Statistical methods in astrology.

1. Introduction.

Recently it becomes more and more clear that astrology is in crisis. It is caused by rapid development of science and civilisation progress - astrology in its present form becames to be an anachronism and so-called serious people associate it with various superstitutions. In this article I presented some remarks about using statistical techniques to astrological research and about application of computers because it makes a wide range of possibilities.

2. Why statistical research ?

The answer is simple: because up to now it is the only possibility ! If we knew the origin of influence of Lights, planets, Signs, houses etc. to us we would not need it. Unfortunately, we do not know the nature of astrological interactions so we need to apply statistics - solution maybe not perfect but efficient. But, however, there may be some doubts - some of them were expressed by Kazimierza Flatau Pozegnanie z astrologia (Farewell to astrology, Problemy Astrologii 1988-1989, Stowarzyszenie Astrologow w Poznaniu).

He made following mental experiment: let us take any horoscope and any element of that horoscope (e.g. Mercury) and shift it 1° in any direction. This configuration cannot be found in any ephemerides so it cannot be associated with any horoscope so it is a nonsense. Similar story with e.g. removing Mercury from the radix. Because the nature of statistics is that it looks for some isolated elements only, it is not a valid way, we should not use it.

It sounds very seriously. But if we follow this way we may say that whole astrology is a nonsense. Why? Because we will never know exact positions of any element in any horoscope, in the best case (time of birth estimated with 0.1s precision, place of birth with 0.01" precision, if we apply the most precise planetary and sidereal time algorythms etc.) we will know planetary positions with precision about 0.1" and cusps of houses with precision about a few arcseconds. In practice, if we know birth time with precision 10 min. (quite optimistic assumption) and we use ephemeris, estimated error for planets is about 1' (for the Moon at least 5') and for houses 1.5° - 5° (for geographic latitudes of Central Europe). I assume that we made no mistakes in calculations. It means that all horoscopes are anhoroscopic (word used by K. Flatau) so instead of doing astrology we should make something useful, e.g. go to look for for mushrooms. Let us have look at the ancient astrology: Uranus, Neptune and Pluto were unknown but they were making horoscopes and these horoscopes seemed to be O.K. Even now we do not take everything: there are planetoids (and astronomers discover more and more), comets, stars (astrology uses the brightest only - why?), gaseous nebulae, pulsars, other galaxies, quasars, black holes ... - can we speak about horoscopes and neglect this enormous amount of objects?

However, I think that K. Flatau may be a bit right. Although equations of classical physics are fully linear, well defined etc. (for simple systems at least) but in quantum mechanics and General Relativity it is not so simple. What does it mean? If an equation is linear, a sum of its solutions is still a solution - even if we do not know exact solution we can estimate it by using some approximate solutions (e.g. for simplier system) and then make next approximations. For nonlinear equations it is not so simple - even a tiny addition may change the solution dramatically. It may be similar in astrology - if it is ruled by strongly nonlinear effects statistical approach may be useless. May, but not necessarily - in order to verify that, it is necessary to make such research, not to sit down and repeat "everything is a nonsense". In ancient times somebody formulated principles of astrology and I do not think that he took them from nowhere, he had to notify some corellations. We can make a little step to statistical methods which are mathematical way of looking for corellations. Apart from that, meteorological phenomena are strongly nonlinear (well known butterfly effect: flight of a butterfly in Hongkong may cause a hurricane in California) but, from the other side, it is very unlikely that in Poland mean temperature in January will be greater than in July. I think that it may be similar with astrology.

3. What is necessary to check?

The answer is simple: everything. It is necessary to verify whole astrology step by step. Of course, negation of whole astrology would be also wrong - in the epoch of Enlightenment they made similar mistake with modern medicine - they rejected whole tradition and now we see a come back to tradition. I suppose that (like in medicine) traditional astrology is O.K. (in approximation) and we need to make some corrections only.

Let us take an example: Zodiac. In astrology it is based on the ecliptic (or plane of Earth's orbit) and vernal equinox point. We see influence of two motions: around polar axis (vernal equinox point is a common point of the plane of equator and the ecliptic) and around the Sun. A question: in astrology Zodiac is based on the ecliptic - maybe it should be based on the Celestial Equator? It would not make a big difference: in the ecliptic the Sign of Aries would start in the same point, Taurus in the point with ecliptic longitude 32° 11' , Gemini in 62° 5', Cancer in 90° (the same point as now), Leo in 117° 55', Virgo in 147° 49', Libra in 180° etc. - differences would be in order of 2°. It may be verified by using statistical methods - if we discover that e.g. owners of canarys have the Sun in Taurus much more frequently than in Sagittarius, if it is true applying right ascensions instead of ecliptic longitudes should enhance this effect; if it weakens effect it would mean something opposite. Another example: aspects. In astrology they are differences of ecliptic longitudes - but (in my opinion) it is valid for objects near ecliptic only, in general we should take real distances at the Celestial Sphere (it would make calculations much more complicated - it would be necessary to include ecliptic latitudes!) - if it is true, for phenomena that depend on aspects applying this theory should enhance effects (or even lead to discover new ones).

