Abhinav Sinha

Systems Thinking – Randomness vs Chaos

In Chaos Theory, Systems Thinking on August 16, 2010 at 3:36 pm

Just four articles old, I had already begun to face the writer’s block, till Bollywood came to my rescue. My last movie going experience was both entertaining and a stimulating one. This Friday, I watched the much anticipated, ‘Peepli Live’.

The story deals with the sensitive issue of farmer suicide, served to the taste of the mainstream audience with a dash of humor and satire. What made me mention the movie here is the chain of events that get rolling by a seemingly trivial issue.

For the benefit of those, who have not yet been to the theaters, the farmer brothers in the story are deep in debt, when they pick up the idea of a suicide. They see it as the easiest way out of their woes, as the government would pay the surviving family an amount of 1 lakh as compensation.

Their decision does not seem to change or influence anything big until their story is accidently picked by a local reporter and published. This triggers of a sequence of events that alters political equations both at the state and at the center, sends national media into a frenzy with army of reporters and cameraman camping at Peepli. The village, with all the attention that it is getting, turns into a land of opportunities for everyone from bangle sellers to coffee vendors from nearby areas.

One single event twisted a large part of the previously existing socio-political system. You will have to watch the movie to experience the pandemonium yourself but at the end of the movie I found myself wondering, whether what happened was just random sequence of events or was it chaos?

You might wonder what the difference is, anyways!

Let me bring in another example that almost each one of us would be aware of (even the non movie goers).

In the US presidential elections of 2000, the Palm Beach county supervisor of elections, Theresa LePore decided to make the typeface on ballots larger for Palm Beach voters, because many of her residents were older and had difficulty seeing small print. She did not notice that it now took two pages instead of one, and that could confuse voters about which button to push when they voted.

As a result 19,120 voters punched holes for both Pat Buchanan and Al Gore, and their ballots had to be thrown out. Another 3,407 people appeared to vote for Pat Buchanan, which he himself found most surprising, expecting only a couple of hundred votes. Ms. LePore’s new design caused about 22,000 votes for Al Gore to not be counted. If they had, Florida would have gone to Gore and he would have been the President of the United States. (Source – CNN News report)

Gore in turn would have likely signed the Kyoto protocol on global warming and probably not have declared war on Iraq. Of course, other things would certainly have happened that we cannot imagine.
What do we attribute such an outcome to? Chance, Randomness or Chaos?

Such condition where, small differences in the ‘initial condition’ of a dynamic system may produce large variations in the long term behavior of the system is called the ‘Butterfly Effect’ in the ‘Chaos Theory’.

There is frequent confusion between chaos and randomness. There are some similarities in the nature of chaotic and random system, but there are also some fundamental differences.

A random sequence of events is one in which anything that can ever happen, can happen next. A familiar example serving as a paradigm of randomness is the toss of a coin. Here either heads or tails, the only two things that can ever happen, can happen in the next throw. The probability of throwing a heads on the next toss is the same as in any other toss. Knowing in addition the outcome of last toss, cannot increase our chances of guessing the outcome of next toss.

On the other end, chaos consists of things that are actually not random, but only seem to be. Knowing the initial conditions well, there outcome can be determined by the known laws of scientific enquiry. But their dependence on the initial conditions is so high, that perfect determinism is a practical impossibility.

As it is popularly understood, chaos deals with unpredictable complex systems. Chaos theory studies how these systems, once thought to be completely random, actually contain hidden ordered patterns.

An example of a chaotic system is the weather forecasting system.

Chaos theory as a field of study in mathematics stems, in part, from the work of Edward Lorenz of MIT, a meteorologist, who simulated weather patterns on a computer. Working with a computer having limited memory, after viewing a particular pattern, he wanted to recover the data. He started the program again, except that this time he put in the initial values of temperature, air pressure, humidity etc. rounded off to 3 places after decimal instead of the original 6.

He was surprised to find a completely different result of weather patterns on his computer, than he had before. The sensitivity of initial conditions in a chaotic system is so high. that it is sometimes metaphorically quoted, that even a flutter of a butterfly’s wing somewhere over the deserts of Rajasthan can create a turbulence miles across, over the islands of Andaman!

This is how the ‘Butterfly effect’ has come to become a popular slogan of the chaos theory. If you make a error while dealing with a random system, the effect would be nothing significant as it would only lead us back to randomness. However, effect of small errors in initial condition of a chaotic system could be explosive.

The same principle applies to human society. Tiny changes in one person’s state of mind can, on occasions, lead to major changes in society as a whole. Or simple acts can lead to unintended consequences.
Chaos is important as it helps us to cope with dynamic, complex and unstable systems (like a few described above, including weather forecast) by improving our ability to describe, understand and even forecast them.

Another arena within which chaos theory is useful is that of organizations.

