.wikipedia.org/wiki/Unit_sphere See exponents of pi stay the same in consecutive integer number of hypersphere dimensions, in the part about gamma function (surface hypervolumes).

Continuum Hypothesis, which says the cardinalities (sizes of sets of certain things in math) are each exponentially bigger than the last (specificly 2 exponent the last size, interesting that its an integer power when talking about the reals isnt it?)

How did I figure it out and know it was important (I'm not saying others dont know it, but Cardinality Of The Continuum is still around)?

Odd dimensions are somehow related to wave, even dimensions somehow related to particle, as in the recursion of gamma function alternating pi the same 2 exponents for volume then move up 1 integer dimension and then the same 2 exponents for surface, and repeat forever. Instead, since pi squared is within the cardinality of the integers (and therefore is an integer, regardless of our view of it having a decimal point and an infinite number of 0s the other direction) we should find ways to use base pi numbers, like Cooley Tukey Fast Fourier Transform (a simple equation and about 20 lines of code, recursively complex numbers in an array). See that youtube video about how to turn a sphere surface inside out http://www.youtube.com/watch?v=R_w4HYXuo9M A sphere has only 1 side. This is why we have complex numbers at odd parity balancing the curve of gravity at even parity (dont they say the graviton is spin 2 or something even about it? I dont know exactly what they mean, but probably this is a view of its most basic part).

Pi squared is an integer

... I wrote another place copied here about the physics math and my progress on open source simulation (can try the basic jello-like unit vector vibrating cube of 400 points at the link...

In physicsmata 1.2.1 (that exact version demonstrates it best, not 1.2.2 which is more about something else) http://sourceforge.net/projects/physicsmata

I created a cube full of 400 random points, and for each chose some near points, observed their exact distance, and put a distance constraint between those pairs. Each time cycle, every point moves the same constant distance in whatever direction its constraints are most satisfied, as if they were springs of constant length, except instead of spring force its not acceleration or force as we know it, instead its a change of position. I have no speed variable, just these vibrating jumps of C (or call it 1.0) distance each. Its C instead of C^2 because if you sum C^2 coin flips each as -1 or 1, its on a bell curve of standard deviation exactly C, as you can see in pascals triangle which is not normally used for that but its where bell curves and circles come from.

When you drag with the mouse the cube of points with distance constraints, angular momentum is conserved as you see by the other half of it rotating the opposite direction you're pulling some point. Drag it along the side of the window and see twisting, bending, and vibrating of that jello-like cube space.

But the electric induction needs an extra step... Instead of manually choosing the distance constraints, which are spread around a sphere with varying radius (so it is compatible with the following math), it would be the inverse distance squared (as in newtonian gravity, electric/magnetic fields, etc), probably with a slight adjustment for the delay in the points at a distance reaching here, but you've got to use a finite set of points somewhere in a simulation.

Whats the 4-vector of it? Light speed appears constant to everyone, happens for the same reason alternating current (AC) squashes together the top humps in the wave and pulls apart the bottom humps (or however you want to name it, since it is symmetric as the phase covers everywhere once per wavelength), so when the 2 sides of a top hump are approaching eachother they are going this constant C 1.0 speed toward eachother, then reversing, back and forth in some combination, whichever way is epsilon less than 0 or epsilon more than 0 (discontinuous, quantum, pascals triangle, converges to bell curve as these forward/back zigzags are like coin flips). The squashing toward the tops see eachother through the denser space, and those farther apart see eachother through the less dense space. This happens when the electric company pushes and pulls on our power lines 60 times per second.

In an induction coil, for example, the many coils near eachother going in the same direction would do the same thing to eachother, cause eachother to jump forward/back/zigzagging 1.0 C that constant distance in some direction. The curl of magnetic field, as perpendicular to the electric field, is lorentzed from choosing a unit vector (from a sphere center to its surface), or maybe its a 3-sphere (as in poincare) with 1 more dimension we call spin or phase or something. Lorentz is just the equation of a circle. Any time you do a sine or cosine, thats the basic idea of lorentz.

There is no total field in a sphere shell. No gravity. No electric. So what does that mean when ball lightning forms a sphere shell, turns invisible, goes through solid objects without much touching them, and eventually explodes with a every loud noise and produces a burned sulfur smell (I read)? I'd say the electricity is moving in these constant distance jumps, back and forth, as it runs into a big blob of lightning and turns sideways starting to cover a sphere, and since its already the amount of positive/negative that lightning would exist there (because a positive charge pulls the negative lightning), I'm not sure if there is a positive charge in its center or not, especially because of that youtube video showing how to turn a sphere insideout without pinching a surface since that means a sphere has only 1 side.

