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 !


What is the purpose of society?

Ants are fascinating little creatures. You drop one little piece of food on the floor and in no time, a swarm of ants will be all over it. Follow their path and somewhere along the line, you will be treated to one of nature’s most interesting formations – an ant colony. This huge pile of earth is like the mirror image of the world that we humans inhabit.

The human society is an organization, much like an ant colony. It is a system that allows us to achieve certain things we otherwise couldn’t have achieved individually. Humans have lived in some sort of society for a long time now. A society serves many purposes. It has helped in hunting-gathering, protection from predators and as human culture evolved societies became more complex.

The main aim of any society is to create a better life for it’s inhabitants. Now better is a qualitative term, every individual’s definition differs. How then can society work towards making lives of its citizens better?

Nature’s great truth – Inequality

Civilization has evolved and throughout history, the structure of the society has existed on a spectrum from closed societies which are authoritative and stress on the “collective” on one extreme to open societies which believe in providing “individual freedom” to citizens or maximizing the utility of an individual on the other. We believe that open societies lead to more productive economies thus benefiting the whole world.

One of the major concerns in a society is the notion of inequality. Inequality is inherent in nature. We can be strong, we can be weak, we can be born rich or poor, we can ace the IQ tests or fail them. Inequality in abilities naturally leads to inequality in returns. But that is not the problem. For a society to exist, it is essential that performance and ability are rewarded. But what a society should aim for is not equality in returns, but equality in opportunities.

Be the creator, be the created

The acclaimed investor, Warren Buffet has a very interesting viewpoint on this issue. Lets see what he thinks:

Let’s say you are given the freedom to design a society structure for the whole world – yeah something like how Morgan Freeman gave the reins of the world into Jim Carrey’s hands in Bruce Almighty (note: you should watch the movie if you haven’t. It’s quite funny).

But there is a catch. You yourself lose your identity and have to pick a slip randomly from a bowl which has 7 billion slips each having the characteristic of a human from the current population. There it is. You could get any slip – A male or a female, A rich guy in America or maybe a poverty stricken person in Congo.

Now this changes things, doesn’t it ? How would you frame the rules of society knowing that you could end up being anyone ? You wanna excessively reward the highly skilled ? What if you turn out to be one of those who isn’t so good ?

So you want to design a society that gives everyone the opportunity to be able to succeed, not knowing what slip an individual gets. As you can guess, it is gonna be a very delicate balancing act. The boundaries of incentives for performance and security for the less-abled are blurred.

Open society

A society striving to move towards the open end of the spectrum, therefore must provide a safety net for the people at bottom, let the top take risk in such a manner that the result of their failure does not affect the general public. Look at the hedge fund industry for example. No player is too big to fail. The industry gains from failure as only the top performers stay in business and are allowed to take risk. The failure of several others does not affect the whole industry like the failure of big investment banks on wall street affected the whole global financial system leading to anger in general public about inequality between the rich and the poor. The middle should be left as it is because they more or less have the same opportunities as anyone in America.

Now the American system may have its faults but it has worked fairly well for many people for centuries.The current political scenario may not be the most efficient in years, but that is where team-work and reconsidering incentives becomes essential.

To create a system that works for everyone, policymakers must put aside their divisive party issues although such games increase their popularity with certain factions of society. Everybody wants different things. Therefore you can lump people in groups, in terms of demographics, race, religion, geography, etc. and appeal to their common issue. But one group’s issue of interest may be radically opposed to another group’s opinions. How does a politician then resolve this conflict of interest so that the policies he puts in place that benefit one group do not harm other conflicting groups? A political campaign can be based and won by focusing on a certain issue that appeals to people’s emotions. But when the politician takes office his policies cannot be divisive, in the sense that they benefit one group at the expense of others. That is being short sighted because in the long run things will normalize and other issues he didn’t tackle carefully will also present themselves decreasing the politician’s popularity.

Only when a politician is capable of thinking of all of these qualities that the“true” population of citizens may be distributed across will he understand the disadvantages of being so short sighted by putting in place policies that put a certain group at an unfair advantage.

