TAO Science
TAO 2 Correlations with Global Stock Market Indices (updated 11/ 05/ 09)
ABSTRACT:
OVERVIEW: This study found a statistically significant correlation between the TAO 2 and the Dow Jones Industrial and SP 500 stock market indices, to greater than 1:10,000 against chance during the time period tested, from 1/1/1999 through 6/30/2008. The TAO 2 is a mathematical oscillator with known planetary longitudinal, angular separations as the sole input. It is inherently mathematical, and thus has the potential to be scientifically useful, across many diverse applications. The TAO 2 is theorized here to be a factor interrelated with global human psychology, that is being measured by stock market price rises and declines.
ORIGIN: The TAO 2 originated from:
1) my studies of the mathematician and astrologer Donald Bradley, who first developed his Sidereoscope that evaluated planetary angular separations using both an objective aspectarian, and subjective planetary evaluations applied it to the movements of the stock market
2) the studies of Sherman McClellan, a mathematician and technical stock market analyst who invented the McClellan Oscillator and Summation Indices--both stock market analytical and trading tools
3) the psychological contrarian sentiment indicators that became popular in the 1970's and 1980's, measuring the percentage of investment advisors who are either bullish (positive, expecting rising stock prices) or bearish (negative, expecting falling stock prices).
METHODOLOGY: The TAO 2 is comprised of five primary integrated concepts and methodologies. First, there is the aspectarian, that assigns positive and negative numeric values to every degree of planetary separation (similar to Bradley), is derived from the numbers 2 and 3 and their harmonics (different from Bradley, and similar to the harmonic theories of John Addey). The harmonics forming the aspectarian are logarithmically weighted to be mathematically consistent, and possibly scientifically applicable. Second, only selected planetary pairs were used (unlike Donald Bradley) both because of the nature of the comparison to the stock market and its psychology, and because of astrological planetary significance. Third, these selected pairs were weighted, related to orbital and periodicity factors. Fourth, for the given time period, the raw TAO 2 oscillator is zeroed, so that the summation of all the raw TAO 2 values equals zero (similar to McClellan, and a critical component of his oscillator.) This step compensates for planetary orbital idiosyncrasies in relationship to the aspectarian and for the limited time frame of this study. Zeroing the oscillator is essential for mathematical and scientific comparisons. Fifth, the zeroed raw TAO values are then both averaged (the Short TAO)(similar to the McClellan Oscillator) and summed (the Long TAO)(like the McClellan oscillator's summation index). The TAO 2 is the average of the Short TAO and the Long TAO. The summation provides an insight into human psychology as reflected in the TAO 2 interrelating with the buying and selling of stocks over a period of time--a sum of the thoughts and actions of people over longer intervals.
NULL HYPOTHESIS: There is no correlation between the TAO 2 and two of the global stock indices, the SP 500 and the Dow Jones Industrial Average.
RESULTS: Since the TAO 2 is a known quantitative variable and stocks prices are another known quantitative variable, and they are independent, then it is statistically indicated to apply the correlation test for two independent variables: the Pearson Product-Moment Correlation. For the Tuesday and Friday data points for both the TAO 2 and the DJIA and SP 500 indices, from 1/1/1999 through 6/30/2008: n=990, the Pearson r for DJIA , r = +0.72; for SP 500, r = +0.81. The Null hypothesis is rejected at greater than 1:10,000 against chance. There is a statistically significant relationship between the TAO 2 and two global stock indices, the DJIA and SP 500.
RESEARCH IMPLICATIONS: There is a need for duplication of this research by an independent investigator, and this will be possible this fall with the publication of a computer program formatted for the TAO 2. Other stock market time intervals can also be studied. Since the TAO 2 is theorized to be an indicator of global human psychology, then correlations to other human events might be studied, such as governmental decisions or disasters affecting large numbers of people. The Aspectarian generated for the TAO 2 verifies some fundamental tenets of traditional astrological aspect analysis (trine beneficial, opposition detrimental, etc.), and suggests further aspect and orb research. There might be a study of a large number of successful/rich/famous individuals correlated with their TAO 2 scores at birth. This type of study, if it shows statistically significant results, could be expanded to include tests of the Angles (Ascendant, Midheaven, Vertex, and more). In a similar manner, astrological theories relating to transits, progressions, and directions can be assessed in a relatively objective format.
Beyond this, once the software is released this fall, it will be seen that there are, literally, an infinite number of TAO's. The TAO 2 is only one of them. The TAO 2 is a limited first step toward an empirical astrological research methodology. Fundamentally, the TAO 2 is applied mathematics and applied astronomy. As this study demonstrates, the TAO 2 correlates with the global stock indices, which makes it useful in a tangible way. Other TAO's might have many other significant applications.
The avenues for future research are virtually unlimited.
TAO 2 Aspectarian: 8/31/09
Degrees of Planetary Pair angular separation and their numeric values: (For degrees 181 through 360, subtract the a.s. from 360: e.g., if the a.s. is 240, then 360-240=120 and use the value for 120 below).
