We become what we do not want

Shakuntala Devi (Hindi; 2020)

A joke that my friend once told me comes to mind. A child, aged 5, will think that his father is some kind of a superman. He is strong and invincible. At 10, he is still looked up upon. In the teenage years, the relationship sours. By 20, son and father do not see eye-to-eye. Father tries to pave the path with his wisdom, but the son thinks his ways are passé. He soon refers to his father as 'your husband' when talking to his mother about him. He only communicates with his mother and does not engage in any form of conversation with his father. Things just happen in a ritualistic manner. Son gets married, has a child, slowly enjoys parenthood. He soon realises the intricacies of parenting. By 45, he is impressed by his father's ability to juggle work, family life and skill to educate his siblings with his meagre income. By 50 or 55, the son tries to make up for lost times. When the son is 60, the father has passed on, and the son starts praising his father again, putting him up on a pedestal. He would say, "my father was a great man. No one can do all the things he did." He once again becomes a Superman, an Ubermensch.

At the spring of youth, wanting to explore newer frontiers, learning new things, looking at things from a different, with the possession of new knowledge, we see our parents as fossilised dinosaurs. We think they are not in sync with reality and are not keeping up with the demands of the changing times. We abhor our parents, are embarrassed and vow never to be like them. After all, with the benefit of education and modern knowledge, we think we can do much better. At the end of the day, we realise how wrong we were!

We go through the mill, traversing the joys and aches that life has to offer and soon realise that at the end of the day, we become the very person(s) that we despise.

Anupama Banerjee, daughter of Shakuntala Devi.

If one were to think that this movie all about the achievements of Ms Shakuntala Devi, a simple girl from Karnataka, who later came to be known as the human-computer, an astrologist, a writer, an activist for the gay community and even as the politician who stood against Mrs Indira Gandhi, one will be disappointed. There are many facets of this interesting lady. The storytellers decide to concentrate on her dilemmas being a woman, a wife and a mother in a world that is not really ready for her outlook of the world.

The story is told from the point of view of her daughter Anupama Banerjee. Many, even those in India are not aware of Shakuntala Devi, the mathematics genius. She has the incredible ability to do swift mental calculations. With ease, she would rattle off roots, square roots of multiple orders in record times, faster than the early late 70s' calculators and computers. She also has the ability to tell the days in a calendar. Give her a particular date any year, and she could tell the day it was. She did all these without any formal education. Her father, a circus man, upon discovering her talent at a young age, decided to bring her around showcasing her abilities like a freakshow for money. He brought her to the UK, and she started her shows there, even in Imperial College. Her fame soon brought to all the four corners of the world. Her skills even find a mention in the Guinness Book of World Records.

This work is licensed under a Creative Commons Attribution 4.0 International License.

You calculate your survival!

BBC Four: The Story of Maths (2008)

Part 1: The Language of the Universe
If one were to look at the history of the world, there was never a time there was peace on Earth. At every moment, there was some turmoil somewhere. In spite of all that upheavals, destructions and loss of lives and civilisations, we as a human race, have progressed on the long run. In the time of peace, people start becoming curious about their surroundings and start trying to understand its intricacies. They try to explain its pattern and perhaps try to predict its recurrence. Attacking forces usurp this knowledge as theirs and try to improve this further when the dust settles after their inquests. Slowly, learning from to count numbers with our digits, we developed formulas and managed to calculate unfathomable numbers of gargantuan proportions.

Mathematics is said to be the language of the Universe. Marcus De Sautoy, a Mathematician, takes the viewers on a journey of discovery of how Mathematics changed humankind. In this episode, he traces the origin of the field of which predates the Greek mathematicians we are familiar.
Economic reasons to quantitate the taxes to be collected and predict weather pattern in the Nile were strong enough reasons to put maths to full use.

Prof Marcus du Sautoy

All the while, I have been wondering why the hour has 60 minutes and so does the minute has 60 seconds. It has to do with the base of 60 that the Babylonians used for calculation. On one hand, the three knuckles on the four finger made 12, and the five fingers eased calculation of bigger numbers. They also had binary numbers. Syrians, which is now in turmoil now, used to the cradle of advanced mathematics. Even before Pythagorean theorem came known to the world, which incidentally may not his discovery, the Egyptian had thought of it.

