D1.0 Introduction

      Perdurabo's treatment of the "astrological complex" (see Block 8: A Challenge for Crowley Scholars and the Ordo Templi Orientis) is much more highly developed and complicated than Nelson's treatment of the "planetary complex". All of Perdurabo's work was done well before any of Nelson's work, but it is clear that they have very similar veins of thought. The concepts that Perdurabo established depend to a very large extent upon observation and experimentation on his part. Seymour provides a theoretical explanation for Perdurabo's concepts in terms of hard physics. All of this is discussed in Appendix E.

      After many years of collecting and analyzing data with respect to a geocentric frame of reference, Perdurabo came to the conclusion that the level of manifestation of the PHENOMENON is a function of the level of manifestation of "astrological complexes". Furthermore, he concluded that the level of manifestation of "astrological complexes" is a function of:

1. The manifestation of planetary aspects, the orbs involved, and the specific planets involved.


2. Where each planet is relative to the eastern horizon, the western horizon, the zenith, and the nadir.


3. Where each planet is relative to the signs of the tropical zodiac along the line of sight from the earth to the planet.


4. Where each planet is relative to the plane of the ecliptic.

      It is the objective of Task 2 of the 1996 TAARP work effort to attempt to find correlations between levels of manifestation of the PHENOMENON and factors 1 through 4. This is a massive pattern recognition problem. The material presented in this appendix is a first cut at a detailed approach to this pattern recognition problem.

      As discussed at length in Appendix E, TAARP is currently of the opinion that Perdurabo is by far the shining light of genius in the area of the PHENOMENON and its relationship with the astrological complexes of geocentric planetary configurations. Unfortunately it is not at all clear from Perdurabo's writings exactly what combinations of features of a geocentric planetary configuration define the manifestation of an astrological complex. Therefore, the real immediate objective of TAARP is to quantitatively and qualitatively investigate the 60-Item Perdurabo/TAARP Data Base, using Perdurabo's writings as primary reference material, in order to arrive at a precise understanding of what he means by the term "astrological complex". TAARP sees this as the first critical milestone that must be accomplished if we are to attain our ultimate current goal of establishing hard scientific evidence for the existence of correlations, if in fact they do exist, between the manifestation of specific levels of the PHENOMENON and the manifestation of specific characteristics of geocentric planetary configurations.

      It should be noted that since our immediate objective deals with manipulations of the 60-Item Perdurabo/TAARP Data Base, the planet Pluto will be ignored for the time being since Perdurabo's data does not include Pluto, and we will only be discussing nine planets of the geocentric frame of reference. These nine "planets" are:

• = Sun
• = Moon
• = Saturn
• = Jupiter
• = Mercury
• = Venus
• = Mars
• = Uranus
• = Neptune

      The fact that the and the are referred to as planets within a geocentric frame of reference will offend some people with rigidly scientific backgrounds. Any reader who is so offended should not waste any more time reading this document.

      It is very important to realize that if TAARP is successful in its pattern recognition work, then by definition the parameter and feature values that manifest as a result of the adaptive processes involved in the pattern recognition learning algorithms will be the primary characteristics of geocentric planetary configurations that correlate with various levels of manifestation of the PHENOMENON. This will be important for two reasons:

1. It should permit predicting dates and times in the future when it is possible for specific levels of the PHENOMENON to manifest.


2. It should provide significant guidance in initiating lines of study into the understanding of any cause and effect relationships between the PHENOMENON and various astrophysical energies, forces, and fields such as magnetic fields, gravity, cosmic rays, and infrared radiation.

      The first step in attacking the pattern recognition problem of interest to us deals with formatting the problem mathematically. To this end, consider the following. In defining the positions of the planets vis-a-vis a geocentric perspective, two reference points can be considered. For diurnal considerations, the eastern horizon will be defined to be 0° in angle with the angle increasing in the apparent direction of movement of the planets across the sky from east to west. For cosmic considerations, 0° of the constellation Aries in the tropical zodiac will be the reference point, with the angle, , increasing in the direction of movement of the planets through the tropical zodiac as time progresses through the year. This later reference is just the point in the sky defining the vernal equinox which is the position of the sun along the ecliptic when it crosses the celestial equator. For the following discussion, the point of the vernal equinox will be used as the planetary zodiacal (or cosmic) angular reference point.

      Figure D-1 presents the general conceptual flow defining a procedure for mathematically formatting the pattern recognition problem of interest. Part "a" of Figure D-1 is an example of a geocentric configuration of the planets. Part "b" is just the result of a mapping of the geocentric planetary configuration onto a straight line. The transformation from part "b" to part "c" is the most critical step in the entire pattern recognition procedure. This mapping consists of creating a function, f(), that is the summation of a set of nine exponential functions, one for each planet, with the peak value of each exponential function occurring at the position of the planet. The parameters x_i and y_i determine the maximum values and the "widths," respectively, of each of the exponential functions. Note that in general, x_i and y_i are themselves functions of factors 2, 3, and 4 above. Appendix E should be consulted for more information on the relationship between x_i, y_i and 2, 3, 4 than is provided here in Appendix D.

