Where’s the science, President ?

When I first started this blog with my friend about 2.5 years ago, it was with an intention to put forward our ideas about science and math. I remember the high school days when we used to discuss vague topics in science, often baffling people around us. Never do I recollect talking about politics though. This blog followed the same trend with scores of articles about astronomy, statistics, economics but hardly any political commentary.

But the extraordinary events going on in the name of the great 2016 American Election have made me sit up and take notice. Everyone of us has an opinion about Donald Trump. I am not here to do any general Trump bashing. Much of that is available on youtube and probably in a more entertaining manner than I might present things here. The angle which I want to cover here is the amazing disregard for science and math that this presidential race has shown.

I have been living in the U.S. for more than 3 years now. Many things have surprised me about this country, but one aspect that has been reinforced is the level of scientific progress here. Countless researchers are involved in working on ground breaking technologies and discoveries all over the country. U.S accounts for more than 30% of scientific publications in the world annually. Equally impressive is the staggering number of students assisting in the endeavor.

But judging from how the presidential campaign is going on, one would hardly think that science is even a subject taught in high school. Right from the primaries, the focus has been on immigration and economics. In the primary debates, the only scientific topic that came up was climate change. It is perhaps the most important concern facing humankind right now. But most of the candidates treated it how a child treats the last 2 problems of his/her homework; they just want to finish it off quickly so that they can go out and play with their buddies.

A look at Hilary Clinton’s webpage shows only a tiny section about climate change as a representative for science. Donald Trump’s page doesn’t even have a mention about it.The whole point of this election has become about two grownups coming close to retirement age squabbling like 10 year old kids over petty issues. Important topics like space exploration, new manufacturing techniques and renewable energy development have been left in the dark.  We can make the world a better place if we give greater impetus to these, but they are almost absent in the hate and blame rhetoric that has characterized this election.

My other big concern is about how numbers and statistics have been blatantly disregarded. Much of this blame has to fall on Trump. Trump has often sought to use his cult of personality to make statements which are blatant lies. One of the many examples of this is how he claims that U.S. unemployment is growing worse. He once claimed that U.S. employment stands at a grand total of 42%. For people who believe in him, that might set big alarm bells ringing. Upon closer examination, his numbers actually include anyone who doesn’t have full time 40hr employment, and that includes high school, college or graduate student, a stay-at-home parent, a job-training participant and even retired senior citizens ! Factor all that out and the harshest number that you can come up with is 16%. That is more than 2.5 times smaller than Trump’s claims. Facts should be the cornerstone of our social lives and if we get blinded by rousing emotions and charisma of the person in front of us, then it can paint a very wrong picture of our society.

Now you might think that a President has nothing to do with science. Let’s leave all that to the universities and industries, shall we ? Well, that’s way off the mark. Let me redirect your attention to Mohamed Nasheed, former president of Maldives, a tiny island nation in the Indian Ocean. Realizing that rising sea levels due to climate change could potentially sink his country, he launched a huge campaign to battle against climate change. He lobbied with leaders of countries far more powerful than Maldives to implement pro-climate measures. He also implemented policies to make Maldives a carbon-neutral nation by 2020. Today he is regarded as a climate change hero all over the world for his tenacity.

If any of the two candidates shows even a fraction of the regard for science as Nasheed showed, U.S could go a long way in helping solve not only the nation’s but the world’s problems, Instead of spreading communal hatred and mistrust, people need to be encouraged to believe in the power of reason and scientific truth. J.F.K’s words in 1961 about sending a man to the moon may have been driven by the cold war, but they revolutionized NASA and has led to a huge boost to space technology which is positively impacting lives all over the world. This once again shows what strong political will can achieve. As Carl Sagan once said, “The earth is but a pale blue dot”; Instead of wasting time on communal tensions, we can let science and math guide our way into a better future.

God gave us integers !


Mathematics has become such an integral part of our lives that we hardly stop to think about it. We check our bill at the grocery store;  even without realizing that the basic math we are doing is actually a great power we have to understand nature.

On one hand, mathematical constructs like series, functions, calculus sound like something which is fit for textbooks and in the hands of engineers and scientists. But the history of mathematical discovery is very rich and diverse; the various branches of algebra, geometry, calculus, probability, statistics etc have had very different origins.

Pascal and Fermat, two Frenchmen basically developed the modern theory of probability in a series of letters to each other. Pascal was a mathematician and Fermat a lawyer, both concerned with the question of fairness in splitting up the prize money of an unfinished game of chance. They calculated the probabilities of outcomes and gave the definition of expected value.

