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Posts Tagged ‘Hilbert’s Infinite Hotel

No reservation? No problem!…

 

Jeff Dekofsky explains Hilbert’s paradox of the Grand Hotel, a thought experiment proposed in the 1920s by German mathematician David Hilbert to illustrate some surprising properties of infinite sets, in this TED-Ed animated lecture

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As a special bonus, another amusing video (via Kottke)– an explanation of why it is that the sum of all positive integers (1 + 2 + 3 + 4 + 5 + …) = -1/12…  Euler actually proved this result in 1735, but the result was only made rigorous later; and now physicists have been seeing this result actually show up in nature.  (Spoiler alert: the answer turns on what one means by “sum” mathematically…)

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As we pray for more fingers and toes, we might spare a thought for Harald August Bohr; he died on this date in 1951.  While materially less well-known than his brother Niels, Harald was a formidable mathematician (founder of the field of almost periodic functions), a gifted athlete (an accomplished footballer who won a silver medal at the 1908 Summer Olympics as a member of Denmark’s team), an inspirational teacher (the annual award for outstanding teaching at the University of Copenhagen is called “the Harald” in his honor), and an out-spoken critic of the anti-Semitic policies that took root in the German mathematical establishment in the 1930s.

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Cogito cogito ergo cogito sum…

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This exploration of the challenges of time travel and five other famous thought experiments (Schrödinger’s Cat, Hilbert’s Infinite Hotel, et al.), all animated in 60 thought-provoking seconds, at the Open University’s “60-Second Adventures in Thought.”

Cogito ergo sum libens…

[TotH to Maria Popova/Brainpickings]

As we lean back in our armchairs, we might recall that it was on this date in 1964 that Sonny and Cher were hitched, if not in fact married..  The duo’s official press information from the early Sixties to the mid-Seventies averred that Sonny & Cher married October 27, 1964 in Tijuana, Mexico.  In the event, Cher herself “married” them in the bathroom of their first home, where they simply exchanged rings and vows without the presence of family, friends or witnesses, or a minister.

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