TAARP - Appendix E - Section E 6.0 - Expanded Discussion of the 2nd Transformation and Part "c" of Figure D-1 in Appendix D

TAARP - Appendix E - Expanded Discussion of the 2nd Transformation and Part "c" of Figure D-1 in Appendix D

E 6.0 Expanded Discussion of the 2nd Transformation and Part "c" of Figure D-1 in Appendix D

(Note: In this section, references will be made to Table E-2. What is really meant to be referenced is the summary table in general of which Table E-2 is an example.)

It is important to understand that the outer adaptive loop of Figure D-2 is not involved with a search over an eighteen-dimensional space (9 planets and 2 parameters per planet) defined by the x_i, y_i of the exponential summation equation for f() in Figure D-1. Instead, the situation is as follows:

For each planetary configuration, there is a set of 9 x_i and 9 y_i (i.e., i = 1, ..., 9 for the nine planets. Pluto is excluded.) So three sets of vector pairs (i.e., one pair for each of the 15 members of the High PHENOMENON class, the 18 members of the Medium PHENOMENON class, and the 27 members of the Low PHENOMENON class) define the totality of amplitude coefficients and the exponential coefficients for the 2nd Transformation in Figure D-1.
3 Sets of vector pairs

^j, ^j; j = 1, ..., n. There are n planetary configurations for the High Class and n = 15.
^j, ^j; j = 1, ..., m. These are m planetary configuration for the Medium Class and m = 18.
^j, ^j; j = 1, ..., p. There are p planetary configurations for the Low Class and p = 27.
t = 2x (n + m + p) = 2 x (15 + 18 + 27) = 120 = total number of vectors = 60 vector pairs.

Each vector has 9 elements, where i indicates the number of the element of the vector and:

i = l for
i = 2 for
i = 3 for
i = 4 for
i = 5 for
i = 6 for
i = 7 for
i = 8 for
i = 9 for

X designates the amplitude coefficient (i.e., the x_is)
Y designates the exponential coefficient (i.e., the y_is)
Examples:

xh = The amplitude coefficient for for the planetary configuration of the first sample of the High PHENOMENON Class.
yl = The exponential coefficient for for the planetary configuration of the fifteenth sample of the Low PHENOMENON Class.
Each element of each vector (e.g., each xh and each yh ) is a function of the factors represented by columns I through XII in Table E-2. Also, another matter that must be taken into account is that each of the columns in Table E-2 has a priority of importance relative to each other column. So, there exists two vectors, and , each of dimension 12 which define the 24 dimensional space that is searched over in the outer adaptive loop of Figure D-2, where:

= the 12 factors of columns I through XII
= the priority of the 12 factors relative to each other.

Twenty-four actually represents the maximum possible dimension of this space. Current thinking reduces the dimension of this space as follows:

The need for two columns for cumulative weight will be reduced to one. The work of Task 1 of Section 7.1 should lead to an "optimum" set of aspect and orb weights for weight Method I, and so weight Method II should no longer be needed.
It may be that the only columns in Table E-2 for which variables are required are columns III, IV, V, and VI. It is not now clear how variables would be used for columns I, II, VIII, IX, X, XI, and XII. One way in which variables could be used for columns III, IV, V, and VI deals with the fact that a planet's proximity with respect to the Four Angles of Rising (R), Zenith (Z), Descendant(D), and Nadir (N) is supposed to be very important. Unfortunately, just like with almost all of the factors in astrology, there is great disagreement amongst astrologers concerning exactly what the optimum position for a planet is relative to these four points. For example, Gauquelin claims that for , , , , and the first 10° just following the positions in question, where direction of movement is from east to west, are the regions of high importance. Classical astrology in general argues for regions just prior to the four positions for all of the ten planets (9 planets plus Pluto equals 10). Alan Leo claims that the nature of the planet must be taken into account, so, for example he says, the heavy tends to work much better near the nadir than near the zenith. Crowley's opinion may be somewhat similar to Leo's, but even with Crowley himself there is significant confusion. In general, Crowley puts much emphasis on planets that are rising and culminating (i.e., in the zenith). For example, he often says how important it is that such and such a planet is only 10° above the eastern horizon. Also, however, he sometimes talks like a classical astrologer and says that such and such a planet is imprisoned in the 12th House, using the term "imprisoned" to connote a squelching of the planet's influence. (Note that the twelve houses are a twelve fold division of the heavens completely distinct from the 12 signs and that the 12th house is located just above the eastern horizon.) Furthermore, Crowley sometimes places significant importance on a planet and labels it as rising even if it is 30° below the horizon provided that there is no other planet "rising before it".
Pursuant to the above, one way to handle this proximity problem, vis-a-vis an adaptive search process, would be to assign an exponential function to each of the Four Angles wherein the "width" and the location of the peak of each of the four exponential functions would be variables. This would give a total of 8 variables as delineated in Figure E-5. So here is the procedure. For each planet in Table E-2 there is an angular position relative to each of the Four Angles of R, Z, D, N. (A negative sign indicates the planet is approaching an Angle as the planet moves through its diurnal cycle. A positive sign indicates the planet has passed an Angle. No data means that the planet is so far from the Angles in question that it is not worth entering into the table. The current cutoff point is 30°.) For any given point in the 8-dimensional space defined in Figure E-5, the locations (as specified by (₁, ₂, ₃, and ₄, in Figure E-5) and "widths" (as specified by w₁, w₂, w₃, and w₄ in Figure E-5) of the 4 exponential functions are specified, and therefore a value can be assigned to each of the 36 planet/position combinations (9 planets x positions for each planet relative to the Four Angles) in Table E-2 for each iteration of the outer adaptive loop in Figure D-2. Note that the importance of each of the Four Angles of R, Z, D, N relative to the other 3 Angles can be handled in two ways:

