September 02, 2011

The number of things

My current effort for my "A Matter of Numbers" column in Mint is titled "The Number of Things". Just in case you were curious, the answer is yes: the essay does mention svelte figures, though perhaps not quite the ones you're thinking of.

There's also a mention of "the beginning of this month, less than three weeks ago" -- which applied when I was writing the essay, but I overlooked the fact that it would be published in September. So if your brow furrows at that, put it down to my own clumsiness with numbers, which is exactly what I'm going on about anyway.

You'll find it here.

Though if you have difficulty with the link, the text is below (with the September mixup fixed).

Some clarifications for those of you who might not know a few references in here: a crore is 10 million. The Mauryan Empire ruled over much of India between about 325 BC and 180 BC. Antilla is the massive mansion India's richest man, Mukesh Ambani, has built for himself in Bombay. The Commonwealth Games were staged in Delhi last year, and turns out to have been one enormous cesspool of corruption.

Comments welcome!


A lady I knew well was warm, well-read and knowledgeable: an all-round sweetheart. Sadly, she also suffered from a far too common affliction. She was a near-total innumerate. She went blank when faced with bank statements. Despite showing her that her investments brought her an income considerably greater than mine, she was convinced she was a pauper.

"I can't understand all these numbers!" she'd say with a helpless smile.

Many of us know about illiteracy, but how many are concerned about widespread innumeracy -- the inability to deal easily with numbers? (The mathematician John Allen Paulos made the term famous with his 1989 book, "Innumeracy: Mathematical Illiteracy and its Consequences"). Think of how often you've heard people saying "I hated maths in school!" Or "I'm a people person, not a numbers person!"

I'm just wondering, do we as easily talk up our difficulties with words? Have you heard people say, echoing the lady I knew, "I can't understand all these letters!"

And yet numbers are everywhere, all the time. Whether in the latest budget, or the latest gigantic scam, or the results from the last Census: numbers surround us, often with plenty of zeroes attached. If we don't understand them, we don't understand their impact. We don't fully understand issues that affect our lives every day.

But fear not! If you merely leap aboard a number wagon with me, we'll look more closely at some svelte figures -- ok, bad adjective -- we've heard of lately.

The Commonwealth Games mess, remember that? One report quoted an official thus: "The total CWG misappropriation may touch Rs 8000 crore, which is quite huge and alarming." Sure, but how huge? Well, let's say a CWG scamster was spiriting money away at the rate of one rupee per second, 24 hours a day, seven days a week. Pretty rapid misappropriation, I'd say. So how long would he take to fill his pockets with 8000 crore?

The answer: more than 2500 years. That is, to be done today, this rupee-a-second scamster would have had to start nearly two centuries before the Mauryan Empire.

Puts 8000 crore in perspective, no?

Rolling right along: In February, Pranab Mukherjee announced a "provision of Rs 1,64,415 crore" for defence services in this year's budget. "Needless to say," our Finance Minister continued, "any further requirement for the country's defence would be met." No doubt this set off the same applause in Parliament that previous Ministers have received for statements like "we will not compromise on national security!"

Applause is good, but what does that figure really mean? What is our military costing you and me?

For each Indian man, woman and child -- all 1.2 billion of us -- we will spend nearly Rs 1400 on defence this year. Compare to the allocation for education Mukherjee also announced: Rs 52,057 crore, or about Rs 430 for each of us. Break it down like that, and it's easier to see that not compromising on security costs our Central Government over three times as much as the imperative to educate you does.

Or try this. All through 2011, we will spend Rs 52,000 per second on defence. Going at that rate, our friend the CWG misappropriater need not have started his spiriting before the Maurya Empire. Nope: the second week of August, less than three weeks ago, would have sufficed, thank you.

And speaking of 1.2 billion of us. That's a whole lot of us, sure. But how many Indians, really, in terms we can understand?

Suppose you are sitting on a stool at the entrance to Bombay's Azad Maidan. Everyone in the country has been asked to file past you into the Maidan and it's your job to count them. Let's say you're ten times as efficient as the misappropriater: in every second that he spirits away a rupee, ten Indians pass and you count them.

If you started today, you'd be sitting on that stool counting Indians trudging past till June 2015. (Give or take a few bathroom breaks). That's how many Indians.

And why are they filing into Azad Maidan? This thought experiment further asks you to imagine building a wall around the ground. The idea is to cram Indians every which way into the resulting enclosure: cheek to fleshy cheek, layer upon bony layer. How high would the wall have to be to accommodate every single person in this country? A metre? Ten metres? Fifty?

The correct answer is -- drum roll please -- about 3 kilometres. There are a lot of us, you know.

