On chaotic systems

This article on deterministic chaos is a nice introduction to the concepts behind it.

The main point here is that -  a system is deterministic if its current state completely determines how it will behave in the future. A simple pendulum is not chaotic and its motion can be described by a simple equation. A double pendulum on the other hand is a chaotic system where the motion of the system is extremely sensitive to changes in the initial conditions. This is the essence of non-linearity: effects are no longer proportional to causes and even small causes can produce large effects.

The most famous illustration of this is the "butterfly effect" described by Lorentz while studying the equations that determine the weather. The weather is a chaotic system where outcomes are strongly dependent on the initial conditions. The tiniest fluctuations in air pressure in one part of the globe may have the most spectacular effects in another part. Thus, a butterfly flapping its wings somewhere in Chicago may cause a tornado in Tokyo.


I present all of this to suggest that astrology is a predictive  model of a chaotic system. They rely on initial conditions (with birth time and location of various planets and constellations) and work on the assumption that small changes in the initial condition can have large effects on the life of the individual.

But there is more to these systems that that. Chaotic systems come in two shapes (source: Sapiens: A brief history of humankind). The weather, for example, is a level one chaotic system. Level one chaos is chaos that does not react to predictions about it.  Though it is influenced by myriad factors, we can build computer models that take more and more of them into consideration, and produce better and better weather forecasts.

Level two chaos is chaos that reacts to predictions about it, and therefore can never be predicted accurately. Markets, for example, are a level two chaotic system. What will happen if we develop a computer program that forecasts with 100 per cent accuracy the price of oil tomorrow? The price of oil will immediately react to the prediction and would consequently fail to materialise. (The mere act of predicting affects the outcomes)


Life, like markets are level two chaotic systems and the mere act of knowing your prediction based on horoscope reading immediately alters the system, rendering the prediction meaningless.

In defence of astrology against snakeoil salesmen

In continuation of the de-bunking of the astrology is pure science myth of the previous episode, I spent a sleepless night imagining what a logically sound explanation for the origin and prevalence of astrology might be. I do not claim to be the first to come up with the theory that I present below but I reckon that this could be the "science" behind astrology.

Evolutionary psychology, a branch of science that attempts to explain the origin of particular mental and psychological traits as the functional products of natural selection, shows that two important natural tendencies in humans are results of evolutionary pressures; namely,  

1.  agency (an event is caused by someone) and
2.  pattern recognition  

These traits are not confined to human species but we can understand the development and strengthening of these traits by imagining the forager experience. The first, agency, was essential for human survival as a threat identifier – you hear leaves rustle, you think there is a predator or competitor in the bushes. All early apes who thought that it was probably the wind got eaten quite rapidly. From a survival point of view, it is better to mistake the wind to be a lion, rather than the other way round. So this leads to a fairly basic heuristic – all things that happen are caused by someone.

Similarly, it is easy to imagine the need for pattern recognition. Humans do not develop pattern recognition because they are so special but rather because they aren’t. Home sapiens have not yet become the apex predator that he is now and is in the middle of the food chain. Pattern recognition, such as the hour at which deer or other prey goes to a particular watering hole or the location of predator territory are all basic survival strategies and are therefore adaptive. Adaptive traits gets passed along to the next generations, just like physiological traits such as opposable thumbs. Given that the early humans who are still hunter-gatherers have these tools in their toolbox helps them in their transition to farmers. It should be noted that modern anatomically correct homo sapiens are at least 200,000 years old but the beginning of farming is relatively recent – 11,000 years ago, representing just over 5% of the history of mankind.

