The Strange story of how there is order in chaos!
Understanding chaos in labelling a "patient"
We all know diabetes, hypertension and increased cholesterol are bad for our health. So its only natural to assume that rigorous control of these values should be good for our health, isn't it?
The ACCORD (Action to Control Cardiovascular Risk in Diabetes) study(www.accordtrial.org) was a US federal government sponsored blinded prospective randomised control study of ten thousand adults with established type 2 diabetes who are at especially high risk of cardiovascular disease. The patients were divided into two groups, one in which diabetes was aggressively controlled ( HBA1c less than 6) and other in which HBA1c was maintained between 7 to 7.9. Based on hypertension treatment also they were grouped into two. Aggressive control group (
Results which came out in 2010 showed that both the aggressive control groups had increased mortality rates. The significance was so high in the diabetic treatment group that the study had to stopped and the aggressive control arm was switched over to normal treatment. What went wrong? The answer lies partly in chaos. Lets see how..
Met department gets it wrong again on monsoon
Forecasting the southwest monsoon is not easy. Till date in the 137 year history of the Indian Meteorological Department, which operationally forecasts the monsoon, has never succeeded in correctly predicting the extremes. To put this in perspective, for 137 years the Indian weather office has never ever been able to predict a drought. In last 100 years, more than 85 per cent of the time the monsoon has been normal. So the chances of a normal monsoon are always high. For last two decades, the IMD has invariably only forecast “normal” monsoons despite the huge variations India has witnessed in bad years like the massive flooding of 1994, and the droughts of 1987, 2002, 2004 and 2009. So is it that the Indian met guys are not upto the mark? Well, interestingly, for the 2012 season, the new numerical model imported from the United States actually predicted a surplus rainfall.
So why can't we predict weather?
Prediction of extreme events is a problem since models that are used for this are faulty, in other words they tend to normalise things. Weather doesn't follow a normal distribution. What it follows can be best explained by chaos theory
What's this chaos theory?
Well to explain it first we should be clear in our mind what it isn't about. In a scientific context, the word chaos has a different meaning than it does in its general usage. in our daily usage we use the word chaos to describe a state of confusion, lacking any order . But a chaotic system is not a random disorderly system without any underlying order. A chaotic system can appear like its random and disorderly though it does have underlying order in its core
In other words chaos theory doesn't mean that complex looking systems like weather, shapes of clouds , evolution etc are unpredictable because they are affected by too many factors and hence have a very complicated mechanism underlying them.
On the other hand , what chaos theory says is that these systems have a simple underlying order which are prone to have an unavoidable element of error/ uncertainty inbuilt in them when we analyse / measure them . When these simple systems then go on to make complex systems by repeating themselves, the error / uncertainty will also increase exponentially making the end result unpredictable. The mathematical word for repetition is Iteration. To iterate means to repeat an operation over and over.
Chaos technical jargon
"Deterministic, nonlinear, dynamical systems" is the correct mathematical terminology for chaotic systems.
Dynamic means any system that changes with time.
Deterministic means these systems have an underlying order in them. Again in contrast to what we mean in common language deterministic doesn't mean something thats predictable but something that follows an underlying order.
Non linear means that output ( end result) isn't directly proportional to input, or that a change in one variable doesn't produce a proportional change or reaction in the related variable(s).
So in short chaotic systems are ones which evolve with time ( dynamic) which have a perfectly understandable mechanism (deterministic ) whose end result as time progresses is unpredictable ( non linear).
So, What are the key features of a chaotic system?
1. Chaos results from a simple orderly deterministic process that’s repeated over and over.
2. It happens only in nonlinear systems.
3. The end result looks disorganised and erratic. it can usually pass all statistical tests for randomness.
4. It happens in feedback systems—systems in which past events affect today's events, and today's events affect the future.
5. It doesn't require an external noise or disturbance to make it chaotic. For given conditions or control parameters, it's entirely self-generated. In other words, changes in other (i.e. external) variables or parameters aren't necessary. So a chaotic system is not a linear predictable system that became corrupted.
6. A chaotic system is not because of any statistical error such as sampling error or measurement error. In others words it's not a linear system that's misunderstood
7. Details of the chaotic behaviour are hypersensitive to changes in initial conditions (minor changes in the starting values of the variables).
8. Forecasts of long-term behaviour are meaningless. The reasons are sensitivity to initial conditions and the impossibility of measuring a variable to infinite accuracy.
