Viswanathan K's Thoughts

Steven Strogatz’s The Joy of x is a “guided tour” from “an adult perspective” to “math’s most compelling and far-reaching ideas”. Each chapter is short (“bite-size”), and the book can be read in any order.   Let’s look at one topic from the book: negative numbers. From early in life, most of us get the “use” of negative numbers. “Minus 1” meaning the basement is self-evident. Or it can mean debt (money owed). But there’s one aspect that doesn’t make intuitive sense to most people: “The most unsettling thing is that a negative times a negative is a positive.” And of course, as adults, we tend to ask “if these abstractions have any parallels in the real world”.   Strogatz gives a fascinating example. Say, you have 3 entities (people, companies, countries, whatever). A solid line designates the connected entities are friends, a dashed line conveys they are enemies. Take 2 such possible arrangements:   Social scientists refer to such triangles that denote rel...

During the first World War, Britain and France were obviously keen that the US join the fight alongside the Allies. Germany obviously did not want the Americans to enter the war. Woodrow Wilson, never keen to get Americans killed in a European conflict, intended to stay away from the conflict. In 1917, writes Simon Singh in his awesome book on encryption, The Code Book , Germany decided (secretly) to launch an all-out offense with their U-boats. Cut off Britain’s supply lines from the US, and they would be forced to capitulate. But what if the Americans joined the war the next time their civilians got killed in this all-out U-boat war, say when a civilian ship was sunk accidentally? Sure, it was possible that by the time the US decided to join, it would be too late and Germany would have already won Europe. But if not? Would America’s entry turn the tide of the war against Germany? A tough choice indeed. And so Germany’s Foreign Minister, Arthur Zimmerman, came up with his ...

When I was a kid, I was blown away by the quality of (a volume of) encyclopedias that my cousin from the US gave us. Before you smirk, remember this was the pre-liberalization, pre-Internet, pre-Wikipedia era when people still put on their loin skins and went hunting for their next meal… An event I was very interested in was World War I. And boy, did the encyclopedia had lots of information of that. The one question that never occurred to me until I read this article by Stephen Walt was the following: “We should also ask why it was so difficult to end.” I realized I never gave it any thought because the answer seemed obvious: the war took as long it took for one side to win conclusively. But Walt is really asking a different question: at some point long before the war ended, he says, surely different leaders on both sides must have felt that the body count was too much, that the eventual economic cost of victory would not be worth it, and that they couldn’t even be certain t...