In general, there are a lot of things to check and I do not know if in 100 years we will know much more.

4. How to do research?

It is necessary to find a well-defined group (e.g. birth dates of members of Association of Owners of Canarys) and then look for common elements in their horoscopes (e.g. what was the most common position of Mars). It is important to pay attention to largeness of the group: more means better; usually good results may be obtained if it is at least 10000. For example, if we would like to verify aspects with precision 1°, it would be necessary to have at least 3602 cases (more than 100000). Of course, it would be necessary to take into account all non-astrological factors like year curve of births, some astronomical dependancies (due to the fact that orbits are elliptical planets are in some signs longer than in the other ones, so e.g. more people will have Saturn in Capricorn than in Cancer) etc. - in other words, compare obtained numbers with the expected ones if we assume that there are no astrological influences.

That is an example that happened to me. I collected some dates of birth and death in order to look for transits to natal positions in days of death and last birthdays. To my great surprise I obtained enormous corellations on last birthdays, especially when looking at transits of Mars to the Sun, Mercury, Venus and opposite - it turned out that there were a lot of conjunctions, semisextilles and sextilles and very few trines, quincunxes and oppositions. Unbelievable! Very strong corellation, in disagreement with traditional data! I was very distrustful about these results and it turned out that I was right, that is the solution:

It turned out that it is an astronomical corellation. Mars when circulating on its orbit around the Sun (S) has almost constant angular velocity so probability that it will be present between the points M1 and M2 is almost the same as between M3 and M4 (not exactly but in this case this difference is negligible); in other words, Mars needs the same time to "pass" through these fragments of its orbit. When looking from the Earth (Z): the angle between the points M1, Z and M2 is much greater than between M3, Z and M4. What does it mean? Opposition of Mars to Sun is much less likely than conjunction (please notice that in the region of conjunction Mars moves much slower with respect to the Sun than in the region of opposition). On last birthday Sun's position is within 1° the same as in the natal chart (and if we calculate solar chart ecliptic longitude will be identical), from the other side Mars would be in conjunction rather than in opposition to the actual position of the Sun - but, as we know, it is close to natal positions to the Sun, Mercury and Venus, so on last birthday Mars will be much more frequently in conjunction than in opposition. Semisextilles and sextilles will be much more frequent than quincunxes and trines.

5. Application of computers.

Finally we move to the main purpose of this article - application of computers in astrological research. Just an example: I have run a test (calculating position of the Sun, the Moon and all planets 10000 times including aberration, nutation etc.) on a PC with 486 DX2 50 processor and it took less than 470 sec. (under DOS, much better optimised OS/2 program calculated it about 235 sec.) and on a PC with Pentium MMX 166 MHz less than 84 sec. (35 sec. under OS/2). Comparaison of already calculated positions would be even faster. If it was made without a computer it would take some months. This example shows that nowadays data processing is not a problem, it is necessary to have proper algorithms and collect data - and it is the greatest problem now. Fortunately, computers are more and more present in everyday life and we can e.g. ask a friend employed in a hospital (especially if he has something to do with computers) if he has access to birth dates of people ill for some particular illnesses. Even more important is to have a program that would be able to calculate planetary positions but in the worst case it is possible to write such program, planetary algorythms are available in the Internet (usually as C codes). I have such algorithms (in C and Pascal) - from simple ones (precision in order of 1') to very precise (0.01", less than measurement error); I can give them if necessary.

Other application - also very important - would be to calculate expected results if so-called null hyphotesis is assumed (no astrological interactions at all, planetary positions are random). In this case computers are extremely useful - please compare two things:

Next example: we have a set of 100000 dates of birth and death. Computer calculates curve of deaths (or probability of death in particular age). Then it takes dates of birth and death, transits in the days of death and last birthday and increases proper numbers of aspects, then (basing on the curve of deaths) calculates random date of death and proper aspects. After processing whole group it compares numbers obtained in both methods (true with "random") and then it would be possible to analyse and interpret these results.

I would like to stress that method of "random results" is used quite often. For example, in High Energy Physics such methods are used when analysing results of accelerator experiments - there are compared experimental results with results calculated in computer simulations under assumption that all possible interactions are known. If there is any disagreement, these results are studied carefully - the difference may be an aparature effect or due to errors in estimates of parameters of used model. If all possible sources of errors are excluded it means that it may be due to something new.

6. Summary.

Dramatic growth of speed of communication and information flow plus the fact that computers went out from closed research centers and they are more and more common in everyday life are making new era in astrological research when the crucial thing will be to collect data (it should become easier and easier) - in other words, we enter the era of information. More and more important are good algorithms, not only to calculate planetary positions - also (even more) methods of analysing collected data. We should not forget about non-astrological factors because neglecting them would lead to improper results.

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