The Butterfly Effect
Scientists during the posts war prosperous years of the 1960s were puzzled about certain dynamic systems such as the weather and fluid turbulence because of their inability to predict the behaviours of such systems. They reasoned that if science could predict the exact dates for the return of Halley's Comet many times over and right to the dot ( Halley's Comet has a circuitous cycle of 76 years ) there should not be any reason why such earthly thing as the weather could not be understood. It turned out that the marvel of a new and universally applicable theory was surprisingly born out of the chaos of the weather. This is a fine example of ' order out of chaos '.
Edward Lorenz was a mathemathician graduated from Dartmouth College in 1938. During World War Two he served in the Army Air Corp as a weather forecaster. He remained working in the field of meteorology after the war. Back in the 1960s even meteorologists treated weather forecasting as educated guesses. So much so that the European Centre for Medium Range Forecasts made the suggestions to scrap weather forecasting altogether to save billions of taxpayers' hard-earned dollars. The centre considered that beyond three days even the world's best forecasts were purely speculative and beyond a week such forecasts would be without any value. Luckily, the appearance of the modern day computer invented by John von Neumann came to the rescue by making rudimentary weather forecast modelling viable. So, the meteorologists kept their job.
There was one Archilles' heel in the scientific method and that is all scientific theories ignore small influences which are supposed to have only insignificant effect on the validity of the predictions of any theory. This method of approximation can easily be seen in the working of the all important mathematical tool of calculus invented by Newton. Small incremental steps are approximated to form a continuous mathematical function. While science is renowned for its logic and precision, it is, in fact, full of approximations and only projects an image of perfection. This is an Archilles' heel because small influences can only be ignored in classical systems which are dominated by linear relationships. In the case of complicated systems with non-linear relationships and feed-back loops and interacting variables even slight changes in their initial conditions can lead to unpredictable results. Such systems which are very sensitive to extremely minute variations in their initial conditions have been called chaotic systems since the introduction of the concept of chaos by Edward Lorenz.
Returning to Lorenz's theory, it was discovered by him in 1961 almost by accident but due credit must be given to him for his shrewd observation and sharp instinct. He was working on his weather forecasts modelling on his first generation computer with a low processing speed. Even with the help of computer modelling, there was no breakthrough. One day during 1961, Lorenz was trying to reproduce just one section of specific data corresponding to a particular time period for further analysis away from the office. Instead of reproducing the data for a whole month from the beginning, he decided to take a short cut by just feeding in the data of the week he wanted based on old printouts. All hardware and software in his computer remained unchanged. To his complete surprise, he came back from his coffee break to find a totally different result from the original printout copy. He immediately took the cue, for a chaotic system like the weather, the final results depended on each and every step of its past history and even seemingly negligible changes in its initial conditions would lead to unpredictable final positions. This was the beginning of the Theory of Chaos with a little kind help from serendipity.
The slight variations in the initial conditions that lead to the final unpredictable chaos and turbulence are commonly known as the Butterfly Effect meaning a sensitive dependence on initial conditions. It is so called because it is said that in theory the flapping of a butterfly's wings in South America can ultimately lead to a hurricane in the Carribbean. This is how it is supposed to happen. When a butterfly flaps its wings this can create a slight depression in the atmosphere around the butterfly. Here is the key concept. When the surrounding conditions are right this small depression will grow into an atmospheric depression that may move out to the ocean to pick up more energy from the evaporating water upon their condensation in the upper atmosphere.This energy originates from the latent heat released by the water vapour when it changes from its gaseous state back to liquid form as rain in the upper atmosphere upon condensation. When the differential between the pressure distributions in the ocean and land mass are big enough a huge turbulence can be formed in the depression as a result of cooler air from high pressure regions with higher density rushes into the depression to fill up the relatively low density areas in an attempt to even out the differences. You must have seen the formation of a turbulent eddy when you try to empty a bath tub by pulling the stopper plug at its bottom. The drain pipe under the plug is the low depression area because it is hollow and provides the space for the water in the tub to go under gravity. As the huge body of water in the tub as compared to the relatively small drain hole scrambles for exit towards the drain pipe, a huge turbulent swirl of water is formed on the water surface above the drain hole. This is a comparable feature to the hurricane. Therefore, the Butterfly Effect represents the small change in the initial conditions of a chaotic system which in conjunction with the numerous existing appropriate conditions including the peculiarities of the past history in the system working in synch in a very complex and unpredictable manner to give rise to the resultant chaotic turbulence such as a hurricane. Not every flap of a butterfly's wing will result in a hurricane but when the conditions are right a hurricane can be born of the flutter of a butterfly's wings.
Recently, there was a new movie in the cinemas called “Butterfly Effect”. It is a sci-fi story dealing with changes in a person's past history and their strange effects on the present. It gives a completely erroneous concept of the Butterfly Effect as applicable to the science of Chaos. I just feel that this is a fair warning to the readers in case they have been misled. The Theory of Chaos is, in fact, an attempt to identify the signs and to understand the working characteristics of chaos. In other words, it is a theory to discover the order in chaos !
