Wednesday, October 29, 2014

Here is a fun equation

4^phi = 3*Pi, to an error of .003.

Wierd? Not sure, but I think it means irrationality might be a spherical definition.  It means that 2Phi = log2(3pi), or the precision of measuring 3Pi-1, assuming Gaussian noise of one is about Phi. That is, when measuring 3Pi-1, one notch on your ruler gets you about Phi bits of precision when notches sample at Nyquist-Shannon rates.

Now if you were to reverse the equation, assume 3Pi-1 was gaussian noise and compute log2 precision you get:

log2(1 + 1/(3pi-1)) = Phi/10, to within .0001.  Wierd? With Gaussian noise, only the one or the other is valid. The Shannon equation, as written, assume perfect orthogonality between signal and noise..

Anyway, spreadsheets are fun.

Talk about stupid

In the battles for smart card dominance:
CurrentC’s maker MCX, for those unfamiliar, is a group of over 50 retailers who have been working to develop their own mobile wallet technology. Essentially, they want to own the mobile wallet experience for themselves, instead of turning it over to a company like Apple, whose Apple Pay mobile payments solution prevents them from gaining access to customer data. Instead, retailers involved with MCX want to use mobile payments as a way to learn more about their customers’ shopping behavior, which could mean they could better target offers to them in the future.

OK, explain to me why a bunch of merchants want to destroy the very fiat system they are creating?   I can see why Apple's Cook is a zillionare, stupid merchants simply want Apple to win the game.

These are them:

Walmart, Best Buy, Gap and others Otherwise known as incredible idiotic executives. Here is a clue to these idiot store mangers. Money is different from spying, they are two different things, you cannot spy using money it will not work.

Tuesday, October 28, 2014

Its about 'one' and 'zero' being equidisant everywhere

This condition sinh^2 + 1 = cosh^2, and the Shannon condition are all the same theory.  That 'one' is a computed quantity, maintained by the motion of matter, the 'one'.  If matter hits close to the 'zero' it degenerates. I have a few drawings almost ready to show how the 'zeros' are moved about so the 'one' has equidistant paths through the linear portion of tanh.  It is all about making the optimum 'yardstick' where the F and 1/F are chosen to keep the zeros at the proper mid-points.  This is the minimum redundancy condition. The system is ultimately limited because the relative ratio of the largest F to 1/F becomes close to the residual irrational error in Pi.

Weinberg knows this, I was listening to one of his lectures, and he got the problem, and knew this was measure theory and warping of Riemann space. So this is real stuff.

Stay tuned, I am going to put up some rough schematics and show how these tear dropped orbitals have the effect of making the zeros equidistributed.  So, the Lattice Chromodynamics folks are on the right track, the idea of a continuous coupling constant is off base a little. The coupling is still quantized, but wave, or the imaginary part of the lattice between grid 'notches'. Things are getting much simpler in physics, its a new world. The folks who did quantum conductance nailed it.  The multiple paths through the linear  tanh is the key link between combinatorics and quantum mechanics.

This graph is the plot of Lucas polynomial L(5,r)+L(6,r)-L(6,r), over the unit circle from 0 to Pi.  The boundary conditions are met, the resultant is zero at angle 0 and Pi. But along the unit circle is a double wave at Pi/2. The vacuum wants to disperse that variation over the whole circumference, so it make an oval, it literally changes the shape scaling of the unit circle x,y axis (still a little fuzzy);  but this distributes entropy. We get the tear drop thing.  What unit sphere is warped? The shell and the 'one' both have complementary distortions. Doesn't that distort the value of Pi? No because of -iLog(i).  In the sum the power series sum remains the same, because the probability of a 'digit' counting is adjusted for the remapping of the grid.

Finite element computations use the concept, matching grid size to the variation  in the function being computed. In Shannon theory this condition makes the baud size, the distance between signals, consistent. In measure theory this condition makes the estimation of 'one' consistent. In physics it makes the total system, in the sum, nearly spherical. In statistics it means you have square matrices and a diagonal identity. In number theory it means you are counting with maximum accuracy using the minimum number of digits. And in network theory it means you have a minimal spanning tree.

How does the vacuum stretch the grid?
It redistributes the Nulls, the little inert elements of the vacuum can be shifted around.  Packing the Nulls makes matter by keep contained light trapped in the limit of the curvature, the Fine Structure limit.. That is the Higgs mechanism. So when stretching the grid, the relative change in curvature, or Tanh'(L(n) + L(n+1), must total Pi in its variation.  That is the total variation in Pi matches Pi, the finite log condition, the Shannon condition, the equal queue lengths condition, etc. Kinetic energy becomes adiabatic.

