## Posts Tagged ‘**infinity**’

## 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…

*email readers click here for video*

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.

## Infinitely cool…

**How to Count to Infinity** (or “Yes, Virginia, some infinities are bigger than others…”)

Many more sixty-second epiphanies at **MinutePhysics’ You Tube channel** (or via ** New Scientist TV**)

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**As we check in to Hilbert’s Hotel,** we might spare a thought for Joesph Fourier; the French mathematician, physicist, Egyptologist and administrator who died on this date in 1830. Fourier introduced Jean-Francois Champollion to the Rosetta Stone, which Champollion subsequently decoded/translated. And after calculating that a body the size of earth, at earth’s distance form the sun, should be cooler than our world is, discovered what we now call “the greenhouse effect.” But Fourier is best remembered for his contributions to mathematical physics through his *Théorie analytique de la chaleur* (1822; *The Analytical Theory of Heat*), which introduced an infinite mathematical series to aid in solving conduction equations. (The technique allowed the function of any variable to be expanded into a series of sines of multiples of the variable– now known as “the fourier series.”)

*True greatness is when your name is like ampere, watt, and fourier—when it’s spelled with a lower case letter.*

- Richard Hamming (in a 1986 Bell Labs Colloquium)