After you read this you are going to want to reach out and kick something, so post a comment, preferably in your native language (this is read all over the world, so don't be embarrassed to admit that you have read it) and I'd sort of like to hear your thoughts. Or don't.
There are parts of it that are not fully addressed, but the basic framework is set out.
There is another F-series model that works within the same theoretical framework as the offset intersecting spiral math and that is the stacked intersecting F-series intersecting spiral. This is not true stacking since it occurs in a dimensionless environment, but occurs based on the order of movement.
In this case the initial framework is the same vibrational framework that was discussed and is only easily envisioned at low values of x:
0,1,0,-1,0,1 which creates the first positive an negative solutions offset by 00 (as well as an opposite value which doesn't prevent an F-series result.
because n=F(n-1) in this algorithm the next solution looks something like this:
(0,1,0,-1,0,1,1,0,-1,-1,0) or (0,1,0,-1,-,1,1,1,0,-1,-1,-1,0). The difference between these two results being the need to move back over the prior solution to get to back to zero. The initial stacking suggests a hybrid which looks like this:
I(A): (0,1,0)+(0,-1,0)+(0,1,1,0)+(0,1,0)+(0,-1,-1,)+(-1,0) or
I(B): (0,1,0)+(0,-1,0)+(0, 1,1,1,0)+(0,-1,-1,-1,0)
What is happening here is a little confusing but it has its own logic. Basically it means that each change has to step over itself to get to the next state, but that zeros do double duty, acting as zero for both positive and negative vibrational F-series results.
Up till now this model has been referred to but not examined in depth for two reasons. The main reason is that there just hasn't been time. The other reason is that the two models are essentially the same except for the vision they produce and the amount of overlap within the models. The broad concept of F-series offset intersecting "spirals" works well for predicting outcomes, especially when it come to inflection points and it makes for a cleaner math model. This vibrational model has some advantages because the results don't have as much built in dimension and stacking is easier to envision over longer periods of time, suggesting a greater stability.
Since each result is "stepped" over the prior result, you get ct1 substitutions of 1 every quantum change which is what is suggested. Let me show that graphically:
1
11
111
11111
11111111
These are the first 5 positive states. We can ignore the negative states for this discussion.
Inherent in this result is the existence of overlap between the top and 2nd of 1, of the 2nd and third of 2, of the 3rd and 4th of 3 and 4th and 5th of 5.
As with the intersecting spiral model, you end up with very long spirals pretty quickly (especially because standard clock time doesn't exist at this non-dimensional state of ct1)
If you jump ahead to where you have the next F-series compression state you get ct2 stacking that looks like this:
11
1122
112233
1122334455
and so on. For lack of a better term, and for reasons that may become more clear in the drawings below, I'm going to call the transition from 1 to 11 and from 11 to 111 "folding." That is you have one bundle of information fold over another to get compression.
The order of solution provides the same type of offset as the spiral solution with the main difference being that the "rest state" where two spirals are parallel to one another (by solution, not by overlap) is absent.
It is important to understand that these are both non-dimensional results so that shapes are less important than other aspects.
If the spirals are only offset by solution order at higher ct states (ct2,3,4,etc) then you have a resting phase built into spiral solutions that are not built into vibrational models, but this can be made up where ct1 spacing takes the place of the rest phase of the spirals.
There are additional issues.
Both of these models can exist together.
A vibrational model can shift to a spiral model and the number of spirals can shift.
By way of example, ct1 may represent a pure vibrational model. Each length of space continues to exist in a time free invironment so that you have space with expansion/contraction phases of 1, 11,111,11111 all existing together so that stacking of these can occur with various half lives (designated as the number of points of overlap (see above) from 1 point of overlap (a half life of stacking too short to have relevance) to extremely long half lives which are, from our vantage point, forever, even though they are finite, presumably in the range of 14 billion years worth of overap from the viewpoint of a ct4 state. In this example, the first spiral would occur when there was a compression level of 256 ct1 states overlapping at once. This does not necessarily create a spiral, but it does necessarily create a "first dimension" because you now get (mathematically this is pre-ordained without a new equation) 11,22,33,44,etc ct2 type results.