And by the time the last Indian -- that's you, finally free of your stool -- leaps onto the quivering pile of fellow-citizens, we'd have built a structure even taller than Ambani's Antilla. About 20 times taller, in fact.

And from somewhere inside that quivering pile, you might just hear the lady I knew: "All right, I understand 1.2 billion! Too damned well! Now let me out!"


Anonymous said...

Good points about innumeracy. Good explanations for most. Although not one of your best "Numbers". Regarding the people stacked at the end - have you accounted for compression and mush when you quote the 3 KM estimate for wall height? Could you not lay the people out end on end, side by side in a matrix and compare that with the area of a state? Your personal coordinates in this 2-dimensional matrix would be (0,0) of course. A much healthier alternative.

Boskoe said...

Read your Fermat's piece with great interest!

Any plans to publish an article on a similar unsolved problem (with a 'simple' problem statement) - Goldbach's conjecture! While on that topic - please do read the book 'Uncle Petra and Goldbach's conjecture' - Good read on the problem.

Also, what about an article on women in mathematics? (Sorry for all the suggestions, but couldnt help it :-) )

- Biju

Suresh said...

The following anecdote concerning Willard Gibbs, taken from here is instructive:

Gibbs was not talkative and not prone to giving public speeches. Once at the faculty meeting, however, after long wrangling - whether the curriculum should be expanded to make more space for language classes (thus cutting down on time given to mathematics), or whether math should be taught to all freshmen instead - Gibbs stood up and defensively said: "Mathematics is a language!” after which he sat down and did not say a word more thereafter.

I mention this classic anecdote only because I feel that when one tries to "explain" Mathematics in "simple" English (or Tamil or whatever), one often ends up introducing new distortions. Take your Rs. 8000 crore example. It implicitly assumes that the value of a rupee remains constant over the counting period which is certainly not true over 2500 years. Note also that if one converts the rupees into dollars, dirhams or whatever, the counting period can change substantially. So should one also take up economic and financial illiteracy alongside "innumeracy"?

Another problem is that "8000 crores" may not always involve money. Suppose I were to tell the sweet old lady that the distance from X to Y is 8000 crore miles (or kilometers or light years), would she be able to grasp it? Your example, in my opinion, gives a false sense of "understanding."

I suppose distortions always arise when one tries to translate from one language to another whether it be Bengali to Tamil or Mathematics to English. The problem is that while many people are aware of the distortions introduced by translation in the former case, the distortions introduced in the latter case often go unnoticed. And for those who are aware, it can be very frustrating. A friend of mine told me that he had stopped reading "popular science" books: it involved too much effort to try and figure out the "maths" behind what was expressed in "simple English."

The issue is whether society (whether Indian, British, American whatever) needs to be worried about the fact that many people don't really understand the language of mathematics. It is worth noting also that there have been articles in the New York Times which have questioned whether society needs to be worried about "innumeracy." I found it interesting that some mathematicians themselves have argued that society need not be worried about widespread "innumeracy."

Boskoe said...

BTW, Antilla is Mukesh Ambani's home (and not Anil's as you mentioned)

B said...

My comment on similar lines as Suresh's. I think you are translating one set of units to another. I dont understand the scale of Azad maidan or the relative size compared to Brabourne stadium. Ambani's house is already tall, so 20 times as tall does not make any difference to me. (On the other hand, it only gives me a scale for Ambani's affluence.)

The same thing with Rs.8500 crores. 2500 years is also a big number that I don't understand. A billion seconds despite bring a very large number is only ~32 years. To me that knowledge is what provides the perspective for 2500 years.

I think like-for-like comparisons work better. I immediately understand the per capita expenditure on defense and education. Feynman has an anecdote of his dad explaining the meaning of a T. Rex being 20 feet tall by saying that if the animal comes to their front lawn it can bring its head near to their second floor window, but it cannot poke its head in because the head is 6 ft wide and larger than the window. Similarly, Rs. 8500 crores is the GDP of Karnataka for a month or the total tax revenue in an year?

But your article makes this clear for me: innumeracy is probably the reason why politicians are involved in scandals of very large sizes. If someone had explained to A. Raja that 50 crores (out of their pockets) would have sufficed to provide everyone in Madurai a color TV (@ Rs. 5k per TV for a million TVs, decent quality wholesale rate). That might have helped explain that all the money from the scam was not worth it.

I don't need news to tell me what's important said...

How can you conflate the education spending of the Central Government with defense spending?!

Education is a state subject (okay, that joker Sibal put it on the concurrent list recently). A majority of the spending on education will be in State budgets. So, unless you take that into account, this is erroneous.