Calculus was formulated by Isaac Newton because the prevalent rules of math weren’t enough for him to explain his work in acceleration and gravitation. Calculus allowed him to explain gravity in quite a beautiful fashion and his science became the bedrock of physics for many centuries to come.

On the other hand, there are many mathematical concepts developed just for sake of logic with no immediate practical relevance in mind; but these turn out to explain physical phenomena in nature which are discovered years later. E.g. the brilliant Indian mathematician Ramanujan published numerous equations and theorems in his brief lifetime in first 2 decades of the 20th century. His work has pervaded many areas of modern mathematics and physics. This begs the question, is math a human invention or is it a discovery of some underlying principles of nature…just like other sciences ?

A perspective that can be useful is to see how math is essential to understanding the complexities of nature. Just consider the simple action of throwing a ball in the air in front of you. Newton’s laws will give us pretty much the exact position where the ball will land. So one might consider math as some sort of tool created by us which gives us the info we need.

But nature is not always as simple as throwing a ball in the air. When we consider complicated systems like nature, we start realizing that our basic laws do not seem to useful in predicting outcomes. So does math have a boundary in which it can’t operate? Well, that’s really not the case; math can actually help us understand why nature behaves so erratically and cause what mathematicians call “Chaos”.

We don’t even need a system as complex as the weather to understand chaos. Let’s consider a simple expression f(x)=1-2x^2. To introduce complexity, we loop this expression by itself in the foll way :

f[x]= 1-2x^2 ; f2[x]=f[f[x]] ; f3[x] = f[f2[x]] … f25[x] = f[f24[x]]…

Let’s graph values for this functions for many iterations. We will use a starting value of x=1/π but once with 16 decimals and once with 15 decimals. The results are presented in the graph below.


We see a very surprising trend after about 60 iterations. Even though the difference between two x values is very small, the function values start fluctuating wildly. Thus we can see how even a small difference in the initial conditions can affect the final result. This is known as the butterfly effect. It is said that a butterfly flapping its wings in one part of the world could possibly kickstart a series of events which can lead to a tornado on the other side of planet. Such is the fine margin that nature operates on. It’s important to highlight that this type of chaos generated is completely deterministic unlike truly random events.

Well one might say that we could avoid such chaos by simply using a perfect value for the inputs in our calculations. But as we will show, that is often not possible. Let’s take the example of the number π.

π is defined as the ratio of the circumference of a circle to its diameter. It is calculated by integrating smaller chunks of circular motion along the orbit. But we can only get results of this integration by approximating it to the best possible decimal. π is an irrational number, meaning the digits after the decimal place do not follow any pattern infinitely. The only way to get a value of pi is to approximate up to as many decimal places as our computing system allows.

Thus there is always going to be an error in measurement of inputs when it comes to any calculation involving π. In applications like space orbits when magnitudes are huge, this can lead to big differences based on what level of approximation that we use for π.

The German mathematician, Leopold Kronecker, once said that “God gave us the integers, all else is the work of man”. It seems to imply that most math is just pure human invention. It might be so on paper, but it is beautifully ingrained in nature and is vital for us to understand it’s mysteries. As we have seen, the best simulator of nature is nature itself and it seems like nature is unaware of its future. But math helps us grasp the depths of this uncertainty; so we can almost say that the closest we can get to nature is through mathematical ‘discoveries’.


Mystery of Pi

Chaos & Self-similarity

Battling with Fear ….

Imagine sitting strapped in a cabin which can barely fit three people. A huge pile of solid rocket fuel containers are below you. Basically you are sitting on the top of a bomb which can blow you to pieces due to just a tiny malfunction. Even if you do launch off safely, your life is at the mercy of a machine. Terrified?

This is the reality of an astronaut every time a spaceship is about to lift off. The whole idea of spaceflight seems inherently so risky. A small spark, a tiny rip in a wire could turn a journey of a lifetime into a nightmare. The images of the smoky flumes of the Challenger shuttle and the visions of the startling, fiery bursts of light of the disintegrating Colombia are still fresh in people’s minds. How do astronauts deal with this kind of fear?

It turns out that the ways astronauts use to deal with fear holds very important lessons for how we can counter fear and insecurity in our daily lives. Nobody describes this better than Chris Hadfield, a senior Canadian astronaut, in his book “An astronaut’s guide to life on earth”. Hadfield, a former commander of the International Space station, says the way to combat this is to embrace the power of negative thinking. Seems strange? Read on..

All that can go bad, will go bad

This is the theme of how astronauts are trained. Each and every part of the proposed space flight is analyzed for things that could go awry. State-of-the-art simulators are built and the astronauts are trained in them until all the operations become second nature to them. An astronaut is not just someone who undergoes a driving test and is a given the license to fly.