The origin of pattern recognition as a predictive tool becomes even more essential for the farmer as his survival depends on knowing when is the right time to plant or harvest the newly domesticated crops. The passage of time which were basically separated as day-night and hot-cold needs further classification. The calendar is born and months and seasons are carefully divided to maximise their yield. But unpredictable events such as floods, droughts, pestilence occur fairly regularly. Here is where the adaptive traits of agency and pattern recognition result in the formation of certain beliefs – floods are caused by flood-gods and droughts by drought-gods. And appeasing these pagan gods with sacrifices (usually human sacrifices) results in the alleviation of their sorrow. Basically the heuristic is that I sacrificed a virgin at the altar of the flood god and three days later, the rains stopped. Post hoc ergo propter hoc. After this, therefore because of this. Confusing correlation to causation is one of the logical deficiencies intrinsic to the otherwise adaptive traits.Just because one observes a pattern does not necessarily mean that a pattern (with causal link) exists.

Simultaneously a predictive model however simplistic is born out of the hard-wired pattern recognition algorithm. The humans who had already become accustomed to marking the passage of time with celestial movements (sun marks day and night, lunar phase marks a month, etc) notice that particular human events occur after certain celestial events. The most famous example being comets, which were seen as harbingers of death and destruction (up until Newton and Halley). So, a simple model is developed – When planet A is in position B, x occurs.  This model is validated when the next time the planet is in the same position, x occurs again. Of course this doesn’t mean that the location of planet had caused the event to occur but merely that they were simultaneous. However, the model is brought to question, when the planet comes to position B the next time and x does not occur. The question then is what is different this time. Then one of the elders points that though planet A  is indeed in position B, planet C which used to be position D (when the event did occur) has now moved to position E (and the event did not occur).

Thus the model is updated at each instance that a given combination of inputs does not produce the expected outcome resulting in increasing complexity. More and more terms added to the equation. A simple three-body interdependent problem will yield

A1x1 + A2x2+ A3x3 + B1x1x2 + B2x1x3 + B3x2x3 + C1x1x2x3

It is like a Fourier series - the more terms you add the more complex and (probably) more accurate. We can therefore understand the sun signs system as a first order approximation, lunar sign system as a quadratic system. And each time we add a planet we increase the order of complexity.

We have what can be described an emergent phenomena where simple rules gives rise to an ordered behaviour in what is a complex, even chaotic system (some notes on deterministic and chaotic systems in next post). Then, predicting what is fundamentally an unpredictable multivariate phenomenon – the future of an individual - is analogous to the prediction of  planetary motion based on simple rules such as gravity. Astrology, then becomes  a predictive model not based on a causal relationship with position of stars - it is an analogous relationship. That is, two complex systems that are equally unpredictable can be solved with same algorithm. By studying the motion of celestial bodies, we study human behaviour -  as long as we can assume that the external and internal pressures in a multi body problem are analogous. Just as planets exert gravitational forces on each other, we can suppose that an individual has pressures and influences of different members of family, society, past, present and future. The planets are incidental to the prediction of the future. One could arguably use Game theory and computer programming to create a model of vectors of numerous interdependent variables to create an analogue but our ancestors did not have those luxuries. Instead they used the only analogue that they had access to and developed a phenomenological model based on observations of celestial phenomena that they updated or fine-tuned over at least 2000 years.  So one believes in astrology not because it is an exact science but because it is an iterative numerical model that has been around for long and has gone through enough iterations to be presumed accurate.

And that is the historical and scientific story of astrology that one could arguably use to believe in it.

But…

This version of history is not conducive for astrologers or the faithful. Firstly, it is important to understand that the democratisation of astrology is a recent phenomenon – astrological models were developed to predict large natural phenomenon. It is the same problem as using macro-economic models to predict individual behaviour. It simply doesn’t work. One can make fairly accurate predictions of populations of people but the models weren’t meant to and aren’t good to predict if I will impulse-buy a purple jumper on a Saturday afternoon in May next year. It is like the climate models that show global temperatures increasing over a period of years. One cannot use those models to predict if it will rain tomorrow. And the models aren’t technically disproved if you have a cold winter.