Now the unfortunate part is that the politician might get away with being short-sighted, depending on the level of transparency and bureaucracy in the system, the appeal of his political campaign may mask his shortcomings. Therefore incentives are important. So that everyone is accountable. For example, if unchecked deregulation in the markets is believed to be the cause of excesses leading to a bubble and then panic eventually popping the bubble and causing enormous damage to the economic system like the most recent recession did, then policies must be put in place that regulate these excesses no matter how much a particular interest group lobbies to have policies set up their way. This is because judging from history, its the taxpayers that eventually end up paying for the repercussions of greed in society.

The system is too complicated and there are lots of variables to get it right the first time, but we must strive to work on incentives that influence people’s behavior. Because only governments can set the rules which lead to excesses and only government can set the rules that minimize the ill effects of excesses.

  1. http://blogs.rhsmith.umd.edu/davidkass

Black holes !

Black holes are perhaps the most mysterious objects in the universe. In layman’s language, it can be said that a black hole is a body with gravitational pull so intense that not even light can escape from it thus making it ‘black’

So if the black hole is indeed ‘black’, how do you see it ? Well, it turns out that you can’t. In fact we have never actually observed a black hole in the same manner as we can view distant stars and galaxies. We can’t see them; but we can definitely predict their presence and detect their strange effects.

To get an understanding of these effects, we first need to visit one of the theories which changed the way we view our universe – Albert Einstein’s general relativity.

Einstein’s Tower Experiment

You throw a ball high up into the air vertically using only your physical strength. What would you expect will happen to the ball? A reasonable person would say the ball will go up for a certain amount of time before it comes to a halt and then eventually it will drop on the ground.

This happens so the kinetic energy(KE) of the ball (KE is highest at the point of release from the arm) is converted to gravitational potential energy(PE) when the ball is thrown up. The ball stops when all KE is converted to PE .Then while falling down, it converts all its PE to KE in the reverse process. All this is basic High school physics !

Here’s where things can get complicated though; what if you are shooting a beam of light from the surface of the earth vertically up? Would you expect light particles (photons) to lose some of their kinetic energy the same way that a ball would?

Turns out that if we assume that light will not be affected by gravity and lose its kinetic energy as it moves up, then using Einstein’s Energy- mass relationship we come to  strange consequences where extra energy is created! This violates the conservation of energy law – energy can neither be created nor destroyed. Therefore, our assumption that gravity does not affect photons must be wrong and calls for a correction. So we correct our mistake by showing that the photon loses energy when moving vertically up. This phenomenon is called Gravitational Redshift.

Now imagine an observer standing at the top of a tower – stationary w.r.t. ground (not free falling). Put a source of light at the surface of the earth and shoot a beam of light vertically up. The photons lose energy due to earth’s gravity. This means that the frequency of the light wave decreases due to the fact that Energy of photons = Planck’s constant*Frequency. As a consequence, wavelength increases (inversely proportional to freq.) and hence it is called redshift as increasing wavelength shifts towards the red part of the spectrum. The speed of light is a fundamental constant of the Universe, it does not vary.Therefore as the photon loses energy while climbing vertically up from the surface of the earth, the observer will see the wave of light redshifted depending on how high he is standing and the strength of the earth’s gravitation1

Check your clocks !

Imagine a clock built out of frequency of light wave and placed at the surface of the earth. As the beam of light shoots up it will be redshifted by gravity, meaning the frequency will decrease and the clock will seem to slow down from the observer’s point of view. The understanding of this phenomenon revolutionized the world of physics.

Black Holes and General Relativity equations

Einstein derived a set of complex equations popularly known as Einstein field equations to describe the geometry of the Universe and how it “curves” due to mass and energy. So, the way of representing this curved space is, a massive object will put a dent in the space-time fabric and light travelling from near the object will have to cover a longer path causing it to “bend” due to the mass of the object (gravitation).

The most extreme prediction of this theory is a black hole. Well, how do these strange objects come into existence ? They are formed mostly from the death of a star. A star goes through a long evolutionary process starting from just a gas cloud. When stars having masses much higher than our sun are in the last stages of their evolution, the star explodes( the phenomenon is called a supernova) and the remaining mass goes on contracting in size. Correspondingly its gravitational pull keeps on increasing until the stage arrives where not even light can escape from it. So this stage of a star is called a ‘black hole’ due to the fact that no light ever can escape it.

