Thoughts to You from Yours Truly - ( TYYT ) - ( 97 ) - Theory of Chaos and Complexity
The most complicated of all structures in this universe is undoubtedly the human brain which consists of over 100 billion cells. The circuitry is so intricate with numerous feed-back loops that it can be considered as a classic example of a chaotic system. The human brain is the motivating force behind human behaviour and by analogy the grand motor of society. Therefore, the Theory of Chaos and Complexity is the most useful of all scientific theories in predicting behaviour in social and economic systems. Let us try to apply the theory socially and economically.
The significance of the theory in human behaviour lies in the fact that human beings are typical chaotic systems being very sensitive to changes in the initial conditions of the inputs affecting their behaviour. As mentioned above, the brain is such a huge chaotic machine with multiple feed-back loops that the predictions of the end results in terms of human behaviour are nearly impossible. However, the theory can predict the trend towards the possiblities of certain behaviour when certain key indicators reveal themselves in the behavioral patterns. An overall note of caution derived from the Theory of Chaos as applied to human affairs is, of course, to take absolute care before initiating any specific action. A corollary from this warning is not to take any action without thinking over its possible consequences.
The key to applying the rules of chaos in human behaviour in a group is to look for tell-tale signs of the key features of a chaotic or turbulent system which are :- the sink, the source, the saddle, the limiting cycle and the bifurcation point. Whenever there is a group of people there are bound to be different types of personalities present. There may be people who are centres of attraction for other people in the group. May be it is the result of their flamboyance or strong personalities. These are comparable to the concept of the sink. Then there may be those who are very keen to initiate some actions in the group. These are comparable to the concept of the source. Others are very often indecisive in their actions and sway between different opinions. These are comparable to the saddle. Still, there are some who prefer to form a small group on their own within the larger group and uphold the interests of the their own small circles. These are comparable to the limiting cycle where no successful policy can be implemented due to a fragmentation of the opinions and conflicts of interests arising between the smaller and the larger group. Finally, the most important feature to note in a small social group like a trade association or a social club is the bifurcation point. There may be some special events like an election of the governing body of the group that may trigger some upheaval such as a struggle for power and control. This situation is comparable to the emergence of the bifurcation point. Extra care should be taken to prevent the situation from deteriorating into a full blown chaos which may have serious ramifications on the stability and peaceful existence of the group as a whole. With different personalities and personal interests and values, it is very often a volatile situation. Any slight changes in the moods and preferences of the individual members of the group can gives rise to different initial conditions that can lead to chaotic and unpredictable results. That is why the Theory of Chaos has been successfully applied to social and economic phenomena.
The most complicated of all structures in this universe is undoubtedly the human brain which consists of over 100 billion cells. The circuitry is so intricate with numerous feed-back loops that it can be considered as a classic example of a chaotic system. The human brain is the motivating force behind human behaviour and by analogy the grand motor of society. Therefore, the Theory of Chaos and Complexity is the most useful of all scientific theories in predicting behaviour in social and economic systems. Let us try to apply the theory socially and economically.
The significance of the theory in human behaviour lies in the fact that human beings are typical chaotic systems being very sensitive to changes in the initial conditions of the inputs affecting their behaviour. As mentioned above, the brain is such a huge chaotic machine with multiple feed-back loops that the predictions of the end results in terms of human behaviour are nearly impossible. However, the theory can predict the trend towards the possiblities of certain behaviour when certain key indicators reveal themselves in the behavioral patterns. An overall note of caution derived from the Theory of Chaos as applied to human affairs is, of course, to take absolute care before initiating any specific action. A corollary from this warning is not to take any action without thinking over its possible consequences.
The key to applying the rules of chaos in human behaviour in a group is to look for tell-tale signs of the key features of a chaotic or turbulent system which are :- the sink, the source, the saddle, the limiting cycle and the bifurcation point. Whenever there is a group of people there are bound to be different types of personalities present. There may be people who are centres of attraction for other people in the group. May be it is the result of their flamboyance or strong personalities. These are comparable to the concept of the sink. Then there may be those who are very keen to initiate some actions in the group. These are comparable to the concept of the source. Others are very often indecisive in their actions and sway between different opinions. These are comparable to the saddle. Still, there are some who prefer to form a small group on their own within the larger group and uphold the interests of the their own small circles. These are comparable to the limiting cycle where no successful policy can be implemented due to a fragmentation of the opinions and conflicts of interests arising between the smaller and the larger group. Finally, the most important feature to note in a small social group like a trade association or a social club is the bifurcation point. There may be some special events like an election of the governing body of the group that may trigger some upheaval such as a struggle for power and control. This situation is comparable to the emergence of the bifurcation point. Extra care should be taken to prevent the situation from deteriorating into a full blown chaos which may have serious ramifications on the stability and peaceful existence of the group as a whole. With different personalities and personal interests and values, it is very often a volatile situation. Any slight changes in the moods and preferences of the individual members of the group can gives rise to different initial conditions that can lead to chaotic and unpredictable results. That is why the Theory of Chaos has been successfully applied to social and economic phenomena.
