I've covered the ground in this essay before, but two things: 1) It bears repeating, it bears repeating, because the myth it seeks to debunk keeps getting regurgitated. 2) I thought I'd explain the actual mathematics behind the debunking.

So here you are. Myth: Muslims are soon going to outnumber Hindus in India. Debunking: below.

Myths need busting, and often over and over again. Often too, it’s a futile exercise, because to some, the myths are more seductive than any busting. Yet especially in this fog of accusations and hatred we’re living through right now in this country — the wrangle over the CAA and NRC, I mean — it’s especially important to keep on with the busting. I’m going to attempt just that in this column, but by using some of what this column is about: mathematics.

I’m repeatedly amazed at how much of the defence of the new Act is couched in terms of extreme hatred of Muslims. That by itself should be a red flag, a sign of something amiss. Yet the hatred keeps flowing. And too often, it finds expression in population numbers. Muslims are increasing their numbers, goes this argument, much faster than Hindus. Which means, goes this argument, that the time is just around the corner when Muslims will outnumber Hindus in India.

This is supposed to be a terrifying thought. One scare-monger spelled out his fears about this in an article, long before we had even heard of the CAA: “Non-Muslims now rarely venture into areas of India where Muslims are in large numbers, fearing unpredictable, irrational behaviour or violence directed at them.” Given that kind of fear, the prospect of Muslims actually outnumbering Hindus in this land, this man wanted his readers to believe, is self-evidently a horrible one for us all.

Well, it is indeed a horrible prospect, but not for the reason the haters like him hold tight to their puny chests. Let me explain, using numbers we actually have rather than empty rhetorical flourishes like “where Muslims are in large numbers”.

In August 2015, the Registrar General and Census Commissioner released population data by religion from India’s 2011 Census. Taken from there, consider the population growth of the various religions in the decade 2001-2011. The Hindu population increased by 16.8% in those ten years, Muslim by 24.6%, Christian 15.5%, Sikh 8.4%, Buddhist 6.1% and Jain 5.4%. The result, as of 2011, was that 79.8% of Indians were Hindu and 14.2% Muslim. Other faiths each accounted for far smaller fractions of our population, which the Census found was just over 1.2 billion.

That is, in 2011 we had about 958 million Hindus in India, and 170 million Muslims.

With me so far? Now if we assume the same growth rates persist (which we cannot, but I’ll return to that) — 16.8% per decade for Hindus, 24.6% for Muslims — we can project both populations to the time in the future when Muslim numbers will equal Hindus. When will that be?

To answer that, we need some relatively elementary, if a little involved, arithmetic. Bear with me as I explain.

Here’s the issue: the 958 million Hindus are growing at a rate of 16.8% every decade, and the 170 million Muslims at 24.6% every decade. One decade from now (or actually from 2011, but let’s not quibble), the two populations will have increased by these amounts:

Hindus: 958m x 16.8% = 161m

Muslims: 170m x 24.6% = 42m

That is, one decade from now the respective populations will be:

Hindus: 958m + 161m = 958m x 1.168 = 1.119 billion

Muslims: 170m + 42m = 170m x 1.246 = 212m

Since we assumed the growth rates don’t change, we can do just the same calculation for the decade that follows. The increments in those ten years will be:

Hindus: 1.119b x 16.8% = 188m

Muslims: 212m x 24.6% = 52m

And thus the respective populations two decades from now:

Hindus: 1.119b + 188m = 1.119b x 1.168 = 958m x 1.168² = 1.307b

Muslims: 212m + 52m = 212m x 1.246 = 170m x 1.246² = 264m

We could keep doing these laborious calculations for decade after decade, of course, searching after every iteration for the point when Muslim numbers will equal Hindus. But no doubt you recognize this growth as equivalent to the notion of compound interest — and we know how to calculate that. Thus, three decades from now, the populations will be:

Hindus: 958m x 1.168³

Muslims: 170m x 1.246³

And to generalize this, some number “n” decades from now, the populations will be:

Hindus: 958m x 1.168ⁿ

Muslims: 170m x 1.246ⁿ

So now we ask, for what value of n will these two be equal? That is, we want:

958m x 1.168ⁿ = 170m x 1.246ⁿ

Rearrange this equation:

958/170 = (1.246/1.168)ⁿ, or 5.635 = 1.067ⁿ

I wouldn’t hold it against you if your eyes are glazing over by now. Lots of calculations, I know. But we’re almost done. Your high-school mathematics memories will tell you that at this point, we use logarithms, and that gives us:

log 5.635 = n x log 1.067, or n = log 5.635 / log1.067 = 27.

