Oct 30 I don't know if it happens elsewhere, but we've seen plenty of fuss over numbers during this pandemic. In May there was the claim that India would have administered two billion vaccinations by the end of this year (I examined that one here: https://www.livemint.com/opinion/columns/when-the-whistle-blows-two-billion-doses-11621541157395.html). Then there was twice when we reached dramatic new peaks in vaccines administered in a day. Again, I examined one of those peaks (June) here: https://www.livemint.com/opinion/columns/the-outlier-must-attract-questions-11624563558482.html - the other was on our Prime Minister's birthday.
Meanwhile, we haven't heard about the two billion mark again, but there's been all manner of hype in recent days over administering *one* billion vaccinations. So in some ways it's all this fuss that prompted my latest column for Mint. What's the meaning of this one billion, and why do such numbers hold such fascination anyway? And of course - What if we had just seven vaccinated fingers? https://www.livemint.com/opinion/columns/what-if-we-had-just-seven-vaccinated-fingers-11635441564960.html Your thoughts, as always, very welcome. cheers, dilip --- What if we had just seven vaccinated fingers? More than likely, you've heard the number 100 crore (1000 million, or 1 billion, or 1,000,000,000) mentioned over the last few days. India has now administered that many Covid vaccinations. This is cause for celebration, so there are hoardings everywhere about it, tweets aplenty, government-issue graphics also aplenty. All thank our Prime Minister. "Let's celebrate accomplishments", someone admonished me on Twitter, accomplishments like this particular "very credible performance". Fair point. But even so, what exactly is 100 crore? Would 116.5 crore, say, or 134,217,278, or 48,560, be "very credible performances" as well? Well, they probably would not generate hoardings and tweets. But for some reason we really like numbers made up of 1 followed by two or more zeroes - not just one zero, and in this case, nine zeroes. We all know that we'll never see hoardings thanking our PM for pushing past the 134,217,278 mark in vaccines administered. Or if we did see one, we'd be seriously baffled. What's so significant about 134,217,278, we'd wonder. Considered this way, there's no reason to applaud the 100cr mark either - what's so significant about 100cr? It's just another ordinary number. Yet I know I won't persuade anyone not to applaud it. Not that I want to. Instead, let's examine the number more closely - especially the way it looks - and then examine the celebration. Why do we like 100cr? It is a large number, of course. But plenty of other large numbers are also ... well, large. What's special about 100cr is the nice pattern, the pretty picture it makes - a 1 followed by nine 0s. There's a satisfying "roundedness" it possesses. And if you think about it, the fundamental reason this particular number makes such a pretty picture is that each of us have ten fingers. What does that mean? Because we have ten fingers, our prehistoric ancestors could count to ten without any external aids. All a particular counter of things needed was her particular set of ten fingers, and that would take her up to ten things - meaning, precisely, 1 set of ten fingers. Now that was pretty useful ... except that the time came, as it had to, when the counter needed to count more than ten things. Then she had to borrow someone else's set of ten fingers. With that, she could count to 20 - meaning, precisely, 2 sets of ten fingers. Borrow a third set and she could reach 30. On and on like that, and at some point she borrows a tenth set to get up to 100. Understand that the numbers as I have written them above - 10, 20, 30, 100 - came to our ancestors much later than the need to count. In particular, the great Indian invention of zero needed to occur for this notation to come into use. But when it did, that's presumably when certain numbers started jumping out at people who were counting. Like 100. Why, that's ten sets of ten fingers, and the way it gets written itself suggests one set of a hundred fingers. Ten of those sets, and we have 1000. Or, one set of a thousand. Onward and upward, like that. Something compelling about numbers comprising a single 1 and several trailing zeros, right? Each feels like a transition to a new realm of numbers, in a way that 70, or 856, or 900, don't. And remember, they are all built on, based on, that first set of ten fingers she started counting with. So call it a base of ten. Also known as "decimal". What if humans had only nine fingers? Apply the same logic. Our primordial counter would use her own fingers to get up to nine things. One set of nine, this time. But think of this - she would write it the same way: 10, meaning, precisely, 1 set of nine fingers. Why not ten in the set? Well, why would she, nine-fingered as she is, think for even a moment that her set should have ten? After all, do we ever count using a base of 11? Anyway, when our counter needs to go past nine-that-she-calls-10, she borrows a second set of nine fingers. That allows her to count to the number we know as eighteen, but that she would write as 20 - meaning, precisely, 2 sets of nine fingers. On like that, till she reaches what we call eighty-one, but she would write as 100: nine sets of nine fingers. Later still, she reaches 1000: the number we decimal types call seven hundred and twenty-nine. See what's happening here? We're working in a base of 9, and maybe the numbers that start with a 1 and have several trailing zeros remain just as compelling. But in base 9, they stand for quite different numbers than we are used to: 100 is our decimal 81, 1000 our 729, 10,000 is decimal 6561. 1,000,000,000 - 1 with 9 trailing zeroes - is our 100cr, but in base 9, it is 387,420,489. That is, if humans had 9 fingers, we'd be celebrating the administration of 387,420,489 vaccines - because that's the number we nine-fingered folks would know as a 1,000,000,000. Extend the logic further. If we had 8 fingers, we'd be operating in base 8, or the octal system, and that number would be 134,217,278 - so now you know why I used it near the start of this column. And if we had just two fingers, we'd be counting as computers do, in base 2, commonly known as binary. In binary, 1,000,000,000 is ... just 512. (Ask your nearest computer that speaks binary). Maybe we'd celebrate 512 administered vaccines by doing a jig and pointing our two fingers skywards. More seriously, the point is that all these are numbers like every other. If one or the other looks a little special, seems worthy of applause, that's because of the particular base we live in - for us, decimal. And that's a direct consequence of the number of fingers we have. Nothing about base 10 makes it more special than base 9, or base 8, or the binary system. So applaud the 100cr milestone, certainly. But it is just another number. Being so, the claim can stand a little more scrutiny. One graphic that made the rounds last week, for example, claims that at the 100cr mark, "India's vaccination drive is larger than all the other continents" ( https://twitter.com/mygovindia/status/1451043075527102465). To back that up, it offers these vaccination numbers: Oceania 41m, Africa 176m, South America 481m, North American 660m, Europe 880m, and India 1000m - which is, of course, 100cr. ("All the other continents" leaves out the bulk of Asia, but let that be). Impressive? But put it in perspective by checking the populations of each continent: Oceania 43m, Africa 1200m, South America 422m, North America 579m, Europe 746m and India 1400m. South America, North America and Europe have all administered more vaccines than their entire populations, and Oceania is close. Africa lags seriously. So in this comparison to "all the other continents", India actually lags as well, if not as badly as Africa. But the real truth here is, again, that all these are just numbers. If we celebrate 1,000,000,000, let's also remember that our population is not just more than that, it's greater than all those other continents too. So in effect, we are celebrating simply having more people than them. Besides, if everyone in Oceania had just 7 fingers, they'd be celebrating 1,000,000,000 vaccinations too. That's just over 40m in decimal. A vaccine for your thoughts on that. -- My book with Joy Ma: "The Deoliwallahs" Twitter: @DeathEndsFun Death Ends Fun: http://dcubed.blogspot.com -- You received this message because you are subscribed to the Google Groups "Dilip's essays" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web, visit https://groups.google.com/d/msgid/dilips-essays/CAEiMe8qohQUE2TW4QUj7Lvq5hWdKb%3Dzun9vPxf2uq418uzB_pQ%40mail.gmail.com.
