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Astrology really works!
This approach really doesn't

Geoffrey Dean

The original review, of which this is a slightly expanded version with an added appendix on declination probability, appeared as "Crooked Thinking is Alive and Well" in Skeptical Inquirer 1997, 21 (2), 46-48.

Astrology Really Works! By the Magi Society. Hay House, Carson CA, 1995.
ISBN 1-56170-134-3. 327 pp. Softcover, $12.95.

Abstract -- This is a strange book. It claims to present irrefutable evidence that astrology really works, but there is no reference to any astrologer, article, book, or published research. It claims to advance astrology into the 21st century by tossing out all chart factors except aspects, parallels and contra-parallels, and by supposedly proving astrology via various observations such as aspect counts among the rich and famous. The observations are restated as Six Challenges To Skeptics, which on close inspection are clearly artifacts and clearly unwinnable. Whatever our opinion of astrology, unbelievable books like this one can only make it worse. Includes a look at the probability (0 through 1) of a contact in declination, which within 0.03 is orb/12.

Anyone familiar with the difficulty of getting positive research results in astrology will be instantly intrigued by this title. The front cover announces that astrology has been "proven by the Magi Society." The back cover announces "The book that advances astrology into the 21st Century!" So might this book represent the research breakthrough we have all been waiting for? The answer is a decisive no. The serious researcher will find nothing in this book worthy of attention except as examples of how not to do research.

A strange book
To start with, it is a strange book. It claims to present irrefutable evidence that astrology really works, so we might expect it to cite some of the many hundreds of published research studies. Not this one. There is no reference to any astrologer, article, book, or published research. The name Gauquelin is nowhere mentioned. The authors are identified only as the Magi Society, "an international association of men and women who know that astrology works" (p.318), contactable only via a New York telephone number (212) 867-2905 (p.61), which is an answering machine. Calls made by a New Yorker on my behalf were not returned, possibly because (as I learnt later) it was receiving 10-15 calls a day. There is a glossary and over 120 birth charts, but no index, so abandon all hope of easy retrieval.

It gets stranger. The text includes scientist-bashing ("no one outside of their own circle is allowed to evaluate or criticize their conclusions" p.227), astrologer-bashing ("there are only a handful of legitimate astrologers in the whole world" p.317), fundamentalism ("the fact that astrology works ... will be the closest thing to proof of God" p.240), and astro-creationism ("astrology proves that the fittest are not those who have the best genes, but they are those who have the most favourable astrological aspects in their natal charts" p.219). Which may explain why, right from the start, the text reads like a sermon complete with breathtaking self-assurance: "After researching the birth charts of all the most successful men and women in America, we found that astrology unquestionably works. But of course, we, of the Magi Society, knew that all along due to our extraordinary and unsurpassed knowledge of astrology, which we call Magi Astrology" (p.1).

Strangely, their extraordinary and unsurpassed knowledge is not without error. Thus aspects (specified angular separations) were not used four thousand years ago (p.10), Newton was not an astrologer (p.16), astrologers do not try to avoid using aspects (p.41), signs were not formulated thousands of years ago (p.131), and Darwinists do not claim we evolved from apes (p.225). But I digress.

The Magi breakthrough
The Magi explain that "astrologers and others have made many failed attempts to prove that astrology works" (p.37), so "we decided that astrology, as it was generally practiced and understood by the average astrologer in 1994, was not yet solid enough to be proven". In other words it needed its own Newtonian revolution "before it could be proven and accepted by most of its critics" (p.39). To make a breakthrough it needed a breakthrough. Therefore "we will take astrology the necessary monumental giant leap ahead by adding a whole new dimension to it; by doing so, astrology becomes provable" (p.39).

The Magi's monumental giant leap consists of (1) tossing out all birth data except the date, and (2) tossing out all chart factors except interplanetary aspects, parallels and contra-parallels. A parallel or contra-parallel exists if two planets have the same or opposite declination (angular distance from the celestial equator). Astrologers who insist that birth times are essential, and that only the whole chart may be used, might well feel compromised. Indeed, on this basis the Magi would fail the elementary exam of most astrological teaching bodies. Declination is the supposed "new dimension", even though it has been used by many astrologers from Ptolemy onwards, albeit with much disagreement over its utility, for example my own survey of over 100 astrological sources found that user opinions were divided roughly 2:1 in favour of it being unimportant. A Magi birth chart (one is shown on the cover) has planetary declinations in the area traditionally reserved for houses.

The justifications for this giant leap are revealing. Birth times are out because "even birth certificates that have exact times are almost always wrong" (p.40, how can they know this?). Declinations are in because "it is impossible to fully interpret birth charts without them" (p.58, most astrologers do it all the time). Which is like arguing that, because wheel alignment is never absolutely exact, cars can do without wheels but not cigarette lighters. Furthermore, because popular ephemerides (tables of planetary positions) do not show declinations, be sure to buy the Magi's one, available from Hay House (p.53), or their software package (p.151). Of course, even in the 327 pages of the present book, there is a limit to what can be said, so "in the future we will be publishing more books" (p.295). At which point the commercial advantages of promoting an astrology dependent only on date and your own publications will be apparent.

