Baron Munchausen and his horse get stuck in a swamp. So, how does Munchausen pull himself out of the swamp?
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Well, Munchausen is a fictional character created by Rudolf Raspe, and is quite a storyteller himself, narrating stories of his unimaginable feats. In one such story, he does something impossible: he pulls his horse and himself out of a swamp by pulling on his own hair.
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In later versions of the story, he does so by pulling himself by his bootstraps. Yes, bootstraps!
But the first documented use of the idiom “to pull oneself by one’s bootstraps” to denote an impossible feat came when someone “devised” a perpetual motion machine.
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A perpetual motion machine can do work infinitely without an energy source. Well, it cannot. Because laws of thermodynamic tell you so. And you should believe the laws of thermodynamics. Why? That’s a thread for another day.
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In 1834, a man called Nimrod Murphree announced that he’d discovered perpetual motion. This claim was justifiably dismissed with the words, “Probably Mr. Murphree has succeeded in handing himself over the Cumberland river, or a barn yard fence, by the straps of his boots.”
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“Bootstrapping” became a common computing term in the 20th century referring to a self-starting process supposed to proceed without any external input. And it continues to be used in multiple different contexts — along with my personal favourite: high-energy physics.
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You know how everything is made up of tiny little particles, a very large number of them — physicists call them a zoo of particles. Quite apt a name, perhaps. In the 60s, physicists were trying to understand ways to fit all these particles within a single framework.
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Then the American physicist Geoffrey Chew came up with a theory where particles do something similar to what Baron Munchausen did — these particles hold on to each other by “exchanging particles”. Difficult explaining it here, but Chew’s theory got a very appropriate name.
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Bootstrap! What was once used as a snarky remark about the “discoverer” of perpetual motion has come to represent a set of ideas instrumental to an entire area of physics. And somewhere along the way is Baron Munchausen pulling his own hair!
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If you want to read about bootstrapping — the one physicists are using in their attempt to understand nature, then you should check out this brilliantly written @QuantaMagazine piece by @nattyover.
Books from Dover have always had a very distinctive feel, and delightfully exquisite covers. The credit, in large parts, goes to its founders Blanche and Hayward Cirker.
The Cirkers began their publishing career in 1941 reprinting out-of-print scientific texts and novels.
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The inexpensive paperbacks — artfully designed — started becoming bestsellers. The Cirkers did not just have a great taste in design but also a wonderful understanding of readership. Their catalogue expanded to illustrations, manuals, music sheets and more.
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At one point, still early into their publishing career, the Cirkers persuaded Einstein to let them publish the out-of-print “The Principle of Relativity”. Einstein was initially apprehensive about the book being dated. But the Dover edition ended up becoming a bestseller.
Causal set theory postulates that spacetime is fundamentally discrete — and not continuous. Abhishek Mathur, Prof. Sumati Surya and I explore an issue central to the theory.
It’s going to be a bit jargon-y. But I’ll try keeping the definitions simple wherever possible.
Causal set theory (CST) replaces the spacetime continuum that we experience by *locally* *finite* *partially ordered sets* — what we call “causal sets”.
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Loosely speaking, a partially ordered set is a collection of elements in which every pair of elements need not be related to each other.
Being “finite” means that there are a finite number of spacetime elements in the set. I’ll not define “locally” to maintain the flow.
Lev Termen, or Leon Theremin, as he was known outside the Soviet Union, was an inventor passionate about both music and physics. His career started with working on problems in electrical engineering and it was during this period that he built the prototype of the Theremin.
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The instrument works on a simple principle: when you mix two signals of close but different frequencies, you get a new signal with a frequency equal to the difference of the two original frequencies.
It is a pity that many Indians take great pride in having "given zero the world” — the origin of which is rather dubious — and do not talk about the decimal number system instead, a more fundamental and ingenious contribution we made to mathematics.
Multiple civilisations had recognised the use of zero as a placeholder for "nothing rather than something". What was unique to the Indian number system was the idea of "putting" that zero after another symbol allowing one to express every number using a set of ten symbols.
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It was the ingenuity of this place-value system that using a set of ten symbols you could represent any number you wanted. Numerals stood for different values depending on their position — units, tens, hundreds, thousands and so on — making arithmetic operations simple.
Those familiar with polyominoes can imagine how interesting their bulkier cousins polycubes — solid figures made of unit cubes joined at their faces — would be.
But if you don't know what a polyomino is, just think of unit squares joined edge to edge. Remember Tetris?
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Let's talk about polycubes now.
Polycubes are three-dimensional equivalent of polyominoes. And like polyominoes, it is extremely difficult to count how many polycubes constructed from a given number of unit cubes there are.
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If you have one or two cubes to begin with, you’ll get exactly one polycube in either case. You add one more unit cube, you get two distinct "tricubes".
Keep adding unit cubes and try to count the different tetracubes, pentacubes and hexacubes that can be constructed.
One name not mentioned often enough when discussing Ramanujan's life is that of Sir Francis Spring.
Spring, an Anglo-Irish civil engineer, was the chairman of the Madras Port Trust when he was made aware of the exceptional mathematical talents his employee Ramanujan held.
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He soon became Ramanujan's champion — helping him with everything from establishing contacts and writing letters to overcoming bureaucratic hurdles to travel to England. He continued to be a strong support throughout Ramanujan's life.
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When Ramanujan's two-year Cambridge scholarship was coming to an end, Spring's was one of the stronger voices back in Madras requesting an extension. He was there to support him again when Ramanujan was back in Madras, his health failing rapidly.