Now some of you are probably having your head hurt like me, because you're asking yourself, what about the 257th overlap which is sure to be there since all of these vibrating lines are overlapping at once. The simple answer is that the shift from 1,11,111,11111,etc to 11,22,33 is discrete. By definition (information theory definition) this shift occurs where n goes from 1 to 2 in the equation F(n)^(2^n) although the information transition is 2^n.
The key to everything in this analysis comes down not to the equation itself, not to the general concept, but to the reason for the transition.
Why F(n)=Fseries(n)?
The solution to this should be so obvious that it hurts, but for whatever reason I don't have it.
In this case it's not a singular problem.
The mass energy equation is e=mc^2. The "reason" for this is because the underlying defining equation is f(n)^(2^n). What I'm looking for is the reason for this change.
The "general" reason is because you transition from 1 informational change at a time to 2, from one "bit" to two bits. That explains the 2^n part of the equation.
However, when this transition occurs, there is no reason to change the F(n) equation.
Stacking
F-series growth is different. It has to come from two parallel points without reference to the history behind those points.
It's important to imagine 256 of these chains so interconnected as to be solved proximately at any level (say at 34) and then for one other chain to then be solved more proximately than one of the 256 as x changes. It is also important to imagine that at this 256 level you are still building at an F-series rate, but that each of the numbers is made of a bundle of bundles, so that you have 8 bundles at 8 so that a single bundle (one of the 8) can be substituted in the sub-bundle. This change allows for relativity and velocity.
The first two parts of this are a the negative 1 and the positive 1 variations. This assumes no net increase in one type of information compared to the other.
This drawing is representative of the type of math that would lead to a result consistent with observations. There are some important ramifications to this drawing which may or many not survive scrutiny.
The 1,-1 and zero may go on, without other expansion with each prior change remaining durable. This is represented by having the "empty" zero states on either side of zero. In this time free environment, there is no reason for other changes, but there is also no other obvious basis for the beginning of the F-series expansion.
Let me explain this. What we are looking for is a model that represents what we observe in an F-series universe. First you have 1, that is easy. Then you have 1-1. If you look at how this model builds it suggests that for modeling, to get to 2 you have to have two 1 states parallel to one another. This parallel isn't because of dimension, but only because of solution order. That means you have a one solution adjacent in time to another. This means that if you start from one zero, you can return back to that same zero and generate the next 1 state as long as the original one remains durable.
It also suggests that unless there is something to stop this process, it will continue, so that at each change in x you produce another 0-1 state, possibly another 0,-1 state, and therefore you are starting another spiral build for every x which is what the model indicates is happening.
This is the same reproducing exponentially that you see in the top drawing.
The first part of the model shows that information comes into existence from the non informational aspects, zero, which presumably would be the time independent information state of god if that is what you want to call the predecessor to the universe as we experience it.
What is important in this model is that after there is the expansion of 1 the repetition of the initial model allows you to get from the moment of linear (yes/no) information to the F-series and you also increase information exponentially which are the two parts of the universe that we experience.
It also suggest that compression can occur as a result of these less expanded versions which build simultaneously at higher and higher concentrations changing at the same rate in higher compression states based on the entire model repeating the process in a form of "folding" so that unalligned states are brought into proximate solution order.
Now for those of you saying, "whoa, what's folding and how can you introduce something new," which is the million dollar mathematical question, you actually see folding above.
Where you add the value of the two adjacent states to get the next number, subsuming the pior lower states (when you add 3 and 5 to get 8 you are basically ignorring the lower values in the chain back to 1 and zero) you are laying the ground work to take 256 of these spirals, grouped together to make bundles of spirals to get to the next compression state.
If this is the way that this happens then expansion would continue along the method presented in the model and you'd see expansion "in multiple dimensions" building the information exponentially form each point even though it would be with dimension.
We've talked about convergence and while at some point in time, the % increase is 618033989 for all intents and purposes, around n=37, the series continues to converge on some number despite the near irrelevance and the change is that is why space appears curved,becuase you quickly arrive at a place (say n=39) where the change is of the order of magnitude that we cannot detect it although it remains mathematically detectable.
I hear you screaming, "make your point." Ok, the point of AuT is that the universe is simple from derivation and complicated by application.