Similar analytical procedures are applicable to financial and economic
behaviour. Investment activities in the stock market and other financial instruments are as
unpredictable as the weather because they are all chaotic systems. The traditional
methods of predicting trends in stock prices based on past data are less than reliable
because very minor changes in the conditions at any particular point on the stock prices
graph can lead to unpredictable results on account of the chaotic nature of investor
behaviour. There was a remarkable story from a well known sharebroker firm on Walls
Street in New York City. A competition was held between two brokers to predict which
shares will rise in prices and which shares will fall in prices. One broker was allowed to
use the high-tech program in a computer for prediction while the other simply used the
primitive method of random chance by throwing a dart onto a list of shares printed on a
sheet of paper glued to the office wall. The results from predicting 100 different shares on
the market using these two radically different methods came out to be more or less a draw.
It almost sounds like a big joke. There are simply too many illusive and related factors with
multilateral feed-back loops to allow a comprehensive and reliable forecast in the financial
market. The Financial Times newspaper once said that :- “ It is a conventional joke that
there are as many different opinions about the future of the economy as there are
economists.”
Having revealed the unpredictable nature of the financial market, there is still some saving grace that is bestowed by the Theory of Chaos and Complexity and that is “ Order in Chaos.“ Let us see how this can come about in the present example. While it remains generally true that economic or financial forecasts are at best guesstimates, there are a few rules which can point us to the right direction. Although a simple projection of the past results to a predicted future trend is not feasible and unreliable, we are reassured by the theory that Past History in the system under prediction is of paramount importance. This is rule number one. In fact, this is where social or behavioral sciences are different from the physical sciences. The latter are not affected by history as you will recall Einstein's all important postulate on the validity of the laws of physics in all frames of references. Secondly, the effects of this past history very often obey a set rules known as the Power Law. Mark Buchanan explains this quite convincingly in his book, “ Ubiquity “ that this Power Law is at work from earthquakes, forest fires, epidemics to money markets which are our present concern. Moreover, this Power Law is the manifestation of Scale Invariance which is the essential element behind the concept of Complexity as revealed in natural phenomena such as the snowflake, natural coastlines, leaves and clouds.
Rather unexpectedly, Mandelbrot also tried to apply his scale invariance concept to price changes in the stock market. He found a very important fact which is contrary to the prevailing beliefs of almost all shareborkers and investment consultants regarding share price changes. It has been a firm traditional belief that price changes greater than some typical size ought to be very rare. This is also in line with our common sense but Mandelbrot had found otherwise. In the 1990s, scientists conducted numerous exhaustive computer research into fluctuations in the stock and foreign exchange markets all over the world and have definitively confirmed that the power rule is actually at work in such systems. To be more specific, one such illuminating research was conducted on the
Having revealed the unpredictable nature of the financial market, there is still some saving grace that is bestowed by the Theory of Chaos and Complexity and that is “ Order in Chaos.“ Let us see how this can come about in the present example. While it remains generally true that economic or financial forecasts are at best guesstimates, there are a few rules which can point us to the right direction. Although a simple projection of the past results to a predicted future trend is not feasible and unreliable, we are reassured by the theory that Past History in the system under prediction is of paramount importance. This is rule number one. In fact, this is where social or behavioral sciences are different from the physical sciences. The latter are not affected by history as you will recall Einstein's all important postulate on the validity of the laws of physics in all frames of references. Secondly, the effects of this past history very often obey a set rules known as the Power Law. Mark Buchanan explains this quite convincingly in his book, “ Ubiquity “ that this Power Law is at work from earthquakes, forest fires, epidemics to money markets which are our present concern. Moreover, this Power Law is the manifestation of Scale Invariance which is the essential element behind the concept of Complexity as revealed in natural phenomena such as the snowflake, natural coastlines, leaves and clouds.