Getting the privilege to go into space requires many years of dedication towards learning every possible thing about spaceflights. For an astronaut, skipping a chapter doesn’t mean just a loss of few marks in a test. That chapter might prove to be the difference between life and death in a bad situation in space.

“People tend to think astronauts have the courage of a hero- or maybe the emotional range of a robot.” says Hadfield, “But in order to stay calm in a high stress, high stakes situation, all you need is knowledge. Sure, you might feel a little nervous or stressed out. But what you won’t feel is terrified.”

Simulating Death

This is one of the stranger components of astronaut training. ‘Death Sims’ is what they call it. Before every human spaceflight, NASA performs some incredibly accurate drills for the possible death of an astronaut. The sim might start with a simple scenario – “ Chris is fatally injured in orbit’. On this the whole of the NASA disaster team revs into action – the ground crew, the medical staff, the program administrators… even the media relations people. Every step from how to inform the family, how to arrange for the safe return of the astronaut to Earth and also how to handle the PR situation that is bound to arise.

What do they gain by this ? Well, strange as it may seem, this drill actually gives reassurance to astronauts that things will be managed just fine in case of their deaths. Everyone always has this thing at the back of their minds. What will happen to my family in case I die ? This death sim gives them that extra boost of confidence when they finally step into the rocket ; a moment which might be the last time they see their families.

Power of negative thinking

“You have to walk around perpetually braced for disaster; convinced that the sky is about to fall” says Hadfield. If he walks into a crowded elevator, he will think about what can be done if the elevator gets stuck. When he puts on the seat belt of a plane, he will wonder what to do in case of a crisis.  

This is not being pessimistic. Rather by anticipating all possible obstacles,we can be more upbeat to face anything which life throws at us. We know what we have to do if things go wrong.  That’s the power of negative thinking.


Is the environment really in danger ?

Maldives – The sinking paradise

A treat for the eyes.. but only for some time now..

Maldives – the place of unrivaled luxury and pristine beaches. A dream destination for every traveler to enjoy few days of complete relaxation. But unknown to the bedazzled tourist, this wonderland is undergoing a ‘sea’ of change. The global rise in the sea levels is slowly eating up the coasts of Maldives.

Maldives, one of the world’s most low lying areas, is one of the few places where we can see the effects of global warming so strikingly. The coastline of the Maldives is being taken up inch by inch every passing day by the rising waves. The pearl of the Indian Ocean might not remain on our maps anymore. To have a chance of preventing this, we can resort to the well documented ways of reducing energy usage and carbon footprints. But primarily, we need to reform our mindsets about climate change and nature. Here are some of the ideas which we think are very interesting in that aspect.

Jurassic Park – Let’s save ourselves !

When dinosaurs ruled the earth..

We all know about Jurassic Park. Michael Crichton’s epic novel and Spielberg’s breathtaking movie has captured the imagination of people all over the world. But Jurassic Park  is so much more than just scary dinosaurs. It  has some very crucial lessons on the relationship between man and nature.

The idea of the park’s creators was to re-create living creatures who have been extinct millions of years ago and try and fit them into a restricted park setting. The point that they missed was that dinosaurs weren’t some species that disappeared because of deforestation or hunting. They have had their shot at dominating this planet. Nature selected that they become extinct. Trying to bring back the past amounts to playing around with nature’s rules which never yields success. This was demonstrated in the end where the dinos broke out of their cages and wrecked havoc on the whole system. If one tries to control nature, then nature will hit back.

Surprisingly the novel also emphasizes on the notion that even in difficult circumstances, life finds a way to survive and thrive as the dinos did even if the humans there didn’t manage to do so That gives us another very important lesson. When we say that we are damaging the “environment”, we should understand what that means. Even if there are catastrophic events on the earth, somewhere, in some tiny place on the planet, life will remain. And given enough time, nature will once again regain its full splendor. It’s not nature which is being put into danger by our actions; it’s us. We do not wield any power over the Earth. The faster we grasp that fact, the better we can plan for saving ourselves from extinction.

Siberia’s Happy people !

Survive in Siberia

How do you think life would be in the hellish cold of Siberia ? Quite taxing, right ? 

Werner Herzhog, the famous German Film director, gives us a very different perspective on one such Siberian community in his documentary “Happy People”.

