BOULEVARD DU TEMPLE I Painting

The title refers to the first known daguerreotype from 1838, an early form of photography. It shows a busy street of Paris. But the street is entirely empty, a lone shoe shiner and his customer are the only signs of life. This was due to the long exposure time (10-15 minutes) which implied that only things remaining stable for a long time, would be rendered visible. The colours of the original are captured in the grey nuances of the painting, and the clear parts make up a single thing that has stood the test of time: Euclid’s proof that square root 2 is rational. This means that square root 2 cannot be written as a faction of whole numbers. Or in ancient Greek: Square root 2 is not commensurable with the unit. The fact is mentioned in Plato’s dialog Theaetetus: Theaet.: Theodorus was writing out for us something about roots, such as the roots of three or five, showing that they are incommensurable by the unit: he selected other examples up t,o seventeen-there he stopped. Now as there are innumerable roots, the notion occurred to us of attempting to include them all under one name or class. The proof is a so-called Reductio ad Absurdum in which one starts out by assuming the opposite of what is to be proved, only to reach a contradiction, whereby the desired result is proved. The proof allegedly caused the collapse of the Pythagorean belief system, as not all numbers could be expressed as fractions, which they had supposed. In modern mathematical analysis, the irrationals are always included among the rest. This work is part of the series THEOREMS AND PROOFS. The works illustrate – directly or indirectly – a theorem with a beautiful proof, according to the criteria put forth by the mathematician Hardy in his classical book A Mathematician's Apology: surprise combined with something inevitable, economy and depth.

Painting:Oil on Canvas

Original:One-of-a-kind Artwork

Size:31.5 W x 39.4 H x 0.7 D in

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