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Business News/ Opinion / The cellerati slowdown
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The cellerati slowdown

Gompertz growth is slow to start with, picks up steam after a while, and then slows again. Which is exactly what happened with cellphones in India

Photo: Pradeep Gaur/MintPremium
Photo: Pradeep Gaur/Mint

In May 1998, India Today had a cover story titled The Cellerati. In that odd need, news magazines feel to identify trends—this one told us that with the coming of cellphones: “Indians are networked into a new lifestyle."

It has always amused me. It was made because in about 1998, “the number of cell phones touch(ed) a million." That’s right: fully 0.1% of India had got themselves phones. Naturally it was time to extrapolate to all 100% of us and suggest that we were networked into a new lifestyle.

But there’s something more intriguing in this than overblown magazine claims. (And not just in the way cellphone is spelled as two words). As the cover story says, that month the cellphone had been “only into the third year of its introduction in the metros, and just a few months in other cities". The “only" and “just" speak of a sense of wonder, that it had taken “only" three years for India to tot up as many as a million cellerati.

Yet the real sense of wonder might have been if we had reread this article in November 2010. That month, yes exactly that month, India’s count of cellerati leaped by—get ready—nearly 23 million; in all of 2010, by nearly 230 million. A million in three years? Laughably snail-paced.

Inevitably, that frenetic pace of 2010 slackened. By mid-2012, it was down to about 5 million a month and falling.

All of which amounts to a classic example of an intriguing mathematical relationship called the Gompertz Curve. It’s named for Benjamin Gompertz, a 19th century actuary and self-taught mathematician who proposed it after studying, of all things, data about human mortality. Meaning, data that spelt out how many of us die at specific ages. His law of mortality predicts this accurately enough that companies use it to decide how much to charge for life insurance.

I’ll return to that; but meanwhile you may already be wondering what the link is between Gompertz and cellphones. Well, Gompertz’s law accurately models a particular kind of growth: one that is slow to start with, picks up steam after a while, and then slows again.

Which is exactly what happened with cellphones in India. When they first became available, the instruments themselves were expensive, as were the charges to make and receive calls. (If memory from 1998 serves me right, you paid Rs16 a minute for air time). Naturally, only a trickle of people—the rich, or those for whom it was an indispensable business tool—bought into the technology. So despite India Today’s wonder at the time, on looking back we know that the number of cellphones in the country grew painfully slowly in those years.

But yes, that’s when we look back. For there was something of a tipping point in mid-2003, when incoming calls became free. Suddenly, lots of people who had never owned a phone decided to get themselves one. Suddenly, cellphones were flying off the shelves. Their declining cost and ever-cheaper airtime fuelled the spectacular growth through that decade.

And naturally this growth peaked, because the customer base neared saturation. Today, the great majority of Indians owns a phone. It’s tough to sell them more phones.

Gompertz for you.

The parallel to mortality? Think of it like this. In your youth, it’s pretty close to sure that you will live through the next year. As you get older, that’s progressively less of a sure thing. But here’s what Gompertz noticed: whatever your age, the odds that you will die within a year—close to zero in your youth—double about every eight years. This is his law of human mortality.

There are ways to at least intuitively explain all this, though I’m not sure we have a reason for the number eight figuring here. But what it boils down to is this: the chance that you will live to a given age is close to certain for infancy and youth, and it decreases pretty slowly for decades—much like the slow growth in cellphone ownership in the late 1990s. The decrease sharply accelerates in your 70s and further—much like what happened to cellphones when incoming calls became free in India.

And here’s the final piece of the puzzle. It’s still contentious, but there’s some evidence that, in extreme old age, the decrease in the probability flattens out again. This is sometimes called the late-life mortality deceleration and it seems to hold for insects. If it turns out to be true for you, me and homosapiens, that slowing growth completes the comparison to the cellphone ownership graph.

Gompertz for you, again. Really, there’s plenty more to explore, if I had the space.

For now, though: One of the things I most love about mathematics is the odd bedfellows it sometimes shines light on. Primes and cicadas, for example. Today, it’s mortality and cellerati. This stuff rocks.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza

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Published: 16 Jan 2014, 05:58 PM IST
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