My quest for ‘Perfection’

Right from the day I stepped into a school, I was told to strive for flawlessness. I was told to dress properly, and speak absolutely right language, to solve all problems to get the right answers, and above all maintain harmonious relations with every one around. I am not sure whether I have lived up to the expectations of my parents and teachers. Now, in the evening of my life, I wish I had also been told to put a filter in my memory through which only the right thoughts would be retained, and the rest consigned to the ‘trash’ bin. I have mulled over these issues for a long time, and I offer this piece as my New Year’s message. 

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1949. I was eight years old, going on nine. Our father was posted to the Indian Military Academy (IMA) as an instructor, and living on the campus of the Academy, was an education by itself. Ever so often, we saw the imposing Chetwode Building. It looked majestic. It provides the perfect backdrop for the training of officer cadets of our army.

                       

Every time I saw it, I was reminded of the parades which we witnessed twice every year.

 

I was struck by the ramrod straight posture of the Cadets and their perfectly coordinated drill movements, which were in perfect harmony with the bands. Nothing ever went wrong, be it clouds, lightning, rain or hot sun. At home, we were taught to emulate the example set by the cadets.

At school, the teachers wanted us to strive for perfection in spellings, tables and the sums which we were required to work out. Soon, I was old enough to acquire a geometry box, with which I could draw triangles, circles and other geometrical figures. Here again, the emphasis was on precision and perfection.

 

It was around this time that I received a globe, of my own. It was a perfectly round object, and they told me that it rotated around its axis, exactly as the Earth. I enjoyed playing with it and looked forward to being able to see  

 

our  Planet from the sky. My quest for striving for perfection continued to grow all this time. I tried to provide absolutely correct answers to every question asked, and I attempted to maintain my room as clean and orderly as the rooms of the IMA cadets.

One day, when we went to Tons River which flows just behind the IMA campus. I was overwhelmed by its beauty, and so we went there as often as we could.  My brother, Surinder and I used to gather stones of different colors from its banks. And then, one day, I observed that the river was neither straight nor circular. In fact it did not conform to any of the shapes which I drew with my instruments. The stones were of different shapes, colors and sizes. Despite being so close to the Academy, there was no uniformity in its architecture, and its motion was far from being ‘perfect’!

In the academy, there were strict rules to maintain pin-drop silence, and here, right next to the military training area, the Tons River was merrily gurgling away to God’s glory!

However, honestly speaking, I liked the sonorous and resonant sound of water, the imperfect shapes, sizes and colors of the river bed and the zigzag path on the mountain across the stream. Whenever we looked at the sky, we saw gorgeous sights. The sunset was always different and whenever there were clouds in the sky, the colors were a treat to see. I discovered that none of these scenes could be drawn with the instruments in my geometry box. Nothing in the nature was either straight or perfectly circular. It was, as though a child had playfully swept a paint brush on a canvas or a piece of paper.

  

Back home, I had another look at my ‘perfect’ globe. The axis of the sphere, I was told, was inclined at an angle of approximately 23.5 degrees, and I also learnt that the earth is NOT a perfect sphere. The diameter at the poles is 44 km less than the diameter at the equator. The ‘North’ which we determined with the compass is not the same as the ‘geographic’ North, and it keeps varying with time.  As I grew up, I discovered many more imperfections. The distance of the earth from the Sun varies between 147 and 152 million kms as the earth makes its annual journey around it.

To my chagrin and dismay, I learnt that not only is our earth imperfect, we actually know very little about the terra firma on which we live. The geologists tell us that the Earth is composed of five distinct segments, as shown below:

The upper crust on which we live is six to sixty km thick, and it is known to have ‘faults’. (it is thin beneath the oceans and thick on the land; beneath the sea surface, the water exerts the pressure to keep it in place) When the crust fractures, we get earthquakes and tsunamis. When I asked why we cannot identify these ‘faults’ and, therefore, predict these disasters, I was told that our geologists have not been able to dig deep enough to investigate even the upper crust.

Imagine, the center of the earth is merely 6,371 km beneath us, and the deepest exploratory well which we human beings have been able to dig so far is no more than thirteen kilometers! The structure which is depicted above is a mere assumption, based on secondary evidence. No human beings, or their instruments can go below, because the earth is very hot below the crust.

 

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I was disillusioned with geography. I found it far too imperfect for my liking, and therefore, I decided to concentrate on Mathematics. Here all answers were exact, and so I felt I was on firm ground. There was a cogent ‘proof’ for all theorems and practical usefulness for everything which I learnt.

