Math of Astrology - 1

Whenever I tell that I am interested in astronomy, there are some who come back with "Oh god! Don't tell me you don't believe in all that crap?". Sometimes I answer with a very serious "Well those are true!". The reality is that while there is a reasonable number of people who don't distinguish between astronomy and astrology, there is an even larger number of people who dismiss astrology as complete fallacy and non-scientific for the wrong reason.

Given that the traditional new year of the Sri Lankan Buddhists and the Hindus which is  based completely on astrology, is around the corner, I thought it would be the right time to start off an article about the mathematical basis of astrology. Astrology consist of studying the movement of celestial bodies and predicting the future (or largely the future of individuals) based on that movement. The predictions made based on astrology have been challenged over and over and have failed to be proven on a rational basis. Margin of error encountered on most (if not all) of the predictions are too large that they can easily be a coincidence when they are right. The predictions are also very vague that they can be interpreted in many ways.

While I do not agree or believe in the predictions made in astrology, I fully appreciate the science and mathematics behind astrology. The entire study of astrology is based on the movement of planets, the Sun, the Moon among the stars. This is a complex task that needs very close observation skills and a good understanding of mathematics.  The purpose of this series of  articles that I am planning to write, is to uncover the basis of mathematics that is used in astrology. For the purpose of this article, I will be analysing the mathematical background of sri lankan astrology, which I am more familiar with.

To start off with, let's try to look at the main aspects of astrology and how modern discoveries contradict them. The objective of this comparison is not to prove that astrology it self is scientific, but to show that the math and the reasoning behind it is not necessarily a fallacy and to understand the basis on which astrology is built.

Let's start with the contradictions that are easier to explain (the more straight forward contradictions, require a longer explanation):

1. There are 13 constellations in the zodiac, where as astrology uses only 12.
This is true. One of the fundamentals in astrology is the movement of the sun through constellations. The collection of constellations that stand in the path of the sun is called the zodiac . If you look at any star map or a software, you will see that the sun moves through 13 constellations throughout the year; Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpius, Ophiuchus, Sagittarius, Capricornus, Aquarius and Pisces. In astrology, there is no reference to Ophiuchus.

This does not necessarily mean that the basis of 12 constellations is wrong. The current constellation demarcation came in to effect in 1930 with IAU finalising the 88 constellations in the sky. The constellations used in astrology are not exactly the same as the constellations we refer to (albeit them having the same name). While the constellations as per IAU vary in sizes, the constellations referred to in astrology are roughly the same in size and span about 30<sub>0</sup> each in the sky. So not having 13 constellations is fine.

2. The nine planets in astrology are not actually planets, and it doesn't account for all planets.
This is also true. The nine "planets" in astrology refer to  the Sun, the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Rahu and Kethu. One of these is a star, another a satellite and two (Rahu and Kethu) definitely don't refer to any planet we know.

As per the essence of astrology, each of these "planets" have an affect on humans. I don't subscribe to this teaching at all, but on the other hand, I think of astrology as a method invented by humans to find patterns in natural world and then trying to extend it to human life. Most of us would have heard about the conjecture ancient Egyptians had with the rising of Sirius and flooding of the lower Nile. Priests in Egypt identified that the lower Nile always floods during the after the first time Sirius is seen rising in the morning in each year. The cause was obvious; seasonal rains, but the Egyptians may not have understood this and may have viewed Sirius as a messenger of the floods to come.

If you are trying to identify cyclic patterns, it does not matter whether you actually deal with planets or stars (or something else). The only requirement is that there is periodicity in motion. So the fact that astrology labels Sun and the Moon as planets is not a problem either (on closer inspection, it can be seen that a long standing "planet", Pluto, lost its status as a planet in 2006 when IAU decided that it is a "planetoid").

What about Rahu and Kethu then? What do they refer to? According to mythology associated with astrology, Rahu is an entity which chases the Sun and devours it occasionally. Its counter part Kethu on the other hand, chases the Moon to devour it. The periodicity of Rahu and Kethu assigned by astrologers coincide with the "Lunar Nodes", the points where path of the Moon crosses the path of the Sun. When the Moon reaches the Lunar Node "in front of" the Earth, it causes a solar eclipse. When the Moon reaches the Lunar Node "behind" the Earth, it causes a lunar eclipse.

Again the astrological stand point on these two "planets" is that they are sensitive points in the sky that have an influence on human life. Regardless of the scientific veracity of this claim, I find the discovery of Rahu and Kethu points to be very important. Given that most of us are unaware of Sun and Moon having different paths of motion in the sky and given that most of the time, you cannot plot the motion of the Sun and Moon on a single star map due to practicality, it takes a lot of careful observations to identify that the Sun and Moon do not move on the same path.

What then about the omission of Uranus and Neptune? Why are they not included? As I mentioned before, I believe that the origins of astrology was in trying to understand patterns in the sky. Uranus and Neptune were not identified up until the renaissance period. What the ancients did was to try make out sense of what they could see. They built a pattern out of what they saw.

3.  Astrology believes that the planets and the sun and the moon rotate around the Earth. We know it is not.The answer to this is that it does not matter. In reality, there is no absolute motion, every motion is relative to the frame of the observer.

 The Earth does not really rotate around the Sun. Both Earth and Sun rotates around each other around the centre of gravity of the two systems. Given that the actual solar system consists of many more bodies, the actual behaviour is more complex. (But given that the mass of the Sun is accounts for 99.9% of the entire mass of the solar system, it doesn't really matter.)
If the intention of astrology was to identify cyclic patterns. Then the only requirement is to find something that has patterns.

4. How can astronomical bodies so far away to Earth, could possibly have an effect on human life?

There have been many explanations given by the astrologers as to the basis of their predictions (i.e. "So why does such things happen when Jupiter moves there?"), but none of them have been accepted by the mainstream academia as plausible.

What is possible, is that (as reiterated several times in this article), that it was a matter of pattern recognition that was extended with divination. Therefore regardless of the great achievements with mathematics, astrology is very unlikely to be useful as a real science or methodology.

With that note, I'll end the first article. Although the intention of the series of articles was to examine the mathematical basis of astrology, not much was done during this article than to discuss some fundamentals of astrology which clashes with current observations. In the next article, we will discuss the mathematical basis of the Buddhist and Hindu new year.