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2022 January 28

Music

Talos Principle OST - Virgo Serena

Maxence Cyrin - Where is my mind (piano cover)

Zbigniew Preisner - Requiem for my friend - Lacrimosa

Haken - Atlas Stone

Mathematical overkill: using Goedel’s compactness theorem to solve a geometry problem by creating a formal system whose consistency is equivalent to the existence of a solution to the problem.

Letterlocking is a security technique of intricately folding and sealing a letter to protect it from inspection or tampering in transit without visibly damaging the letter. Letterlocking has been used for more than 700 years and folding methods were often personalized by individual letter writers. Recent work has allowed researchers to defeat historical locked letters using xrays and computer modeling to inspect them without damaging them.

In Penney’s game, for a fixed n > 2, two players sequentially name a different sequence of coin flips of length n (e.g., the first player might say TTH, and then the second player might respond HHH). Remarkably the second player always has a winning strategy, making this a non-transitive game.

Herbert Dingle (1890 - 1978) was a respected physicist who became reputed as a crank in his later years. However, it seems he had no idea what he was doing all along:

At this point his colleagues were convinced that Dingle was insane through age or loneliness […] But there is a small point. Dingle was not crazy. For 35 years from 1920 to 1935 (that is before starting his campaign against Relativity) Dingle had written, held conferences about and lectured on a theory of which he’d never understood any part.

[…] Nor is [it] a novel event for a famous scientist to start supporting an absurd or ‘heretical’ theory, completely losing any credibility, maybe for ideological or political reasons, or out of academic rivalry. Here, though, we face a different matter, and an even more chilling one: someone who is a supposed expert in a sector in which ‘peer reviews’ exist with all the accolades and the respectability that entails, who shows that he hasn’t understood a word of things that he’s been left to discuss for years. […] if one looks at his books on the history of scientific philosophy, they are full of blunders. In practice, it’s not that Dingle forgot some things, or was acting under false pretences. He really didn’t understand some things.

That blog also has a fascinating mini-biography of Alexander Grothendieck, one of the greatest and most independent mathematicians of the last century. I hadn’t really internalized just how unusual it is to go to North Vietnam during the US-Vietnam War to teach mathematics in a war zone, just one of many oddities of his life.

Grothendieck seemed indifferent to the danger. When the bombings got too violent, his hosts moved their classes to the jungle. It wasn’t a problem for Grothendieck. He dressed as a Vietnamese peasant, wore sandals made from old car tires, and slept on the ground. The math lessons were very advanced, and Alexander hove into the sights of the western secret service, which continued to track him for years. But his Vietnamese visit had an important outcome in that Grothendieck became the rapporteur of the dissertations of Hoàng Xuân Sính, the first important female Vietnamese mathematician and founder of Than Long University [and first female professor in Vietnam of a technical field], who gained her doctorate under Alexander’s supervision in 1975.

Images

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The first prototype computer mouse. It was demoed in 1968 at The Mother of All Demos, which also demonstrated hyperlinking, windows, version control, video conferencing, and real-time multi-user text editing.

From False Knees.

Halos around the sun observed from Rhone-Alpes, France. Refraction through ice crystals is responsible for most of the features seen.

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