Let the 4 amplitude coefficients of the 4 exponential functions each have a value of 1 as shown in Figure E-5, and let the priority elements p₃, p₄, p₅, and p₆ of the priority vector be varied in the outer adaptive loop search process.
Let p₃ = p₄ = p₅ = p₆ = 1, and extend the 8-dimensional space of Figure E-5 to 12-dimensions, where the last four dimensions represent four amplitude coefficients for the four exponential functions.

If there is anything to astrology, and if an adaptive, self-organizing algorithm can separate very capable people from regular people, then the algorithm should, by its very nature, reveal some correct facts about astrology. In other words, the algorithm should self-organize into a form whose characteristics are astrological laws. For example, if the algorithm is successful then the final set of priorities, , that is established by the search process in the outer adaptive loop of Figure D-2, should provide critical information on how to interpret the individual horoscope of any particular person.

It is important to understand that the columns in Table E-2 must be normalized with respect to each other if they are to be combined using a polynomial function (i.e., if the x_i and y_i are polynomial functions of and ). If Boolean functions are used to combine the columns into one factor, then this normalization is not required. In this latter case, the value in a column will be compared with a threshold value appropriate for that column.

If a polynomial function is used, the normalization may operate something like the following:

The maximum normalized value for any column is 100.
For the CW column (this assumes that there will only be one cumulative weight column instead of the CWI and CWII columns now in Table E-2), the normalization number will be the largest CW weight that manifests for the aspect/orb optimizing work of Task 1 in Section 7.1 of The Main Body of the Report. Currently this number is 440 and is from the current Method 1 cumulative weight for Neptune and for the Sun for Louis Pasteur. (In other words, for the aspect and orb weights in Table C-2 of Appendix C, Louis Pasteur has 440 for the Method I cumulative weight for both Neptune and the Sun. Furthermore, 440 is the largest Method I cumulative weight in all of the quantitative analysis work reported on in Appendix C). Every value in the CW column for every individual would thus be divided by the maximum number and then multiplied by 100.
For the lord of the rising sign column ( i.e., column VII) do the following:

If there is no competition between planets for this position, then give the lord of the rising sign planet a value of 100 and all the other planets zeros.
If there is competition for lord of the rising sign, then figure out some way to equitably split 100 between them. For example, if 25° of is on the ascendant (i.e., the Rising Angle which is the Eastern Horizon is 25° ) and the 1st House is 21° wide, and all of the 1st House except for the final 5°, which are occupied by , is occupied by , then maybe the split should be:

(Due to ) = 50 (note that rules )
(Due to ) = 50 (note that rules )

For the column dealing with the number of planets in a sign/s ruled by a given planet (i.e., column IX), the situation may call for a saturation phenomenon. For example, the assignment of values for this column may be something like:

For one planet in a sign, the ruler of the sign gets a value of 10.
For two planets in a sign/s, the ruler of the sign/s gets a value of 20. (Here is an example of what the plural term "signs" means: One of the two planets is in Aries; the other planet is in Scorpio; Aries and Scorpio are both ruled by Mars; so, for this column the Mars row would get a value of 20.)
For three or four planets in a sign/s, the ruler of the sign/s gets a value of 40.
For five or six planets in a sign/s, the ruler of the sign/s gets a value of 60
For seven or more planets in a sign/s, the ruler of the sign/s gets a value of 100.

A first reasonable assignment of heuristics for guiding the adaptive search process for determining and will not be available until after the completion of the qualitative assessment of the Famous 1, the Famous 2, and the Others.

