C3.0 A Method for Optimizing Aspect and Orb Weights

      This part of Appendix C will present the first phase of development of a simple adaptive algorithm designed to optimize a set of aspect weights and a set of orb weights for Weight Method I so that a more definite cumulative weight distinction between High, Medium, and Low PHENOMENON geocentric planetary configurations can be established than was demonstrated in the third analysis attempt.

      Figure C-11 presents a plot of the highest Method I cumulative weight versus the next to highest Method I cumulative weight for all of the 60 geocentric planetary configurations. The data in this figure are based on the aspect weights and orb weights in Table C-2. There is definitely no clear clustering of the data into three groups corresponding to High, Medium, and Low PHENOMENON, but the mean values do conform to the trends discerned in the CW I Mean Chart of Figure C-9.

      The next step in the development of the cumulative aspect weight work will be to construct an adaptive learning algorithm that is designed to find a set of orb weights and a set of aspect weights which will permit a clear and concise classification of a geocentric planetary configuration as corresponding to a High, Medium, or Low level of manifestation of the PHENOMENON based on Method I cumulative weighting. The first phase of development will only deal with the High and Low PHENOMENON data items. For this first phase, the Medium PHENOMENON data items will be ignored. The objective will be to search for a set of aspect weights and a set of orb weights that drive the mean values of the Method I cumulative weights for High PHENOMENON geocentric planetary configurations far apart from the mean values of the Method I cumulative weights for Low PHENOMENON geocentric planetary configurations.

      Each of the cumulative weight curves corresponding to a single geocentric planetary configuration will be considered to be a vector of nine elements with the first element representing the largest cumulative weight and the last element representing the smallest cumulative weight. For example, let ¹ be the Method I cumulative weight vector corresponding to the first High PHENOMENON geocentric planetary configuration. Then,

1=

350 293 290 235 226 157 84 81 58

=

Method I Cumulative Weight Vector for the First High Phenomenon Geocentric Planetary Configuration

• H = High PHENOMENON
• L = Low PHENOMENON
• j = Data Item Indicator
  • There are 15 for High PHENOMENON
  • There are 27 for Low PHENOMENON

      Let and represent the cumulative weight mean vectors for the Method I cumulative weights for High and Low, respectively. Therefore HM_i will be the i^th element of vector .

      The objective will be to maximize the Euclidean distance between the cumulative weight mean vector for High and the cumulative weight mean vector for Low by adjusting the aspect and orb weights for Weight Method I. Note that the cumulative weight mean vectors have nine elements, so that the Euclidean Distance, ED, between the cumulative weight mean vectors will be:

V1 = AW1 = Aspect Weight for
V2 = AW2 = Aspect Weight for
V3 = AW3 = Aspect Weight for
V4 = AW4 = Aspect Weight for
V5 = AW5 = Aspect Weight for
V6 = AW6 = Aspect Weight for
V7 = 0W1 = 0rb Weight for Orb From 0° to 1°
V8 = 0W2 = 0rb Weight for Orb From 2° to 4°
V9 = 0W3 = 0rb Weight for Orb From 5° to 8°
V10 = 0W4 = 0rb Weight for Orb From 9° to 10°
V11 = 0W5 = 0rb Weight for Orb greater than or equal to 11°.

      We must do a search of an 11 dimensional space in an attempt to reach an acceptably large value of ED.

      For Weight Method I and the current set of aspect and orb weights for Method I (i.e., the weights in Table C-2):

=

311 285 261 237 212 178 136 119 75

=

268 227 208 192 175 154 133 107 75

=

10 2 5 10 10 10 10 7 4 1 0

1. For each of the 11 variables (i.e., the elements of ), do the following:
• Draw a number from a uniform random distribution on the interval -1 to +1.
• Add the random number to the current value of the variable.
• If the new value of the variable is less than zero, then set it to zero.


2. Calculate ED for the new variable vector. If the new ED is less than or equal to the old ED, then repeat A). If the new ED is larger than the old ED, then take another step in variable space in the same direction and the same magnitude as was done in A). For an example of this, see Figure C-12.
   
   
3. As long as ED continues to increase or stay the same, then keep taking identical incremental steps in the same direction. After ten successful such steps, then double the increments of each element of . After another ten successful steps, then double the increments again. Keep up this ten-step/doubling process. For any step, if ED (new) < ED (old), then return to the previous and go to Rule A.

      Note that if heuristics were added to the search process in order to try to drive the two mean vectors apart so as to further enhance the current trend in the CW 1 Mean Chart of Figure C-9, which has the mean curve for High PHENOMENON above the mean curve for Low PHENOMENON, then the underlying assumption of the heuristics would be that what distinguishes High PHENOMENON from Low PHENOMENON is that for High each of the nine cumulative weight positions is more heavily weighted than is the case for Low.

      Based on Perdurabo's observations (see Appendix E) that for High PHENOMENON everything in the geocentric configuration tends to center around one or two planets, whereas for Low PHENOMENON there are usually three or more important planets, it might be the case that for an accurate set of Method I aspect and orb weights, for High PHENOMENON the cumulative weight curves are low and flat for the first 7 or 8 cumulative weight positions and then rise suddenly for the last one or last two cumulative weight positions, while for Low PHENOMENON the curves have a more constant upward slope.

      However, note that the way the current perforrnance function is designed (i.e., simply to maximize the Euclidean distance between the two mean cumulative weight vectors), the mean vector for High PHENOMENON could be driven to a low point in the nine-dimensional cumulative weight space and the mean vector for Low PHENOMENON could be driven to a high point.

      What has been presented here is in reality nothing more than a rough idea of the kind of thinking that should go into the development of an adaptive process for optimizing a set of weights for aspects and a set of weights for orbs vis-a-vis the Method I weight scheme.

      Current TAARP plans call for the purchase of AbTech's AIM Statnet Software (see Addendum 3), and its utilization for various optimizing tasks such as the one presented here for Method I weights. Appendix D and Section E6.0 of Appendix E present a much more complex approach for adaptive computer algorithms as applied to quantitative astrological studies.