The second problem is of course that doing penance or visiting a temple dedicated to a particular planet is not going to make the planet forgive your sins or allow you to buy the Mini Cooper that you have always wanted. So the predictive models, while interesting intellectual exercises are not prescriptive. There is no ‘do this and everything will be fine’. Unfortunately.  We live in an indifferent universe. This is our future. The future is uncertain for the most part and the only thing we have is the now, this moment. And to spend this precious moment on hypothetical futures is futility. We could succeed. We will fail at times. We might be happy. We will be sad. Yes, Fear and especially the fear of the unknown is a strong emotion  and knowledge (however imperfect) can empower us. But it can just as easily lead us to fatalistic despair.  The only certainty is that we will definitely die. We will be forgotten. To quote one of my favourite authors’ view on oblivion -  “There will come a time when there are no human beings remaining to remember that anyone ever existed or that our species ever did anything. There will be no one left to remember Aristotle or Cleopatra, let alone you. Everything that we did and built and wrote and thought and discovered will be forgotten and all of this will have been for naught. Maybe that time is coming soon and maybe it is millions of years away, but even if we survive the collapse of our sun, we will not survive forever. There was time before organisms experienced consciousness, and there will be time after. And if the inevitability of human oblivion worries you, I encourage you to ignore it“  

Also, some infinities are bigger than other infinities.

In defence of science against the astrology snakeoil salesmen

It all started when my father ill-advisedly sent me this article on astrology

The crux of the argument was that astrology was pure science and that any failings that are there in the predictive capability is because the astrologer is not skilled at handling the complex calculations. This in itself is an old bit of excuse and it wouldn't have made any impact on me. But the author mentions things like neutrinos and tidal tugs and pissed me off enough to respond. In excruciating detail.

I would posit that whether astrology has physical basis or not, it is not a science. Even granting that the bulletproof argument that any failings that astrology has is not the fault of astrology but the imperfections of astrologer. 

Words have meanings. science has a very strict definition. Primary of these definitions of what makes science science is 'repeatability'. If I make the claim that the perforation force of a glass fibre sandwich composite is 5000 N (with s.d of 200 N), it means that if I test another composite plate tomorrow I expect it to be 5000 N. Another of the primary characteristics of science is user-independence. If my claim cannot be verified by another scientist using his equipment in another lab, then my claim is pretty useless. If the other scientist finds a perforation force of 2000 N, I can't with a straight-face say, "I am still right". Another feature of science is 'provability or disprovability'. If I make a claim that an unknown ray with unknown attributes is causing things to happen in unknown ways, but it is totally true, then it is not science. 

So even if we accept for arguments' sake that cosmic background radiation and neutrinos are perfect predictors of human destiny and the only problem is that we don't have capable astrologers to do all the math correctly, it still doesn't follow that astrology is science. believe, don't believe - i really don't care as long as you call it something else but science. 

And please don't joke around with terms like neutrinos or tidal tugs. sure to non-physicists these strategically placed jargon give the aura of true science but last time i checked the Higgs-Boson field does not cause tidal tugs on brains to emit neutrinos. here is more jargon to make your head spin - quantum mechanics, string theory, dark matter. Tachyons. Midichlorians.

Just so you know that I am not just being 'close-minded', I'll tell you what will make me a true believer. Let Nature, Science or The Astrophysical Journal publish an article that they have measured xrays, gamma rays, cosmic rays or whatever to affect the course of our lives because of the moment of our birth, I will, after critically reading those articles and not finding any leaps of faith, accept the scienciness of astrology. Well, I might even consider his arguments if Shivakumar can give me the link to the extraordinary claim that he has made (technically he has pointed that someone else has made a claim) that gravitational tugs has a measurable impact on brain of foetus. I regularly browse recent developments in cognitive neuroscience and I have friends who work in some of the best labs in the world on neural imaging. I have not heard of any scientific research that proves anything close to a done deal. In fact, I have spent the last hour on scientific databases and I can't find the research that they are referring to. 

So, what would take an open-minded person like you to question the validity of astrology?