Viswanathan K's Thoughts

At the end of World War II came the “ long divorce ” of physics and maths. Physicists only worked with well-established maths; and mathematicians had no interest in physics. Neither side looked to advances in the other field for new ideas or seeds that might be relevant to their own fields. Why had this happened?   Part of the reason was that mathematicians feared that their field was becoming a “ragtag of unconnected ideas and results”. Kurt Godel’s theorems had struck a dagger at the very heart of maths – maths seemed to be in tatters. Best for mathematicians to decide how their field could proceed, they felt. Another reason was that physicists found they were able to make progress with existing maths. And lastly, applied physics was in vogue, esp. solid state physics. The engineering mindset – approximations were acceptable as long as they worked – was becoming the norm. This, of course, made theoreticians in both physics and maths wary, uncomfortable and even contemptuous o...

There are a lot of unsung heroes. That’s life. But it’s always good to see the odd, sincere acknowledgment of such folks. Shruti Rajagopalan does just that in case of Dr C Rangarajan, the RBI deputy director in 1991 and then the RBI director from 1992-97; along with the bureaucrats and technocrats behind the scenes.   Typically, a country on the verge of bankruptcy (like India in 1991) ends up with a “tin pot currency”. Desperate countries, in such circumstances, take IMF loans. Those loans come with conditions to restructure the economy. The country can’t or won’t restructure (internal pressures, political compulsions, ideological aversion), and so the cycle repeats itself.   India itself went through such cycles in its past. Why didn’t history repeat itself in/after 1991? Because, this time, says Rangarajan, the desire to reform the economy came from within. It was not just something, unlike the last few times, when it was being imposed from outside . As Rangarajan ...

The next part of the physics-maths story starts with quantum mechanics. When Heisenberg tried to explain things, he ran into mathematical array with strange properties. To him, they were strange. Mathematicians, however, had known it for long by the name of array matrices .   Dirac entered the quantum mechanical story late. He was more mathematician than physicist. When he investigated Heisenberg’s and Schrodinger’s equations, he “bent the rule of mathematics”. He made extensive use of a “mathematical function that made purists blanch”. Dirac didn’t care. If the physics worked (as quantum mechanics did), then any mathematical implication of it, however weird it may seem, must be true, argued Dirac. Dirac was reversing the directionality – so far, maths had helped physics; but now Dirac was saying physics could lead to new maths too. Oh, that function that made purists blanch? Decades later, other mathematicians would prove the function was correct.   Dirac wasn’t do...

There are so many who rave about AI, and its many forms like ChatGPT. Yes, the output of many of these AI’s is very impressive. And yes, they hallucinate too (cook up facts). All that’s well known.   What’s less well known is that many AI’s make mistakes with these two simple questions. The first one: Which is bigger? 9.2 or 9.11? The other one is just as simple: How many r’s does the word “strawberry” have?   Believe it or not, a lot of AI’s get those two questions wrong! What is going on? As you know, the AI’s can (on many topics) explain their reasoning. So they were asked to explain how they come to the wrong answers.   On the 9.2 v/s 9.11 question, the AI’s say there are multiple interpretational patterns to evaluate the question. The maths way is just one of them . The maths way leads to the obvious answer (9.2 is the same as 9.20; and so 9.20 or 9.2 is bigger). But there are other ways to look at the question. One such way is to read them as “2” and “...

I was thinking of the entire sequence of events that was set off when Hamas invaded and kidnapped those 100+ Israelis in October, ’23. Since then, in response, Israel has practically wiped out Hamas, bombed Gaza to the ground, attacked Lebanon, weakened Hezbollah enormously, and most recently, attacked Iran’s military leaders and its nuclear sites. A righteous war taken too far? ~~   All this reminded me of a point the standup comedian, Trevor Noah, makes in  his autobiography, Born a Crime . The Holocaust was a terrible and evil act, no doubt. But there have been plenty of other terrible and evil acts through history, many of which are not even disputed. Why is it that the Holocaust gets so much disproportional attention?   A key point, he says, is that the Nazis maintained meticulous records of the numbers and methods they used to exterminate Jews. When the perpetrator maintains records, well, the data cannot be disputed. No such luck for the Africans of Congo...