Rather unexpectedly, Mandelbrot also tried to apply his scale invariance concept to price changes in the stock market. He found a very important fact which is contrary to the prevailing beliefs of almost all shareborkers and investment consultants regarding share price changes. It has been a firm traditional belief that price changes greater than some typical size ought to be very rare. This is also in line with our common sense but Mandelbrot had found otherwise. In the 1990s, scientists conducted numerous exhaustive computer research into fluctuations in the stock and foreign exchange markets all over the world and have definitively confirmed that the power rule is actually at work in such systems. To be more specific, one such illuminating research was conducted on the
New York Stock Exchange in 1998 by Gene Stanley of Boston University based on price
fluctuations of all the shares included in the Standard & Poor's 500 stock index. Stanley
and his team studied prices recorded every 15 seconds over a period of 13 years from
1984 to 1996. There were a total of 4.5 million readings taken for his graph depicting this
13 years' trend showing very complicated and irregular ups and downs. The researchers
found an underlying Power Rule behind all these crazy fluctuations. What they found was
that price changes became 16 times less likely each time one doubles the size of such
price changes. This applies to the New York Stock Exchange only while other markets
may be governed by power rules of different magnitudes. As mentioned above, as far as
the power rule goes it is not the number or quantitative side that is important. Rather, it is
the qualitative aspect that is critical. The clear conclusion to be drawn from this lack of
qualitative differences between the large and small fluctuations is that the power rule
inevitably implies that there is no such thing as a typical fluctuation and, hence, no reason
to assume that the larger fluctuation can be considered as abnormal. This is because
there is no such thing as normality in any chaotic system. In the technical terms of Chaos
and Complexity, there is Scale Invariance in the Stanley's graph depicting the share price
changes meaning all fluctuations whether large or small are ultimately made up of similar
patterns just like when you are magnifying the finer details of the coastline. All coastlines
in the world are composed of bays and inlets separated by headlands. Scale invariance
as applied to the stock market can be translated to mean that the investor should not be
surpised by sudden huge upward or downward fluctuations in share prices for no apparent
reasons at all. The simple reason is that large fluctuations can be expected in the same
way as a small fluctuation since there is no such thing as normality in the market. The fact
that you occasionally guess correctly on the price increase or fall based on all available
market information ( there is, of course, no perfect information as there is no perfect
market ) is merely a matter of serendipity. From the foregoing, you may now appreciate
why the throwing of darts and the use of a computer program to predict share price
changes can come out even handed. Further analysis of investor behaviour will be
forthcoming in the next chapter on the Science of Networks. Meanwhile, let us proceed to
other seemingly eccentric applications of the Theory of Chaos and Complexity.
The key concept and the most useful one revealed by the theory is “ Order in Chaos “ which is the crowning glory of this scientific theory. It has an almost universal application because chaotic systems are all over the place in our society. Without going into the details of the particular scientific research, we are given to understand that the following power rules apply to various natural phenomena as indicated. For earthquakes as measured by the Richter Scale, scientists have discovered that for earthquakes with twice the energy level of another it has 4 times less likelihood of occurring. It appears to be a square rule. Furthermore, the longer one waits for an earthquake to occur the longer one seems to have to wait for the next. Although this seems to be against our common sense yet this has been borne out by the Omori Law in seismology which has established that the waiting time for an earthquake is 2.6 times more if the period of non-occurrence is doubled. Finally, the initial movement in the earth's crust leading to any particular quake is usually irrelevant to the end results. That means a catastrophic earthquake can start as a minor tremor. The catastrophic result depends on the appearance of Critical State ( similar to Bifurcation Point ) which in turn is dependent on the Past Histrory of the build-up of the seismic tension in the related rock strata. Any system that obeys the Power Rule has no normal or typical behaviour. In other words, they are all chaotic systems.
Another example is forest fires. Based on over 4000 fires in national parks between 1986 and 1995, the US Fish and Wildlife Service found a fairly reliable power rule. Every time the area covered by a fire doubles, it is about 2.48 times less likely to happen. This power rule holds true for fires varying in sizes to a million fold. The qualitative indications of this rule seems equally stunning. The layout of trees in any particular park appear to organize themselves into a Critical State in which the next fire might be of any size that can lead to a big disaster or even total destruction of the area.