Secondly, defense spending and education cannot be compared for another reason: defense is a monopoly of the Government. Education is not -- and rightly so.

Please make these adjustments and you'll probably find that the defense spending is dwarfed by education.

So what is worse than no breaking things down is breaking them down wrongly.

Anonymous said...

I agree with the previous comment on education and defense spending. Given the number of private institutions involved In education, comparing the govt spending on education vs the spending on defense is not fair. But perhaps dilip can justify that by saying that he's not writing about logic/reasoning, but only about comparing numbers.

Jai_C said...

expanded numbers is one way to go. Like a newspaper recently ran the 2G scam story with the loss headlined as 167,00,000,00,00,000 rupees or something.

take the crore and billion out and the scale becomes apparent almost immediately.


Dilip D'Souza said...

Thanks for responses, people. Yes, Mukesh: I don't know how I messed up. Will correct as soon as this comment is done.

Anon at top: Yes, I could have done the matrix thing. Would it have worked better?

Boskoe: Goldbach is certainly a possibility. One of these days. And women too. Tell me more, and keep the suggestions coming, always.

Suresh and B: There's only so much I can fit into a 850-word piece! Yes, I'd like to take inflation into account, or to explain how things will be different with other units (monetary or otherwise). But I have to pick and choose, as well, what to focus on. Some of this is how I try to make sense of a number like 8000 crore. May not work for everyone, of course.

I am unable to see how I have "conflated" defence and education spending. Mukherjee mentioned those two figures, so I picked them out to use in this example. I have made no erroneous pronouncements on state subjects etc: after all I did use the phrase "Central Government".

Comparing defence and education spending is certainly something worth attempting, but not here. Some other time.

I don't need news to tell me what's important said...

You reduce numbers with a claim that they make more sense relative to each other. I point that you have missed in that process of reduction 2 important aspects that make the relation to each other. You claim that is irrelevant. I am left wondering then what are you even saying.

So extend your argument and say the government of India's spending on each person on education is X. Then compare it to the Government of India's payment of Income Tax for every person. That will be 0.
I fail to see how your reduction is any different than the absurdly trivial case above I cite. In other words, the reduction needs a rationale -- without that, it makes no sense.

And to top it all, you have the absolute lack of modesty to condescend and tell me you can comment on X separately?!

Okay, I don't even know why I am still here. Bye.

Dilip D'Souza said...

I am not allowed to pick out two numbers from a public government budget and compare those two numbers?

There are plenty of other numbers I could have picked up too: for example Mukherjee said he would provide Rs 3000 crore to NABARD to help weaver cooperatives, and Rs 20 crore to IIM-C for a new lab. (And there are plenty of non-rupee amounts in there I could have chosen as well). I chose the two I did solely because they are not round numbers, therefore a little more interesting to play around with.

Your objection is really that I picked on defence, of course. You're allowed to say it.

Comparing what the amounts are spent on is not what I'm attempting in this article, so when I say that much, I am being condescending and lacking modesty?

Hard to say anything to this contortion, except welcome back, and then, in turn, bye.

I don't need news to tell me what's important said...

I really don't care what was spent on defense. My annoyance is completely from the perspective of context and not from political ideas on what ought to be spent. You suggesting that it must be case throws you in rather poor light, I must say.

When you say X is c1/ person and Y is c2/ person, it follows that c1 and c2 be in the same units and are taken in entirety. That's what 6th standard school children are taught. I merely pointed that c1 and c2 aren't being taken in entirety.

Anyway, I don't know why I came back. This seems petty arguing with you when you have this annoyingly smug approach to basic units when you are clearly made an error. I am sorry I came back.

Dilip D'Souza said...

Welcome back. I'm not sorry you came back, not just in a matter of two hours, but after some months. Is there a mention of emotions coming up?

The line in question reads: not compromising on security costs our Central Government over three times as much as the imperative to educate you does.

Which part of this sentence suggests to you different units, or things not being taken in their entirety? This is, after all, about the Central Government's own publicly declared plans about its spending intentions: 1,64,415 crore on defence, and 52,057 crore on education. Are you saying these figures are not in rupees? That they are not in their entirety, whatever that may mean?

And in any case, I'm not allowed to take two random figures and compare them? Why not?

Chandru K said...

"1,64,415 crore on defence, and 52,057 crore on education."

You can blame two awful entities in India's neighbourhood, for that supposed anomaly. Pakistan and China. India is positively not ideologically predisposed to spending such amounts on defense preparedness. India would be very happy to allocate 20 times as much for education as for defense. But alas, the awful neighbourhood. What to do?