Scientists during the posts war prosperous years of the 1960s were puzzled about certain dynamic systems such as the weather and fluid turbulence because of their inability to predict the behaviours of such systems. They reasoned that if science could predict the exact dates for the return of Halley's Comet many times over and right to the dot ( Halley's Comet has a circuitous cycle of 76 years ) there should not be any reason why such earthly thing as the weather could not be understood. It turned out that the marvel of a new and universally applicable theory was surprisingly born out of the chaos of the weather. This is a fine example of ' order out of chaos '.
Edward Lorenz was a mathemathician graduated from Dartmouth College in 1938. During World War Two he served in the Army Air Corp as a weather forecaster. He remained working in the field of meteorology after the war. Back in the 1960s even meteorologists treated weather forecasting as educated guesses. So much so that the European Centre for Medium Range Forecasts made the suggestions to scrap weather forecasting altogether to save billions of taxpayers' hard-earned dollars. The centre considered that beyond three days even the world's best forecasts were purely speculative and beyond a week such forecasts would be without any value. Luckily, the appearance of the modern day computer invented by John von Neumann came to the rescue by making rudimentary weather forecast modelling viable. So, the meteorologists kept their job.
There was one Archilles' heel in the scientific method and that is all scientific theories ignore small influences which are supposed to have only insignificant effect on the validity of the predictions of any theory. This method of approximation can easily be seen in the working of the all important mathematical tool of calculus invented by Newton. Small incremental steps are approximated to form a continuous mathematical function. While science is renowned for its logic and precision, it is, in fact, full of approximations and only projects an image of perfection. This is an Archilles' heel because small influences can only be ignored in classical systems which are dominated by linear relationships. In the case of complicated systems with non-linear relationships and feed-back loops and interacting variables even slight changes in their initial conditions can lead to unpredictable results. Such systems which are very sensitive to extremely minute variations in their initial conditions have been called chaotic systems since the introduction of the concept of chaos by Edward Lorenz.
Returning to Lorenz's theory, it was discovered by him in 1961 almost by accident but due credit must be given to him for his shrewd observation and sharp instinct. He was working on his weather forecasts modelling on his first generation computer with a low processing speed. Even with the help of computer modelling, there was no breakthrough. One day during 1961, Lorenz was trying to reproduce just one section of specific data corresponding to a particular time period for further analysis away from the office. Instead of reproducing the data for a whole month from the beginning, he decided to take a short cut by just feeding in the data of the week he wanted based on old printouts. All hardware and software in his computer remained unchanged. To his complete surprise, he came back from his coffee break to find a totally different result from the original printout copy. He immediately took the cue, for a chaotic system like the weather, the final results depended on each and every step of its past history and even seemingly negligible changes in its initial conditions would lead to unpredictable final positions. This was the beginning of the Theory of Chaos with a little kind help from serendipity.
The slight variations in the initial conditions that lead to the final unpredictable chaos and turbulence are commonly known as the Butterfly Effect meaning a sensitive dependence on initial conditions. It is so called because it is said that in theory the flapping of a butterfly's wings in South America can ultimately lead to a hurricane in the Carribbean. This is how it is supposed to happen. When a butterfly flaps its wings this can create a slight depression in the atmosphere around the butterfly. Here is the key concept. When the surrounding conditions are right this small depression will grow into an atmospheric depression that may move out to the ocean to pick up more energy from the evaporating water upon their condensation in the upper atmosphere.This energy originates from the latent heat released by the water vapour when it changes from its gaseous state back to liquid form as rain in the upper atmosphere upon condensation. When the differential between the pressure distributions in the ocean and land mass are big enough a huge turbulence can be formed in the depression as a result of cooler air from high pressure regions with higher density rushes into the depression to fill up the relatively low density areas in an attempt to even out the differences. You must have seen the formation of a turbulent eddy when you try to empty a bath tub by pulling the stopper plug at its bottom. The drain pipe under the plug is the low depression area because it is hollow and provides the space for the water in the tub to go under gravity. As the huge body of water in the tub as compared to the relatively small drain hole scrambles for exit towards the drain pipe, a huge turbulent swirl of water is formed on the water surface above the drain hole. This is a comparable feature to the hurricane. Therefore, the Butterfly Effect represents the small change in the initial conditions of a chaotic system which in conjunction with the numerous existing appropriate conditions including the peculiarities of the past history in the system working in synch in a very complex and unpredictable manner to give rise to the resultant chaotic turbulence such as a hurricane. Not every flap of a butterfly's wing will result in a hurricane but when the conditions are right a hurricane can be born of the flutter of a butterfly's wings.
Recently, there was a new movie in the cinemas called “Butterfly Effect”. It is a sci-fi story dealing with changes in a person's past history and their strange effects on the present. It gives a completely erroneous concept of the Butterfly Effect as applicable to the science of Chaos. I just feel that this is a fair warning to the readers in case they have been misled. The Theory of Chaos is, in fact, an attempt to identify the signs and to understand the working characteristics of chaos. In other words, it is a theory to discover the order in chaos !
