Reading The Signal and the Noise: The Art and Science of Predictionby Nate Silver, the other day (a book which has nothing to do with the occult), it occurred to me – how would Astrology stand up against analysis in terms of Bayesian Probability? Bayesian Probability is the art of updating original estimates of probability in the light of new evidence. This can be expressed in the following terms.
Let X be the estimated probability of The Outcome which we had before we had the new Evidence (the “Prior”);
Let Y be the probability that the Evidence is conditional upon the Outcome being true;
Let Z be the probability that the Evidence is conditional upon the Outcome being false.
The probability of the Outcome given the Evidence (the “Posterior”) can therefore be expressed as:
Now let us suppose the following hypothetical situation:
Let us suppose that by some fluke someone has obtained evidence tending to prove that people with Sun in Leo do in fact behave like typical Leos 100% of the time. The probability that people born with Sun in Leo behave like typical Leos in the light of this evidence is not 100%. This may sound counter-intuitive, but real astrologers who know the limitations of the Sun-sign astrology – the kind that gets published in newspapers and vapid glossy magazines – will begin to see why. We can quantify actually quantify these limitations by using the Bayesian formula above to work out a more accurate probability. I.e.
Let X be the probability that we would have ascribed a person with Sun in Leo behaving like a typical Leo, had we not had the new evidence. Logically, by pure chance alone we know that this can be no lower than 1/12.
Let Y be the probability that the results of the evidence are conditional on our Prior being true. Now here is where the Skeptic will depart from the True Believer. The Skeptic will claim that Y = 0, on the basis that he would not accept the evidence nor indeed any evidence as tending to support the reality of Astrology. The True Believer, on the other hand, will want to argue that Y = 1.00, i.e. that it definitely does support the reality of Astrology, and moreover, the correlation in our hypothetical situation is 100%. Let’s assume – for the moment at any rate – that we are not Skeptics, and that we accept that Y = 1.00.
Let Z be the probability that the results of the evidence are conditional on our Prior being false. Duh, well where did the evidence come from then if this is so? This is where the limitations of Sun-Sign astrology come in. The real Astrologer will be aware that a person could display some Leonine-characteristics if any one of the planets fell in Leo on their chart – or if one of the major angles such as the Ascendant or Mid-heaven were in Leo. So along with the Ascendant and MC there are ten other planets in Astrology: Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Therefore we could say that Z = 11/12, the probability that it was caused by either the Ascendant, MC or at least one of the other planets falling in Leo. This of course is an approximation: a quick look at world demographics by age will tell us that not everyone on the planet can have seen the slowest moving planets pass through all 12 zodiacal signs: even the world’s oldest human being has only seen Pluto move through half the zodiac during her lifetime.
Anyway, if we crunch these figures, we will find that even if we are True Believers and we have the best evidence possible, our updated probability only works out at 9.08% – which is only a little better than by chance alone (the prior, 1/12, by comparison, is 8.3%). The Skeptic however would have arrived at a figure of exactly 0% i.e. impossible, because anything multiplied by zero is zero.
Or to put it another way, if you are reading your daily horoscope in the paper and it’s written by a competent astrologer who knows his or her stuff, and has evidence to back it up, there is still only a 9.08% chance it will apply to you! And that’s being generous!
However, we now know how to scientifically test the proposition in order to come up with more realistic figures. Take a sample of any amount (e.g. 1000) who are all the same sun sign (e.g. Leo). Calculate the Horoscopes of each one – this will give us a more representative Z figure, because then we will know to what extent we can exclude the influence of other planets in the results. Devise a test to see whether the test subjects react in a way typical of that sun-sign, and if so to what extent. This will give us a more representative Y figure.
What we would expect to see is that once the influence of the other planets in each person’s chart has been been determined, the resulting Z figure would probably be lower than 11/12. However, there is also no reason to suppose that the Y figure would be as high as 1.00. If the test results turn out to be less than 100% – which, except in the case of a sheer miracle, will be most likely – the maximum possible value of Y would decrease accordingly.
If we then crunch the numbers according to Bayes’ Theorem and come up with any number greater than 8.3%, that would be a justification for further investigation. If however the Posterior comes to less than 8.3% (the prior, what we would have expected by chance alone), then we know that the hypothesis has not been proven.