"Folding" has to occur in exactly the same way for each state for this to be the case. That is, you cannot, as in pre-AuT mathematics, insert another equation, another "force" whenever you run into a road block. That would be cheating. While someone is saying, "universal field theory, then;" that is not the point, because "field" or "force" are effects and not causes. You can add, indeed we see the addition of fields with stages of compression and these are durable up to the point, at least, that neutrons and protons begin to break down, but behind that, in supersymetry you have to use the same equation applied the same way.
Folding, in the drawing above, is accomplished by the two lines from two different "1's" connecting to a two and from the "2" and "1" connecting to form a 3 and so on into infinity.
This same folding occurs in bundles (of 256) of these chains of folded solutions. Otherwise, you'd be injecting another mathematics into the process and you might as well throw everything into the garbage can and say, the universe is made up of forces and revert post Parmidean, Pre-AuT mathematics.
In practice, as x changes, one chain from a folded bundle is exchanged with another chain for each change in x to achieve velocity at least in ct2 states. Where the substitution of one change for another in a higher compressive state is shared between compressed states, you convert velocity to "history1" since the overall structure is preserved. You can have histories 2 through infinity as the compression increases.
Put another way, Relativity arrises by having overlap between these chains in the same fashion to build 256 chains changing together in terms of value and solution order although you have have "universal" relative change and proximate change and they amount to the same thing although they are experienced vastly different. Let me explain.
Let's say that you have two solutions (a+b(1)) in proximate order adjacent and you have two solutions (a+b(2) that change in proximate order on opposite sides of the univerese but that both are changing at the same rate. Both of these form a type of matter for each change in x even though we recognize a+b(b1) as being tangible and a+b(2) as being entangled.
a+b(1) can be folded, a+b(2) cannot be folded but both are otherwise similar no matter what scale of compression they are in and the underlying state is not affected.
The top drawing insists that growth occurs from every point, but observation tells us that expansion only occurs at ct1 and that at higher states, in place of expansion you get historyl in the form of a changed position in solution order along a single dimension up to 3 in ct4 states where we happen to abide.
The building of chains occurs with folding according to the F-series; the building of compressive states builds according to the F-series but relativity is inserted by having the sharing result from information states increasing (1 to 11 to 111) so that the number of solutions occuring together increases. There is not change in information in any of these states but relative change allows for the results to be experienced differently relative to ct1 states and for the longest time everyone but Parminides and a few people who talked to him, interpret this, incorrectly as a thermodynamically driven universe.
| Rabbit Trails |
You can ignore what follows, because it just represents some examples of why I don't believe other models work well.
Here are problems with other models for dealing graphically based on simple math.
One way to match the overlap suggested by F-series compression is where 0,1,1 match (as opposed to a higher state.) If you look at the example I(A) above you can see the 0,1,1,0 pattern necessary for this result (F(n)=0+1+1 for ct1).
Now for ct2 you somehow have to transition from 0,1,1,0 to 1,1,2,0. This transition only occurs where there is stacking, ie where you go from 1 to 11.
In this case you have stacking in place so that 0,1,1 is stacked with 0,1,1. In such a case, for any two vibrational states the choices are 0,1 or 2 (0+0,0+1,1+0,1+1).
There are several ways to look at this.
This is an oversymplified analysis. If you applied it to the other state, you'd have:
Any two stacked states would have (0,1,1,2) plus (0,1,1,2) would have (0,1,2,3,4); (0+0,0+1,0+1,0+2,1+0,1+1,1+1,1+2,1+0,1+1,1+1,1+2,2+0,2+1,2+1,2+2)
0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4
This doesn't work the same way, because you are not stacking like cases, instead you are stacking 11 cases.
Another way to look at this is that there is 1 0,0 state, one 2 state and two 1 states (1,1,2) which also provides no solution.
The problem is solved because what you are really doing here is stacking the 0,1,1,2 solution with another 0,1,1 solution, not another 0112 solution).
This gives you possible solutions of 0,1,2 and 3.
Now you cannot add a 0,1,1 solution, but another 0,1,1,2 state
yielding a 0,1,2,3 grouping of solutions.
If you add another 0,1,1 solution you get
0,1,2,3,4
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