The number 300 has been repeated by all kinds of people over the years as the number of families entering Mumbai every day, leading to overcrowding. However, research shows the real figure is approximately 48 families; 300 is our own Goldilocks number. Photo: Abhijit Bhatlekar/Mint
The number 300 has been repeated by all kinds of people over the years as the number of families entering Mumbai every day, leading to overcrowding. However, research shows the real figure is approximately 48 families; 300 is our own Goldilocks number. Photo: Abhijit Bhatlekar/Mint

How Goldilocks numbers distort the truth

Goldilocks numbersnot too large, not too smallare misleading when they falsely become part of the public discourse on an issue like immigration

Try asking an average middle-class resident of any large city in this country where the ubiquitous street kids, the slum dwellers, come from. They’ll likely say, with a measure of middle-class distaste, “outside". Meaning, they think they are migrants from elsewhere in the country. Nice urban shibboleths get built up around this belief.

For example: Hordes of “outsiders" are flooding into Mumbai; this is likely, in some hand-waving way, illegal; they are the reason the city is so overcrowded; they are taking away jobs that rightfully belong to the “sons of the soil"; and it’s these hordes who end up in slums and on the streets.

So how large are these hordes anyway? “You know", people here will say, shaking their heads in mild consternation, “about 300 families a day enter the city." Hold on to that number—I’ll return to it.

My late father, who spent his career in the Indian Administrative Service, thought the first mention of this figure 300 came courtesy the late Vasantrao Naik, chief minister of Maharashtra in the 1960s. It’s been repeated by all kinds of people in the years since, with occasional inflation too. In 1997, the state’s urban development minister, Ravindra Mane, announced in the assembly that “350 families migrate to Mumbai daily and now even the creeks (are) not free of slums".

In 2005, Newsweek wrote about “migrants who are still pouring into the city at the rate of some 400 families a day." (Ron Moreau and Sudip Mazumdar, Bombay Dreams, published 24 April 2005). And in her closely-observed, finely-sketched and tautly-written story of slum life in Mumbai, Behind the Beautiful Forevers, Katherine Boo has the same number. A young man in her book is, she writes, one of “roughly five hundred thousand rural Indians who annually arrived in Mumbai." If you do the mathematics, that’s about 300 families a day. (At a Delhi seminar in 2006, I heard the industrialist Vijaypat Singhania inflate the number substantially more: 8,000 people, he said, were entering Mumbai everyday. That’s 1,600 families, Mr Singhania).

It’s a compelling, almost frightening vision. All those probably unwashed immigrants, illegally thronging an already bursting city! How will we cope?

Compelling, yes. But it’s a number that’s completely wrong. It was proved wrong, to my knowledge, at least as long ago as 1995. That’s when an organization called the Centre for Research & Development (CRD) published its Socio-Economic Review of Greater Bombay. CRD comprised senior bureaucrats and respected economics professors, bank directors and police officers. Their data came from state and city agencies, census figures and more.

In the entire decade 1981-91—3,650+ days—said the Review, a total of 283,000 people migrated into Mumbai. That is, each day of that whole decade saw, on average, 78 people coming into the city. Taking the generally accepted norm of five people per family (hold on to that number as well), that’s fewer than 16 families each day. Not 300 or 350 or 400 families, but 16. The data also showed that migration was at its peak in the 1970s, when fewer than 60 families a day entered.

(Aside: the Review itself remarked on the startling decline in migration in the ’80s—60 families, down to 16. CRD speculated that the 1991 census had undercounted the population to a degree. But even with their “more plausible" projections, the ’80s saw 241 people, or 48 families, entering Mumbai each day. Not 300, but 48.)

This is the truth behind that number 300. But as these things go, the number sticks in the mind far more firmly than its refutation. It is still trotted out every now and then. (Like in this 2014 article: So why does it live on like this?

To answer that, I’m going to enlist the help of another number: 50,000. Some years ago, the journalist Brooke Gladstone wrote a book called The Influencing Machine, examining various aspects of the media. (Interestingly, it is a graphic book — written like a comic book, the pictures and speech balloons telling its story.)