Now look at above figure representing a black hole and let us analyze it from the General relativity point of view. The black hole does not merely dent the space time, but it puts a hole in it called singularity. This singularity could be interpreted as a point (no dimension) where all the BH mass is squeezed into and has theoretically infinite gravity2


As a result of light having a finite speed, there may exist a gravitational field so strong that light coming from the mass creating the field will lose all its energy before reaching a stationary observer outside the gravitational field. Such a gravitational field is created by a Black Hole and the corresponding area (no escape zone for light) known as the event horizon is proportional to the Schwarzchild radius3(SR). Information from inside the event horizon cannot reach outside. This is because the speed of light is a fundamental limit that we know on how fast anything can be transmitted from one point to other.

Does that mean BH is a vacuum cleaner that sucks everything inside? If suddenly the Sun turns into a BH would the Earth be sucked inside? No! Things will orbit around the black hole just like they orbit around a star if they are moving fast enough outside the event horizon. If they are moving too slow near the BH gravitational well they will fall towards the center. If they are moving too fast they will get deflected but continue moving in the same direction until acted upon by some other force. Inside the event horizon all world lines lead to singularity!

Astronaut freezes in time !

Go back to tower experiment in the earlier section. This time imagine an observer standing outside the gravitational potential of the Black hole, beyond gravitational potential of BH – stationary w.r.t. the BH. An astronaut is free falling into the black hole. As the astronaut is getting closer and closer to the event horizon the light emitted by his suit is getting more and more redshifted when it reaches the external observer. Hence the astronaut’s clock appears to be moving slower and slower w.r.t. external observer’s clock. But this is only relative, the astronaut perceives his own time moving normally. Now this clock slows down until the astronaut reaches the event horizon at which point the slowing-down-factor approaches infinity, in other words the external observer sees the astronaut frozen in time at the event horizon!

From the astronaut’s (assuming he manages to survive the immense tidal forces created by BH) perspective, all light from outside reaching his eyes will be blueshifted (opposite of redshift, photon gains energy) increasing frequency of wave more and more as he approaches the event horizon. Hence he sees the external observer’s clock moving faster and faster (frequency increases). At the event horizon he sees the observer’s clock moving infinitely faster!

The world’s biggest lenses

Of course we cannot send a person inside a black hole to test these theoretical predictions. Strong tidal forces of the BH are more likely to just rip a person apart before even reaching the event horizon. Instead lets look at what we can observe with telescopes and light sensitive detectors as a result of black holes.

A fascinating phenomenon Black holes (or any massive object creating spacetime curvature for that matter) can produce is called “gravitational lensing”. Imagine a black hole obstructing our view of a further object in some direction in space. The light from this object will bend due to the black hole’s gravitational well – as we saw earlier, light takes longer path to travel due to the curvature in spacetime. This bending may lead to distorted image of the object in the background.  The nature of the distortion and how the image will appear depends upon the angle the lensing object makes with the distant object and an observer on earth. See image below4

Ever since the discovery of gravitational lenses, astronomers have been interested in studying them. These lenses apart from being fascinating may be helpful in making more accurate measurements of distant objects.

Goodbye, Newton?

So there it is, the expansion of physics from Newtonian or classical mechanics with its notion of absolute time to theory of Relativity which integrates 3D space and time into a 4-Dimensional fabric of space-time. Space time has changed the way we look at the universe and it’s workings.

So do we just discard Newton’s classical laws of physics? Absolutely not! Relativistic calculations are not always practical or fruitful in improving our level of accuracy in cases of small influence of gravity (or small velocities we are dealing with). Classical mechanics is still very useful in making several deductions in the field of astronomy.

1. This has been experimentally verified by putting extremely sensitive atomic clocks at various heights from the surface of the earth and measuring the differences in time due to earth’s gravitational well.
2. Humans have a hard time imagining infinity. It can be said our physics is insufficient at this point to understand this gravitational singularity
3. The Schwarzschild radius is the radius of the event horizon surrounding a non-rotating black hole. If any object is compressed to a physical radius smaller than its Schwarzschild radius, then it will become a black hole. Formula for the Schwarzschild radius is Rs = 2 GM/c^2. M is the mass of the body, G is the universal constant of gravitation, and c is the speed of light.
4.In the formation known as Einstein’s Cross, four images of the same distant quasar appear around a foreground galaxy due to strong gravitational lensing

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