The story of Mathematics spreads beyond these shores. Alexandria used to the centre of Mathematics with people like Euclid and Hypatia. Legend has it that Hipassus, a member of the Pythagorean cult, was drowned when he could resist the temptation of telling the world about irrational numbers! It is interesting to see how long it took for Man to comprehend concepts that we look at today as a known fact.

Part 2: The Genius of the East

Chinese calculation with rods

The colonial masters who landed on this side of the world came with a chip on their shoulder. In the eyes, they saw themselves as saviours of humanity who came to liberate them from dark ages. They spread their cultures to the offspring of their subjects who in turn also looked up highly at the masters' knowledge whilst being ashamed of their assumed ignorant past. Little did all of them, barring a few, knew that beneath their history lay a rich past with a wealth of mathematical knowledge.

The Chinese had their way of calculating big numbers with sticks and symbols, volume approximation and complicated equation. Mammoth structures like the Great Wall of China are testimonies of their engineering feats. The Indians introduced the decimal system, the number zero which paradoxically helps to calculate big numbers and even added another plane of number- the negative numbers. Civilisations before them, like the Babylonians and Chinese, only left an empty space to denote nothing (zero). The concept of infinity, pi and trigonometry were thought of by Indians long before 15th century Europe.

The 5th century Islamic Era was a time when knowledge from other regions to bring mathematics to yet another level. Algebra was introduced. Omar Khayyam, the poet, also tried his hand in solving equations.

The first modern European mathematician can be said to be Fibonacci. His endeavour to replace Roman numerals with the easier Hindu-Arabic numbers was met with scorn and suspicion. Fibonacci's number helped to explain many patterns in nature. Bologna was the place where mathematical sorcery took place and from it borne complex cubic equations. The history was rewritten by the Europeans.

Part 3: The Frontiers of Space

Descartes thought of this!

As the Golden Age of the Eastern civilisations takes a back seat, modern European mathematicians, many of whom wear many hats, as scientists, painters, philosophers and even sword-yielding sorcerers, go on to discover many peculiar traits of mathematics. Their practical use of this field helps them to propel their race to greater heights. 

Many of the icons who thought of new ideas were actually men of faith. The beauty of the thinking trend at that time was that thinking was allowed. They did not feel that humankind had learnt everything that needed to be learnt. They were receptive to changes and had the burning desire to reach even greater heights. Complacency was not the order of the day. Thinking outside the box was allowed. Everybody was trying to outdo each other to show-off their discovery, sometimes with disastrous outcomes.

Fermat's number play

Piero Della Francesca used mathematics to perfect his painting of 'The Flagellation of Christ'. We always think of Rene Descartes (of 'I think therefore I am' fame) as a philosopher. He actually started off as a mercenary soldier. In his spare time, I suppose, in between killing people, an epiphany of sorts must have flashed upon him. He tried to merge geometry and algebra, describing curved lines as equations. Marin Mersenne, an ordained priest, was also an accomplished mathematician who even corrected Euclid's calculations. Pierre de Fermat discovered that a prime number which will give a remainder of 1 when divided by four could be rewritten as additions of two squares. His other patterns in maths are used in credit card encryption.

Isaac Newton, besides being a physicist was also a mathematician who was interested to know about acceleration. He had a long battle with Leibniz accusing him of plagiarism. Gottfried Wilheim Leibniz must have been an extraordinary individual. A philosopher, a lawyer, an engineer, a learner of languages, he must also be the first computer engineer for venturing into the binary system through his interest in the Chinese language.

The Bernoulli family from Basel, sympathisers of Leibniz, were great in their own right, introducing the subject of the calculus of variation. One of their student, Leonard Euler, left his mark in St Petersburg. One of his many discoveries is that the addition fractions of squares in descending order equals to π2/6.

The documentary goes on to talk about Gauss, who challenged Euclid geometry which is based on flat topography, János Bolyai with his hyperbolic geometry and Riemann with his high dimensional geometry. I was surprised that there was no mention of Blaise Pascal, who spoke of probability and was instrumental in the discovery of modern calculator.

David Hilbert

Part 4: To infinity and beyond
The final part of the series talks about complicated mathematic theories. In 1900, a German mathematician extraordinaire, David Hilbert, put forward 23 unsolved problems that needed to be tackled. Over the years many experts contributed in one way or another to solve them one by one.