There we have it. At those growth rates, it will take 27 decades, or 270 years, for the Muslim population to catch up to the Hindus.That is, the hate-mongers are quaking in their shabby boots — and asking us to do so as well — about something that will happen as we, or actually our descendants many generations over, close in on the 24th Century. Are you really going to worry about what might happen in the year 2290 AD?

But even if the haters do quake about that, let’s ask another question: assuming these growth rates, how many Hindus and Muslims will there be in India in 2290? In other words, what is 958m x 1.168

Answer: 64 billion. 64 billion Hindus and 64 billion Muslims. Think of it. This, in a nation that today has a total of 1.3 billion Indians. This, meaning 100 Indians for every single Indian living today: 100 Indians crowding that spot where you sit reading this, 100 Indians jostling for the tiny standing space you occupy in the 8:27 Churchgate fast, 100 Indians sharing one seat to watch Deepika Padukone in a rerun of Chhapaak, just as they were going to do this week. This, and remember we have not accounted for Christians and Sikhs and Buddhists and other varieties of Indians, not forgetting other denizens of India such as cows and dogs, cars and bookshelves, trees and playgrounds.

This is the mirage-like prospect that a deep-seated hatred drives people to dream up and fear.

The truth should be apparent. The really horrible, fearful prospect is not that Muslims will outnumber Hindus. Instead, it’s that hundred-fold increase the calculations above suggest. If we are actually going to rack up numbers like those, we will have died out from overcrowding long before getting to that moment in 2290 AD, that dreadful prospect of Hindu-Muslim parity.

And here’s what makes that prospect even more mirage-like. The reality is that we cannot assume the same growth rates — Hindu 16.8%, Muslim 24.6% — will hold indefinitely. In the earlier decade, 1991-2001, Census 2001 figures showed that the Hindu and Muslim populations increased by 19.9% and 29.5%, respectively. Those numbers decreased to 16.8% and 24.6%, respectively. Obvious from those numbers is that growth rates are decreasing. There’s nothing unusual here; this is exactly what happens as a country develops. (Note too that the Muslim growth rate declined faster, decade to decade, than the Hindu growth rate). So since the country has continued to develop since the 2011 Census, the 2021 Census will certainly show further declines in these growth rates. That means even greater population projections than 64 billion, an even longer time to population parity than 270 years.

Welcome to the overcrowded wasteland of 25th Century India, perhaps. The pity is that the hatred in too many of us reduces us to such a wasteland right now.

So here you are. Myth: Muslims are soon going to outnumber Hindus in India. Debunking: below.

***

Myths need busting, and often over and over again. Often too, it’s a futile exercise, because to some, the myths are more seductive than any busting. Yet especially in this fog of accusations and hatred we’re living through right now in this country — the wrangle over the CAA and NRC, I mean — it’s especially important to keep on with the busting. I’m going to attempt just that in this column, but by using some of what this column is about: mathematics.

I’m repeatedly amazed at how much of the defence of the new Act is couched in terms of extreme hatred of Muslims. That by itself should be a red flag, a sign of something amiss. Yet the hatred keeps flowing. And too often, it finds expression in population numbers. Muslims are increasing their numbers, goes this argument, much faster than Hindus. Which means, goes this argument, that the time is just around the corner when Muslims will outnumber Hindus in India.

This is supposed to be a terrifying thought. One scare-monger spelled out his fears about this in an article, long before we had even heard of the CAA: “Non-Muslims now rarely venture into areas of India where Muslims are in large numbers, fearing unpredictable, irrational behaviour or violence directed at them.” Given that kind of fear, the prospect of Muslims actually outnumbering Hindus in this land, this man wanted his readers to believe, is self-evidently a horrible one for us all.

Well, it is indeed a horrible prospect, but not for the reason the haters like him hold tight to their puny chests. Let me explain, using numbers we actually have rather than empty rhetorical flourishes like “where Muslims are in large numbers”.

In August 2015, the Registrar General and Census Commissioner released population data by religion from India’s 2011 Census. Taken from there, consider the population growth of the various religions in the decade 2001-2011. The Hindu population increased by 16.8% in those ten years, Muslim by 24.6%, Christian 15.5%, Sikh 8.4%, Buddhist 6.1% and Jain 5.4%. The result, as of 2011, was that 79.8% of Indians were Hindu and 14.2% Muslim. Other faiths each accounted for far smaller fractions of our population, which the Census found was just over 1.2 billion.

That is, in 2011 we had about 958 million Hindus in India, and 170 million Muslims.

With me so far? Now if we assume the same growth rates persist (which we cannot, but I’ll return to that) — 16.8% per decade for Hindus, 24.6% for Muslims — we can project both populations to the time in the future when Muslim numbers will equal Hindus. When will that be?

