The poetic beauty of Fourier series

Mathematics is the essence of life, which has helped in all the human endeavors by establishing an order among the mystical set of parameters governing the universe. There are umpteen instances in nature which explicitly display the presence of mathematics making us believe that god created the universe based on the result of an infinite set of complicated equations. To give you a whiff of what I intend to say, I will give you an example of a beautiful equation.

Generalized Fourier series:

Y(t) = A1*X1(t) + A2*X2(t) + A3*X3(t) + ……………………… + An*Xn(t);
where the vectors Xr(t) are independent with each other.

The equation simply means that any signal can be represented by weighted sum of the N number of independent vectors. These vectors can uniquely represent any kind of signal. For a layman the equation is simple in its essence and possibly may not interest him. However looking deeper, it is a beautiful piece of poem expressed not in words but in terms of variables.
Essence of the poem:

* Every human being is a wonderful creation of nature with unique characteristics that define him and only himself.
* As in the case of the equation, the number of parameters should tend to infinity to completely describe the person.
* A list of these parameters would include the physical, emotional and intellectual aspects of a person.
* The low frequency contents, which contain most of the energy, are the ones given most importance in mathematics. In humanistic terms the low frequency content represents the obvious parameters such as the height, weight, accomplishments in life etc.
* These high frequency contents are analogous to the finer aspects of a human being and are the ones that truly define a person’s identity and his wonderful idiosyncrasies. They are generally overshadowed by the other cruder parameters (in cases such as compression in mathematical terms).

For those who in the same frequency band in which I am in would be able to enjoy the essence of this article and for others my advice is: Try to modulate or demodulate yourself to required frequency band to enjoy the spirit of mathematics.

The Bodhi Tree a.k.a The Date

The Bhodhi tree:

Burrrrrrrrrrrrrr, a loud burp diverted the attention of the group whose focus was on the meek fresher being ragged. The serious mood created by the group to create an atmosphere of intimidation, which is an essential factor of ragging, was completely lost in the laughter created by this unexpected act from the surprising visitor Ram.

Ram, a person who is strictly against ragging, was taking a casual visit to the notorious place – the television room known for its ragging sessions. The ever-curious mind of his had made him surprise his group of friends with this visit to a live ragging session, as he was patiently sitting in the room and observing the proceedings silently. The junior student was forced to hang from iron bars of the window with one hand. Looking through this window, one could observe a few students sitting on the benches adjacent to the mess under the shade of the neem trees, with the company of a group of goats, all relaxing after a heavy meal. There was also this old lady a bit farther in the picture hooting and whistling to catch the attention of her goats .

A photograph of the junior posing like a monkey was taken with the new NOKIA 5800 mobile. Suddenly Ram started feeling vibrating sensations from his stomach. The strenuous climbing of three floors of stairs had kick started the process of digestion. He got up and went straight to his room to get a tablet of digeine. As he entered his room, the timetable stuck on the wall reminded him of the next class he had to attend in a short while. With a sigh he fell on his bed deciding against it as there were too many obstacles. The after lunch laziness, the kilometer walk to the department, the boring lecture all aided by his inherent laziness kept him on his bed.

His idle mind was racing through randomly each thought widely different from the next one, a singular image flashed through his mind. It was the image of the old lady holding a wooden stick slogging through the thorny pathway and grazing a herd of goats. The frail looking lady with a long pointed nose , wrinkles crisscrossing all over her face with traces of flesh all over her body, a few strands of hair jutting out of the exposed scalp all these along with a small stoop made her resemble a witch. Ram had seen her couple of times walking through the same path through the window of his room.

The thing which fascinated him the most about this old lady was the answer to one big question about her? What was the driving force for the granny to be able to carry on such an arduous, never ending passage of time called life? Life is filled with peaks and troughs, each one nicely complementing and providing an essence for the existence of the other. When analyzing her life what he saw through his eyes and processed through his mind, with his limited experience in life, did not make sense as he could see only a flat line way below the normal.

As his cold, calculative brain was processing all the information and trying to reason out things, an idea popped out. The question needed to be answered at any cost. The key is to know more about her of how she leads her life, her views on it and other related things. It was not like he could ask her out on a date to coffee day. So he conspired with his friend Shyam and came up with a plot.