Bakhtia is a region in the Siberian Taiga known for its extremely cold weather where a group of villagers have been living for centuries in their traditional way. Every year in winter when the Yenisei River freezes, the men of the village go hunting in the woods where they live a life of solitude. Every hunter has his own cabin and has to be completely self reliant in order to survive. Most hunters carry dogs that are tremendously helpful in hunting. Other than using some modern technology such as guns to kill larger prey and motorized snow sledge to cover vast distances of the Taiga, these hunters rely mostly on traditional traps to catch small animals. They then carry their game back to the village during spring time to sell and/or eat. Even after these hardships, they are quite content with this lifestyle and are glad to have their life so intertwined with nature.

Now these people who are dealing with natural uncertainties for centuries using more or less traditional methods are better equipped in dealing with climate volatility than people living in urban areas who are mostly just exposed to a constant controlled environment through their lives.

For most part of human history majority of human population has been living in rural societies that were more in touch with nature than ours. These communities have developed basic age-old methods to solve many problems nature poses them whereas urban societies have grown disconnected from natural forces. With the growing disconnect comes more and more dependence on technology that works best in normal times but it has forced us to keep our natural survival instincts aside.

Lets survive!

We have to realize here that there are parts of climate change that we can affect and there are parts that we cannot control or predict to a certain degree, but humans have tackled climate change all the time and what has been a powerful tool for our survival is our ability to think about and plan for the future.

Human behavior has been shaped by variations in climate change and the question of our survivability on this planet still remains, but we have a chance to answer it. For our own good, we better take it.  

Reference for the documentary: 


Evolution in Everything !

We are standing in the dense forests of Ranathambore in Northern India. This iconic national park is renowned for its tigers. Yet now, the forest guide has taken us to the edge of a big clearing.

He asks us to stay quiet and points to a herd of deer drinking water at a pond. The deer look nervous. Some are drinking, while some are looking around.

The guide makes a gesture towards one of the deers who is looking around. We follow the gaze of that deer and suddenly from some distance away, a majestic yellow and black striped animal jumps out of the grass and gallops towards the herd. But the watching deer had anticipated that. The herd of deer instantly take off and gallop away. It’s now unlikely that the tiger will get deer meat for lunch. The naturally developed survival tactic employed by the deer saved them.

Darwin’s Natural Selection


Galapagos Islands – The rich ecological diversity here influenced Darwin’s ideas

Many years ago, a British naturalist, Charles Darwin observed countless such animal interactions on his voyage to the Galapagos Islands and formulated his now famous theory of natural selection or evolution.

Natural selection is often known in popular culture as the “survival of the fittest”. Well, what do we mean by the “fittest” ? Is it the most strongest fellow around ? Generally it would indicate something like that. But in ecological terms, “fittest” has a whole different meaning.

Lets consider the example of a peacock. The peacock has a quite astonishing set of colored feathers. These don’t help it to gather food; but they do perform another very important function – attracting a mate. For a species to survive, it is extremely essential for it to mate and produce offspring. So an animal that may be fit for its environment in every other way, but fails to pass along its genes to the next generation has no effect on the future of its species. That’s how evolution by natural selection works – the species which prosper are the ones which develop the best genetic mutations to aid the cause of their gene pool growing. The rest just die out.

Evolution in sports


More interestingly, Darwin’s landmark theory not only applies to ecology, but also to various spheres of human life. Competition is an integral aspect of most areas of human interaction.

This competition is as ruthless as the one we see in nature. The ones who develop ways to keep on changing and adapting to the environment around them will ultimately prosper.

Lets look at a recent example in the world of English football. The champions of the last two seasons (Manchester City in 2011-12 and Manchester United in 2012-13) failed to recruit top class players in the summers following their titles and both failed to retain their crown next season. Of course there were other reasons like the retirement of United’s iconic manager Sir Alex Ferguson. But inactivity in the transfer market was a vital factor.

Manchester City lost their title to United whose capture of talismanic striker Robin Van Persie proved to be the difference between the two sides. But United repeated the same mistake in the summer of 2013 when they failed to make any world class additions to their side. Now they are languishing in the 7th spot in the league while City are flying high in the top 3 positions due to their decisive signings in the summer of 2013.

The last two years in the English Premier League have been stark examples of the fact that even the most mighty teams need to keep on evolving and bringing in fresh blood in order to keep on prospering.

Evolution in the business world

When you think about investment the first thing that comes to your mind is probably growing your wealth over a period of time. Now we classify time as past, present and future, three distinct things. Hence when we think about investment we are thinking about how our investment would last over time. Now how does one grow wealth over time? By investing in assets that are growing in value over time. Businesses are a source of investment.