Max Planck is known as the founder of quantum theory. He came up with the idea of the quantum as “an act of desperation”, to explain weird experimental observations that could not be explained by theory. He found he could explain the observations “only by butchering the mathematics of the underlying theory”, by assuming the existence of “quanta”. But to him, quanta were just mathematical constructs, not real-world constituents.   Albert Einstein , in trying to explain the photoelectric effect, concluded that the energy of light (and all electromagnetic waves) was quantized. Quantization was real, argued Einstein, not just a mathematical convenience.   Many had noted that Maxwell’s laws were “symmetrical” in certain mathematical ways. Einstein went further than others. Not just Maxwell’s laws, he said, (mathematical) symmetry applies to all universal laws of nature . Conversely, he said, if a universal law isn’t symmetrical, it’s wrong. So far, all experiments show th...

You can’t do physics without maths. It’s been that way since Newton. But has it gone too far, many have asked, to a point where physicists fall in love with “beautiful” mathematical theories and stop caring if it aligns with the real world? Phrases like “fairy tale physics”, “not even wrong”, and “lost in math” capture that sentiment.   Farmelo Graham’s book, The Universe Speaks in Numbers , traces the history of the relation between physics and maths. The story starts with Newton ’s theory of gravity – the equations matched observations, but, complained the critics (even back then), it didn’t describe the physical mechanism behind gravity. This was also a case of Continental envy – the British worshipped Newton, while the Continent felt he was a mathematician, not a physicist.   A generation later, the roles reversed. Frenchmen like Laplace advocated and advanced physics via maths, while the British dismissed such an approach as “flowery regions of algebra”. Not jus...

In his autobiography, Born a Crime , the comedian Trevor Noah talks about the names of black South Africans. Since the whites could not pronounce African names, the natives would have to (also) take on a name for whites to use, the so-called English name. This English name was chosen at random – “plucked from the Bible or taken from a Hollywood celebrity or a famous politician in the news”. Thus, names like Napoleon, Mussolini and even Hitler.   Such names offend whites, but Noah is unapologetic. The whites came, invaded, occupied, treated the natives like crap, did not educate them, and then act offended by the fact that the blacks don’t know history (of whites) and pick names like Mussolini and even Hitler. Whereas, as Noah says: “Many black people in South Africa don’t really know who Hitler was.” Noah’s own grandfather thought Hitler was a tank since all the news said it was crashing through Europe! Many South Africans considered Hitler good because he had white Europe...

Tim Harford wrote a thought-provoking article on the inflation numbers calculated by governments: “The consumer price index, or CPI, aims to measure the average price paid by UK consumers.”   The devil lies in the details. What basket of items you use for the calculation matters. Is it truly representative? But wait, here are further nuances: some items matter more to poor people than others (e.g. food prices).   And then there’s the problem that humans change their behavior. If the price of certain items goes up, they shift to cheaper alternatives. In which case, the increased price of the item doesn’t affect them anymore: “They might pick up some cheap carbohydrates. Rice one week, spaghetti the next — whatever was on special offer.” Even if you could magically factor in for such changing preferences, it’s not enough. After all: “It makes sense to calculate inflation by looking at the same goods, month after month.” But if you keep changing the list of ite...

While reading Freedom at Midnight decades back, I was too young and so taken in by the flow of the events and characters that one question never occurred. If all the princely states of British India had to make a choice (India or Pakistan?), how come Kashmir got to not make a choice at the time of independence? Surely, Sardar Patel and the British could have forced Kashmir to make a choice, the way they did with all the other princely states, right?   Shashi Tharoor answers that in An Era of Darkness . While highly critical of British rule, one area he acknowledges the positiveness of British rule was to introduce and allow for continuation of the printed news. While not fully free, they were still allowed to criticize the “policies and actions of the government in a responsible manner”. For the most part, that is (There were obviously times when the British would step in and censor or even ban entire outlets. And structurally, the British demanded a sizable “security deposi...