To answer that, we need some relatively elementary, if a little involved, arithmetic. Bear with me as I explain.

Here’s the issue: the 958 million Hindus are growing at a rate of 16.8% every decade, and the 170 million Muslims at 24.6% every decade. One decade from now (or actually from 2011, but let’s not quibble), the two populations will have increased by these amounts:

Hindus: 958m x 16.8% = 161m

Muslims: 170m x 24.6% = 42m

That is, one decade from now the respective populations will be:

Hindus: 958m + 161m = 958m x 1.168 = 1.119 billion

Muslims: 170m + 42m = 170m x 1.246 = 212m

Since we assumed the growth rates don’t change, we can do just the same calculation for the decade that follows. The increments in those ten years will be:

Hindus: 1.119b x 16.8% = 188m

Muslims: 212m x 24.6% = 52m

And thus the respective populations two decades from now:

Hindus: 1.119b + 188m = 1.119b x 1.168 = 958m x 1.168² = 1.307b

Muslims: 212m + 52m = 212m x 1.246 = 170m x 1.246² = 264m

We could keep doing these laborious calculations for decade after decade, of course, searching after every iteration for the point when Muslim numbers will equal Hindus. But no doubt you recognize this growth as equivalent to the notion of compound interest — and we know how to calculate that. Thus, three decades from now, the populations will be:

Hindus: 958m x 1.168³

Muslims: 170m x 1.246³

And to generalize this, some number “n” decades from now, the populations will be:

Hindus: 958m x 1.168ⁿ

Muslims: 170m x 1.246ⁿ

So now we ask, for what value of n will these two be equal? That is, we want:

958m x 1.168ⁿ = 170m x 1.246ⁿ

Rearrange this equation:

958/170 = (1.246/1.168)ⁿ, or 5.635 = 1.067ⁿ

I wouldn’t hold it against you if your eyes are glazing over by now. Lots of calculations, I know. But we’re almost done. Your high-school mathematics memories will tell you that at this point, we use logarithms, and that gives us:

log 5.635 = n x log 1.067, or n = log 5.635 / log1.067 = 27.

There we have it. At those growth rates, it will take 27 decades, or 270 years, for the Muslim population to catch up to the Hindus.That is, the hate-mongers are quaking in their shabby boots — and asking us to do so as well — about something that will happen as we, or actually our descendants many generations over, close in on the 24th Century. Are you really going to worry about what might happen in the year 2290 AD?

But even if the haters do quake about that, let’s ask another question: assuming these growth rates, how many Hindus and Muslims will there be in India in 2290? In other words, what is 958m x 1.168

^{27}?Answer: 64 billion. 64 billion Hindus and 64 billion Muslims. Think of it. This, in a nation that today has a total of 1.3 billion Indians. This, meaning 100 Indians for every single Indian living today: 100 Indians crowding that spot where you sit reading this, 100 Indians jostling for the tiny standing space you occupy in the 8:27 Churchgate fast, 100 Indians sharing one seat to watch Deepika Padukone in a rerun of Chhapaak, just as they were going to do this week. This, and remember we have not accounted for Christians and Sikhs and Buddhists and other varieties of Indians, not forgetting other denizens of India such as cows and dogs, cars and bookshelves, trees and playgrounds.

This is the mirage-like prospect that a deep-seated hatred drives people to dream up and fear.

The truth should be apparent. The really horrible, fearful prospect is not that Muslims will outnumber Hindus. Instead, it’s that hundred-fold increase the calculations above suggest. If we are actually going to rack up numbers like those, we will have died out from overcrowding long before getting to that moment in 2290 AD, that dreadful prospect of Hindu-Muslim parity.

And here’s what makes that prospect even more mirage-like. The reality is that we cannot assume the same growth rates — Hindu 16.8%, Muslim 24.6% — will hold indefinitely. In the earlier decade, 1991-2001, Census 2001 figures showed that the Hindu and Muslim populations increased by 19.9% and 29.5%, respectively. Those numbers decreased to 16.8% and 24.6%, respectively. Obvious from those numbers is that growth rates are decreasing. There’s nothing unusual here; this is exactly what happens as a country develops. (Note too that the Muslim growth rate declined faster, decade to decade, than the Hindu growth rate). So since the country has continued to develop since the 2011 Census, the 2021 Census will certainly show further declines in these growth rates. That means even greater population projections than 64 billion, an even longer time to population parity than 270 years.

Welcome to the overcrowded wasteland of 25th Century India, perhaps. The pity is that the hatred in too many of us reduces us to such a wasteland right now.