I figured that the Fine Structure Constant was a variation in volume.  I may be wrong, and physicists should clarify. But, it really should be computed as the variation in the value 'one', for spherical systems. It  itself is a 'constant' with the same proportional variation. Given the constant, the laws of physics should fall out from the equal distribution of entropy.  What if one built a system with a different number? Hmmm.... It may not be possible, the set of combinations may always be open. This was Shannon's world where cables were infinitely long. Recursive sequences tend toward Phi in their ratios, though I cannot prove this always that case. Making the variance in the value 'one' larger just causes the system to scale up and work with an nth root of 'one',

Monday, October 27, 2014

So how many units of 'Disorder' in the atom?

The Lucas system is circular, but it would accumulate the 1-tanh^2 as it spirals through the orbit. That gets Pi/2. But it is scaled and so may actually be getting Pi or 2* Pi, who knows? Anyway, that accumulation is a volume as the hyperbolics are circular. So the fine structure residue is a volume, and I am not sure where physicists have the 3/2 in their formula.

To get the total number of those, take (Pi/Fs) or (pi/2*Fs) and so one; you numbers like 215, 430 etc. Call these the total volume of the sphere in units of Fs, and you have it, I think.

Do I have units upside down? Could be.  Previously in that spectral chart, I could count up or down, it wasn't hyperbolic.  Now I have to be careful.  But Tanh is linear around the small angles, and that is where most most measurements of Pi will take place.  So we may have to count from the center out. The system will always try and operate along the linear portion.

Atomic Orbitals:

This makes sense regarding the atomic orbitals because the first two Lucas polynomials have no zero, so the shell is spherical,  Add another Lucas number and we get that inner and outer shell. How does the Lucas system handle the higher s orbitals with no angular or magnetic moment? Most likely the Lucas polynomials that have congruent zeros are used in series, as if it can skip intermediate polynomials.  

Magnetic moment:

  But you can see the set of Lucas polynomials can satisfy the n,l,m system in standard use. Magnetic moment probably happens then the center no longer is a point source. So the Lucas numbers no longer count by 2,4,8 etc.  They will snap too on the odd numbers.  When the incongruent polynomial appear, it is mismatched with the s orbital and has to curve the shell to realign them along the tanh linear, and that means splitting the outer shell into separate regions, each region having the same odd curvature.

The thing seems to be driven by surface distortion on the surface of the unit spehere, wherever that is, near the center. So the orbitals compensate for asymmetry in the nucleus, I would think. It likely make Pi by making the zeros as symmetrically out from the some center as possible. The vacuum does not have direct access to both sinh, and cosh. It basically adds, and even then can only add maybe three numbers at a time. So the vacuum simply redistributes the interts and imbalances to make a 3 bit adder work at any one time.  In other words, it does not do sophisticated math to meet some human regular complex plane, it just warps the local vacuum to do simple straight line adds.

I hate to spoil the party, be we are dealing with  something having an IQ of 1.5.

Tie in Shannon to Lucas

Look at  log(1+entropy of Pi), a version of Shannon.  A slice of the entropy is 1-tanh(n*a)^2 where a is log(phi).  The idea is that the electron moves such that is separates out the integer values of Lucas at the surface (or center?)  of the orbital shell, where the Lucas polynomial is at x=1.  We want to know how the Lucas numbers are paired to make orbitals. The electron angular motion would effect a transfer to balance out the phase and match motion to phase imbalance.

So we get:

log(2-[sinh^2/cosh^2]) or  log(2*cosh^2-sinh^2) - log(cosh^2).
The first term becomes:  log(sinh^2+2)

Then converting to the Lucas system which scales the unit circle we find that sinh^2 = L(2n) because the integer 2 goes away with the square of sinh. But L(2n) is cosh(2n)* sqrt(2) so we end up with:

log(cosh(2n*a) - 2*log(cosh(n*a)) + log(sqrt(2), and these come out to integrals of tanh, which is a sum in out discrete system.  So it may be that the system is working with copies of Lucas in n and 2n to balance Pi.

I think I have most of this, but errors abound, so be careful.

Another way to check this is go to the spread sheet and use irrational Phi, and take the logs of 1-tanh(n)^2 for the power series and directly construct a two binary digit system.

This is not something I should be working on, it is a critical piece of the puzzle and the pros need to be on this.

Sunday, October 26, 2014

Handling the Bohr model

I am trying to match counting directions for quants with the Bohr model. This is about aligning the axis between this and the Lucas model and converting the total energy of the Bohr model into delta energy per level in the Lucas model. On top of this is the angle matching between hyperbolic and trigonometric with the Lucas model. Bohr also counts negative energy, the amount of energy needed to remove the electron.   I am trying to straighten this out, see below.