Shyam, a good friend of Ram was a youthful adventurous person and the first one who heard most of his unconventional and unique ideas. Though they did not share a similar wavelength in terms of their thought processes they have gelled along well. Shyam had been a part of the execution of many of his pranks and crazy gimmicks. However the current plan of stalking an old lady was way too much for the simple mind of his to comprehend and comply to. With a lot of persuasion from the side of Ram and also because of the faith he had had on Ram from his earlier experiences that it will always be interesting, made him reply in positive.

A detailed plan was charted with the help of his good friend Shyam. They started from their hostel at four in the evening the next day. It was a three kilometer long drive by a bicycle to the village where the granny lived. The travel was first through a short kutcha road which was testing their cycle balancing skills. As they entered the village the road was relatively smooth. It looked like a typical village with hens flocking around, friendly looking people clad in dhotis and sarees standing beside their thatched houses staring at them curiously, semi naked children trying to race ahead of the people on the cycle, in their self imagined race, skillfully driving their vehicle -a single tire pushed and steered by a small wooden piece. The two cycles stopped in front of the local tea shop as they started with the execution of their plan.

They introduced themselves as representatives of the youth wing of the local party and that they were here on the orders of the M.L.A. of the constituency to take a survey in the village to enquire about the problems they face in their day to day life. They started their survey with the tea shop workers and few of their customers and proceeded to the other houses slowly moving to the right of the main street of the village, towards the house of the granny.

The whole business of surveying the other houses was to make the whole plan look natural as they could not directly knock the door of the granny. They spent about one sixth of an hour in every house asking questions related to the basic amenities. Ram was the person asking the questions and shyam noted down some points on a scrap paper. Though all these were part of the drama, talking to these people exposed them to a whole new world. Some of the villagers opened up and started sharing their personal problems. They spent about two hours talking to the people before they stood in front of the granny’s house.

It was nearly dusk as they approached the small thatched house. The two old ladies sitting outside cut short their discussion and welcomed the young men with a pleasant smile. The granny was leaning on a lamp post munching on betel leaves. The other lady started the conversation by enquiring the purpose of their visit. They were offered a seat on a shaky old wooden rope cot. Ram was partially resting himself on the wooden frame with his upper body bending forward and focusing all his attention on the granny, as he introduced himself. Imagining himself as Sherlock Holmes, he tried using his self-professed powers of astute observatory and deductive skills to extract all the information he would need. The conversation between Ram and the granny went on for over half an hour. Shyam was a silent spectator in the whole time amazed at the ease with which Ram proceeded. They were offered some butter milk before they started the return trip back to the hostel.

The lighting was poor as it was nearly eight o clock at night. They walked back to the tea shop to get their cycles which were parked there. Only after the first pedaling of the cycle did Shyam notice that his back tire was punctured. It was going to be a long walk to the hostel and that too with the burden of having to maneuver the cycle. As they were ambling along Shyam wanted to desperately break the ten minute silence. He was a bit puzzled and very curious to know what Ram thought about the whole incident. Most of his earlier experiences of assisting Ram were exciting. They were events which were etched in his memory and those which he would be proud about for their level of craziness and element of adventure and especially the embarrassment or the risk factor involved. This was quite different from the rest.

The reply to Shyam’s whole set of questions was just a smirk – a wicked smile, one which is indicative of a sense of enlightenment, a sense of relief of having rested the obsessive mind by finding the solution, a sense of humor thinking about the answer which was ironically simple. Ram in turn enlightened Shyam with his explanation.

“Brother the whole thing started because I as a curious person wanted to know how the granny carries on with her difficult life without having anything to expect from it. Once I started speaking with all those villagers I could get a sense of what the answer would be. I confirmed that this was the answer after speaking to the granny -which is the nothing but the five minutes of happiness they get. If you had noticed the kind of hospitality we got from those people, of how their eyes sparkled. You know what? Those five minutes we spent in each house, the attention we gave them, how we unknowingly helped to soothe their pain temporarily by patiently listening to them. Those packets of five minutes of pleasure come in different ways in what they call as the journey of surprises called life and [a pause] these people live on, expecting those little cute surprises…We were lucky to provide them with one such packet today. [with a grin and a long pause]The answer is so bloody simple is it not….. K lets keep moving fast. I am really hungry”.