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The Mathematics Of The Holidays

Proved, why math is the best date for you.

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It’s that time of the year again.

Fairy lights, holly, party favours: it’s holiday season, but we’re here with an interruption. Don’t worry yet, it’s still a celebration – we’ll be loving something we’ve hated most of our lives. December 22 – Happy National Mathematics Day. Who says we can’t invite math into the festivities?

Probably everybody who has ever hated math – and that seems to be a pretty sizable chunk of the population. Is it so, though? Mathematics, as a subject, is not even defined. Translated from Greek, all it means is knowledge. Are we really spreading hate over something we don’t really know?

Statistics show that we’re not. Contrary to popular belief; a mere 24% of the population hates math. Double, 48%, actually loves the subject. The rest are indifferent. It’s probably been explained by Hardy best: “most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.” Sounds familiar?

There you go then: math is humanity’s mistress, our secret love affair, something we can’t – and don’t – wish to give up, really. It’s been with us since the beginning of life – animals brushed with math when they recognised that 3 apples and 3 acorns have something in common. Prehistoric man began to record days, seasons, with tallies on bones. By 3,000 BC, the Egyptians had math as a crutch for finances and construction. By the 6th century BC, the Greeks had a system of study in place.

Hence, proved. You can come out of the closet today – it’s okay to love math, society has been approving for a very long time. Is the holiday season your excuse to push it to your new year’s resolutions? But we just invited math in – plus, as you’ll see, we’ll actually need math to celebrate.

Deck the halls with boughs of holly – 2,5 arrangement of leaves; here’s a Fibonacci sequence for you. More Fibonacci in the double set of spirals of the pinecones you hang on your Christmas tree. And your lovely golden tinsel star on the top – it’s likely to be a pentagrammic dipyramid, or if you’re more fancy, a great dodecicosacron.

Then there’s pie – we’ve got to give analysis, applied math, discrete mat, cartesian geometry, matric algebra, combinatorics, topology, and order theory each a slice – how do you split a pie into eight, using three strokes? More math. How much is each getting? Let’s bring in the other pi! Fun fact: the first three numbers, 3.14, read in reverse… gives you pie. Maybe you’re a bit more modern – choose pizza, over pie – say you have enough dough for a cylinder of radius ‘z’ and height ‘a’, you can make a pizza of volume, well, pi.zz.a.

Not convinced yet? Let’s get to business: we’re handing you your trump card. Numbers. Yes, they do work in your favour if you know how to; you can use math to get yourself winning streaks at Monopoly, Pac-Man, even tic-tac-toe and classic Christmas chess. Winning at chess, for example, is easier if you’ve gone through the data analysis of over 2.2 million master chess games. Or if you’re more badass and plan to hit the casinos this New Year’s, who says you can’t tweak the odds in your favour? Math can be the ace up your sleeve, your shady contact – trust us, you won’t need luck this time. Here’s an example: you’re likelier to win in Paris, not Vegas; the American roulette has double the zeroes, and double the long-term loss, than the European. (Disclaimer: these are expectation values; a math system might work a couple times, but sticking by it is a one way trip to bankruptcy.)

If you’re looking to kick back after hitting the jackpot – it’s a numbers game again. There’s math even in sleep! The length of non-REM and REM sleep periods in humans, and most mammals, follows an exponential distribution: the log of the probability of a period of a certain length is distributed linearly with the log of its length.

Moving on, let math be your date to that NYE party. Do you need your perfect outfit? You’ll need math to figure out the holiday sales. Or maybe you chose to economise this year – don’t worry, permute and combine to pick out from those thirteen shirts, five pairs of bottoms. Now that you’re here, perhaps you’d like a drink (although you shouldn’t: processing alcohol is actually harder on your brain than math is!) – and want to know if you can drive back next year? Math will take a look at the percentage alcohol by volume, the glasses you had, and decide for you.

It’s almost time – are you looking around at all the couples in the room, wondering if you’ll find the one this time? Well – assuming your soul mate is set at birth, and it’s love at first sight, mathematical estimates indicate that the odds of you finding your soul mate are only 0.010%. It’s okay – math will hold your hand as you do what it first taught you, count down from ten, nine, eight, seven, six, five, four, three, two, one…

Happy Mathematics Day to you too!