It was good going until I learnt about zero and infinity. I was told that:

            1 divided by infinity = zero          ( 1 ÷ ∞ = 0 )

            This led me to conclude that :  1 = infinity multiplied by zero. ( 1 = ∞ × 0 )

So far, so good. But when I divided my age, 12, by infinity, I was floored, and consequently led to the ridiculous conclusion that 1=12! Since, by the above logic, 12 is also=infinity multiplied by zero ( 12 = ∞ × 0)

My teacher was not able to give me a cogent answer. He sent me back, saying that division by zero and infinity is not permitted. When I asked why it is not permitted, he flung me away in scorn. But my doubt lingered on.

I was destined to pursue mathematics to the post graduate level at the IIT Delhi. And there I learnt that Mathematics is also imperfect! As for the concept of zero and infinity I did some research and found a satisfactory answer. My analysis is contained at the end of this story. For the moment, let me state without any reservations that as far as I know the physical science which we teach and learn is as imperfect as the Geography about which we talked a little while ago. I discovered many areas of a perfect disconnect between analysis and practical observation. Physics and Chemistry are far from perfection.

The engineering designs with which I have been associated are often based on approximations, which in turn derive from experience and proven designs, which are based on ‘gut’ knowledge. Rigorous mathematical and analytical calculations rarely yield practical solutions to real life problems.

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In the old age, and especially after retirement, I have turned my energies to the study of history. I have been told that if you learn ‘historical’ facts, you can guide the future generation to proceed in the right direction. I started with the world history, but soon turned towards our own past. For a while, it was good going. But once, I stumbled on a copy of “The Golden History of India” published in 1945 in a library. To my horror it said very clearly that in 1857, some disgruntled and misguided soldiers had gone crazy, but the consequent “Sepoy Mutiny” was effectively put down and order was restored. This was only one of the differences between the Indian history which we taught and learned before independence and what our books say now. As seen by our British rulers, ‘Netaji’ Subhash Chandra Bose was a rebel and ‘Shaheed’ Bhagat Singh was a ghastly criminal. This difference is understandable, but what I found difficult to digest was what I read in a history text book which I obtained from Pakistan. It is of High School standard, and the cover page prepares you for what lies ahead. The title of the book is “A New History of Indo-Pakistan”

 

The very first thing you observe is that as far as Pakistani historians are concerned, their history begins with the advent of Babur. All that happened before, including the Indus Valley civilization (which lies in Pakistan) and the history of the period of Lord Buddha and Ashoka the Great are ‘prehistoric’ events which need not be taught. The name “Indo-Pakistan” suggests that the concept of ‘Pakistan’ has existed since several centuries.

The table of contents tells the rest of the tale with sufficient accuracy. Please read it with care.

After this there was no great surprise in store for me. I was prepared for what I read. The students in Pakistan are taught what their rulers would like them to learn. Jinnah and the Muslim League are for them what Gandhi and Congress are for us. Ranjit Singh who ruled  a significant part of ‘Indo Pakistan’ from Lahore finds a very brief and listless mention.

The 1965 war was, in this book, tipped in favor of Pakistan. Despite the inferior numerical strength, the Pakistani soldiers faught with great courage and captured a large part of Indian territory.  8 September is celebrated as the ‘victory day’ and the ‘uprising’ in East Pakistan was a ‘misunderstanding’ 

What our students in India are taught in history is quite different. Even though the story should be identical up to 14/15 Aug 1947, the two books have very little in common, even for that period. My immediate inference is that history is as imperfect as geography and mathematics.

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History is as ‘imperfect’ as Geography and the pure sciences.  However, the consequences of inaccuracies in history are far more serious than the errors in other branches of knowledge. Biased history has a tendency of injecting venom in the minds of children at an impressionable age. About history, a wise old man said,

      “Whenever God wishes to change history, He connives with the historians!”

There is no way by which we can improve the defects in science and mathematics. But I think there is an urgent need to set the historical records straight. For this, here is a humble suggestion:

The history of warring nations should be written by dispassionate historians. Just as we have neutral umpires and referees in sports, we should requisition the services of completely unbiased scholars from distant lands to record history. In our case, historians from Argentina, Iceland and, Norway may foot the bill. And until we are able to organize that, history books written in India should be made compulsory reading in Pakistan with a reciprocal agreement in India.

