Sunday, 28 August 2016

The Whole Purpose of Education

For most of us, the first image that is conjured up in our minds upon hearing the phrase ‘educated’ is probably that of a studious, bespectacled guy who holds at least a post-graduate degree in his chosen field. Many of us might go on further to speculate that this figment of our imagination probably epitomized being a model student during his school and college days - always turning in his assignments on time, being the first to answer questions in class, and topping every god-damned examination! He has diligently hoarded up knowledge over the years, which he applies rather well In his professional sphere, and most likely gets paid handsomely for it too. However, the question we need to ask ourselves is: while our imaginary friend is no doubt a highly respectable citizen and deserves every bit of the success he has worked hard to achieve, does all that automatically entitle him to be called ‘educated’? In case you are tempted to answer ‘yes’ to that, then I would definitely beg to differ with you.

Firstly, having a degree and being successful professionally is not, and should never be the criteria for judging how well educated a person is. After all, whom would you consider more educated - a street urchin who picks up a plastic wrapper off the street and deposits it into the nearest trash can, or the high-profile corporate magnate who just chucked it out of the window of his swanky sports car? The latter is almost sure to be more knowledgeable in most respects - after all, he probably had access to better schooling and holds a professional degree - but he is just too engrossed in pursuing his materialistic dreams in order to be a responsible citizen; in my opinion, this makes him quite ill-educated, despite paradoxically having a greater amount of knowledge at his fingertips! On the other hand, the street urchin, despite his rather limited exposure to any formal schooling, has successfully assimilated the lesson imparted to him regarding his responsibilities as a citizen, and crucially, he decides to act upon it and performs his civic duties when the opportunity presents itself. That, I believe, is one of the hallmarks of being a truly educated person - when you learn to think beyond your own narrow circle of existence, and apply whatever knowledge you have acquired for the greater good of the society that you are a part of. This has been expressed brilliantly by Sydney J. Harris through the following metaphor: "Most people are mirrors, reflecting the moods and emotions of the times, but few are windows, bringing light to bear on the dark corners where troubles fester. The whole purpose of education is to turn mirrors into windows.”

Another intrinsic quality that marks out the truly educated is their insatiable curiosity and thirst for knowledge; they come to realize how vast the boundless ocean of knowledge really is, and how little of it they have actually explored. No one could have put it more aptly than the legendary Socrates when he said: “I am the wisest man alive, for I know one thing, and that is that I know nothing.” This constant inner drive to keep learning and growing is an essential character trait for a person to qualify as ‘educated’.

A proper education not only makes a man strive to constantly update himself, but it also teaches him to accept every new bit of knowledge only after rigorous verification and cross validation. This is especially relevant in the light of today’s educational system which tends to encourage rote learning by not providing enough incentives for students to question deeply what is being taught. This is quite disturbing, since a society which pushes men to merely hoard existing knowledge, without making any attempts to refine or add to it, is bound to stagnate sooner rather than later. The constant progress of human civilization down the ages has always depended on our ability to push the boundaries of existing knowledge, which ultimately leads to the creation of new technologies that benefit society as a whole. But the main impetus towards this expansion of knowledge has to come from the students belonging to the new generation, who must be taught to cultivate the habit of questioning ferociously before accepting any new piece of knowledge. For the sake of mankind’s progress, they simply cannot afford to be docile and accept calmly every new fact or solution that is thrown at them by their teachers; instead, we must strive to create an environment that promotes healthy debate in the classroom and encourages students to offer alternative solutions. For that is what education is truly about: it was never meant to be a one-way communication channel for passing down knowledge from a teacher to a student; rather, it was designed to be a two-way interaction that enriches and refines the knowledge of both the teacher and the student!

Friday, 4 March 2016

An interesting application of the pigeonhole principle

Suppose 2016 points of the circumference of a circle are coloured red and the remaining points are coloured blue. Given any natural number $n \geq 3$, prove that there is a regular n-sided polygon all of whose vertices are blue. (Source: INMO 2016)

Consider a regular $(2017 \times n)$-gon on the circle, say with vertices $A_1, A_2, A_3,\dots, A_{2017 \times n}$. For each $j$, such that $1 \leq j \leq 2017$, consider the set of points $\{A_k : k \equiv j \mod 2017\}$. Note that these are the vertices of a regular $n$-gon, say $S_j$. Thus, we get 2017 regular $n$-gons: $S_1, S_2,\dots, S_{2017}$. Since there are only 2016 red points on the circumference, by pigeonhole principle there must be at least one $n$-gon among these 2017 which does not contain any red vertex. But then, all the vertices of this regular $n$-gon must be blue. Hence proved.