Proving Magi astrology
Having taken this giant leap, the Magi then proceed to prove astrology by various observations. Along the way they give particular aspects Capitalised Names to indicate their Connections. The super rich and famous (eg Rupert Murdoch, Clint Eastwood) "almost always have at least one, and on the average, two to three" of twelve Super Aspects so powerful that "anyone who possesses even one of these aspects has a jump start on achieving great success" (p.67). The average champion athlete has two Super Aspects plus two of seventeen Sports Champion Aspects (p.205). The difference between Super Aspects and Sports Champion Aspects is complicated and confusing (seven aspects are common to both), but in broad terms Sports Champion Aspects involve Mars and Super Aspects do not. Among other things planetary aspects affect the stock market (p.113), the success of companies (p.245), personal relationships (p.271), and business opportunities (p.293). Positions midway between planets in celestial longitude or in declination behave like planets and are just as important (p.147).

Unfortunately these observations are presented uncritically without controls or statistical tests, ie in a manner that will be drearily familiar to readers of astrology books. Nevertheless the Magi assure us that everything has been subjected to "rigorous scientific statistical tests", the details being conveniently omitted because they are "beyond the interest level of most of our readers" (p.304), which I suppose is an interesting commentary on their target audience. However, "anyone who wishes to obtain the study can contact us", although just asking for it implies "a very deep-rooted skepticism of astrology. In such a case no amount of statistical validation may be enough" (p.305). So in February 1997 I wrote for details of their study but to no avail.

Six challenges to skeptics
At which point astrologers and skeptics alike might justifiably view the Magi's observations as beyond the pale. But what makes the Magi's book worth at least passing attention is that their observations are restated as Six Challenges To Skeptics. To my knowledge no other astrology book has challenged skeptics so directly. "Astrology really works and is proven unless the skeptics can meet all of our challenges" (p.317). Which at first sight seems fair enough. Two of the six challenges involve predicting the future, and are discussed later. The rest are as follows:

- List famous long-established athletes who do not have a Neptune enhancement of the Sun. The Magi will list those that do. You lose if your list is not ten times longer than their list (p.61).

- List American sports champions who have no Sports Champion Aspect and not more than one Super Aspect. The Magi will list those who have at least one of each. You lose if your list is shorter (p.206).

- Choose a number of two-year-old horses who have no Sports Champion Aspect, no multiple aspect involving Mars, not more than one Super Aspect (here choice is limited to nine), and who have not raced. The Magi will choose an equal number who have at least one Sports Champion Aspect or at least two Super Aspects. You lose if your horses win less money than theirs during the next two years (p.221).

- List successful corporations with no Super Aspects in their charts. The Magi will list those with at least two. You lose if your list is shorter than theirs. "If skeptics do not meet this challenge, we have the right to say that astrology is proven" (p.246).

The middle two challenges are immediately ambiguous because the Magi do not explain how to deal with those Sports Champion Aspects that are also Super Aspects. That aside, the twelve Super Aspects (p.68) and eleven of the seventeen Sports Champion Aspects (pp.204-205) are all "enhancements". An enhancement exists when two planets are mutually in conjunction, trine, parallel, or contra-parallel. The orb (permissible inexactness) is 3 degrees for the aspects and 2.5 degrees for the rest (pp.52,71).

Probability calculations
The orb is crucial because it determines the probability of occurrence. For a parallel or contra-parallel the probability also depends on where the planets are in their orbits, because like a person on a swing each spends more time at the extremes of declination than at the mid-point, which of course increases the probability of occurrence. The probability will also depend on retrogradation (the apparent reversal of planetary motion as seen from the earth, which increases the time spent at whatever declination the planet happens to be at), and on planetary latitude (which shifts declination up or down as a whole).

In short there are so many complications that controls are essential. But as a guide my computations indicate that the long-term probability of an enhancement is something like 0.26, most of which is due to the declination component, see Appendix. So, with twelve enhancements to choose from, the average chart will contain about 12 x 0.26 = 3.1 purely by chance. The Magi's observed average of two or three for the rich and famous is therefore unremarkable. More to the point, their first challenge is unwinnable -- if the total population of famous athletes is N, then purely by chance (irrespective of any astrology) the Magi will find 0.26N with an enhancement, leaving us to find 2.6N with none, which is impossible. It would be easier to toss coins and always get heads.

In the other challenges (ignoring ambiguities) we need to find cases with no enhancements while the Magi need to find cases with at least two. For the twelve Super Aspect enhancements, the probability of finding none will depend on the time period, but will generally be something like (1-0.26)12 = 0.027, whereas the probability of finding at least two, calculated binomially, is given by

the sum from r=2 to r=12 of 12Cr x 0.26r x (1-0.26)(12-r), where 12Cr = 12!/(r!(12-r)!),

which comes to 0.86. In fact the Magi later include a handful of other aspects as Super Aspects (p.142), so in effect the 12 in the above calculation should be increased, which means that the above difference in probabilities is conservative. Similar probabilities apply to the seventeen Sports Champion Aspects.