There is the company/site/app called FlightAware that provides real-time and historical flight tracking data (flight paths, statuses, cancellations, delays and predictive analytics). It is popular among both aviation enthusiasts and travellers.   Ben Burwell wrote this piece on the eternal problem engineers have to deal with: “While we as engineers might hope for aviation data to be clean and well-standardized, the real world is messy.” All kinds of assumptions about standardized data types and schemas (formats) turn out to be false, making the development of FlightAware very challenging. He lists examples of invalid assumptions from multiple categories, some unsurprising, some downright weird. Click on the hyperlinks below for examples.   Flights . Flights depart from a gate. Flights leave their gate only once. Flights take off and land at airports . Flights are never longer than a few days . Flight numbers consist of an airline’s code plus some numbers, like UA...

Ekta Kapoor once said: “I think success is what you make of it - of course there is always the factor of luck, but one should always be equipped to seize the moment when opportunity knocks.” That is obviously true. But can one do things to be better positioned to take advantage of the elusive opportunity/luck when it comes one’s way?   Shane Parrish certainly thinks so : “The answer is as simple as it is frustrating.” You’ll see what he means as he elaborates.   First, it is an accumulation of a large number of small steps that gets you to that stage where you could seize the opportunity. But none of those small steps carry immediate rewards (or penalties): “The ordinary choices that guarantee a strong future go unnoticed. There is no pat on the back for doing the right thing just as there is no slap on the wrist for doing the wrong thing. Eating a chocolate bar right now won’t make you unhealthy. Just as not eating it won’t make you healthy.” Not getting a...

I was hesitant to write on the Iran-Israel war because everything would change dramatically if the US entered the arena. And who knew whether and when the US might join the war? Now with Trump announcing a 2 week period after which he will decide, it might be “safe” to write one… (Of course, as Iran rightly fears, the US may be lying about that to lull Iran into a bit of relative security, but I’ll ignore that possibility and write this anyway).   Personally, I don’t think Trump greenlighted Israel’s attack for a couple of reasons. First , if this was part of the US plan, why the 2 week wait period? They’d have had a plan ready. Second , the US would have lined up its ducks, By that, I mean their intelligence agency would have said (lied?) that Iran was close to having a nuke, whereas their spy chief, Tulsi Gabbard said the opposite . Yes, Trump said she was wrong but that just supports my point – you wouldn’t have these kinds of contradictory statements if the Israeli attack w...

Joe Daigle wrote an interesting article on the issues found when someone tries to replicate a research publication: “A shocking fraction of published research in many fields, including medicine and psychology, is flatly wrong—the results of the studies can’t be obtained in the same way again, and the conclusions don’t hold up to further investigation.”   He then turns to a field which should be immune to this problem – maths: “In experimental sciences, the experiment is the “real work” and the paper is just a description of it. But  in math, the paper, itself, is the “real work” .” Unlike other fields, where it takes money to try and replicate an experiment, one can just go over the other guy’s proof in maths (and spot errors), right? Nope: “It’s reasonably well-known among mathematicians that published math papers are full of errors . Many of them are eventually fixed, and most of the errors are in a deep sense “unimportant” mistakes . But the frequency with whic...

Rare earth minerals . No, they don’t refer to gold or silver. They are the lanthanides (lanthanum, neodymium, cerium, europium etc), scandium, and yttrium. Never heard of them? Well, they are critical for a whole host of industries, which is why they have been in the news for a while.   Importantly, China is the world’s largest producer of these vital minerals. A key point here is that the rare earth minerals aren’t really rare. Rather, they are found in low concentrations, which makes their extraction economically unviable. So did China just get lucky in having higher concentration ores in its territory? Like how the Middle East lucked out by having oil under its feet?   Nope, that’s not the case here. Rather, China got to this point via its deliberate economic policies. First, China heavily subsidized the rare earth mining/extraction industry. These subsidies made it cheaper to extract in China.   Second , China doesn’t allow its exchange rate to be decide...

