Towards a Proof of Astrology An AstroSignature for Mathematical Ability Copyright © 2004 All Rights Reserved by David Cochrane Preliminary Discussion of Astrological ResearchThere are several extremely important keys to conducting astrological research. The following rules are my own based on my experience as an astrologer, conducting astrological research, and knowledge of the scentific method. All of the rules may not apply to your style of reesarch, and the following rules are my personal rules, and it is possible that you can conduct research in some other manner that will succeed. I am listing these rules here because a huge amount of research, in my opinion, fails because these rules are not followed. (1) The experimental group, i.e .the group of people who have a trait that you are studying, should be highly homogenous. Consider, for example, a study of athletes versus non-athletes. Athleticism is the trait to be studied, and the control group is the athletes, and the control group is the non-athletes. Athleticism is not a good trait for astrological research because it is too broad. A soccer player, baseball player, and tennis player utilize very different skills. Even the category of baseball players is very broad. One baseball player runs fast and relies more on agility and speed and may like to take more risks, while a different player may be a power hitter and not particularly fast. Different positions require different skills. A pitcher, for example, does different things than an outfielder. (2) The trait being studied preferably is one of the most important and conspicuous traits of the person. A study of people who are in the military, or people who have advanced college degrees, is not likely to yield positive results because people make these kinds of decisions for many different reasons, and the variation in colleges and military service makes it difficult to define a particular trait which all of these people have in common, and the most important and conspicuous characteristics of many of the people being studied may have little to do with the fact that they served in the military or received advanced academic degrees. (3) The trait should be one that is not primarily defined by non-astrological influences, such as heredity or the environment. How does a person become a great baseball player, or a great mathemetician? A complete scientific answer to these questions is not available, but you should use common sense, intuition, and research to figure out what kinds of behaviors are likely to have a strong astrological indicator. (4) Your chances of being successful in research are greater if you are, or were, an astrological consultant, or in some other way have worked intensively with the language of astrology. You have a much better feel for how to interpret results, and come up with hunches for what to pursue if you do. Progress in science is generally achieved by people who are intensely devoted to the research, not by people who have a passing interest in the subject. Dedication to a field of study and research over a period of time brings wisdom and a sensitivity to subtle issues that others will miss. (5) If possible, study an area that you have some knowledge of. Perhaps in your astrological consultations you worked with many people who had a particular psychological problem, and suupose also that you have studied the literature on this psychological problem . A research study in this area is hopeful. There are some areas that we all have at least a fairly good sense of what is involved. For example, you can study athletes in various kinds of sports without actually having much direct experience in the area. Obviously, boxing requires physical endurance, strength, and aggression. However, consider an area like alcoholism. If you have read the literature on alcoholism, and have some experience with alcoholics, you will have a much better sense of what kinds of dynamics are involved than if you are almost completely unacqainted with the area. (6) Conduct pilot studies and informal investigations first. Keep an open mind and explore many possibilities. If you jump into the research with a narrow set of expectations, you are likely to have little success. For example, if you expect that boxers will have Mars and Uranus in square aspect with a 5 degree orb, you are likely to obtain disappointing results. Astrological influences work through much more complex means and a more integrated view of the chart is needed, rather than one or two simple factors. Do some exploration by looking at charts of people who have this trait first. (7) Choose an area for which there is lots of available data. Obviously, if you study boxers, then you need charts of boxers. This requirement, unfortunately, can almost never be met, so we have to make due with the data that is available to us. Also, if possible, do not study all of the charts during your initial studies. Keep some charts untouched so that they can be used later, as explained below. (8) You must devote a great amount of time to the research project. Tremendous perseverance is needed. Thomas Edison did not invent the light bulb after one or two attempts. Proof of astrology is very elusive, so elusive in fact that a great many highly respected and excellent astrologers do not believe that astrology is amenable to scientific proof or that astrology can function in a manner similar to other scientists. Any advance in moving astrology towards a scentific discipline is a historical achievement, and one that many