Cantor explained the pattern in the infinite set of whole numbers and fractions. Poincaré worked on geometry, the topography of 2D surfaces and inadvertently suggested the chaos theory and butterfly effect. Leonard Euler used the seven bridges in the town of Kaliningrad to study topology.

Perelman in 2002 finally used flow studies to appreciate 3D shapes.

Euler's problem of crossing Kaliningrad through all its

seven bridges without missing a bridge or passing it twice.

Gödel used logic to answer one of Hilbert's question through his 'Incompleteness Theorem'. The death of many mathematicians during WW2 with the dissipation of experts away from the continent marks the end of Europe as a powerhouse of Mathematics.

Europe's loss is Princeton's gain. Many Jewish exiles gain employed at Princeton's Institute for Advanced Studies (IAS). IAS saw Gödel working with Einstein and Paul Cohen, an American. The narrator goes on a spree of name dropping of doyens in the field - Julia Robinson, Yuri Matiyasevich, Galois, Andre Weil, the fictional author Bourbaki and Gronthedieck.

The unsolved problems in Mathematics are the one that makes it a living subject.

Never thought running could spur philosophy!

Running on the treadmill can be a daunting task, but it had to be done. Unpredictable working hours and inclement weather make it imperative for one to rely on this monotonous method of training. To ease the task of repetition risking premature retirement, many have devised their own means to beat boredom. I depend on the cable TV. That too sometimes lets me down. Thanks to the tropical weather and highly negatively charged weather clouds, transmission ceases more frequently than it should.

I devised my own method to cut my runs into halves and a further half it. Say, I plan to 7kms (~4.2miles) that day. First, I aim to reach half the distance (~2.1miles). Then, I aim for half that distance, another ~1.05miles, then another ~0.5, then ~0.25, then ~0.125 and so on. Before I know it, I am drenched in perspiration and joy for reaching my target.

Never in my wildest dream did I think that what I was essentially doing was what Zeno of Elia was trying to tell people around him. In his philosophical treatise which was finally termed Zeno's paradox, he advocated that by halving the distance your destination, you will never reach your intended endpoint as there will always be a void between you and the target.

Just like a moving arrow is actually static at every moment of time but in relation to space and time is seen to move from point A to B.

If Achilles set his target to reach the point where the tortoise is, he will never be able 

to overtake the animal as the tortoise would always one step ahead no matter what!

Then what?

Anand Kumar and his students

My brother from a different father and mother sent me a mail recently about a certain Mathematics tutor from Patna, Bihar, who would tutor students pro bono for them to pass the coveted Indian Institute of Technology entrance examinations. He hand picks a group of 30, motivates them, arranges hostel facilities, cooks healthy meals and literally drills them day and night to achieve 100% pass rate.
The students swarms in from remote and impoverished regions of the land to slog it out for about 7 months with the sole intention of passing the test. A pass, to them, is the panacea of their woes. A rewarding career and perhaps a post in a multinational company or even an overseas posting is a sure way to uplift their living conditions and their immediate loved ones. 

The spill over effect can be seen even to the relatives whose background and caste is irrelevant anymore. I can relate to the hopeful eyes of the illiterate parents who put all their hope, putting aside their difficulties and poverty, to educate their offspring. In the year that the documentary was shot, 29 of the 30 students passed their exams.

Audience with President Kallam

A little melodrama occurs after that. You can watch it below if you have the time.

So what happens afterwards? The teenagers go on to IIT, get a comfortable job, parents continue their  tortuous job albeit at a less strenuous pace. Then what? They get married, perhaps stay in a big mansion or migrate to a developed country and enjoy the fruit of their labour. They themselves would have offsprings who after growing up guarded against poverty and shielded from harsh reality of needing to acquire street-smartness and survival skills, would think that it is their birthright to demand for luxuries that their parents tried to offer to the kids. Whatever they missed, they did not want their children not to have.

On the part of the children, hard work and motivation would be alien vocabularies. They would talk about enjoying life. having a complete life, not to miss out on finer things of life and the now well renowned phrase of that it is their life and they can live any which way that they please!

In the immortal words of Confucius, wealth in a family would only last 3 generations. And the cycle of life would go back to square one!