Dilip D’Souza (for Info only, not official)

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Dilip D’Souza

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    ...Plenty in it thrilled me and left me thirsting for more. It features explorations and explanations of chance and approximation, topology and the golden ratio and plenty more. But towards the end of the book is a pair of images that I always stopped at in wonder, because I always found them oddly mysterious. They may constitute the reason I quietly abducted that selfsame book—now considerably worse for wear—and today it resides proudly on my shelf. The first image has two sheets of paper, identical except one is yellow and the other blue. They are both printed with a 12 x 10 grid, filled with the numbers from 1 to 120. The yellow sheet floats an inch or two above the blue one, so you can see the numbers on both. In the second image, the yellow sheet is crumpled and lies forlornly on the blue one. Here’s the text that accompanies the pair: “First, a numbered paper sheet is placed over an exact duplicate so that all points on both the sheets are aligned. ...

    Live Mint on Dec. 1, 2017, 2:45 a.m.

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    ...H.G. Wells probably did the most to fire public imagination over the idea with his 1895 novel, The Time Machine. And there have been plenty of other efforts too. The idea being, as you’ve no doubt guessed, time travel. Few other themes can and do inspire as much romance and speculation. And while going into the future has its attractions, the past arguably raises the really interesting questions. What would happen if you could travel back in time? To when in the past would you choose to go? How would you explain your presence to those you meet? How might you affect the course of history? That’s not so grandiose a question as you might imagine, actually. Think of going back in time to that day in 1948, for example. To Birla House in Delhi, venue of Mohandas Gandhi’s last prayer meeting. You know what’s about to happen, of course—that comes with the privilege of actually having lived several years in the future. ...

    Live Mint on May 19, 2017, 12:49 a.m.

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    ...More recently, we’ve seen it—and learnt much more about it—via images taken by the Cassini spacecraft, which was launched in 1997 and has been orbiting Saturn for 13 years now. While the hexagon was quite a find, we’ve learnt much more about Saturn via Cassini than just an unexpected shape at its north pole. But as I mentioned in that previous column, the doughty little spacefarer is coming to the end of its fuel. So its bosses at the National Aeronautics and Space Administration (Nasa) planned a year-long farewell tour for Cassini. It began one last orbit around the planet last September. A few days ago, it embarked on the first of some final manoeuvres that will last till next September. Cassini’s swansong is a series of dives through Saturn’s famous rings—that is, between the planet and the rings. The first dive started on 26 April, the second on 2 May, and there will be one every week until September. ...

    Live Mint on May 5, 2017, 12:57 a.m.

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    ...How many times does it appear in this paragraph? Twice still, though you’re probably already wondering why I’m asking silly questions. But what if I asked these slightly different questions instead: Which word appears most frequently in this article? Which word appears second most frequently? Almost certainly, the answers will be “the” and “of”, respectively. This holds for any reasonably long piece of English text, and “and” is third-placed. Bear with me for a few seconds more. Let’s say you picked up a novel that’s about 100,000 English words long. “The” will indeed appear more often in it than any other word. If you actually counted, you’d find about 7% of its words are “the”, or 7,000 occurrences. That’s just a feature of the language. But here’s something for you to chew on. “Of” will appear about 3,500 times, or 3.5%. That’s also a feature of the language, but does that number wrinkle your brow at all? What would you have guessed: That second-placed “of” would appear just slightly less frequently than “the”? Or about half as frequently? ...

    Live Mint on April 21, 2017, 12:10 a.m.

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    ...Yes: As is evident, I really had nothing to do. Still, it wasn’t a total waste of time, for I actually learnt something from the ant. This: For its size, it scurries along nearly four times faster than Usain Bolt at his fastest. If that makes you splutter in your coffee, note that I’m not suggesting that if we put the ant and Bolt on respective starting blocks and fire the starting gun, the ant will pound a path to the 100m finish line four times faster than Bolt will. But what I am saying is, if you give the ant a distance to cover that is, relative to its size, the same as 100m is to Bolt—well, the ant will indeed win that race. Hands down. How can I make such a claim? Well, consider that Bolt is about 2m tall. His signature race, the 100m, is about 50 times as long as his body is. His world record at that distance is 9.58 seconds, which means he runs just over 5 body lengths every second. Nobody on the planet runs faster. I should say, no human on the planet runs faster. But ants, now…. ...

    Live Mint on April 7, 2017, 12:13 a.m.

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    ...As he writes in an essay I read recently, he “intoxicatedly explored the endlessly rich world of integer sequences”. Doing so, he ran into all kinds of patterns. What patterns? Well, before exploring his, consider some others for yourself. Take the multiples of 9, for example: 9, 18, 27, 36, 45…. As innumerable children learning multiplication tables have found, the first digit here increases by 1 and the second digit decreases by 1 at each step. Makes it easy to remember. Or the squares: 1, 4, 9, 16, 25, 36…. Check the gaps between them: 3, 5, 7, 9…. We have the odd numbers! Perhaps these are trivial; certainly they are so well-known that they would excite only children learning numbers—not that that’s to be sneered at (I believe it’s to be celebrated). But there are others. In fact, there’s no end to the patterns you can discover in numbers. You might even stumble on one that nobody has seen before. That’s Hofstadter’s “endlessly rich world”. ...

    Live Mint on March 9, 2017, 11:20 p.m.

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    ...The colleague had the annoying habit of picking up and reading pretty much any file or paper on the desk, even those marked “Secret”. Gentle reprimands had no effect. So the officer—incidentally, a mathematician by training—found another way to get the message across. He got a red file with “TOP SECRET” written prominently across the top. He put just one sheet inside, with these words on it: “Some people are in the habit of reading papers, like this one, that are not meant for them.” He set the file down on his desk, in full view. Sure enough, it wasn’t long before the colleague wandered in. Sure enough, he picked up the file and read the words. I wish I had been there to see his face. What did he think: Was the note meant for him? What do you think? Somehow that story always reminds me of Raymond Smullyan, mathematician and puzzle-crafter extraordinaire. ...

    Live Mint on Feb. 24, 2017, 1:14 a.m.

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    ...I relaxed for a while, below another blue sign that said: “Tinnai Pial—Visitors wait here. Place for relaxing in the evening.” The next morning, Kathleen and I arrived at 9.15am, expecting to find it open. It was still padlocked. A genial old man sat where I had sat the previous evening. When will it open, I asked. “11,” said the old man, smiling and helpfully holding up two index fingers, in case I hadn’t understood his Tamil “11”. Then he shouted: “Paati! (Grandmother! ), “come here! There are guests to see Ramanujan’s home!” A wiry old woman appeared, shaking her head. “You can only go in at 11,” she said, also holding up two index fingers. As we resigned ourselves to waiting, she tottered away and returned with a number on a sheet of paper. “Call it,” she said, pointing. When I did, Suresh at the other end listened, asked a few questions and said, suddenly: “OK, OK. Wait 10 minutes. I will send someone to let you in.” Just so did we finally enter a great Indian’s home. ...

    Live Mint on Feb. 10, 2017, 4:25 a.m.