TAO 8   Aspectarian


Richard F. Schulz               02/26/2014©

                The focus of this paper is the history and nature of the TAO 8 Aspectarian.   The TAO 8 is formulated from selected and weighted transiting planetary pair aspects, and is theoretically a measure of human psychology as it changes over time.    On any given day, all of the pairs have an angular separation, and as calculated by the TAO Aspectarian mathematical cosine formula (based on the cosines of weighted Harmonics of the numbers 2 and 3) these separations generate corresponding Aspectarian values, positive or negative, for that selected Planetary pair.  .  For the given day, these Planetary Pair numbers are summed, and that is their absolute TAO 8 number for that day.    Multiple Planetary pairs are used to create the current TAO 8 model (there are theoretically an infinite number of possible TAOs), and their aspectarian generated values are summed to be the TAO number for that day.  Later papers will describe in depth how these raw TAO daily numbers are transformed into the Quick, Slow and TAO 8 oscillators.

                The TAO aspectarian is one of the 6 primary keys to unlock the mystery of how the TAOs generate graphs that reflect human activity on Earth over the recent decades.  The other 5 are: 1) selecting the Planetary pairs used in the daily calculations, 2) weighting these Planetary pairs,  3) averaging the daily TAO values over time, 4) selecting the type of averages to be used, and 5) mathematically integrating and refining those averages for both graphing and application purposes.  The original TAO 8 Aspectarian originated in 1984, and programmed in Apple Basic, on an Apple IIe.  It used a semi-arbitrary square root function based upon fundamental astrological aspect theory.  The 12th harmonic aspects were positive: 30, 60, 120, and 150 degrees.  The 8th harmonic aspects were negative: 45, 90, 135 and 180 degrees, with the 0 degree conjunction given a positive or negative effect dependent upon the Planetary pair (e.g., Venus/Jupiter positive at conjunction, and Mars/Saturn negative at conjunction).

                I puzzled over this for a long time, since scientifically and mathematically having different values for the conjunction of various Planetary pairs would necessitate a different Aspectarian for them as well.  I eventually chose to primarily emphasize the Aspectarian in its pure mode, regardless of the given Planetary pair.  A conjunction of Venus/Jupiter and Mars/Saturn would be valued the same according to a neutral Aspectarian.  Given my astro experience as a tropical and Jyotish practitioner I had multiple perspectives.  As time went on, I grew to weigh aspects, especially transits, more than signs.  I had remembered that Mars, Jupiter and Saturn had made tight conjunctions during both the early 1980 and mid 1982 stock lows.  So I assigned the conjunction a relatively negative value, and constructed the initial Aspectarian accordingly.  0 degrees was -20, 30 = +10, 45 = -10, 60 = +20, 90 = -20, 120 = +40, 135 = -10, 150 = +10, and 180 = -20.  There was a 180, and back to 0.

                I calculated and entered the Planetary angular separation numbers by head and hand.  I wasn’t proficient in spreadsheets at the time, so I also hand graphed the results.  For statistical significance, I compared each Planetary pair with the Dow Jones Industrial Average (DJIA).  I was a bit amazed that the trio of Mars, Jupiter and Saturn (3 Planetary pair combinations) all were significant using the Pearson Product-Moment Correlation (PPMC) statistical test for two independent variables.  I came to realize later that this PPMC correlation was partly skill (the Aspectarian combined with 3 Planetary pairs that happened to be significant longer term) and mainly luck, with a favorable limited time frame selected.  Regardless of the actual merit, the results greatly encouraged me to continue working on the project.  Had I known how difficult, tumultuous and lengthy this project would be, I might never have proceeded.  However, I did.  The TAO 8 results have come from over 20,000 hours of investigation over the last 30 years.

                I did this work with a scientific result in mind




 I then took this a step further in my research:  averaging these transiting numbers over time (the collective psychology of decisions over time), and then further, zeroing those averages.  When the averages (Quick, Slow and TAO 8) remain positive, optimism dominates (for stocks, rising prices).  When negative, pessimism dominates, and more selling (and asset losses, such as home values) tends to occur.   The Pearson Product-Moment Correlation (as applied to 2 independent variables) for the TAO 8: 1/1/1980 through 08/31/2013, n = 3602, r = +0.48, the p < .0001, with the odds of this correlation occurring by chance are less than 1:10,000 (the source of analysis is http://vassarstats.net/textbook/ch4apx.html).  The TAO 8 correlations extend beyond the economic field into other aspects of human global life, into the social, political and mundane realms.  The latter are not addressed in this introductory paper.


There are several primary components to the TAO 8:  1) Some (24, at present) planetary pairs are selected for inclusion in the calculations, 2) Each selected planetary pair is then weighted: 0.01 to 1.00.  3) The Aspectarian formula transforms each daily (or bi-weekly) planetary pair aspect into a positive or negative number.  4a) The daily TAO is exponentially averaged to create the Quick TAO, and 4b) the daily TAO is averaged for a year to create the Slow TAO, and 4c) then finally the Quick and Slow TAO are averaged to create the TAO 8. 

                The TAO 8, as with the previous TAO versions, is the average of the immediately responsive Quick and the longer trending Slow TAO.  The Quick TAO is calculated by applying an exponential moving average (0.05 ema) to the sequential transiting TAO values, and responds immediately to value changes, while maintaining a positive or negative bias during prolonged net positive or negative transiting values.  The 0.05 ema thus measures both immediate changes in psychology as well as net positive or negative psychology over time.  The Slow TAO has been revised.  On any given date, the Slow TAO is the average of the transiting TAO values for the previous and subsequent 6 months (a one year equal average).  The Slow TAO is a view of TAO values over a longer period of time, and includes the past (6 months) psychology, present, and future (6 months).  Thus the Slow TAO includes both lagging and leading planetary pair sentiments.   The TAO 8, being the average of the Quick and Slow TAO, theoretically measures both the peaks and troughs of shorter term (weeks to months) sentiment and human activity (buying and selling relative to the SP 500), and the probable longer term (months to years) trend.   

