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 The Story of The Unit Simulacrum and Whole PI     Chapter Three —The Unit Simulacrum — Page Three
 In the simulacrum solution to the Fibonacci Series, the ratios are nested such that the sum of the simulacrum at each level becomes the largest value at the next level, and the largest of the variables at each level becomes the smallest value at the next level. From this, the simulacrum sum at each level equals the denominator of the ratio in the next simulacrum. These ratios are similar to the Critical Ratios in the Bottom Up Solution. The Case 1 solution is given as the inverse of the inverse of the observed ratio (A/B)*, as A(1+(1/(A/B)*), assuming B ³ A. When I saw how the Fibonacci Series could be solved using a simulacrum solution, I started to realize that any sum of two numbers could be expressed either as the sum of two numbers or as one value times the sum of 1 plus a ratio of the numbers. I also noticed that one part of the equations used above has been seen before.  It is the Golden Equation, S(A+B) = A(1+(B/A)*).        The Golden Equation equals the Case 1.1.1.1 case, in the updated Case identification system. These mathematics describe an increasing sum. This is a case of growth, or increasing numbers. The process of deriving each ratio from the preceding ratio by making the numerator of one ratio into the denominator of the next, and the sum of the preceding into the new numerator of the next ratio causes a self-replicating growing system. This can be seen as: 1) the first ratio = (A/B), with B³A ; 2) then C = (A+B); 3) and the new ratio is = (B/C). This continues on and on, giving an infinite series of Fibonacci values and Fibonacci ratios. The Simulacrum relates each ratio to the next.  Figure 23. The generalized equations based on an observed (A/B)­ ratio, without the limits imposed by mass spectrometry. A variable may take any value, but at least one value must be greater than 0. In the Case 1.1.1 solution, A £ B, B ³ A, (A/B)£1.
 When I first started generalizing the equations, and saw how well they applied to logic and probability, I got excited. But when I saw that they also could easily be used to describe the Fibonacci Series, the hair on my arm stood up and I knew that I was right in the middle of something incredibly fundamental and important. The Fibonacci Series was just a 1.1.1.1… nested simulacrum. That was based on the post-Alignment Cases. Before aligning the Cases with the Many and the One, I first described the growth in numbers described by the Fibonacci Series as a Case 2.2.2 solution. When I found the Fibonacci simulacrum equations, I first started to suspect that this new construct could be huge.        I soon realized that the First Mass Spectrometry Simulacrum only represented one of several greater possibilities. The first possibility, or permutation, is to remove the requirement that no value can be greater than 1. If one or both values are greater than 1, the larger value can always be taken as a ratio to the lesser value, and that ratio will be ³ 1. Or, the smaller value can be taken as a ratio to the larger value, and that ratio will be £ 1. So it works out that a sum can be taken as one value and a ratio greater than one, or a value and a ratio less than one. In short, the sum of any two values can be set equal to a number times the sum of one plus a ratio greater than or equal to 1, or a number times the sum of one plus a ratio less than or equal to 1. 