But the key idea here is that, if we look into the past we can observe that businesses have evolved much like species have evolved on this planet by competing in business and economic environment. But history only gives us retrospect. So when asking the question, how much would a certain investment in a certain business yield over time, one must consider how effective the business model and the management would be in the future and how would the business withstand potential extraordinary changes in its environment.

The analysis is similar to asking whether a group of organisms would grow in population over time or be able to survive a potential catastrophic event . If the tiger population in a forest increased, it will probably lead to a decrease in deer population. Can that much be said with some degree of confidence? The organism’s survival depends on its ability to withstand change, which involves changing behavior as well as physical changes over generations that are favored by nature. In a company’s case it survival depends on how good a company is at having a durable competitive advantage. Now what may be durable in the future can be deduced from looking at past scenarios. But there will always be uncertainty.

Evolution is wonderful !


The mighty dinosaurs !
Courtesy:National Geographic

Some truly awe-inspiring species like the dinosaurs have roamed our Earth for millions of years. Yet, despite being so successful, they died out because nature didn’t generate enough mutations in their bodies for them to co-exist with the changing environment. They have never really died out though. They have evolved and are all around us. When you see a bird flying majestically in the sky, feel privileged. You have just seen a descendant of the great dinosaurs of the past !

Bradman – the best ?

Wherever we have sports, we have stats. Many actions in a sport can be quantified. Players are often defined by the numbers they generate. The greatest players often have the most glittering collection of stats against their names. Even in this number laden world, one statistic towers above all – Sir Donald Bradman’s batting average of 99.94 in the sport of Test cricket.

Over the ages, legendary sportsmen have churned out extraordinary performances and have accumulated staggering numbers. But here we will try to justify why the legendary Australian’s feat is often heralded as one of the greatest achievement for any sportsman in a major sport.

Why is Batting Average so important in cricket

Cricket is all about scoring more runs than the opposition. Batsmen need to score as many runs as possible in an innings and the fielding team needs to limit the scoring. So players who can make tons of runs are the stars of any team. Cricket has multiple formats, but the five day game of Test cricket is the oldest and arguably one that requires the most skill.

It has been widely accepted that batting average is the most accurate among the stats that we have in order to judge a batsman’s consistency. Batting average denotes how many runs a player scores per inning on average. It can be calculated for any period of time during a batsman’s career. And to illustrate Bradman’s remarkable achievement, we use a statistical diagram called a box plot to compare his batting average to his peers’. 

What the boxplots reveal

When players are compared, it is often debated about how the game has changed over the years and so it is unfair to compare two players from different eras. Every era has had differences in playing surfaces, quality of opponents, and pressure from the audience etc. But there is a way in which players can be analyzed. This way is by comparing the dominance a player exerted over his contemporaries. So for this analysis, we decided to compare players from a similar timeframe so as to greatly reduce era bias in the numbers.

We picked three eras – 1925-50, 1965-90, 1991-2013 and obtained the batting averages for each of these eras1. When we plotted the averages as points in a box plot format, we got these results – 









The grey box represents 50 percent of the data with 25% on each side of the middle line which is the median2 of the data. These 25 % areas are called ‘quartiles’. The top and bottom tails represent the rest of the data. 

A box plot is a good way to see how data is distributed and represents it’s variance. The lengths of the box and the tails and the position of the median line tell us about how skewed the data is.  If the median line is near the top that means there is less variance in the top data and vice versa. Similarly if the top tail is smaller it means there’s less variance in top data and vice versa.

In this case, you can see that the batting averages in the last two eras are quite identically distributed. But in the era 1925-50, you can see that there is a point at the top which is far away from the box plot. This point represents Bradman’s average of 99.94.

Bradman – A batsman like no other

This diagram not only reflects Bradman’s staggering dominance over his contemporaries, but it also illustrates how far away from the pack Bradman was as compared to dominating players from other eras.

Such was Bradman’s influence on his rivals that in 1932-33, the England team devised a whole new negative bowling technique called ‘Bodyline’3 specifically to combat Bradman’s extraordinary batting skills.

More than the numbers, this is a fitting tribute to his abilities. To put it simply, no other player has dominated his age like Bradman has.



[1] We picked three arbitrary eras. Calculations can be done for other choices too. The data was collected from Cricinfo.com.
[2] Median – If we sort the batting averages in ascending order, then the median is the middle average point in the sorted data. 
[3] A bodyline delivery was one where the cricket ball was bowled towards the body of the batsman on the line of the leg stump, in the hope of creating leg-side deflections that could be caught by one of several fielders in the quadrant of the field behind square leg. This was considered by many to be intimidatory and physically threatening, to the point of being unfair in a game once supposed to have gentlemanly traditions