XIII I: Role of Mathematics behind disorder in nature.
[Contd. A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri.]
" Chaos is the score upon which reality is written"-----Henry Miller.
Up till now we observed that the natural world in which we live and an inseparable part,is essentially orderly.The laws of physics and other sciences along with dictum of mathematics are followed there satisfactorily. We call them " laws of nature". But does nature always obey rules or in other words can we predict nature? For example,can we predict whether will it be raining? It can be said if it will happen within few minutes or even within an hour but not possible to predict it for the next twenty four hours or within few days.
There were many discoveries of paramount importance in the world of science during the last two centuries.As a result,now we are able to predict many events which were once unpredictable. But we should not be complacent and over confident about our power of prediction and explanation of cause and effects of all natural events.In this context the remark of the great French mathematician Laplace (1749--1827) is worthy to note,"If we were to know with precision the position and speeds of all the particles in the universe then we could predict the future with certainty." This is echoed in the "uncertainty principle" of the renowned German physicist Werner Heisenberg articulated in1927 which states that:The position and the velocity of an object can not both be measured exactly,at the same time,even in theory
There were two epoch-making,astounding and even puzzling discoveries in the early part of the twentieth century. One of them is:Theory of Quantum Mechanics advocated by Max Plank .The other is Theory of Relativity propounded by the greatest scientist of this century Albert Einstein.The quantum world is extremely bizarre.Can you imagine that you may be present at a number of places at the same time? Or can you think that something may appear all on a sudden from an empty space and then disappear again like a ghost? Yes all these are possible in a quantum field, of course for minutest particles with which this world is made of.
So how funny and ghostly is this world in which we live!
Then just imagine the extent of ignorance and helplessness of common people like us,in this quantum world.So are we not in an utter quandary in predicting laws of nature?
[Contd. A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri.]
" Chaos is the score upon which reality is written"-----Henry Miller.
Up till now we observed that the natural world in which we live and an inseparable part,is essentially orderly.The laws of physics and other sciences along with dictum of mathematics are followed there satisfactorily. We call them " laws of nature". But does nature always obey rules or in other words can we predict nature? For example,can we predict whether will it be raining? It can be said if it will happen within few minutes or even within an hour but not possible to predict it for the next twenty four hours or within few days.
There were many discoveries of paramount importance in the world of science during the last two centuries.As a result,now we are able to predict many events which were once unpredictable. But we should not be complacent and over confident about our power of prediction and explanation of cause and effects of all natural events.In this context the remark of the great French mathematician Laplace (1749--1827) is worthy to note,"If we were to know with precision the position and speeds of all the particles in the universe then we could predict the future with certainty." This is echoed in the "uncertainty principle" of the renowned German physicist Werner Heisenberg articulated in1927 which states that:The position and the velocity of an object can not both be measured exactly,at the same time,even in theory
There were two epoch-making,astounding and even puzzling discoveries in the early part of the twentieth century. One of them is:Theory of Quantum Mechanics advocated by Max Plank .The other is Theory of Relativity propounded by the greatest scientist of this century Albert Einstein.The quantum world is extremely bizarre.Can you imagine that you may be present at a number of places at the same time? Or can you think that something may appear all on a sudden from an empty space and then disappear again like a ghost? Yes all these are possible in a quantum field, of course for minutest particles with which this world is made of.
So how funny and ghostly is this world in which we live!
Then just imagine the extent of ignorance and helplessness of common people like us,in this quantum world.So are we not in an utter quandary in predicting laws of nature?
We have so far been acquainted
with natural patterns like symmetry, spiral, fractals and marking on animals
skins like spots, stripes all of which maintain regularity and more or less
obey mathematical rules. But perhaps nature’s greatest and least understood
paradox is that she is both ordered and chaotic. This paradox represents the
core reason why we cannot predict or control nature.
As naturalists, it is important
to have some understanding of both order and disorder in nature. With that
understanding we are better equipped to make sound ecology decisions that
inculcate knowing what we can and cannot do.
The actions of nature cannot always
be defined as effects that are directly related to causes.Many natural phenomena seem to be very unpredictable;for example, the weather and long term effects of climate change.Yet we are not a
mute spectator of these natural phenomena. We tried our best to bridge order
with disorder and as a result ‘chaos theory’ emerged. Chaos is the study of
order within a system that exhibits apparent randomness. But what is chaos
theory? It is a part of mathematics that looks at certain systems that are very
sensitive. A very small change in the initial conditions may make the system
behave completely differently. Very small changes in the starting position of a
chaotic system make a big difference after a while. For example, dynamic or
chaotic systems like weather condition, cloud formation, rainfall, direction
and severity of storms etc. are largely influenced by a very very small change
in the conditions at the outset.
This insignificant cause behind
a large event is called “butterfly effect” in chaos theory. The name was coined
by Edward Lorenz (1917 – 2008), an American mathematician, meteorologist and a
pioneer of chaos theory. Initially it was used in weather prediction but later
the term became a metaphor used in and out of science. Butterfly effect
originated from the metaphorical example of details of a hurricane such as
exact time of formation, actual path etc., being influenced by minor
perturbations such as the flapping of the wings of a distant butterfly several
weeks earlier.
Many of us now know that the
chaos theory was propounded by Edward Lorenz. But quite amazingly much before
him Jagadish Chandra Bose (1858 – 1937) the famous Indian Scientist, wrote a
story on similar theme which is entitled to be the first true science fiction
story written in Bengali published in 1896 and entitled “Palatak Toofan”
(absconded tempest),. The story described how a severe surge of the sea could
be appeased by even a drop of oil and could save a ship.
Chaos theory helps us to
understand nature’s systems. It has been used to model biological system
imaginable. Chaotic patterns show up everywhere in nature, including mountain
stream, cloud patterns, the currents of the ocean, the effect of air
turbulence, the flow of blood through fractal blood vessels, the branches of
trees, astronomy, epidemiology. ecosystem,the human society.In all of these examples we see forms of order amongst a lot of disorders.
Chaos theory may invoke philosophical thoughts. It may also rouse mathematical thoughts which will lead us to worthwhile investigations.In our practical life chaos theory may have some roles to play:After heart attack our heart behaves chaotically. Rigorous investigations are going on to find ways whether chaos theory may help to predict this in advance and a suitable pace maker might be designed to bring the fibrillating heart to normalcy.There are many cases which depend on chaos, such as,laser,power systems,fluid motions,disease epidemic,capsizing ships,particle accelerators, computer graphics etc.But one thing should be borne in our mind that the chaos theory by no means can be used to predict the future.
[To continue]
Chaos theory may invoke philosophical thoughts. It may also rouse mathematical thoughts which will lead us to worthwhile investigations.In our practical life chaos theory may have some roles to play:After heart attack our heart behaves chaotically. Rigorous investigations are going on to find ways whether chaos theory may help to predict this in advance and a suitable pace maker might be designed to bring the fibrillating heart to normalcy.There are many cases which depend on chaos, such as,laser,power systems,fluid motions,disease epidemic,capsizing ships,particle accelerators, computer graphics etc.But one thing should be borne in our mind that the chaos theory by no means can be used to predict the future.
[To continue]
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