Remembering Che: A Life Characterized By Its Death

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Fifty two years ago on this day, i.e. 9th October 1967, Che Guevara was executed by Bolivian soldiers at the age of 39. 

He was a Marxist revolutionary and guerrilla warfare genius who played a pivotal role in overthrowing Cuba’s US-backed dictator. He helped bring about a new popular government in his country.

However, his disposition for rebellion lingered and so he left Cuba to ignite revolution in other countries. There, he was subsequently captured by CIA-assisted Bolivian forces. He was kept tied-up and guarded in a village school. He refused to respond to any interrogation by his captors and only spoke quietly with the common soldiers. A soldier recounts that even though he was deathly sick and shot in the thigh, “Che held his head high, looked everyone straight in the eyes and asked only for something to smoke.”

On the following morning of 9th October, he asked to see the teacher of the school, who later gave an account of the interaction. She described Guevara to be an “agreeable looking man with a soft and ironic glance.” She recalled that she had found herself “unable to look him in the eye” because his “gaze was unbearable, piercing, and so tranquil.” Guevara had pointed out the poor condition of the schoolhouse, stating that it was “anti-pedagogical” to expect school students to be educated there. He contrasted it with the “government officials driving Mercedes cars”, and declared, “that’s what we are fighting against.”

Thirty minutes before he died, he was interrogated by an officer as to the location of his comrades. He did not oblige. One of the common soldiers asked Che if he was thinking of the immortality of his own name. “No,” he replied, “I’m thinking about the immortality of the revolution.”

When his executioner arrived to shoot him, Che spoke his famous last words: “I know you’ve come to kill me. Shoot, coward! You are only going to kill a man!”

Even though more than 50 years have passed, his iconic image (frequently described as the most famous photograph in the world) still endures in our minds and lives. After his death, Che became a symbol, not only of communism but that of all revolution and rebellion. As we increasingly slip into a world where the sovereignty of poorer countries is being undermined by first world agendas, Che’s life serves as a reminder of standing up and making our point, regardless of repressive policies. 

Nine days after Guevara’s death, Fidel Castro, a fellow revolutionary and a great friend of his famously quoted:

“If we wish to express what we want the men of future generations to be, we must say: Let them be like Che! If we wish to say how we want our children to be educated, we must say without hesitation: We want them to be educated in Che’s spirit! If we want the model of a man, who does not belong to our times but to the future, I say from the depths of my heart that such a model, without a single stain on his conduct, without a single stain on his action, is Che!”

 

The flap of a wing

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‘All actions have consequences’. This is something that every person has learnt at a young age, in one way or the other. If you punch a wall, you will injure your hand. If you push your brother, he will push you back. If you stay awake all night, you will feel lethargic the next day. But in these cases, the actions propose pertinent consequences of more or less equal magnitudes. Something that a normal human mind can conclude beforehand. However, what we don’t realize is that the most insignificant and seemingly indifferent actions can be the ones that shudder the whole world in every aspect there is.

“Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”. Nearly 45 years ago, Edward Lorenz put forward this ambiguous question during a meeting of the American Association for the Advancement of Science. Although intended to be rhetorical, this question spurred the minds of people across the globe. This idea later went on to be the basis for a branch in mathematics, called the Chaos Theory. This highlighted the idea that some complex dynamical systems, such as the ecosystem we inhabit, possess erratic behaviours such that a minute disturbance in the system can have profound effects on the stability of the system.

Imagine a young man in the early 20th century leading a normal life with his family. He has gained an interest in painting and wants to learn more about the art. He applies to the Academy of Fine Arts, Vienna and hopes to pursue his career over there. But, the academy deems that man unsuitable to be a painter and rejects him, twice. Upon the death of his mother, he finds himself trapped in Vienna and has to live in the slums. Because of the living conditions, that man became anti-Semitic and decided to join the German army. This man is none other than the infamous Adolf Hitler, the leader of the Nazi party. In simple words, rejection of an application by a Fine Arts academy led to the assassination of countless Jews and consequently, the second World War!