What the probabilities tell us
So what do these probabilities tell us? As before, if the total population of cases is N, then whether we count corporations or cats, we will find around 0.027N cases with no enhancements. But purely by chance (irrespective of any astrology) the Magi will find around 0.86N cases with at least two enhancements, or over 30 times as many. Which means that the Magi will have over 30 times as many horses to choose from and a correspondingly better chance of picking winners. It also means that we cannot possibly exceed the Magi's count of 0.86N because only 0.14N non-Magi cases remain. In other words the corresponding challenges are unwinnable. Or as the Magi Society says, it "has examined the birth charts [sic] of EVERY superstar of American sports, and we know skeptics cannot meet this challenge" (p.206). The skeptics' failure to win will of course have nothing to do with astrology and everything to do with statistical probability. In effect the deck is stacked absolutely in the Magi's favour, which did not stop a reviewer in the Astrological Journal (1996, 38, 263-264) concluding that the Magi's evidence is "certainly persuasive."

The Magi generously offer to reduce the orbs to 2.33 and 1.83 degrees for aspects and declination respectively, thus supposedly making success "harder for the Magi ... and ... easier for skeptics" (p.312). This increases our count to around 0.06N, but reduces theirs only slightly to around 0.76N, so the deck is still stacked absolutely in their favour. In effect skeptics are being challenged, not to show that butchers differ astrologically from bakers, but to show that butchers tend not to have two arms and two legs. Note the irony: Even if this were possible, it would say nothing about astrology.

Challenges involving prediction
The remaining two challenges involve predicting the future by transits and progressions (future planetary positions judged in relation to birth positions):

- Make money on publicly-traded stocks and commodities (no real estate) by investing on days when, by Magi rules, there are bad transits to your birth chart. "The Magi Society will tell you when you cannot make money. Contact us and we will prove it" (p.123).

- Choose any well-known group of American athletes and predict their performance over the next few years better than the Magi Society. You cannot choose athletes who have favourable transits and progressions (future planetary positions) according to Magi rules. "We are very anxious to compete with skeptics on this challenge. Please do not disappoint us" (p.129).

The first requires actual investment, not pretend investment, so you will need plenty of spare money. But in both cases there is a severe problem, because "until you read one of our subsequent books, you will not know how to correctly evaluate your transits and progressions" (p.272). This means we cannot make any probability calculations or check what the Magi Society tells us. Even though these essential books were published after this review was written, there seems no reason to suppose that either challenge is more soundly based, or less stacked, than the others. No sensible person will bother.

Gullibility really works!
So what might skeptics conclude? "After they have read this book, only those skeptics who want to be unreasonable and do not want to accept the truth will continue to refute the validity of astrology. We know that they cannot meet our challenges. Nonetheless, we expect to be attacked and vilified by the most diehard of skeptics. What we have written will be misrepresented, taken out of context, and nitpicked" (p.316). Well, maybe. But whatever our opinion of astrology, unbelievable books like this can only make it worse. Until the Magi abandon their sermons, stacked decks and naive counting in favour of scholarship, controlled studies and adequate reporting, their "irrefutable evidence" for astrology is evidence only that crooked thinking is alive and well. Gullibility really works!

Appendix: Probability of a contact in declination

The plot below shows how the probability of a parallel or contra-parallel with a planet (in this case the Sun) depends on where the planet is. Each dot is the mean probability during a full 360-degree cycle by the other planet, and for the sake of demonstration the orb in declination is 2 ° 20 min or 2.33 degrees. Start on the left.

Probability of a parallel or contra-parallel

As the Sun moves from left to right, the probability is minimum at 0 (= 0 Aries), where the Sun has zero declination. As soon as the Sun moves away from zero declination it allows contra-parallels to exist, which causes an initial steep increase in probability. As the Sun moves towards 90 (= 0 Cancer and maximum 23N declination), the probability slowly rises to a peak and then falls somewhat as the orb extends past the limit of travel. As the Sun moves past 90 the probability plot is a mirror image of the first half. As the Sun moves out of the graph into S declination, the entire plot is repeated.

The maximum probability is 0.405, more than six times the minimum probability of 0.064, and the mean probability is 0.216 (halve this to get the mean probability of a parallel or contra-parallel only). If the two bodies differ in latitude by two degrees, which is often the case, the mean probability is slightly decreased to 0.211. The probability of a conjunction or trine of orb 3 degrees is about 3x(3x2)/360 = 0.05, so the probability of an enhancement is about 0.21 + 0.05 = 0.26. The variation of declination probability with orb is not straightforward, especially if the planets have latitude, but the approximate probability is within 0.03 of orb/12.

Because the probability of a contact depends on where the planet is, it will also depend on the time period, which for slow-moving planets can cause severe sampling problems. For example Neptune had zero declination in 1862, maximum N declination in 1903, zero declination again in 1943, and maximum S declination in 1986. So if our charts happen to come from the 1860s or 1940s they will necessarily contain fewer declination contacts to Neptune than if they happened to come from the 1900s or the 1980s.

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