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The Story of The Unit Simulacrum and Whole PI 
Chapter Three — The Unit Simulacrum — Page Eight
By working out the equations for the three Critical Ratios chosen to provide information and follow the rules of mass spectrometry, it allowed me solve equations nested three levels deep. The mass spectrometry solutions were each seen to be special cases of one ratio observed at each level, although the inverse of that ratio could equally well be observed. The simulacrum sum of each ratio is the sum of (A(1 +(1/(A/B)_{*}))) or B(1+(A/B)_{*}). Or it could be (A(1 +(B/A)_{*})) or B(1+(1/(B/A)_{*})), depending on perception. There are two inverses based on observing different values, A_{*} or B_{*}, (value perception) and there are two ratio perception inverses based on perception of (A/B)_{*} or (B/A)_{*}. When I had the full First General Form of a Simulacrum, it seemed like this related to everything in the world. It seemed liked YES! This shows that the sum of any two values can be expressed as a value and a ratio. If one value is equal to 1, only a ratio is necessary to describe the sum, when operated in the simulacrum. One characteristic that I mentioned, but that I had not planned, was that the ratios for mass spectrometry are nested. I had set up the Critical Ratios for mass spectrometry to get the maximum amount of structural information from the ratios available from the data. And it turned out that the ratios of ions that provided the most information about the structural characteristics happened to be nested ratios. For instance, for an ABC TAG, the two abundances that make up the numerator and denominator of the third Critical Ratios for the ABC TAG, the [BC]^{+}/[AB]^{+} ratio, make up the sum that is in the denominator of the second Critical Ratio, [AC]^{+}/([AB]^{+}+[BC]^{+}). Similarly, the three abundances that are in the numerator and the denominator of the second critical ratio, the [AC]^{+}/([AB]^{+}+[BC]^{+}) ratio, make up the sum that is in denominator of the first Critical Ratio, [MH]^{+}/S[DAG]^{+}. The S[DAG]^{+} equals [AC]^{+}+[AB]^{+}+[BC]^{+}. Thus, each ratio is nested into the denominator of the next higher ratio. Finally, the sum of all ions, S(I^{+}) equals the sum of the numerator and the denominator of the first critical ratio, the [MH]^{+}/S[DAG]^{+}. S(I^{+}) = [MH]^{+} + S[DAG]^{+}. The ratios are nested one into the next, into the next, three levels deep for an ABC TAG. Every ratio is nested into the denominator of the next higher ratio, and the last ratio nests into the total sum. We can see that at each of the three levels deep that the ion abundances were nested, a decision was made about which ratio to construct next. Thus, decisions were made and other possibilities were ruled out. One can imagine that if we wanted to see the sum of possibilities at each level, we would have to construct the FGFS at each level, and at each level the sum could be substituted with the (1+ ratio) equation for each possibility for observation. There are exactly eight possibilities for observation at each level. One level can be related to the next by either a single number (ratio) or by a value and a ratio. Typically, the simulacrum sum of a ratio at one level is nested as the denominator of the ratio used in the simulacrum at the next higher level. We have to have to expand two levels to see the pattern. We start out with two variables, and these two variables form a third, the sum of the first and second. Then, the larger of the two variables carries the sum up to the next level. 
NomenclatureAs I mentioned earlier, time is something that can be kept track of in the simulacrum, and each variable must be kept track of, so that the construct can be complete. For instance, the TAG lipidome needs three Critical Ratios. I had showed the nested solution equations in the TAG Lipidome, but needed a way to express the sum at each level, to keep track of time, and to keep track of the variables. The choice of the symbol Sigma for the Simulacrum Sum was the natural choice for the sum. But the Simulacrum Sum needed to be differentiated from the simple sum, and to convey the information necessary to reconstruct the data at any time from the ratios.
This is confusing and hard to figure out. The decimals used in the ratios are confused with the decimals used to separate simulacrum variables. It would make more sense to use dashes between simulacrum terms, as follows:
The first (leftmost) 1 is because this is the first simulacrum construct (first order at the constructed level). The first 1 is the simulacrum number. It can be used to keep track of the level of the simulacrum. Then a dash separates this first simulacrum term from the next term. The second simulacrum term is time. It has a value of zero if we are not keeping track of time in the simulacrum. Or, it can be incremented to keep track of the position within the simulacrum cycle. Assume the time increment is zero for now; we are not keeping track of time. Then there is a dash that separates us from the first variable. In the example above, the first variable has a value of 1.5. This is separated by a hyphen from the next variable, which is a ratio of 0.6125. The second variable is separated from the third variable by a hyphen, so that the 3.25 in the example above is the value for the third ratio in a simulacrum construct three levels deep. You can see that using the decimal notation for the simulacrum in the first example equation, it would be difficult to pick out the proper arrangement of terms. However, when dashes are used to separate simulacrum terms, it becomes much more clear that this is a first level simulacrum with three variables that is not keeping track of time. This notation was chosen because it was simple and conveyed all of the requisite information to reconstruct the mass spectrum using a simulacrum with three ratios. The notation of using hyphens to separate simulacrum terms was therefore adopted.