The energy of the n-th level for any atom is determined by the radius and quantum number/ An electron in the lowest energy level of hydrogen (n = 1) therefore has about 13.6 eV less energy than a motionless electron infinitely far from the nucleus. The next energy level (n = 2) is −3.4 eV. The third (n = 3) is −1.51 eV, and so on. For larger values of n, these are also the binding energies of a highly excited atom with one electron in a large circular orbit around the rest of the atom.

Lets try to nail down down direction in counting Lucas numbers.

1) The highest order Lucas number matches the Fine Structure.
2) The fine structure constant must be the high end band limit of light from the electron orbital. Isn't that limit a radial frequency?

3) The atom gets heavy toward the center, high Compton frequency goes with higher heaviness,  λ=h/mc and high Gamma frequency comes from the atam center.

4) The Lucas quants counts layers, it is not an integral.  I mean light is a power spectra and all of its cylinders are firing. So the Lucas atom will be a power series, going from the exterior to the center.

That means Lucas numbers count up from the outer shell toward the more inert center. This is the way I have been counting exponents, but Hyperbolic says we can count symmetrical anyway. 

And, the Lucas polynomials are equally defined over the interval zero to one, and are not a radial function, so that variable has to be scaled.  And the hyperbolic angle will be scaled.

I likely got a lot of this backward, but that is going to be my first effort, so you experts out there, feel free to jump in.

This equation says it all

In the fields of electrical engineering and solid-state physics, the fine-structure constant is one fourth the product of the characteristic impedance of free space, Z0 = µ0 c, and the conductance quantum, G0 = 2e2/h:

Its on the Wiki site.  This tells me that finite combinatorics and group theory are superseding Isaac's rules of grammar and relativity.  I think this generation of physicists and mathematicians have everything together.  The next step would be to define the first order of light entropy as the unit of momentum for engineers, then let them divide up straight line light, distance, mass and time as they see fit.  Physicists can move on.

We are at a great turning point in science and amateurs and 'numerologists' like myself cannot keep up. The  new constructions of the orbitals, based on Lucas theory, are already in the computers of these brilliant minds.

My numbers

These numbers are me using the rational ratio for Phi. If I use the limit of Lucas  and actual Phi, I get -137.1590861574, which about right. Using rational ratio, my entropy in pi is a lower than the actual fine structure, .006 instead of .007.  However, that is likely a selection error on my part. I have the titles and Fibonacci  numbers both in the chart. I think there is a trade where adding more degrees of freedom and suffer a bit of error in Pi yield a better stability for the atom. The odd orbital shapes happen because the entire power series is not used everywhere. The Lucas number do not actually divide out a rational ratio, they count up to the maximum degree, (L number)  then count down, in a quantum oscillation. Everything is done by n, the Lucas quant, no time or space. It looks like everything in the nucleus and orbitals is composed of just 16-20 integer counts.  Separability by primes insure that they combine in the proper two or three integers near the surface of a sphere.

1.619047619   rational ratio.
n Ph()^n p^n-p^-n/p^n+p^-n 1- ratio^2
1 1.619047619 0.4477144646 0.7995517582
2 2.6213151927 0.7459121502 0.4436150642
3 4.2440341216 0.8948023173 0.199328813
4 6.8712933397 0.958518851 0.0812416123
5 11.1249511214 0.9839698039 0.031803425
6 18.0118256252 0.993854207 0.0122538153
7 29.1620033931 0.9976509898 0.0046925025

sum of 1.5677944879

Rational phi sum of 1.5724869905
1 2

2 1.5 error from pi/2 0.0030018388
3 1.6666666667 error from pi/2 -0.0016906637
5 1.6

8 1.625
13 1.6153846154

21 1.619047619

34 1.6176470588

55 1.6181818182

89 1.6179775281

144 1.6180555556

233 1.6180257511

377 0

Here is where I think we are headed

Some of this will be wrong, but its a start.
This is the atom, I have marked the Lucas four and three quant levels. I have also marked what I think are the charge vector, Cosh and the magnetic vector, SinhNote: The magnetic vectors will be remapped by the odd zero set, so this diagram is more a schematic. The sinh is always a half angle off from the cosh, and, and the sinh always has odd zeros on its bounding circle. The Lucas numbers appear on the bounding circle for that quant level and goes to zero toward the proton center.  Lucas numbers are quant values of light.

The blue and yellows circles are the zero points of the Lucas Polynomial, with respect to what real and complex axis?  I think the axis will have to be relative to the dominant vector of radial motion.  I also am still confused about mapping this to a sphere, but I think Reimann sphere packing is on its way.