      The mapping from Part "c" to Part "d" is the standard Fourier transform. The mapping from Part "d" to Part "e" is simply a method for establishing a procedure whereby the amplitude and phase of the Fourier transform of f() can be (adaptively) sampled in a search process to try to find features which permit the assignment of a given f() to the High PHENOMENON class, or the Medium PHENOMENON class, or the Low PHENOMENON class. The values of the c_is and d_is will be adjusted in an adaptive learning algorithm that will try to find , vector pairs which are unique for each of the three PHENOMENON classes.

      The pattern recognition problem can now be summarized as follows:

1. For each of the items in the 60-Item Perdurabo/TAARP Data Base, there is:
1. Either a High or a Medium or a Low level of manifestation of the PHENOMENON.


2. The particular geocentric planetary configuration that manifested along with the manifestation of the given level of the PHENOMENON.
• "Along with" means that the manifestation of the specific level of the PHENOMENON occurred at a specific point on the surface of the earth on a specific date and at a specific time of day, and that on the same date and at the same time a specific geocentric planetary configuration also manifested, and the exact center of reference for the geocentric planetary configuration is the same specific point on the surface of the earth where the specific level of the PHENOMENON manifested.


2. For each geocentric planetary configuration, and for any given set of x_i and y_i, there is a corresponding f().


3. For each f(), there is a corresponding Fourier transform G().


4. The Fourier transform data, G(), is to be processed with a learning algorithm in an attempt to define Fourier features which are distinctly different depending upon whether f() corresponds to the High PHENOMENON class, or the Medium PHENOMENON class or the Low PHENOMENON class.


5. Each dual set of c_i, d_i parameters defines a particular sampling of G(). For each particular sampling, a dual set of Fourier feature vectors , are defined. These feature vectors must be processed in an adaptive learning algorithm to determine if a dual set of weight vectors , can be found and applied to , in such a manner that it is obvious which PHENOMENON class (i.e., High, Medium, or Low) any given f() belongs to.

      It should be noted that there is a very good reason for choosing the Fourier transform as the mapping from Part "c" to Part "d". The underlying assumption for this entire effort is that there are specific patterns in the geocentric configurations of the planets that correspond to the levels of manifestation of the PHENOMENON. This is the basic thesis of Perdurabo's work. The word "pattern" implies global qualities. Therefore, if f() is properly constructed, it should have global qualities that can be correlated with levels of manifestation of the PHENOMENON. Furthermore, a local quality in Fourier space maps into a global quality in "regular" space (i.e., the space of f()). Hence, by adjusting discrete elements of Fourier space, global properties of "regular" space can be scrutinized. In other words, Fourier space makes it convenient to grab onto global features of "regular" space and manipulate them in various ways.

      In particular, note the following. Assume that the diurnal and cosmic positions of the planets are not an issue (i.e., are not germane to the level of manifestation of the PHENOMENON). Furthermore, assume that Perdurabo is absolutely correct about his conclusion that aspect angles between pairs of planets of 0°, 30°, 60°, 90°, 120°, and 180° are important for specifying the level of manifestation of the PHENOMENON. Then, the pattern recognition methodology presented here should find that x_i = 1 and y_i = l for all i, and should find that integer multiples (except for the 5th) of the 12th harmonic of f() are in some manner correlated with the level of manifestation of the PHENOMENON. (360° + 30° = 12 and l x 30° = 30°, 2 x 30° = 60°, 3 x 30° = 90°, etc.) Note that there is at least one error in this line of argument. It is as follows. Even if the diurnal and cosmic positions of the planets are not an issue, an effective adaptive algorithm could find that x_i is not equal to l and y_i is not equal to l for some or all "i", if indeed it is important which particular planets form close orb aspects of 0°, 30°, 60°, 90°, 120°, and 180°. For example, it may be significant in terms of the level of manifestation of the PHENOMENON that and are in close orb aspects that are integer multiples (except for the 5th) of the 12th harmonic of f(), but absolutely insignificant that and form close orb aspects. If this kind of thing is true, then the adaptive mechanisms of the pattern recognition approach of Figure D-1 should find that x_i = 1 and y_i = 1 for some or all i.

      It is apparent from Figure D-1 that the pattern recognition mechanism will involve three, nested, adaptive loops. The outer loop will adjust values for x_i and y_i, the next loop will adjust values for c_i and d_i, and the innermost loop inward will adjust the weights that comprise vectors and .

      Section D2.0 presents more details on the general nature of the three level, nested, adaptive mechanism implied by Figure D-1.

      Section D3.0 presents one specific example of how the innermost adaptive loop could be handled.