What is science? Thanks to the insane accuracy of physics, many people believe that that science means the ability to predict . But is that the right definition, wonders Mitchell Waldrop in Complexity . Or is the ability to explain things the correct measure of a science?   He cites several good examples in that context. “Was Darwin “unscientific” because he couldn’t predict what species will evolve in the next million years? Are geologists unscientific because they can’t predict precisely when the next earthquake will come, or where the next mountain will rise? Are astronomers unscientific because they can’t predict precisely where the next star will be born?”   Then Waldrop cites everybody’s favorite problem field – economics. When the market and the economy is unpredictable, why do economists insist on making it like physics? Why come up precise mathematical equations, built on the assumption that all humans are perfectly rational (and thus predictable), when (a...

One of Isaac Asimov’s tales is titled The Final Question . Well into the future, the very hi-tech inhabitants of the future are worried. By the second law of thermodynamics! Or rather, the implied consequence of that law.   Without getting into the details of what the law is, let’s focus on the consequence that is scary. The law implies that everything in the universe will eventually cool down and decay. In that setup, no free energy will exist to drive any further processes. It is called the “heat death of the universe”.   Or as TS Eliot poetically put it: “This is how the world ends. Not with a bang, but with a whimper.”   So these hi-tech inhabitants ask their cosmic supercomputer: How can the second law of thermodynamics be overturned?   The supercomputer starts working on the question. Eventually, long after all life has ended, the stars have died out, and as nothing new emerges in the universe, and the universe is on the cusp of the gloomy end...

I’ve never been a Scrabble fan. And yet I found this extract from Oliver Roeder’s book fascinating. He hits the nail on the head as to why kids dislike the game: “The problem when you start playing Scrabble— ​ especially if you start as a kid — ​ is simply that you don ’ t know many words… You spend a lot of time trying to figure out how to make a word, any word, with the tiles on your rack, and then trying to figure out where to play them, and discovering that the whole enormously frustrating effort was worth, like, six points.”   One has to rise “one step above beginner” to begin to enjoy the game: “Anagramming is an addictive intellectual rush. Unscrambling AAABLOPR, DFGGHIOT, or EILLMNOU for the first time feels like exercising a minor superpower.”   But if you want to be really good, like competitive good, then the process begins to sound like chess: “One must study. One first learns the “twos,” or two- ​ letter words… Many of them are already familiar: AN...

The immune system is something to marvel at. It is in a state of continuous alert and is fighting (minor) wars all the time, and wins most of its battles (which is why we are healthy most of the time). But it has its flaws, writes Nathan Lent in Human Errors .   The most well-known flaws are the diseases where the body attacks itself. No bacteria, virus, or tumours are the culprits. They are called autoimmune diseases. “Autoimmune diseases are the result of mistaken identity… It’s a tragic case of friendly fire.”   Surprisingly, allergies too are an immune system “error”: “An allergy is the result of the immune system overreacting to a foreign substance – one that is totally harmless.” Redness, swelling, fever, pain – all signs of an allergic reaction – these are also signs of the immune system on overdrive. As Lent wryly remarks about those allergic to bee stings: “Even if bee stings were truly dangerous (which they’re not), suicide seems like an overreaction....

We tend to think of people as being one of the two: optimists or pessimists. At best, we are willing to concede the same person can be optimistic about some things while being pessimistic about other things .   But founders of mega-successful startups need to be both: audaciously optimistic about their company’s prospects while simultaneously pessimistic that they could get wiped out by some new upstart who rises the way they did. Let’s see a few examples of the pessimism of such founders.   Andy Grove, as CEO (and one of the co-founders) of Intel, wrote a famous book titled Only the Paranoid Survive . He calls events that can kill businesses as ‘strategic inflection points’. These happen at high speed; and don’t creep up on you incrementally. It could be technological advances (like what the iPhone did to Nokia), or a deep pockets player moving in (think of Reliance or Amazon entering any new market), or a regulatory change, to name just a few reasons. There is a ...