nlc-part huit of the discussion of ct3-And now for some math

This section is to provide some limited relief to those of you who are dissatisfied because there is not enough math.  A discussion of algorithms without math formula is like having cereal without milk.  It's ok, but it leaves something to turn it into mush.  For reasons that will become clear as you read through this, not only do we have to pick which models to pursue, but you have to stop the analysis pretty quickly since its hard to find math for a 4 dimensional spiral.  The concept is pretty simple (you just take the spiral function and add another variable and integrate it relative to the prior variables) but there are several approaches (radians and degrees just to give an example where only the units change) and to decide at this point in time which one is the better solution to pursue would be to add a certainty to the process it doesn't deserve.  Worse still, there are so many dimensions (as many as there are bits of information in the universe or at least half that many) that attempting to get a complete solution would be pointless, what I am going for is a general solution.

I could spare you this analysis, of course.  I could write a nice poem.  But since you don't spare me, I will not spare you.  I wonder if I could complete this with you here.  I'm reminded of the Seinfeld episode where everyone gets either smarter or dumber by abstinence (you can go either way, but in the episode the men get smarter and more sophisticated while Elaine loses the ability to complete even minor tasks.  It is, admittedly sexist, but its pretty funny).  I'd rather be having sex, in case you are wondering.

It is, for me, a beautiful morning, sunny, but cool on my Charleston deck.  I feel particularly isolated from you and melancholy.

This section (in the book) which I have now reached section 8 of the rewrite (hit) is actually called "CT2-NLC a spiral explanation of the one source universe".  It got carried away and self important in the re-write, but if you look earlier you'll see the basic spiral equations.  There is a better equation, I think, for the spiral inward and the negative of that equation would represent the spiral outward (ct1).  There is some conflict for what the intersect would look like in my mind.

There are a surprising (who really cares about this stuff other than me?) amount of information on spirals and  a few links are worth mentioning other than those already given as leading to the three dimensional spiral in one direction, I haven't yet found one with an intersecting spiral going in the opposite direction.:

http://www.mathematische-basteleien.de/spiral.htm is a good "general" spiral equation source.

This link provides a method of adding volume to the line drawings of that prior set:
** http://webee.technion.ac.il/~ayellet/Ps/11-HararyTal.pdf.  If you want to draw two intersecting spirals of the type we've discussed, you can do so with this model.

Then there is this one for spirals which we can also use to simplify the issue related to time orbits-stacked time states.
http://math.stackexchange.com/questions/804702/equation-of-a-3d-spiral

Several good background articles
http://www.algebra.com/algebra/homework/formulas/Geometric_formulas.faq.question.250579.html
http://www.dma.ulpgc.es/profesores/personal/aph/ficheros/investigacion/ficheros/chaos4.pdf
http://mathworld.wolfram.com/LogarithmicSpiral.html

None of these deal with 4 dimensional or 5 dimensional spirals, but the basic idea is there and there are probably better articles, you can always point them out to me if you want.

Because there are "so many ways" to "skin this particular cat" and because I'm not of a mood to skin the cat today, I'll just give my favorite.  My (1) "combination" of the two (outgoing and incoming) overlapping spirals and (2) the decrease (by one quantum unit with each quantum step inward) is significantly the only difference between what is already there if  you ignore (3) the removal of dimensions and quantum compression at each point of intersection.
Spirals and the math of them, quite possibly including this relatively minor manipulation, predate NLC as written although adding these two features is not immediately known to me and the methodology of "floating" the lost width of the three dimensional spiral is open to interpretation.  I use a helix for no particular reason below which is why I provide links for those who want to experiment with different combinations.

That is by overlapping the positive and negative spiral and by (at each point of intersection) taking of a diameter and spiraling it outward you come up with one of many, many models using spirals for the algorithm that defines linearity.  The helix coming off of the primary spiral go up and then return at the point at which they either "recombine" for increased compression (fusion=energy to mass; matter to black hole material, etc) decreasing further the width of the inward spiraling three dimensional helix or where they fission in a more complex arrangement where they increase the width which is otherwise diminished by other compression since there "must" be constant movement in one direction in a one way universe.

This is going to be a little nauseating for me, since I have this whole blindness-inner ear thing, so bear with me:  If it is hard for you to follow, it's even harder for me to write:

Since we're using a three dimensional spiral (note that the number of dimensions is largely irrelevant from one to a zillion plus) for modeling purposes you come up with something along these line:

We're sticking with the logarithmic spiral, but you can use whatever spiral you want or whatever helix since this is a model for an algorithm and not an actual drawing.  You can, for example, look at a deflating sphere going in and coming out.  You'll note that the exponential information equation (x=2^n) appears throughout even though this is an "information equation" and not a "spiral equation" although the basis of both is mathematically identical, the derivation is quite different but which I said was predicted earlier in this section even though we knew the answer had to be there in order for NLC to work.

For the logarithmic spiral you have: (2pib for separation)
r(t)=e^(.1t) or r=a^b(theta)-the simpler, but less exponential (we need exponential for nlc) spiral is r=a+b(theta) for the Archimedean or perfect spiral.
Polar equation: r(t)=exp(t)
Parameter form: x(t)=exp(t)cost(t), y(t)=exp(t)sin(t)
central equation y=xtan[ln(sqr(x^2+y^2))].

To move along this from t=1 to x=maximum information in the universe in either direction for this single spiral is a "relatively simple" application of additional spirals to these along their length.  As you add dimensions to in and each of the dimensions either increases or decreases (typically each added dimension is h, h1, h2, etc).  The article with the two ** does this for a three dimensional spiral and, quite frankly, it's a little more than I could do even given a month.

