I'm tired and blind so this is a rough draft of part 1, and yet it is so important to an understanding of the quantum universe, that rather than wait for me to rewrite something which I may never finish, you should put down everything that you're doing and read this. I'm just kidding, of course. So much jibberish jibber jabber.
The Archimedes Spiral vs the logarithmic spiral
Rather than work with degrees, we chose radians to focus on the importance of Pi. Pi serves two functions necessary to NLC. The first is that it disproves linearity. The second is that shows there is a limit to the amount of information.
It ultimately leads back to the conclusion that the universe is a fixed entity. Rather than Einstein's "without time everything would happen at once" there is no time. Time is the non-existent dimension that is merely the recognition that all fixed data points continue to exist and can only change in one direction. This post continues the discussion that the direction is an ever increasingly compacted spiral.
Pi is an infinite series and since it defines a circle it shows that in a non-digital universe, it cannot exist. There must be a quantum limit to the infinite series which can only occur if there is a minimum quantum distance beyond which division is impossible and the existence of an indivisible length requires that space is illusory, i.e. it does not exist. Further, perfect non-quantum circles could not exist in "real space" since the solution is impossible. If however, there is a minimum distance and indivisible distance, then pi can be solved down to that distance. This "quantum pi" solution means the universe is not what we experience, but is instead individual coordinates which yield, through changing sequential compression states, the illusion of space-time. This shows that the universe cannot exist except as a fixed, non-moving entity. This will apply equally to spirals which we know result from a cursory discussion of the universe (the solution to pi is given in an earlier post) which is what Parminedes and Xeno argued 2500 years ago in Greece. There is a limit to the information in the universe results from there being discrete features of the universe.
The question to address is which (of many, many different) spiral is the better model for NLC or is it a combination of the two. The choice suggested by nature, by the galaxy is the logarithmic spiral, with radius governed by Fibonacci series. It would be reassuring and we will discuss later, if these gave rise to compression states represented by information (FS-0,1,1,2,3,5,etc-one unit defined by the two preceding units) However, there is another consideration. The other consideration lies in the nature of the galaxy and the fact that there is no ability for variation.
However, as you will see shortly, in a non-linear environment, there is no difference between the two.
The size of the spiral is also misleading since it has no real dimension and since information may be displayed in quantum bands, the maximum initial spiral may be very small and shrink, not expand, from there as compression increases. Further the actual spiral need not exist, except as a model through which non-linearity can be seen as a linear construct. We can, therefore, look at the universe as a single curve spiral.
But what the details of the spiral? Oh, how much I'd like to edit this before I post it, but I have to get this stuff written. Some definitions are in order but for purposes of this discussion, I will include involute and Archimedean curves together to compare to logarithmic spirals for expediency.
Involute spirals have successive curves with constant separation distance between the curves. Related Archimedean spirals are defined by having any ray from the origin intersect successive turnings in points with a constant separation distance (r=2Pib)
b=ln(Phi)/(Pi/2). Another way of looking at it is b=ln(phi)/90 degrees. Note that as r doesn't change for Archimedean spirals we are working with a single formula. But for logarithmic spirals b is a growth factor defined by a Fibonacci series (0,1,1,2,3,5,etc-two prior numbers added to make each third).
r=ae^(btheta) where a and b are arbitratry positive constants, in this case a and b approach zero and are the quantum distance. Another way of looking at this is theta=1/b(ln(r/a) which makes theta (the angle) a linear function as the distance constants (a and b) approach zero which is what you'd expect given the illusion of linearity in the universe.
The initial quantum radius, the only radius, in such a spiral universe is defined by: r=ac^theta where c=e^b.
For the so called golden spirals, theta=1/b(ln(r/a).
For logarithmic spirals the arc length changes L=a/x*t1^2 for 0 (less than or equal to) t (less than or equal to t1)
We have these two types of equations:
For Logarithmic spirals
r=R(pi/2)n as r+R is greater than zero. In this case n is the number of turns of the spiral and this applies backwards to the spiral outward (n goes negative)
For archimedean spirals:
r=a+b(Phi)^1/c or r=2pib where b controls the distances between successive turns.
Why a universe of one type or the other? In this case, if there is a single turn, the difference between even these very different spirals seems negligible, but in our universe, we see a reflection of one, not the other.
In pine cones and sunflowers and spiral galaxies we see logarithmic spirals, and for pine cone and sunflowers, we see these running in intersecting opposite directions to form a matrix, just as we observe dimensional and force characteristics run in opposite directions in at least some of the equation hypothesis of NLC.
All natural spirals are logarithmic. If linearity is a reflection of non-linearity, it makes a lot of sense that nature would imitate the underlying symmetry of the universe. So for the moment, the prize goes to logarithmic spirals which makes sense since we are dealing with exponential compression which is indicated by the solution c=e^b. As mentioned, quantum separation where the minimum distance is 1/x where x is the total information at any point in the universe, means that compression may be the compression of a single coordinate at one time as long as the total change in the universe (assuming certain data can be changed by speeding or slowing it down, but not by going backwards) is equal to a single quantum change from the prior state.
Going back to our **'s, you can go from:
***.****.*** to ****.***.*** or ***.***.**** or **.*****.*** etc but only one change can occur overall per quantum length along the spiral, otherwise you'd have a gap and there's nothing to fill it with because this spiral doesn't exist except as a mathematical formula governing the expression of data as it goes from a state of minimum compression to maximum compression (10^n as n goes from zero to x where x is all the data in the universe which may express slightly differently according to the spiral rule by change in one direction only at any quantum moment).
In the next post, if it is ever posted, we will take the prior discussion of a universe of quantum lines spiraling down to non-linearity and the equations for the spirals and combine them to give a better description of the universe than has ever been given before! Just kidding, but I will put them together, assuming I decide to post it.
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