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
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.
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.
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.
separations: Sirius program, from www.astrosoftware.com
SP 500 prices: www.yahoo.com financial, historical prices,
both for the SP 500 and SPY
Statistics: www.vassarstats.net/textbook/ch4apx.html for the n and r entries, yielding the p