We can, however, draw out a few equations/definitions:
3D Definition 2 – Geometrical spiral: A spiral for which the length of the radius R increases in geometrical progression as its polar angle θ increases in arithmetical progression, where R = p x 2 +y 2 +z 2 and θ = arctan(y/x) (Figure 3(b)).

Definition 4.1 The 3D logarithmic spiral is the curve that satisfies the initial conditions for s = 0 and the following: 1. d~T(s) ds = 1 r0 +∆rs ~N(s), 2. d~N(s) ds = − 1 r0 +∆rs ~T(s) + 1 σ0 +∆σs ~B(s), 3. d~B(s) ds = − 1 σ0 +∆σs ~N(s), 4. |r0 +∆rs| > 0 and |σ0 +∆σs| > 0. To understand this definition, observe that 1–3 are the Frenet-Serret Equations [dC76] with our condition for the curvature and the torsion. ~B is the cross product of ~T and ~N. By the definition of the tangent, the spiral C(s) is: C(s) = int (from zero to s)[T](v)dv+x0=int(from 0 to s)[int (from zero to t)d[T](u) du du+[T](0)]dt+x(0) where [T] is a line product (represented mathematically as a T with an arrow over the top..

This definition for NLC is complicated further because as we move outward from zero to s and zero to t in this case we lose part of the definition of this spiral in favor of another spiral "off" of this primary spiral.  Worse still (better still) this model only works towards the center of the sprial and we have a transition from the two dimensional spiral equation to this three dimensional spiral at the point of contact at the third outward overlap, presumably getting down to a one dimensional spiral (a spinning spiral towards nothing) at the first outward overlap of the two spirals.  As we move out from the third overlap, we have another overlap where we have a 4 dimensional spiral, then a 5, 6, etc all the way to the maximum amount of information with the total information remaining the same as, in this case, s and t make a sum that never increases and as additional dimensions are added those variables (eg x, y, z) take away from s and t so that for I=total information in the universe the integral constants s, t, x, y=I and also equal s,t,x,y,z=I

The negative spiral (going out or in depending on perspective) is merely the negative but if you allow it is only one spiral going outward, then this one spiral is decimating the many dimensional sprials as it goes in.  You can imagine a plane on team x shooting down multiple planes on team y.  The planes on team y have many flights (a,b,c).  Each flight, c for example, is shot down during the course of a single spiral so at each interesection, an entire dimension (a,b,c) is taken out so that one flight c of planes is shot down by a single x plane on each rotation.  Since information is conserved, these “shot down” planes during each rotation have to be stacked somewhere, and under the theory these planes are “loaded” into other planes at each rotation, but between the rotations they are merely stacked together.  Its an imperfect analogy at best. so what I chose instead is to have the spirals stacked together (one spiraling off of another, adjacent spiral) until another dimension is added at the next intersection to allow the stacked information to be spread out along that other dimension.

As if this was not enough, there is the possibility that instead of shooting down flights, that as it moves outward the ct1 spiral plane picks up the flights.  While enchanting in its way, I’m not going down that path yet because the information spiraling in remains constant, there is no reason for the outward spiral which also contains all of the information, albeit “traveling” in the opposite direction, to “pick up” information or increase in the number of time states; but it remains a possibility among many others.

   The place where the last intersection occurs headed inward and defining the point where the spirals "collide" in the center is defined by the minimum size of radius which is the minimum quantum length (you can use planck length, for example, although there is a suggestion that quantum time would be the better unit).  Another way of putting this (not mine, alas) is that the spiral has two arms, one for theta>0 and one for theta<0 which connection smoothly at the origin for archemedian spirals, more violently for our logarithmic spirals..The reason for the violent, non-violent dichotomy is because of the "ever shrinking" nature of one versus the fixed diameter of the other.  The difference is made up by having a quantum beyond which one does not shrink, i.e. the solution point for pi which is suggested by NLC.

You want a discussion of this violent intersection and, not surprisingly it's explored indirectly.  You can look to https://books.google.com/books?id=AiDwbEINsNcC&pg=PA110&lpg=PA110&dq=what+is+the+equation+for+a+three+dimensional+spiral&source=bl&ots=VSWH6sctXm&sig=_kE4VyhnlbV7k7vI9QNhdWeNZjk&hl=en&sa=X&ved=0CE4Q6AEwBmoVChMI2YiGwrbixwIVg10eCh02qAZi#v=onepage&q=what%20is%20the%20equation%20for%20a%20three%20dimensional%20spiral&f=false but it's a little thick for me to attempt to apply it without a lot more time than I'm willing to spend Sunday morning!

In continuing to pick from among the many cat skinning methods, we're first going to go from ct2 (ct1 goes outward in this model) to ct3 in the classical sense-adding dimensions (height is the first one) as a continuous function of theta with the radius going down by one each time and at each point a helix going off and then at each intersection the single helix combine to make a new spiral coming back down.

Unfortunately, this changes at each dimension and if we are using a point source for the collisions, the ct1 spiral outward, there is no clear explanation of how this effects the entire spiral moving inward.  Two ways of looking at this is that the ct1 outward spiral carries some dimensional feature that allows it to (along each quantum movement) “stack” a corresponding quantum movement of the multi-dimensional spiral before pushing it up to the next compression state.  Complicating this further, is the movement between states representing fission and fusion, wave to particle energy, matter-black hole material, and back for example which we experience in the middle ground.  Since the primary direction is believed towards compression, the limited about of “backwash” doesn’t ruin “net” one directional movement, it does make for a fairly complicated equation and begs the question of what imperfections exist within the spirals allow for this.  It is important to distinguish between “random” imperfections which are rejected and “intentional” imperfections which are governed by physics/math in a universe which is as fixed as any drawn spiral.

I will pause to take a breath here.