Applying chaos theory to organizational behavior allows strategists to take a step back from the management of day-to-day activities and see how organizations function as unified systems. An organization is a classic example of a nonlinear system (i.e., a system in which minor events have the potential to set off grave consequences or chain reactions, and major changes may have little or no effect on the system whatsoever).

In order to exploit the chaotic quality of an organization, one needs to try to see the organizational shape that emerges from a distance. Instead of pinpointing causes in the organization for organizational problems, the company is better served, according to chaos theory, by looking for organizational patterns that lead to certain types of behavior within the organization.

  1. This chaos theory is something new for me. I hope the theory could be of use in the disease prediction models which are mostly based on weather parameters such as temp., R.H., rainfall, cloudiness, dew etc. The presence or absence of pathogen propagules, the the inoculum load, physiological state of the pathogen and susceptibility/resistance of the host are other important factors that will govern epidemic build-up. I would be able to comprehend it better if the Chaos theory could be further elaborated in a situation of this type.

    • Dear Dr. Singh,

      You have indeed added another dimension to the applicability of the chaos theory.

      As far as my limited understanding of clinical biology and pathology goes, where chaos theory can help is in providing the young interns an understanding of the limits of predictability in a clinical situations.

      Carrying on from the weather prediction example, we know that the system remains chaotic yet within finite boundaries. We can be reasonably sure that it would be cold in Delhi in December and warm in May. However the predictability decreases sharply as we start getting into specifics.

      A stochastic mathematical model of the epidemic can be developed. This may incorporate factors like humidity, temprature etc. and factors such as number of contacts that an infected person makes with non-infected people, and the chances that the infection will be passed on during one of these contacts.

      Such models help us understand the factors that whether an epidemic is going to catch up and effect a large population or is it going to die down soon.

      Same model can also throw up scenarios that will emerge if lets say half the population was vaccinated.

      Other than epidemics, Chaos may some day soon help model the erratic cardiac rhythms. The pacemakers can start using technology that is derived from the stochastic models of cardiac rhythms during severe fibrillations.

  2. good one……..

  3. Well, thoughts well executed….. The brilliance of this article is that, the very thoughts which were coming to my mind while reading, were dealt with beautifully, in the following paragraphs…
    But one thing’s for sure that except for man made things like coin n dice, where one knows the number of possible outcomes there by claiming the system to be “random”, most of the incidents/events tends to be chaotic in nature since all of their possible outcomes are not known, leading to the very existence of “Butterfly Effect”.

    Now the crucial thing is if we can know and there by alter that tiny n seemingly insignificant event which has a potential to lead to large variations in the dynamic system in future, then we can hope for an organized, more evolved and much better world. Though we are aware about few tools which can do alterations in the event, though they are still a distant reality, like Time Machines, or a very recent tool of Idea Inception in mind, undertanding and knowing the very event, which has a potential of causing large variations, is still beyond our realm.

    • Hi Alakh!

      Many many thanks for the powerful words of encouragement and most importantly your participation in sharing your own views on the subject.

      While it may not be possible, with current set of tools to alter any event, post facto. The study of chaos theory certainly helps us in making informed predictions about the nature and behaviour of complex systems. The systems can ofcourse be a weather system or a social system like the one we live in.

      The chaos theory also makes us counscious of the limits of predicatbility in such systems. Please check my response to the comment made by Dr. Premjit Singh.

      An interesting fact:
      A friend of ours and a reader of this blog, informed me on email that there are DVD movie rental companies, who have been using models based on chaos theory to identify the choice of movies that their customers are likely to make and order.

      Knowledge is power! Think.

  4. Wonderful description, You should write a book !!

    • Thank you Suvi!

      Good to have an admirer and a subscriber of the blog like you! About the book, long way to go still.. but the motivating thought makes me feel really good!

  5. Interesting topic.. and a great linkage to Peepli Live!

    • Thanks Mayank!

      It feels good to find you in the reader’s list. Lot of motivation indeed! Would love if and when you choose to participate and share your thoughts as well!

  6. Very well written….

    • Thanks varun!
      The value of this effort would be best realized, if and when I am able to simulate a thought process amongst the readers. More importantly, invoke participation!

      Keep in touch and keep sharing!

  7. I have been working on randomness and chaos for the past 6 years by using a Roulette model and RNG. The concept has been converted to software applications. The latest version is currently under construction and will be posted on my website. The results are quite phenomenal! A clear distinction can be seen between chaos and randomness…the bottom line is this: our only reference is order. Order is only chaos with meaning and purpose maybe?!

  8. You have pertinently responded to my query. Most of the forecast models are based on the assumption that initial foci of infection are present. Once this assumption is satisfied, then the outcome of an infection can be more easily and accurately predicted using such models. However, if infection/disease is not to be found, or is not likely to develop in the near future, it is more difficult to to forecast an epidemic. I shall appreciate if you could give some guidelines on long term predictions and the techniques to be adopted to interpret data for such studies.

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