When I look around, I have to admit that is requires a certain credulousness to see a telephone post bent at just such an angle and the standing straight up.  That result must be repeatable.  That is, there must be no randomness to get to this result.  That appears so unlikely, but AuT seems to require that result.  Randomness, however, being an illusion anyway, is built into the system.  Does this mean that our universe represents a result with randomness even though randomness is an illusion.  AuT requires a yest answer to this question that seems to defy yes.
I'm not sure that I can accept this answer although logic demands it.  Does that mean that I cannot accept my own theory?
I"m almost half way through the edits of the new portions of AuT.  These posts form the first 15% perhaps, but the most important parts have been posted already.
So much of this is philosophical because I don't have time to finalize this (or anything else it seems some times).
Next year is getting easier for me although more complicated.  Things have never been better for the world and yet we are facing twin disasters with opposite effects; man made global warming and volcanic caused global cooling.
We both know where we should be and yet we do nothing to get there.
Under such circumstances is credulousness so valuable?

AuT-Building an algorithm 6 Calculus 5 of 6

Trying to force AuT into Calculus abandons true, non-linear math to get to the relative math of our view of the universe which allows us to solve for all the prior points because we are going to ignore history.

If we are using Newtonian concepts we are ignoring the movement through space and what is happening on either side of the solution.  This works fine for us.  It is predictable within limits.  We are adding the movement through space but we are not including the past.  We “fake” our way into a solution by using relativistic changes only relative to other points in existence within our time frame.

AuT merely adds the solution over time which is not really time at all, well it is but it also includes the mechanism for the creation of time, the variable x and the relative changes of different ct states to prior states carrier algorithms which all exist at once and not be solved together.

Tangent line-y-y0=m(x-xo) where m (the slope of the curve) is l.  In a two-dimensional framework of the kind found in ct3; y0=f(x0).  Of course, there is no y in a one dimensional framework.  Dx takes the place of time and is altogether appropriate where x is an underlying variable but the change for dimensional purposes is the change of alignment of ct1 states in ct1 and the changes are along ct1 states for higher states.

This may be viewed as 1,ct2; 1,ct2;2,ct2,3,ct2;5,ct2;8,ct2 which can further be looked at as 01,11,12,21,31,52,81 for example which shows the existence of a carrier in conjunction with a fixed ct2 state.

Later, this might look like something quite different 011,112,123,231,351 and so on although other variations are possible.

  No matter how many different ct1 states are involved, x changes sequentially and sct time, dx in calculus, only cares how many carrier points along the various ct1 carrier lines are traversed.

A point becomes (x0,f(x0)) which is pure logic for x0,y0 where y is a function of x and HERE y is F-series for ct2 relative to ct1.

The slope of tangent line to y=f(x)=m=f'(x0) the derivative of x.

tangent=limit of secant lines p-q as q tends to p (p fixed, q varies)

df/dx=slope of secant (not tangent).

Now you have to apply limit

limit as dx approaches zero of df/dx is slope of tangent.

From point P to point Q you get:

P=x0, F(x0); P=x0+Dx,F(x0+Dx)  Something happens HERE between x0 and x0+dX which is that the underlying geometry changes and in some cases the F-series changes although the may be according to a formula for stacking that can be applied across the board.

Derivative for a fixed point in the universe:

m=f'(x0)=limit as Dxgoesto0 of [f(x0+dx)-f(x0)]/dx

F(x)=Sum(geo(Fseries(x')^2^x)) where geo is solved for pi at the fundamental level to separate all points and for each carrier state and x' is the value for each x (for ct1 it is either 0,1 or 1) for each sum.  The summation includes both the original state and the carrier state that is made of all the underlying states and rather than rotate between 0,1,1 the carrier goes 0,1,1,2,3,etc so you have two numbers [1] one of which operates within the same range but [1a] changes the range for different states where each state represents a carrier formed by the lower state according to the 1,11,111 F-series exponential function and [2] the other steadily increases based on an F-series rate as the carrier of the underlying base rate based on the F-series function (1,1,2,3 etc).  While a set sum is derived, the individual parts of the sum define where things are in the universe and how fast they are moving.

In this case the sum of the parts is greater than the whole…solution.

The difference quotient df/dx=Sum(geo(Fseries(x'+dx)^2^(x+dx)-Sum(geo(Fseries(x'^2)^2^(x/dx) where x' and geo change in part according to [1] and [2] internally for each point in the solution.

At small values of x the geo function changes at a higher level since it is a function of pi (or more correctly it is a function that yields pi for any value of x or x' where x is the total value of x and x' is the effective value of x' for any point based on the amount of compression and both apply to different points in sum just as different [1] and [2] states apply as both states are made of fundamental points defined by [1] and carrier states defined by [2].

There is symmetry at any value of x, but the symmetry is destroyed as x changes because the solutions are offset by a converging series

A simple equation y=1/x gives a slope of -1/x^2 of the type we see here, a converging series.

There is one last variable which is the negative -df/dx determined in the same fashion and for the same value of x which determines whether there is a diverging or a converging symmetry (between the positive and negative spirals so defined) which determines if the system is governed by gravity or anti-gravity.