In the book, Gladstone writes about something she heard on a NBC TV news programme in November 2005: that at any given moment, 50,000 “predators" are online, looking for children to target. This number was quickly repeated by others and at some point Gladstone decided to track down where it came from: a process she likened to “following Hansel and Gretel’s trail of breadcrumbs." (Aside: How many columns about numbers mention Goldilocks and Hansel and Gretel?)

She asked the NBC journalist who had reported the number, Chris Hansen. He said he had discussed it with Ken Lanning, a former Federal Bureau of Investigation (FBI) agent who now studies crimes against children. Lanning “couldn’t confirm it (but) couldn’t refute it either." He thought it was a reasonable figure, but was curious because the same number had “popped up in the past": in the early 1980s, it was regularly cited as the number of American kids abducted by strangers each year.

But this number was also cited as the number of human sacrifices every year by Satanic cults in the US —which raised Lanning’s eyebrows, because he also knew that there were about 20,000 murders in that country annually. Were these Satan followers really killing over twice as many people as “all the other murderers combined", and somehow contriving to have their murders unreported?

This dilemma apart, Gladstone couldn’t stop thinking about Lanning’s mention of the number popping up before. So she did some digging. Her astonished reaction: “50,000 is a death magnet!" As she writes: “Every year, 50,000 die in road accidents … and from secondhand smoke … and from trans-fats in America (and) from snakebite in India, and from malaria in Asia, and from pollution in Pakistan, and from car-noise-induced heart attacks in Europe … and every day 50,000 children die from global hunger and poverty, not to mention annual human sacrifice. What’s the deal?"

When the same number shows up again and again like this, journalists’ and mathematicians’ antennae start quivering. In each case, another journalist explained to Gladstone, the number may start off as a quote from someone who just uses it off the top of their head. Then it may be mentioned to some government authority, from where it might make its way into some academic study and then the press, gathering credibility with each step. Once it’s in the press, some other government authority will cite it, some other publication will use it … merry-go-round fashion, it has now become firmly part of the public discourse. (This is not to suggest that all these numbers are false, only to suggest that sometimes a source for them can be hard to track down).

But here’s the question: why 50,000? Why not 20 kids abducted by strangers every year? Why not 7.5 million deaths from snakebite in India? Well, 20 is so small that nobody would believe it. Similarly, 7.5 million is so large that people would scoff. So if you are really picking a number off the top of your head for such a phenomenon, 50,000 sounds about right: Not too small, not too large.

A Goldilocks number, in fact: Not too hot, not too cold. (In the famous children’s story, Goldilocks tries to decide which of three bowls of porridge to eat. One is too hot, one is too cold. The third? Not too hot, not too cold: just right).

So I think that 300 families figure is our own Goldilocks number. Three families a day? Too few; nobody will see it as a serious threat to the well-being of this city. About 5,000 families a day? Too many; nobody will believe it. Thus Vasantrao Naik, if it was him, settled on 300: not too small, not too large, but just right to both be believable and set alarm bells ringing in middle-class circles even decades later. A number you can confidently cite and not only will you not be challenged, you’ll come across as knowledgeable, maybe even scholarly.

And if that’s a good example of a Goldilocks number, what about that other number I asked you to hold on to—five, as the “generally accepted" size of a family? That might be a Goldilocks too. Clearly, one or two are impossible as a family’s size, and three—meaning one child—seems small too. And clearly, 10 is too large. So let us settle on—I mean let’s generally accept—five.

Though as we do that, we might consider that on average, Indian women have 2.4 children in their lifetimes. Thus on average, the size of an Indian family is likely to be not five, but about 4.4.

Similarly, we might also consider: if it’s not hundreds of unwashed families flooding into the city, what does account for Mumbai’s growth? The old recipe, of course: people making babies. At a rough estimate, somewhere close to 1,000 babies are born in Mumbai every day. What’s more, said the CRD Review, “migration’s relative contribution (has) been declining… since 1951." In fact, it sank below 50% in the 1960s, though “the absolute volume of net migration declined only in the 1980s."

All of which means that the angst residents of the city feel about jobs and crowds is probably best directed not at the bogey of migrants, but at other sons of the soil. The ones making babies.

Bandying about Goldilocks numbers, on the other hand, helps not at all.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners.

His latest book is Jukebox Mathemagic: Always One More Number. His Twitter handle is @DeathEndsFun.