Or maybe, I need not worry my old and rotten head. The Internet is already doing that. Sooner or later, the borders are going to become irrelevant, in as far as transfer of knowledge and information are concerned. We are rapidly moving from imperfection to perfection at least in this case! 

But are we moving in the right direction and fast enough??? I am not altogether sure!!!

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A Note on Zero and Infinity

The discussion on Mathematical concept of zero and infinity was getting a bit heavy. So I checked myself. Actually, the explanation is simple. Zero and Infinity are not numbers: they are concepts, and they are relative in nature. Consequently these two ‘quantities’ are required to be treated differently. We take a few examples.

• Consider that you are standing on the bank of a river. You have a grain of moist sand in your hand, and let us assume that its diameter is one millimeter. Now compare its mass with that of the earth. The ratio of the volumes will work out to 1: 1,728,000,000,000,000,000.  To save time, we can save effort by stating  that the Earth is infinitely larger that the grain of sand.

• Now, compare the size of the earth with that of the Sun, or better still the largest known star, Antares. I am placing their relative sizes below in the form of diagrams. It does not need to be mentioned that the Earth is infinitely smaller than the largest star.

 

 

And now compare our Sun with Antares. It is less than one pixel  in comparison, on this scale!

You will have to strain your eye to see the Sun, and Jupiter is invisible.

 

Now let us get back to the tiny grain of sand with which we began all this. Has it ever occurred to you that it is infinitely larger than the thousands of molecules of which it is made? To give you a rough idea, here is a picture.

Molecular structure of a grain of sand

 

 

And these molecules are, in turn, infinitely larger than the atoms, each one of which is a vibrant replica of our universe! It has a nucleus and electrons revolving around it at an unbelievable speed.

More recently, we are told that the electron itself is made up of three parts, and there is sufficient reason to believe that the electron will turn out to be infinitely larger than something which a scientist will find, soon! Here is a quote from a recent post on the Internet,

In 1996, American physicists C. L. Kane and Matthew Fisher made a theoretical prediction that if you confine electrons to individual atomic chains, the Wiedemann-Franz law could be strongly violated. In this one-dimensional world, the electrons split into two distinct components or excitations, one carrying spin but not charge (the spinon), the other carrying charge but not spin (the holon).

And, of course, there is no reason to believe that we have been able to explore the limit of the universe. Each new probe into the space shows us more stars and constellations. In fact, cold logic suggests that the space has no limit. In fact an outer shell is beyond the realm of imagination.

Indeed, if there were to be an ultimate limit to the cosmos, and we accost a large wall or screen on which there is a clear signpost in alll languages, which says, “There is nothing outside this limit” our intelligent human beings will ask, most humbly, “What is beyond this?”

It is therefore quite unlikely that either the microcosm or the macrocosm can be fathomed by human intelligence. Perfection exists only in the ‘imperfect’ minds of our erudite scholars.

To Sum Up the discussion on Zero and Infinity, let us put it this way : The tiny speck of sand is infinitely larger than the electron (and its constituents, spinions and holons). We can see it and even play around with sand particles. The Giant stars are infinitely larger than the speck of sand and they emit enormous light and heat, but we need a telescope to see them. The Earth is somewhere in between. I leave you now to decide, which of these objects is ‘zero’ and which one shall we describe as infinitely large.

 Zero and Infinity are a lot like the Creator…He is large enough to build the entire Creation, and yet so tiny, that we can not see Him. The Lord in the Heaven is Infinity and Zero rolled into one!!!

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Epilogue : A Plea to my Friends and Foes on the New Year’s Day

I have never mulled more over any issue as this one. The quest for ‘perfection’ began to bug me sixty years ago, and I have felt for a long time that the nature never wanted perfect straight lines or circles. Nothing is ‘exact’ or ‘quantifiable’ in the universe. Everything, including truth is relative. It is in the cosmic scheme of events to create, destroy and create afresh. Nature does not keep a record of events. Even the animals do not retain memories of friends and foes. We human beings need to learn from the Creator. And the one message I have for mankind is to resolve that we shall learn to unlearn the ‘imperfect’ history which we have laboriously written over the years, and re-write it, after removing all that is negative in it.

Let us record all that we have written so far on the electronic medium, and press the ‘delete’ key. All history books published so far should be consigned to flames. Alternately, let us learn to read what our adversaries have to say on the subject.At least in personal relations, let us remove from our memory screens all the bitterness we have gathered for our friends and relatives, and begin afresh on the New Year’s day!