I'm going to try simulating ball lightning, coil inductor, capacitor, etc... Something simple like a blob of bell curves I'll call wire and metal plates, and coil the wire in the middle, and for the lightning that would take a slower but very worth it to see what happens simulation. Science is also good for games. The jello-like cube of 400 points runs realtime graphics fast without even much optimizations. This is because I found the right math instead of needing to evolve possible solutions to the constraints. You just calculate it right away each time cycle. Try it.

While its still too early to say how practical, I think we will eventually learn to use something like a tesla coil with maybe a grid of digital radio transmitters wired into its power source, to generate precise electricity balls around a person with no space suit or protective gear, hold it stable by preventing any one part of the bubble from vibrating in the direction of radius since it should be stable while its parts move randomly or any near balance, then somehow tune it into the N dimensional simultaneous combination of waves (theres only 1 wave, the universe) and go with the ball lightning wherever it goes when it becomes near transparent. You cant approach light speed because you never reach an event horizon as viewed from anywhere outside, but you can slow down until you're faster than light, which I think of as a sphere surface has only 1 side (see youtube video "how to turn a sphere inside out). Light speed is a sphere surface because its area is squared of its radius (times a constant if you dont use base pi, see gamma function http://en.wikipedia.org/wiki/Unit_sphere gamma function (surface of nsphere) for continuation of parity of alternating dimensions, but we dont need to get confused this early. I am very confused on that), but I am sure light speed is sphere surface of C^2 (variance is stdDev squared, see pascals triangle above) because if you multiply the height of bell curves you get a 1 less dimensional hypersphere of constant density at each radius. In quantum, light speed is C^2 and shaped as a hypercube 1 quanta per side, or in qubits light speed is C because you are using scalars which are made of many bits. Its all derived in pascals triangle which is well known math for integrating continuously X choose Y (cardinality of integers but theres still infinity of them and you get to exponentiate by squaring... pascals triangle is generally useful). Sorry officer, I cant obey the speed limit because time is on the other side of the black hole and I dont see how I could have a speed without knowing if I'm going forward or backward in time. Maybe thats what they meant by imaginary velocity or imaginary time (complex number) Its always the other side. Thats why you fall toward the black hole as you increase in time. But since a sphere has only 1 side, its meaningless if you're going forward or backward.

...

Also, they probably already do this, but it appears to me, in a vague way to be explored later maybe, that in computer CPU and GPU hardware they are probably using (and if not should look into it) something very similar to Cooley Tukey FFT in scheduling which NAND ops (or whatever primitive of general computing logic, which are all capable of running all possible software if you hook enough of them together) occur simultaneously when adding, multiplying, exponentiating, and forever on superexponentiating (see very small and complete continuation in Church Encoding of Lambda Calculus) scheduling the NANDs which can not get in eachothers way (or gambling that you wont have to backtrack with some extra cycles in less common cases)... Maybe they had their AIs and 3SAT solvers generate it, but there is a method to the madness, start half way into it, branch half way again, or something like that. Cooley Tukey FFT has pictures of the data flow http://en.wikipedia.org/wiki/Cooley%E2% ... _algorithm For a short time, I was looking for a way to use Max Xor constraint of NPComplete to implement a variable number of bits of accuracy lazy evaluated fractional fourier, like your numbers would be functions that look for relevant bits a few objects deep which also know about other objects, standard Lisp kind of stuff. A supercomputer will only take you so far if you dont know what math it should use. What I was looking for was something similar to the way the fourier of a bell curve is another bell curve (at constant location, phase varying), and how bell curves are generated by coin flips as in pascals triangle. Theres an infinite depth of more advanced math than the powerset number of calculations you get in some cases from 2^qubits (minus the lost accuracy of scalars since you're working in the model of C (quantum is hypercube of 1 quanta per side) as the speed of light instead of C^2 the continuous sphere view. Can't completely defeat heisenberg uncertainty, but I imagine if you throw the mass of a black hole on top of it, held by some carefully designed structure, it will get certain enough for practical use. Or maybe not. Things to explore.
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