Note that specific values that must be assigned to some of the elements in Figure D-1 by a human analyst and specific details of the microscopic structure of Figure D-1 will develop over a period of time as a consequence of the synergistic interplay between the evolution of Figure D-1 and the ever-growing astrological knowledge of the TAARP analyst. For example, present plans are to use an adaptive mechanism to select optimum weights for the six major aspect angles and various orbs in order to maximize the Euclidean distance between The Famous 1 Method I mean cumulative weight vector and The Others Method I mean cumulative weight vector. This is the objective of Task 1 of Section 7.1. The results of this task will permit "optimizing" each of the cumulative weights in column I of Table E-2 and eliminating column II. The cumulative weights thus produced for each planet in Table E-2 for each of the 60 planetary configurations in the 60-Item Perdurabo/TAARP Data Base will be used as input for the initialization of the outer adaptive loop of Figure D-2.

If Crowley is correct about highly capable people having fewer and tighter orb astrological complexes than ordinary people, then when the columns in Table E-2 have been correctly normalized and prioritized, and coalesced together, a comprehensive weight curve constructed along the lines of the current CWI and CWII curves should separate highly capable people from regular people as follows:

The curves of highly capable people should be flat and low for planets at the low end of the comprehensive weight scale and in the middle of the scale, and then rise very dramatically at the high end of the scale.
The curves of regular people should in the first place be much flatter in their totality than the curves of highly capable people. Also, it may be that the absolute value/s of the highest one or two comprehensive weights for highly capable people are significantly larger than is true for regular people.

If in fact the correct way to incorporate all of the columns in Table E-2 into one quantity (i.e., one comprehensive weight) for each planet is some Boolean function/s or is some high order polynomial, then the ideas presented above about normalization and prioritization vis-a-vis Table E-2 may have to be modified. Current plans are to find a set of priorities (p₁, ... , p₁₂) for the columns in Table E-2, and to find a set of normalized values for each column/row element in Table E-2, so that a proper comprehensive weight (PCW) can be assigned to each planet by simple summation. So,

PCW (Planet) = p₁c₁ + p₂c₂ + ... + p₁₂c₁₂
PCW () = p₁c₁() + p₂c₂() + ... + p₁₂c₁₂()

PCW () = p₁c₁() + p₂c₂() + ... + p₁₂c₁₂()

The p_i's are the priorities for the various columns and the c_i's are the normalized values of the column/row elements in Table E-2. Note that this formula assumes the same set of priorities, , is proper to use for each planet. In fact, this may be an unacceptable simplification, and it may be necessary to have 10 sets of s, one for each planet. Also, it may be that one is proper for all of the planets, but that the form of PCW (Planet) should be a complicated polynomial. Note that this assumes that the same polynomial function is proper for all of the planets, but in fact it may be that a different polynomial function is required for each of the planets.

CAUTION!! It is very important to understand that there is the possibility of a real problem existing if, as proposed above, the data in Table E-2 is used to determine the x_i's and y_i's of the 2nd Transformation in Figure D-1. The possible problem deals with Column I of Table E-2. (We will assume that Task 1 of Section 7.1 optimizes column I, and thus permits the elimination of column II.) Here is the problem:

Task 2 of Section 7.2 is dependent upon Figures D-1 and D-2 of Appendix D. Figures D-1 and D-2 are suppose to represent an adaptive mechanism that permits the synergistic evolution of a set of features and an accompanying classifier. The current design for the adaptive mechanism is such that the features are by definition artifacts of the Fourier transform of f(). This function, f(), is comprised of the sum of a set of exponential functions, one for each planet in the geocentric planetary configuration. Furthermore, the "locations" of the exponential function in space corresponds to the "locations" of the planets in space. The harmonic content of f() is to be scrutinized by the adaptive processes in LOOPS II and III of Figure D-2 in the hopes of finding harmonic characteristics that permit the classification of a particular f() as belonging to the High Phenomenon Class or the Medium Phenomenon Class or the Low Phenomenon Class. So far there is no problem with any of this.
Task 1 of Section 7.1 is to be performed prior to Task 2, and the results of Task 1 are to be used as input for Task 2. Task 1 deals explicitly with optimizing the utilization of the six major aspects of , , , , , . Thus the 1st, 2nd, 3rd, 4th, and 6th integer multiples of the 12th harmonic of f() have in a certain sense already been manipulated in a specific way prior to the initiation of the very adaptive mechanism (i.e., the adaptive mechanisms of Figures D-1 and D-2) that is suppose to identify which harmonic characteristics of f() are important for the classification job of interest.
So, the question is:
- Does feeding the results of Task 1 to Task 2 corrupt Task 2 or does it simply make Task 2's job easier?
- If the correct answer is that corruption occurs, then using Column I in Table E-2 as input for determining the x_i and y_i in the 2nd Transformation if Figure D-1 will have to be abandoned.

(Note: In this section references were made to Table E-2. What was really meant to be referenced is a generic summary table of which Table E-2 is an example.)

Figures E-6 through E-9 present more ideas for the 2nd Transformation in Figure D-1.