Thursday, 3 March 2016

Which one is greater - $e^{\pi}$ or $\pi^{e}$?

Recall that: $ e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots $

Therefore, $ \forall x > 0 $, $ e^x > 1 + x $.

Substituting $x = \frac{\pi}{e} - 1$ in the above inequality, we get:

$ e^{\frac{\pi}{e} - 1} > \frac{\pi}{e}
 \implies e^{\frac{\pi}{e}} > \pi
 \implies e^{\pi} > \pi^{e} $

Tuesday, 1 March 2016


His mind was being invaded, and he was powerless to resist!
Where once resided only dry logic, rationality and offensive practicality,
A single innocent face started making its presence felt -
Never deserting his thoughts for even a single moment in the day.

Like a cancerous growth, the image kept spreading throughout his consciousness;
Day by day it expanded, taking up more and more space in his mind,
And pushing out every other thought till they were left tottering on the brink -
Dangling at the edge of the precipice by one last tenuous thread of reason.
Ultimately, it evolved into a burning passion that threatened to consume him -
Consume him and the entire universe of his existence in one raging inferno!

He was at a total loss to figure out what was happening to him;
The gears and cogs of his desperate mind whirred uselessly, and then fell silent;
But he was no closer to finding an explanation, and felt himself drowning in utter confusion!

Initially, he fought hard against this invasion -
Chided himself for this inexplicable madness,
Rebuked himself for this illogical obsession,
Scoffed at himself for chasing daydreams and fantasies!

Yet, little by little, he found himself unable to resist;
Till finally he was forced to abandon his ineffectual struggles and give in.
And then, he was surprised to find himself relishing this strange alien sensation,
Though he knew not what it was, nor could he find a name for it!

However, as She slowly poisoned the cold, terse rationalist to death,
And freed the poet long imprisoned in a deep, dark corner of his mind,
Realization dawned at last inside his half-paralyzed brain;
Realization of what he had become:
A hopeless addict, full of delusions!
And She? His intoxication!


Friday, 5 February 2016


Let the darkness engulf me,
Please don't light the lamp.
No need to give me shelter;
I'm better off being a tramp.

I've learnt to endure my thirst;
To quench it, please don't bother.
Just learn to save yourself first-
There's no point sinking together!

Inflict more pain on me,
Put aside all bonhomie;
Pour vitriol in my heart-
Just tear my world apart!

Monday, 1 February 2016


Shall we never again sit together on the rocks by the sea -
Waves punctuating the silence, while your eyes speak to me?
Shall we never again take a stroll together in the rain -
With your hand in my hand, and happiness numbing my brain?
Shall we never again sit and talk the entire night away -
Losing all track of time till we see the dawn of a new day?
Won’t you ever come ? Won’t you join me again?
Won’t you come to end my solitude and my pain?

Will I never more experience the warmth of your embrace -
Or get to inhale the sweet scent of your hair on my face?
Will you never more help me find peace in times of strife -
With your magic smile will you never more light up my life?
Won’t you ever come and end this long, torturous wait?
Won’t you come to restore my belief in fairness of fate?

Tuesday, 5 January 2016

When the Lights Go Out

As the floodgates snap open,
And the memories rush by,
I fight to hold back the tears -
Try not to cry!

Toss and turn,
Rage and burn,
Till you're too numb to feel the pain!
Toss and turn,
Rage and burn,
Until weariness takes you again!

As the veil of courage flutters,
And old fears come crawling out,
I fight to master my senses -
Try not to shout!

Toss and turn,
Rage and burn,
Till you're too numb to feel the pain!
Toss and turn,
Rage and burn,
Until weariness takes you again!

As steely resolve wavers,
And the doubts start to whisper,
I fight to regain control -
Try not to surrender!

Toss and turn,
Rage and burn,
Till you're too numb to feel the pain!
Toss and turn,
Rage and burn,
Until weariness takes you again!