As another example, imagine that two asteroids collide with each other in the Asteroid. As a result, a miniscule meteor is formed which advances towards the Earth. As it plummets to the Earth, Constantine is fighting a Civil War against Maxentius. Constantine’s army is outnumbered and hope is little. But, before the conclusive fight commences, he notices the bright light in the sky and assumes it to be a ‘trophy’, a sign from God to not give up until the very end. Consequently, Constantine wins the battle and goes on to become the Emperor who passes the Edict of Milan, leading to the widespread of Christianity. The flashing of a meteor across the sky in the 4th century gave rise to the highly prominent Christian religion!

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Vienna State Opera House, Adolf Hilter, 1912. Source: The water colours of Hilter, 2005

As depicted by the butterfly effect, everything in this universe has a specific purpose that contributes to the stability of the system that we all reside in. All of the vicissitudes in our life can be explained to be the aftermath of an unimportant, indifferent event. Any change that is made right now is going to have an explainable, yet wondrous cause-and-effect ramification of the future. In fact, if you do not get up and get yourself a cup of coffee right now, pandas will become extinct within the next few decades. This effect justifies how little of a room there is for errors in this world. As the renowned author, Kevin Michael suggests, “Small shifts in your thinking, and small changes in your energy, can lead to massive alterations of your end result.”.

A papal tweet and what it says about climate change

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It’s ludicrous how an impending disaster that puts 7.3 billion people at risk, the largest of its kind, is treated more as a myth by people than anything else. Climate change despite strong scientific backing has a hard time being taken seriously. It’s a polarising and absurdly even a partisan issue in some developed countries. But perhaps the greatest danger of climate change is its sheer lack of credibility to hold debate even in the highest forums.

In 2015 Dr. Virabadran Ramanathan, an atmospheric scientist had convinced the Vatican to let him have a 3-minute audience with the pope outside his residence. It was quite literally a parking lot pitch. To save time, he memorized a monologue in Spanish to explain the dangers of climate change but as the car pulled over and the greatest religious leader of the world stepped out, he blanked out. Not a word of Spanish came to him, so he resorted to a translator and got straight to the heart of the issue. He told the Pope that the richest 1 billion were causing more pollution than the rest of the world and that poorest 3 billion are going to suffer the brunt of the consequences. Even though they had contributed little to the issue. The pope listened to the scientist and asked what he could do to help. This was not how Dr. Ramanathan had thought it would go. He told the pope that climate change was a moral issue and that as the moral leader of the world he must urge the world to be better stewards of the planet. The pope was rather quite convinced, he mentioned this message in his letters to the Catholic world but more importantly, he tweeted it to his 40 million followers.

That one act of changing the lens through which we see the issue from a scientific to a humanitarian paradigm and propagating the message through something as mundane as a tweet had the most profound impacts. Almost half of all Americans had heard of the Pope’s message, 1 in 10 Americans had it discussed in their place of worship and 17% of Americans had gained a better understanding of the issue. This phenomenon was called as the Francis effect.

Graphs and data do little to persuade people. To have people deliberate on an issue, the issue must first permeate the ethos of their society. The differentiating factor between climate change and other issues is that climate change has its cause(pollution, waste, etc.) more detached from its effect(population displacement, loss of habitat, water shortage, etc.). Therefore, a hole in the ozone layer doesn’t intuitively translate into a humanitarian issue. Scientific papers cannot change what a society considers as their ethical responsibilities and do not reflect on the humanitarian issue that climate change will create. At the crux of it, climate change is an impending humanitarian disaster and one tweet from the Pope made us the world populus a more socially and ethically aware than decades of scientific reports or research.

Fool’s Paradise

Eudaimonia. Felicidad. Contentezza. Bonheur. Happiness. An emotion that is supposed to transcend the barriers of language and culture. Unite people and spread joy. But is happiness such a one-dimensional shallow feeling? Something for which we always wander never realizing what it truly means. Men far greater than me have tried to define happiness within the confines of a few words. Aristotle put it eloquently when he called it a state of activity. Eleanor Roosevelt elaborated on her definition elaborating upon criterions to achieve happiness.

“Someone once asked me what I regarded as the three most important requirements for happiness. My answer was: A feeling that you have been honest with yourself and those around you; a feeling that you have done the best you could both in your personal life and in your work; and the ability to love others.”

