Exponential growth can be a terrifying thing. We all know the story of the king who was foolish enough to grant a boon to one who was familiar with the concept of exponential growth. To recount, the king said, “Ask and I will grant it to you.”

The man said, “All I want is a few pennies. I want one penny on the first square of a chess board, two pennies on the second square, four pennies on the third, eight pennies on the fourth, and so on till we reach the 64th square of the chess board.”

The king, like our present day innumerate kings, was immensely relieved. Here was this idiot asking for pennies when he could have asked for a ton of gold.
“Done,” said the king and asked his minister to make the arrangements.

The minister soon reported that he had finished counting the total amount the king had promised and it turned out to be around 184,467,441,000,000,000 or $185 million trillion. The annual GDP of the
US is $10 trillion. It would take the US about 18.5 million years to get that amount together.


We are talking large sums when exponential growths are concerned. It does not matter what the value of the exponent is. It could be as little as 2%. In a matter of just 35 years, the world population of 6 billion would increase to 12 billion at a 2% growth rate. It is estimated that it took all of human history till the year 1804 CE for human populations to hit the billion mark. The latest billion was added to the human population in about 12 years — a million times faster.

World Population

Population      Year    Interval
----------      ----    --------
1 billion       1804    all of human
2 billion       1927    123 years
3 billion       1960    33 years
4 billion       1974    14 years
5 billion       1987    13 years
6 billion       1999    12 years

India’s population was around 350 million in 1947. Now we have three times as many people alive in India. Bihar, UP, Rajasthan, and MP make nearly 45% of India. They are also among the poorest states of India.

India has more people than all of Africa,North America and South America combined. And all these people, more than a billion,
or around 17% of all humanity, are jammed into only 2.4% of the world’s landmass.

It is crowded as all heck and still every year we add more people than the population of Australia.

Population in India density has risen concomitantly with the massive increases in population. In 1901 India counted some seventy-seven persons per square kilometer; in 1981 there were 216 persons per square kilometer; by 1991 there were 267 persons per square kilometer–up almost 25 percent from the 1981 population density. India’s average population density is higher than that of any other nation of comparable size. The highest densities are not only in heavily urbanized regions but also in areas that are mostly agricultural.


[Continue to part 2 of Numbers.]

Author: Atanu Dey


2 thoughts on “Numbers”

  1. Might your numbers be a little off?

    1971: July 16 – The four billionth baby was born.

    Data also shows that the growth in population over the last 50 years has been more linear than exponential.

    The rate of growth has also considerably slowed down in the last 10 years.

    Ofcourse population analysis needs other factors like aging of population, effect of fertility, birth rates, the effect of AIDS/HIV to be a complete analysis.

    The above no way tries to prove that we are not facing a looming crisis. Just trying to refactor some of the data and include other parameters.


  2. very true, prashant. The world population seems to be heading more towards a linear plateau region of growth than the exponential graph we all believe in. Particualrly in the western countries there is no real danger of population outgrowing natural resources. In India though the situation is a bit different. But yet, somehow I believe a country’s population growth slows down automatically with economic development. I don’t have figures as of now to support my conjecture, but I do think that higher birth rates are more associated with poverty than with a particular culture or civilization. As poor people learn the virtues of smaller families, as and when they get literate, as and when they can afford to dwell on future planning because they dont have to worry abt their next meal,lower birth rates show their effect. Also, sex as a cheap source of entertainment also loses its charm, and the willingness to use contraceptives also increases. The issues of birth control and rural upliftment are essentially interwined particularly in a democratic set-up like India( in China its a different story) and there is more a need to take a holistic view of the situation than trying to make sense of one domain in isolation.


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