One final important example of the amazing predicting ability of the Power Rule is the KT Event that caused the distinction of the dinosaurs. This mass extinction event took place some 65 million years ago. KT comes from the words Cretaceous ( in German, Kreide ) and the later period of Tertiary.It was caused by a huge meteor 's impact on our planet. Apart from KT there were 4 big extinction events in earth's natural history so far. Going backwards in time, they happened 210, 250, 365 and 440 million years ago. The power rule they revealed is this. If you double the size of the extinctions the disaster is 4 times less likely to happen. This regularity holds true from extinctions involving just a few species to the worst event destroying thousands. The rule does not tell us when just how often with no numerical data in terms of years.
The key concept and the most useful one revealed by the theory is “ Order in Chaos “ which is the crowning glory of this scientific theory. It has an almost universal application because chaotic systems are all over the place in our society. Without going into the details of the particular scientific research, we are given to understand that the following power rules apply to various natural phenomena as indicated. For earthquakes as measured by the Richter Scale, scientists have discovered that for earthquakes with twice the energy level of another it has 4 times less likelihood of occurring. It appears to be a square rule. Furthermore, the longer one waits for an earthquake to occur the longer one seems to have to wait for the next. Although this seems to be against our common sense yet this has been borne out by the Omori Law in seismology which has established that the waiting time for an earthquake is 2.6 times more if the period of non-occurrence is doubled. Finally, the initial movement in the earth's crust leading to any particular quake is usually irrelevant to the end results. That means a catastrophic earthquake can start as a minor tremor. The catastrophic result depends on the appearance of Critical State ( similar to Bifurcation Point ) which in turn is dependent on the Past Histrory of the build-up of the seismic tension in the related rock strata. Any system that obeys the Power Rule has no normal or typical behaviour. In other words, they are all chaotic systems.
Another example is forest fires. Based on over 4000 fires in national parks between 1986 and 1995, the US Fish and Wildlife Service found a fairly reliable power rule. Every time the area covered by a fire doubles, it is about 2.48 times less likely to happen. This power rule holds true for fires varying in sizes to a million fold. The qualitative indications of this rule seems equally stunning. The layout of trees in any particular park appear to organize themselves into a Critical State in which the next fire might be of any size that can lead to a big disaster or even total destruction of the area.
One final important example of the amazing predicting ability of the Power Rule is the KT Event that caused the distinction of the dinosaurs. This mass extinction event took place some 65 million years ago. KT comes from the words Cretaceous ( in German, Kreide ) and the later period of Tertiary.It was caused by a huge meteor 's impact on our planet. Apart from KT there were 4 big extinction events in earth's natural history so far. Going backwards in time, they happened 210, 250, 365 and 440 million years ago. The power rule they revealed is this. If you double the size of the extinctions the disaster is 4 times less likely to happen. This regularity holds true from extinctions involving just a few species to the worst event destroying thousands. The rule does not tell us when just how often with no numerical data in terms of years.
These three examples are just a few among the numerous ones including
more mundane things such as magnets, sand pile avalanches, potato shards experiments,
epidemics, population growth and even population distribution, etc. Despite the lack of
prediction in absolute quantitative terms, concepts such as Order in Chaos, Past History
and Citical State do testify in favour of the existence of Universality and Ubiquity in our
universe. This alone sends us a very important message and that is, this miraculous world
of ours is ultimately comprehensible to a great extent. One word of caution is in order. My
personal opinion regarding certain mathematical models used to simulate the emergence
of life is that they are as yet rudimentary and have a long way to go before I am convinced
that it was the actual course taken by life on this planet of ours if life originated on Mother
Earth at all. Einstein once said :- “Things should be made as simple as possible, but not
simpler. “ No other comment can describe the Theory of Chaos and Complexity more
aptly. The theory gives us qualitative trends and indicators to follow but the Golden Rule is
nothing but a qualitative Power Rule and here lies the real revolutionary nature of the
theory. Ever since the establishment of modern science in the Age of Reason some four
hundred years ago everything about science and scientific theories have been nothing but
quantitative. Finally, we are offered a qualitative approach to science through the Theory
of Chaos and Complexity. This has not only broadened the scope of the discipline by
making illusive phenomena accessible to science but has also provided a very powerful
tool to analyze complex human behaviour and social phenomena.