astrologers and non-astrologers are skeptical is even possible. (9) Eventually you will need to develop an AstroSignature. For example, suppose that you are interested in researching the astrological influences that correlate with extensive travel. You can define extensive travel as, for example, the number of times that the person has flown in an airplane outside the USA and the study can be of only people who live in the USA. Explorartory research followed by pilot studies are likely to indicate that various astrological factors show promise of correlating with travel, rather than just a single astrological factor. You may find that Sun, Mercury, and Jupiter in the 9th house or ruling the 9th house, as well as Sagittarius rising, all incline towards travel. You may also find that some astrological influences correlate more strongy than others. Fortunately, there are various astrological software programs, such as Kepler and AstroDatabank, for example, that provide tools for assumptionless research (that can be used during the exploratory phase of research) and development of sophisticated AstroSignatures that involve many different kinds of astrological influences. These astrological influenes are combined together in different ways with different weighting assigned to them. The ability to obtain AstroSignature scores for groups of charts provide the average scores for the entire group. Also, as discussed in more detail in item 11 below, an AstroSignature that consists of a coherent or consistent set of rules is preferable to an AstroSignature that consists of apparently unrelated and disparate astrological influences. (10) Study an area that has a clear operational definition (measurable manifestation) of the trait or energetic property being studied. For example, consider whether a study that compares astrology charts to people who get certain scores on an IQ test or Myers-Briggs introversion-extroversion scale, or who are great mathematicians. I am more inclined to study the mathematicians because the need for mental concentration and studiousness is a trait that, to me, is more tangible and specific than a score on a psychological or intelligence test. However, my determination of this is largely based on my own common sense and intuition and experience in analyzing birth charts. You must find a measurable way to study an intangible trait. From my experience as a teacher and from charts I studied, I am inclined to use mathematics as a relatively good operational definition for mental concentration, studiousness, objectivity, and intensity of thought. There are other operational definitions for these traits that may be even better. (11) If you can develop a theory based around a consistent and simple astrological principles, this is much more likely to be repeatable in future astrological studies. For example, suppose you find that boxers have Mars-Uranus in square, sextile, or sesquiquadrate aspect, but they do not have Mars and Uranus in trine or semisquare aspect. Such a finding may be vaild, and you do not need to discount it. However, there is little precedence in astrology for including in a seemingly arbitrary manner some hard and soft aspects and leaving out others. Such a finding should not be thrown out! However, when you attempt to duplicate the study with another group of boxers, there is a good chance that the aspects that you found in the first group do not show up in the second group. I am giving you this advice based on personal experience! You should be a little more skeptical of your findings if there is little conssistency to them. On the other hand, these findings should not be ignored, and should simply be analyzed again with a new set of data to see if there might be validity to the theory. (12) To prove astrology, you must eventually conduct a study using the scientific method. The most critical features of the scientific method is that you must clearly state your hypothesis before you look at any of the chart data! Then you collect the data, compare the experimental group (the charts that have the trait) with the control group (charts that do not have the trait). There is a great deal of astrological research that is very interesting and impressive, but has not followed these strict rules for scientific research, and therefore the findings should not be construed as scientific proof, but they do offer exciting and hopeful theories. The Magi Astrology books and a recent book by Dr. Mitchell Gibson are examples of these kinds of works. They provide some exciting findings but do not quite meet these strict requirements for research. The proof of astrology will come when a study can be replicated numerous times with success. This is the gold standard for scientific research. There are other required details of scientific research to ensure objectivity of the study, and peer review is required, etc. but this simple requirement to state the hypothesis clearly, and then conduct the study is a basic tenet of the scientific method that has not been followed in most astrological research, so therefore most astrological research is of a "piolot study" or "exploratory research" level, and not a final scientific study. There is nothing wrong with this. In fact, I have already emphasized that exploratory research should precede final studies. The only problem is in misidentifying exploratory research as a finished experimental validation of astrology. SUMMARY:Below I will summarize the research that I did on mathematicians, physicists, and alcoholics. This