The TAO 8 is designed to be a 100% scientific astronomic aspect oscillator.  A true scientific oscillator is zeroed, over any defined time period, which means that the average of its values is zero.  For statistical comparisons, zeroed oscillators have their intrinsic merits and demerits.  For the TAO 8, one primary use is to compare it with a linear, non-zeroed set of numbers: SP 500 stock index.   For 1/1/1980 through 08/31/2013, using bi-weekly data, the n = 3602, r = +0.48, p < .0001, for odds against chance greater than 1:10,000. 

Correlation is not causation, although this level of significance suggests a mechanism of causality that is not yet known in modern physics (evolving string theory offers a multi-dimensional possibility).  The TAO 8 is pure numbers in, numbers out.  The methodology, data sources (footnotes) and statistical correlation is sound and replicable. 


                The primary difficulties for a zeroed oscillator appear when it reaches extreme positive or negative values.  For the TAO 8 the positive extremes happened in end 1980, fall 1987, end 1995, 1999-2000, mid 2005, end 2007, and now, end 2013-2014.  A maximally peaking zeroed oscillator must, inherently, subsequently decline toward to and/or then remain negative for a period of time.  Equities rose into the TAO 8 peaks of 1980, 1987, 1995, 1999-2000, 2005, 2007, and were accompanied usually by falling SP 500 prices after.  The 1987 peak occurred in Aug/Sep 1987 Crash, and stocks troughed 4 years later in 1990.  The greatest decline for the TAO 8 occurred from 1989 into 1990, coincident with the US 1990 recession and the great fall of Japan.  The rise from the TAO 8 late 1990 bottom (near -9000, not shown) into end 1995 is the greatest on the graph, with a normalizing oscillator decline back to the zero line into end 1996, ending with another rise into the triple head-and-shoulders peaks of 1998-2000—the period of the historic Tech bubble peak. 

The TAO 8 major troughs have indicated, with 90% accuracy, SP 500 buying opportunities.  These occurred end 1982, end 1985, end 1986-early 1987, end 1989-early 1991, and those shown on the graph.  It is for a future paper to quantify the dates, and compare various investment strategies relative to the absolute performance of the SP 500 over that time.  It is apparent from the graph that buying at the troughs, exiting at the TAO 8 peaks and going into cash, money market, short term CD’s or T-notes would have had greater returns than just buying on 1/2/1980 and holding until now.   While the corresponding magnitudes of the TAO 8 and the SP 500 rises and declines are not always similar, the directional movement correlates highly.   The TAO 8’s 1:1,000,000 odds-against-chance merits some attention and mathematical, scientific analysis and review.

Fundamentally, the TAO 8 is 100% mathematical and astronomical.  For those who may be interested, the Aspectarian does verify some astrological aspect tenets.  The 2nd Harmonic cosines (the formula could equally use the sine function) produce negative or minimal TAO values at 0 (-7.2), 45 (-10.1) , 90 (-0.7), 135 (+5.5) and 180 (-36.1) degrees of separation (aspect).  The 3rdHarmonics produce positive or maximal TAO values at 30 (+6.0), 60 (+18.9), 90 (-0.7, moderating the negative square value), 120 (+47.8), and 150 (+6.0) degrees.  A full explanation of this will appear in another paper.    

The TAO 8 uses primarily (90%+) longer cycling planetary pairs (Lunar north/south nodes, Mars, Jupiter, Saturn, Chiron, Uranus, and Neptune).  The TAO 8 is thus comprised of cycles within cycles within cycles—multiple unique periodicities interrelating with each other, forming longer rhythms.  These correspond with the economic flow of money into and out of equities, globally. There are other economic (such as home values and consumer or investment sentiment), social, political and mundane correlations as well.  These, too, will be discussed in another paper.  The TAO 8 now sets a framework from which numerous discoveries can evolve.  

I wish the 1600’s Astronomy pioneers were alive.  They created planetary laws through observation, laborious hand calculation, and unique insights.  It remains for time to tell what path the TAO 8, and analogs, proceeds on from here.  This research and development has held my fascination for the 28 years of its development.  Now I move into more specific articles concerning the TAO 8’s practical applications, further research and refinement, and am always open to new ideas and avenues for exploration.

                                                                                                                                                Richard F. Schulz






1)       Planetary angular separations:  Sirius program,  from www.astrosoftware.com

2)      SP 500 prices:  www.yahoo.com  financial, historical prices, both for the SP 500 and SPY

3)      Statistics:  www.vassarstats.net/textbook/ch4apx.html  for the n and r entries, yielding the p values.



Schulz on Market Cycles

                                                                                                  Richard Schulz

10-04-20  1500 cdt

NYSE   Bi-Daily  10-01-18 through 10-02-20 close

10-04  1500:   More of the same, with accelerating lower values this week.  If there is an early week rally, it will quickly reverse.

09-27  1100:    The Bear is returning.  Selling rallies primarily.

09-20  1100:    The graph is self-evident.  ExpO Y is the primary focus, now that ExpO Z is crossing ExpO X.   The ExpOs are now forming a series of lower highs and lower lows.

      The 3 year perspective sees a gradually rounding recovery from the Feb plunge.   This is one of the most reliable formations for a return to substantially lower values over the next few months; in effect, the return of Bear market activity is imminent.