Without going into further such wordplays, the commonalities can be seen emerging from these definitions. Though this does beg the question that can this unequivocal feeling be put into words that might apply for the everyday John or is it defined by unique parameters for every individual. After all you cannot judge a fish by it’s ability to climb a tree and neither can you put a millionaire in a pauper’s place and ask him to find happiness there.

We often hear about parameters that state how happy the general population of a country might be. The United Nations Sustainable Development Solutions Network has been providing us with a World Happiness Report outlining the state of world happiness and causes of both happiness and misery. In addition to this, in the last thirty years, more than 3000 empirical studies have been conducted, some of them bearing questionable titles like ‘How much happiness is there in the world?’ and ‘Causes and correlates of happiness’. Most of these use factors like GDP and surveys among the demographic to quantify something that might just be unquantifiable. But to what extent are such measures valid and reliable as they seek for an answer to a seemingly abstract question. U.S.A which is seemingly the 14th happiest country in the world continues to be ravaged by unemployment and dissatisfaction with the government bringing into question the validity of such reports.

In spite of its vague nature, happiness is something we strive for in our day to day lives often making it an end goal for us. “I just want to be happy”, a line often heard from the millennial generation a they navigate through the creeks and crevices of life. Most of our decisions are guided by our pursuit for happiness, often failing to identify happiness right when it is staring us in the face. This never-ending pursuit goes on and many end up losing track of the path they set out on often settling into the monotonous idiosyncrasy of their life. Other try and look for happiness in material possessions or perhaps in the arms of a loved one. But if you cannot find happiness on just your own from within yourself, how can you expect things or people to fill the void that might be bubbling under your skin?

A wise man once said that you will always find the answer in your heart where it has been long waiting since before the question. Maybe that is where our Pursuit of Happiness is supposed to lead us too. And in that moment of contentment, flourishment and fulfilment, we might end up discovering the fruits of our strenuous pursuit for the all elusive Happiness.

Human 3.0

The dominance of humans on this planet has been greatly due to their abilities to use inanimate objects, engineering them to meet their desires. To a certain extent these objects or more precisely tools have been more useful than the animate ones itself. The process of evolution took time but the development of these tools was gradual with a very steep slope. Unarguably, the tool that has led us to discriminate other creatures against humans has been the technology. Life has never been this easy in the human history all credit goes to the level of technology around us. Even today it is impossible to predict the point of saturation of it. But the stretch of one of the fields in technology that has startled humans is Artificial Intelligence. Fundamentals laid on the ground to describe the human thinking based on very clever manipulation of sequences of 1s and 0s. This field of intelligence has seen lot of ups and downs during the course of its development. But this giant was never out of scope and its mammoth possibilities to transform human lives even further gave us the taste of every colour.

 

AI is not the technology of any other generation but now. It might be either “Siri” or “Alexa” assisting you right on your demand or spotting the driverless car in traffic beside you. For instance, the smarter web browsing experience whether the filtering of junk mails or personalising the web, our dependence on it narrates the story . With every sunrise we are not only gifted with a brand new day but also with better experience due to new and improved algorithms heavily influenced by this technology. The ability of these machines driven by AI – – to show advanced cognitive skills, to learn, to perceive,  to process data – has made them capable to perform any task with high accuracy.

 

On 1st january 2016, the dream for a better future took off driven by 193 nations. The dream is to see a better world by the end of 2030 revolving around the development of economy along with attention to the amelioration of the environment. The United Nations ‘17  “Sustainable Development Goals” is set to promote prosperity in the country and at the same time protect the planet, economic growth and the social needs for the same including education, health, social protection, and job opportunities along with checking the climate change and environmental protection.  The concept of “AI for good” is to explore the implementation of it for the greater good of society and ultimately using it to cut the problems faced by us.

 

If the coin gets flipped, we might end up with the very last invention of the human race. We consider ourselves supremely intelligent from our primitive animal cousins, but in reality we are only fractionally more intelligent than them. But that tiny fraction had led us to develop tools, language , civilisation and much more. When AI gets more intelligent than us, not fractionally but by million times called the “singularity”, our breath could be the price we pay. All that is needed now is to be very careful with this technology but the twist being the impossibility of the situation in predicting it before it actually happens.