research is weak in regard to items #7 (large amount of available data) and #11 (final research phase) above. Nevertheless, I am describing this research here because I think it is among the most important research studies ever done in astrology. I know that such a claim sounds grandiose to an extreme, and furthermore I believe that in time this kind of research will lead to repeatable experimental studies as described in #11 above, an even more grandiose claim! In other words, we are approaching the ability to validate astrological theory, which is of such immense signficance as to be history-making. Advances in science are almost never the work of one or two people. Hopefully the publication of this research will inspire others to continue along similar lines and eventually lead to the transition of astrology from a sea of theories and conjecture to a science. One last note before summarizing the research study: the word "science" conjures up different emotions, attitudes, and even meanings to different people. The extraordinary advances in science in the late 19th century, the 20th century, and no doubt continuing also in the 21st century which we have just entered, have brought wondrous miralces to us. At the same time, the heart and soul of the sciences has been trampled upon by a disregard for the spirit of the people who developed these disciplines. Our schools and academic institutions often emphasize only the final result of the work, a kind of "bottom line", and leave the student with only the husk or shell, and leave out the wonder, awe, beauty, inspiration, and magic of the process of discovery, and of the formulae and the functioning of creation. For example, there is not time to wonder in amazement that the circumference of the circle is always proportionately larger to its diameter in a non-repeating real number value, but we just memorize that Pi equals 3.14 and plug it into the formula to pass the test. The lives of Euclid, Newton, and Einstein are fascinating, but there is no time for that either in our rush to pass the exam and produce the correct answer to the formula. I hope that the soul of astrology and the soul of astrology students is not sacrificed in the march forward, as has happened in many other disciplines. Theoretical Basis for the Research: Tools Used: First Stage of Research: Exploratory Research of Physicists Second Stage of Research: Exploratory Research of Alcoholics Third Stage of Research: Exploratory Research of Mathematicians I decided to start over with an approach similar to the analysis I used in the 1970's as an astrologer, but with the improved software available now. I looked at harmonic charts 1 (the "normal" chart), the 5th, 7th, 8th, and 64th harmonic charts. The 8th and 64th harmonic charts are particularly important because they are "octave harmonics" or "hard aspects". Hard aspects are harmonics 1, 2, 4, 8, 16, 32, etc. In the harmonic chart wheel are drawn the following aspects: opposition, square, trine, sextile, semisextile, quincunx, semisquare, sesquiquadrate, 1/16, 3/16, 5/16, and 7/16 aspects. A semisquare or sesquiquadrate aspect appears as a conjunction in the 8th harmonic chart, and similarly a semisquare or sesquiquadrate aspect in the 8th harmonic chart appears as a conjunction in the 64th harmonic chart. By looking at the hard aspects in the 1st, 8th, and 64th harmonic charts I can actually see all octave harmonic patterns up to the 1024th harmonic very quickly. I can also see the soft aspects (semisextile, sextile, and trine) as well as quincunx as well. I also included the 7th harmonic because I associate the 7th harmonic with discipline, chronic situations or determination, sobriety, and deep inner probing, a liking for things that are humble and ponderous, sometimes almost mystical or ancient. From my experience teaching math to children and adults, the 7th harmonic pattern seemed very likely to be strong in the charts of mathematicians. I found some evidence of this in the chart of physicists but not as strong as I had hoped, and other harmonics, like the 17th and 19th were often stronger. The 5th harmonic is the harmonic of culture, play, dislike of tedium, creativity, and freedom. While the 7th harmonic loves discipline and knows that practice makes perfect,the 5th harmonic excels in creativity and play. The 7th harmonic likes to work and the 5th harmonic likes to play. The 7th harmonic is ponderous and deep, while the 5th harmonic is light and exuberant. I doubted that the 5th harmonic would be strong in the charts of mathematicians but the creative freedom of the 5th harmonic gives it an intelligence which more mundance and steady types typically lack, so it would not be impossible for the 5th harmonic to be important as well. The first 12 harmonics can be seen in the harmonic charts I constructed as follows:
Many other harmonics can also be seen. For example, the octaves of the 7th (7th, 14th, 28th, 56th etc) appear as conjunction, oppositions, squares, semisquares and sesquiquadrates, etc.) respectively in the 7th harmonic. I changed the color of Mercury to red in the chart wheel, and left the other planets black, so that I could quickly see Mercury in each chart as I browset through them. My theory was that I would see many aspect lines to Mercury from Mars, Saturn, Uranus, and Pluto. This was what I had found in the study of physicists but there were too many exceptions to the rule to be really impressive. As I browsed through the charts of the mathematicians I was amazed and delighted to see that in almost every 7th and 8th harmonic chart the aspects appeared. Now, at last, the expected patterns appeared conspicuously in almost every chart of mathematicians! However, having spent hundreds of hours of research this year, and countless hours researching before this, I have learned not to jump to conclusions. There are a seemingly endless number of perils in the quest to validate astrological theory! The importance of the 7th and 8th harmonic charts was exactly what I expected. In my work with clients in the 1970's I did not expect a great deal of information from the normal astrology chart! I know that this sounds strange, but every astrologer has his/her own unique way to analyze charts, and I rely on a number of harmonic charts and midpoint patterns to analyze the chart. The 8th harmonic chart, in many ways, is more fundamental than the 1st harmonic chart because it reveals the inner dynamic patterns within the person. Each harmonic chart fills in the coloring of the chart; the basic personality is built on a structure of the octave harmonics. One additional note on harmonic charts: the orbs used are different from other forms of astrology. A 16 degree orb is used for conjunctions, 8 degrees for oppositions, 4 degrees for squares, 5 1/3 degrees for trines, etc. The orbs must be proportionate. If you change one orb, you must change them all. An orb greater than 2 degrees is not very strong because it is above the 8th harmonic level which is a threshold point for digging deep within the core of the person's personality and energy dynamics. I then created an AstroSignature for mathematical ability. I gave 1 point to a conjunction, opposition, or square in the 7th or 8th harmonic charts for each of the following planetary patterns: Mercury-Saturn, Mercury-Uranus, and Mercury-Pluto. I dropped Mercury-Mars, which was in my original hypothesis, because it did not show up nearly as strongly as the 3 other planetary pairs. I also refined my original hypothesis to be specifically these 3 aspects (conjunction, opposition, and square) in these 2 harmonic charts only. Additional analysis showed that trines, sextiles, semisextiles, and quincunxes also occurred frequently in the charts of mathematicians in the 7th harmonic chart, so these were also added. Hypothesis reformulated and restated from this exploratory study The beautify of this hypothesis, as compared to the hypotheses that I had earlier created for physicists and alcoholics, is that it is very consistent, as described in rule #11 above. I use all traditional aspects (the multiples of 30 degrees or 12th harmonic, or in other words conjunction, opposition, square, trine, sextile, seminsextile, and quincunx) in 2 harmonic charts between Mercury and the planets Saturn, Uranus, and Pluto. This is very consonant with astrological theory. I hypothesized that Mercury would aspect thse planets because this was my observation as an astrologer, in my rsearch with physicists, and the choice of these planetary pairs conforms reasonably with the expectations of most astrologers. The orbs used and harmonics used does not conform with what most astrologers expect but it does conform with my hypothesis. RESULTS OF THE STUDY:The results of the study were stunningly more consistent than any other research that I have done. In the table below if the percentage of charts that have each of the 3 planetary pairs conjunct in each of the 6 harmonic charts: Percentage with conjunctions of 3 planetary pairs in 6 harmonics:
The individual totals for the planetary pairs were not calculated for the 21st, 42nd, and 84th harmonic. These harmonics were added later and by this time it was decided that all 3 planetary pairs would be used, so individual totals were not needed. The octave harmonics (8, 16, 32) showed a mild correlation with mathematical results. 29% of mathematicians have Mercury-Saturn or Mercury-Uranus or Mercury-Pluto in 8th harmonic as compared to 23 percent of alcoholics. In the 16th harmonic the percentage is 33% for mathematicians and 21 percent for alcholics. The 32nd harmonic, however, showed no correlation, in fact a slightly inverse correlation with only 18 percent of mathematicians having the planets in 32nd harmonic. The incredibly impressive results are in the 7th harmonic. Not a single planetary pair occurs less often in conjunction in the 7th, 14th, and 28th harmonic charts of mathematicians than in the chart of alcoholics. A comparison of the total for all 3 planetary pairs in each 7-based harmonic is amazingly consistent:
By adding the harmonic totals for alcoholics (23+21+22+27+28+31+28+25+21) and dividing by 9, we obtain the average percentage for a harmonic for alcoholics = 25.1%. This value is precisely what is expected because a 16 degree orb for the conjunction aspect was used, so there is a 32 degree area (16 degrees on either side of a planet) where Mercury would be conjunct the other planet, or, in other words, 32/360, or 8.8% of the zodiac. Three pairs are used and 3 x 8.8 = 26.67 so mathematically we calculate the random probability of any aspect pair being conjunct in one of the 3 harmonics as 26.67%. The actual probability of alcholics for all 9 harmonics is 25.1%, very close to the mathematical random expectation of 26.7%. The distribution of these 3 conjunctions in these 9 harmonic charts in the 167 charts of alcoholics was random. The minimum value was 21% (16th harmonic) and the maximum value was 31% (28th harmonic). These values appear to be random fluctuations around the expected averageof about 