0 -5 60 +18 120 +36
1 -5 61 +15 121 +34
2 -5 62 +12 122 +29
3 -5 63 +9 123 +24
4 -5 64 +7 124 +21
5 -5 65 +4 125 +19
6 -5 66 +1 126 +20
7 -3 67 -1 127 +19
8 -3 68 -1 128 +16
9 -4 69 -1 129 +12
10 -7 70 +1 130 +10
11 -7 71 +1 131 +8
12 -7 72 +1 132 +6
13 -3 73 +2 133 +3
14 +1 74 +4 134 +1
15 +1 75 +4 135 +1
16 -1 76 +4 136 -1
17 -3 77 +1 137 -1
18 -5 78 -3 138 -1
19 -6 79 -4 139 -1
20 -7 80 -5 140 -1
21 -9 81 -3 141 -1
22 -9 82 -2 142 +2
23 -8 83 -2 143 +2
24 -7 84 -4 144 +1
25 -5 85 -5 145 -1
26 -2 86 -5 146 -1
27 +1 87 -5 147 +1
28 +2 88 -6 148 +4
29 +5 89 -6 149 +6
30 +7 90 -6 150 +7
31 +5 91 -5 151 +4
32 +2 92 -4 152 +1
33 -2 93 -3 153 -3
34 -4 94 -2 154 -5
35 -5 95 -1 155 -8
36 -3 96 +1 156 -11
37 -3 97 +2 157 -14
38 -3 98 +4 158 -14
39 -6 99 +4 159 -15
40 -8 100 +2 160 -14
41 -8 101 +3 161 -13
42 -9 102 +4 162 -13
43 -10 103 +10 163 -12
44 -10 104 +13 164 -10
45 -10 105 +16 165 -9
46 -10 106 +14 166 -11
47 -8 107 +14 167 -14
48 -6 108 +13 168 -19
49 -5 109 +14 169 -20
50 -4 110 +13 170 -20
51 -2 111 +13 171 -18
52 +2 112 +13 172 -18
53 +4 113 +14 173 -18
54 +4 114 +17 174 -20
55 +3 115 +20 175 -21
56 +4 116 +24 176 -22
57 +6 117 +26 177 -22
58 +11 118 +30 178 -23
59 +15 119 +33 179 -23
60 +18 120 +36 180 -24
AREAS for Potential Research:
1) Financial: From 1/1/99 through 8/31/09 the published TAO 2 demonstrates statisitically significant correlations with stock market indexes (the DJIA and SP 500). The TAO 2, as a global psychological indicator, has potential applications to other financial sectors (such as gold, interest rates, employment, etc.).
2) Natal planetary analysis. Each planet in the birth chart can have a TAO 2 total score, and that can be applied to personality, or any part of a person's life (work, health, finance, etc.).
3) Progression analysis. The progressed aspects (using any of the standard progression or direction techniques) can be totaled independently, or their scores relative to the natal chart, with quantitative analysis of life events possible.
4) Transit analysis. Same as #3, only using transiting planets relative to the natal chart.
5) Medical. For the first time, quantitative medical research is possible because of the numerical aspectarian inherent in the TAO 2. Do highly positive or negative TAO 2 natal, progressed or transiting scores result in specific medical conditions.
6) Cosmobiological/Midpoint analysis.
7) Returns. Solar and Lunar, Parallax or not, Precessed or not...all can be quantifiably and statistically compared for results.
8) Mundane. Ingresses (both Tropical and Sidereal) with locality impacts and aspect analysis. What angles are the most active or potent?
9) Eclipse charts.
10) Ingress studies. One potentially effective means of comparing the Tropical vs. Sidereal zodiacs is by using the TAO 2 scores of the Asc/MC/Vx angles of the two (or more) dramatically different charts evolving from the two zodiacs.
11) Aspectarian analysis. The TAO 2 aspectarian is only one of an infinite number. The TAO 2 aspectarian uses only the numbers 2 (negative) and 3 (positive) for its final form. The harmonics 2, 4, 8, 16, 32, 64 and 128, and 3, 6, 12, 24, 48, 96, and 192, in decreasing weights, add up to the values assigned to the degrees from 0 through 180. The TAO 2 aspectarian supports traditional interpretations for the primary aspects.
12) Harmonic analysis. Other harmonics can be explored aside from 2 and 3. Vedic/Hindu astrology is replete with references to and use of various harmonics, especially the 9th (Navamsa). David Cochrane's work with the 7th harmonic documents its relationship with the price of gold. Further work is needed.
13) Tests of the angles. This might prove to be one of the more fruitful areas of TAO 2 research. Does a high or low TAO 2 score for the natal MC relate to employment choice or success/failure? Does the Asc relate to personality or health? Does the Vertex actually attract certain types of people into a person's life?
14) Asteroid, Uranian, Jaynian planet analysis. Do these bodies, both the physical and hypothetical, have demonstrable effects? Does a positive Midas produce wealth? Is Chronos associated with leaders? Does a positive Ceres produce a "green-thumb"? The possibilities abound.
This is only a preliminary list of potential avenues for quantitative astrological research. It is my intention to provide the TAO 2 aspectarian as a building block in the foundation of statistically sound and effective methodologies for astrological inquiry. My work is dedicated to expanding that awareness and inspiring future work by others. The published work on this website ideally serve those functions. Your ideas are welcomed.
Schulz on Market Cycles Richard Schulz
TAO 3 Graph on Publications page