9. Short-term predictions, however, can be relatively accurate.
What causes chaotic behaviour?
In-spite of knowing the simple event/ system which caused the complicated system / behaviour, wewon't be able to predict the characteristics of the complex system due to the inbuilt error/ uncertainty in the simple event that started it . This known as the butterfly effect or sensitive dependence on initial conditions, which many consider to be the cause of chaotic behaviour
Sensitive dependence on initial conditions (butterfly effect) means that a seemingly insignificant difference in the starting value of a variable can, over time, lead to vast differences in output. Measurement error, noise, or roundoff in the data values are the usual causes of this. For eg, computers, in particular, are susceptible to sensitivity to initial conditions because of their binary system, operating system, software details, the way they are built, and so on.
So as James Gleick put it, chaos in nothing but "Order masquerading as randomness" or to paraphrase Richard Kautz , "chaos is predictable random motion!" Now that sounds like an oxymoron, but it isn't . how can one predict something that's random?.
In short, complex systems like weather pattern , stock market behaviour, shapes of trees , maps of continents , occurrence of earth quakes, shapes of clouds and ice flakes have an underlying order which will be simple. But understanding this simple elements wont help in predicting the behaviour of the concerned system.
Why should one try to understand whether a system is chaotic or not?
1) Once we understand that a random looking phenomenon is chaotic, then that means there's a discoverable law involved, and a promise of greater understanding of underlying mechanism.eg; fractals in formation of shapes of clouds, trees, shape of continents, (keep in mind though that this doesn't mean we can predict these shapes in long term)
2) Identifying chaos can lead to greater accuracy in short-term predictions and at same time we can confidently say that long-term forecasting is largely meaningless.
3) Once we have understood the basic principles of chaos theory we have to modify what we expect when we deal with these complex non linear systems. For eg; The basis of weather forecasting is looking from a satellite and seeing a storm coming, but not predicting that the storm will form
Chaos in medicine
Just controlling one number doesn't decrease mortality/ morbidity risk. ACCORD study is the classical example. It showed that over enthusiastic maintenance of numerical limits like glycated Hb below 7, BP of 120 / 80 or cholesterol value less than 200 doesn't significantly reduce risk of mortality . Just cuz we know the mechanism by which say increased glucose levels, lipid levels or hypertension can harm our arteries doesn't mean we can easily predict their impact in from of a single number
Another major issue of making cut off marks like above is that these values are in fact really close to the normal mean value of population. This means that a huge percent of normal population suddenly becomes "patients". Now once diagnosed as patient, you have to medications for the "disease". So one leads to another and wide spread usage of certain drugs are started which inturn does more harm than good as the rare adverse effects of these drugs (eg; fragility fractures in bisphosphonate therapy) becomes not so rare entities .
In short not understanding chaos can deceive clinician and patient into inverting the risk benefit ratio of treatment modalities
So now it's clear why all surgical instruments are routinely checked / replaced after specific time periods even though they are working quite well. It's because we are unable to detect or avoid all butterfly wing flappings that will later during repetitive (iterations) usage through chaos theory mechanism present as a random catastrophic event
How has chaos theory changed the way we view world around us?
Realising that a simple, deterministic equation can create a highly irregular or random system has forced us to reconsider and revise the long-held idea of a clear separation between determinism and randomness. In other words, many of what we thought were random processes have turned out to be not so random in the sense that they have an underlying order
The separation between determinism and randomness have definite philosophical undertones.Determinism is a philosophy that says that for everything that we decide or do there are conditions such that, given them, we could have decided or done nothing else. This is often contrasted withconcept of free will which assumes we have ability to make random choices free of constraints.
Chaos shows how something that’s very deterministic in its origin can have a random appearance in the end. This concept throws light on origins of what we feel as free will
Moral of the story
So, the lesson one learns from understanding chaos is that knowing in depth about something doesn't necessarily mean one can predict its future with reliable certainty. The inverse too is true, just because something looks like random doesn't mean its random and hence there is no point in studying it!
To conclude one can say, chaotic systems though are deterministic in root cause become probabilistic as they iterate and appear as random. So its important when we deal with systems not only to know the underlying mechanisms, but also to know in-spite of their basic ,mechanisms, whether they are deterministic or probabilistic as they evolve. Physics , chemistry are deterministic sciences while medicine and social sciences like economics, politics, epidemiology & geographical sciences are probabilistic in nature due to chaos.
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