But lets continue anyway.  The zeros are spots where phase imbalance is zero!, they would be likely spots that the electron would appear, I think.  The half angle difference and the Lucas numbers result from the fact that unit spheres, the proton and electron, are finite, not point charges, and that is why we have magnetism vs charge. The magnetic is mostly tangent to the unit sphere, the charge vector perpendicular. But they are both made of light bubbles, the magnetic bubble having an odd set of zeros, that is why we think it is dipole.

The motion of the electron is out from the page, a cross product of the sinh and cosh vectors. The electron itself is composed of Higgs elements and trapped light, as are the rest of the atom, its all these two things. The electron will spiral in and out from the center, its momentum determined by the angle of the two vectors. In this chart, the electron bounced between the L4 and L3, driven by the half angle difference. The odd and even zeros will cause spiral in two dimensions.

The movement of the unit sphere follows the vector cross product until force is drained then reverses motion, so the electron climbs from L3 to L4, and back again. The light bubbles follow the reverse circuit.

And of course we would have the complementary motion in the quarks. This stuff is very vague to me, and a lot of work needs to be done here. The Lucas values are reusable at higher energy levels, and will deform as we see in existing orbitals.  This is mainly because the degrees of freedom for light are nearly orthogonal.  As the bounding circles warp into tear drops and rings, the zeros are redistributed, we get a remapping of the grid.  And the magnetic vectors will assume the normal pattern we are used to, being curved by the odd number of zeros.. 

But, no fields in this thing, just bunches of local bubbles packed in a sphere.

Saturday, October 25, 2014

How close can Fibonacci get to the fine structure constant?

Well the maximum deviation Fibonacci has from Pi/2 is -0.0072908055, and its inverse is -137.1590565066, the physicists have:
I call that close. We need to dig up Prof Lagrange and Lucas for the Swedish Banana. This had to be true, the degrees of freedom are equally utilized, so Lagrange estimation will be spherical and that makes Phi a winner. The Fine Structure is simply t the variance of light exchange rate and given the size of the universe, the quasars simply got the vacuum optimum to the degrees of freedom that match.

It came out to a power series in tanh', the derivative, because tanh is the allowable motion, and the variance in that has to be split up to minimize redundancy.  The variance in that value is of course the spectrum of fundamental light, its sample rate noise.

This number is theoretical based on using Phi to the limit of my spread sheet.  When a finite rate is substituted the number is between 0.0002269164 and -0.0045091191. My finite ratio for Phi is 89/55. So the universe can compute Pi and implicitly Ln(Phi), so it has enough know how to do Isaac's grammar to a finite limit of .00729 = dx. Is this the limit? I dunno if the quark system is more accurate, this only applies to outside the proton shell as near as I can tell, but do not quote me, check with Weinberg and Higgs.

How does this fit with my spectral chart? The chart was just a computation about how much would fit if there was no structure, no electron, no quarks.  The came me trying to find applicable recursive power series which the vacuum could do with only local knowledge and maximum entropy. Most of my blundering about was ignorance and application of things like primes and power series, most of which I barely understood.  Lucas did the real work here when I realized his integer series was cyclotomic.

There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!
Richard FeynmanRichard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 0-691-08388-6.

Packing spheres, Richard, packing spheres. 
Charge is offset, is the electro dynamic entropy in a sphere, composed of what seems to be a fifth to sixth order power series. By offset I mean the exponent in the power series when phi is the base. It is the contribution to the entropy of pi from each of the 'digits'. Free light in 'space' is the spectrum of light without enough Higgs density to be meet the Compton limit, and that is conductance. {ut in other words, Conductance is the ability to move charge without moving Higgs elements.

There should be up to six configurations in which the elements of light can be packed against Higgs elements. But, like I say, I am not sure how the fine structure is split between the proton and the electron. But all the measurements of the constant seem to be along a single axis, but do not quote me, I am still reading up.

What about magnetism? Not sure, but I am looking at the cosh(n*w) plus i*Sinh(nw-n), the two being one delta angle separated.The motion of the unit sphere needing to avoid zeros when an electron is involved. Look at the Lucas sequence and note the alternation between cosh and sinh.  The quant, the ln(Phi),  is built into the cross product I think.

What about size difference?
One of my incomplete ideas.  Light (or the Higgs) can change shape and that gives us the seven degrees of freedom.  That seven determines the degree of the power series.  So that problem melted away.

Who is doing numerology here?
The physicists who assume the number line goes to infinity. Not the finite element, finite order wave folks like me.