Archive for May, 2007

Fifteenth century surrealism

May 24, 2007

One painting I hope to see one day, for instance this summer, is The Garden of Earthly Delights by Hieronymus Bosch. It is in the Museo del Prado in Madrid and the following picture is a small (breathtaking) detail of this marvel

The Garden of Earthly Delights (detail)

taken from the excellent Web Gallery of Arts.

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Actual infinity, the Banach-Tarski paradox and the Axiom of Choice

May 18, 2007

Many years ago, when I was an undergrad, I stumbled upon the Banach-Tarski Paradox (BTP), aka “one can cut a sphere into two disjoint parts which both have the same volume than the initial sphere“, and was quite puzzled by it — all the more since none of the courses I attended back then discussed it.

This is typically the kind of statement that, if not explained carefully, can drive people away from math (and sadly it probably has done so many times already). And of course it provides the perfect occasion to point out differences between physics and mathematics, as well as modifications of the undergraduate curriculum, so I’d like to discuss this a little bit. Comments welcomed (especially on the issue whether or not the countable version of the Axiom of Choice (AC) is enough to prove the BTP).

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Fourier’s memoir 200 years later

May 6, 2007

Exactly 200 years ago, in 1807, Fourier submitted to the Académie des Sciences his famous memoir on his theory of heat propagation. It was controversial at the time and was finally published only in 1822. Since Gallica has a digital copy of that book, I’ve spent a little time reading it.

The style is in fact not that dated, especially for a physics book where one has to discuss at length one’s motivations, which Fourier does very carefully. It’s fascinating to see all the nowadays famous equations pop up gradually. In the second chapter, the heat equation first appears on page 123. This is followed by a table describing the dimensional analysis of the various quantities he introduced.

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