26.7%. Note that planetary motions are not linear and are complex due to retrogradataion so this calculation of an expected mean of 26.7% may not be the actual expected mean, and is only a rough estimated value. Note, however, that in harmonic charts, the actual random distribution of planetary angles is much more evenly distributed than in the 1st harmonic, or normal chart, and typically the obtained average from a control group is close to the expected mean calculated by this overly simplified formula, and in this case, as usual, the obtained average score of 25.1% was close to the calculation of an expected average using this rough estimated value of 26.7%. The fact that the rough estimate from calculation and the alcholic data produce similar results confirms these values of 25% to 26% to be an accurate estimate. Analysis of Numeric Totals: The lowest 7-based harmonic value for mathematicians is 37% and the highest value is 70%, with an average percentage of 51.8 (37+56+48+48+52+70 divided by 6). Therefore, of the six 7-based harmonics, the highest percentage for alcohlics (31) was less than the lowest score for mathematicians (37), and the average for mathematicians (51.8) compare to the percentage for alcoholics (25.1%) is about twice as great! The consistency of the result across all 3 planetary pairs for all 7-based harmonics analyzed is even more impressive. A statistical analysis of the results is not necessary because this study does not meet all of the criteria for scientific study in that the hypothesis was formulated only in general terms, but not articulated in detail. The hyothesis has now been articulated in detail, and a subsequent study can be carefully carried out, and results can be analyzed statistically to test the null hypothesis. AstroSignature Analysis: After the AstroSignature is created, a Mathematical Aptitude score for any person can be produced. The Mathematical Aptitude score for mathematicians using this formula calculated for the 27 mathematicians was 16.37. The average score for the 167 alcohlics was 8.54. The ratio of these scores is 1.92. In other words, mathematicians scored nearly twice as high as alcoholics. Astrological Conclusions: The octave harmonics (8, 16, and 32) showed promise of having some significance, but not as strong as the 7-based harmonics. This finding was not expected, but the positive indications of the octave harmonics were consonant with the original hypothesis as well. Indications for Future Research: Current astrological literature consists of an almost endless number of possible variables, and a synthesis of some of the most important variables into a coherent formula that can provide a platform for further research is needed for astrological theory to make a transition from unverifiable hypotheses to supported theories. This pilot study initiates the process of this transition. The synthesis of relevant variables into a supportable theory is a daunting task, but this current pilot study shows great promise of providing this foundation for further astrological research. Note that the experimental group used in the current study was a group of highly accomplished mathematicians. A study of less accomplished mathematicians or those who work primarily in pedagogical pursuits or applications of mathematical theory may not have the exceptional qualities of mental discipline and mental intensity that these noted mathematicians have, and therefore may not have the strong 7th harmonic patterns that was found in the current research study. I hypothesize that astrological influences represent a complex web of energetic patterns. These energetic patterns develop in response to environmental stimulation and decisions made by the individual. Each person is endowed with a wide range of capabilities and from this palette of potentials creates a life pursuit. The astrological influences do not magically represent behaviors, but rather represent energetic patterns. We are now at the initial stages of unraveling these complex patterns, and over time the capabilities of astrology may prove as awesome as the advances of other sciences and arts. The interweaving of variables is complex, and the interaction of astrological, environmental, genetic, and possibly other influences involves a system of influences that cannot be fully appreciated by simple methods. Nevertheless, the domain of astrological theory is tractable and amenable to scentific research, and with care and persistence, a scientific pursuit of astrology can lead to successful advances, and this new body of supported theory is applicable to a wide range of human conditions, and can prove to be a benefit to humanity. No doubt further research would refine and expand the number of harmonics and planetary pairs used. Inclusion of other astrological variables could further refine the formula, and finally a solid basis for further research would begin, and the initiation of astrology as a field amenable to scientific analysis can begin. Huge research group sizes of thousands of charts are not needed. However, all research is time consuming and without the support of academic institutions and publicly funded research projects, progress in astrological research, as with research in any other discipline, will be very slow. Hopefully, a paradigm for future research has been established in this study. Only future studies will clarify the extent to which this pilot study provides a robust and stable platform upon which to build a scientific study of astrology. AUTHOR: David Cochrane |