This is a beautiful short film celebrating M.C. Escher (1898-1972), the Dutch artist who explored a wide range of mathematical ideas with his woodcuts and lithographs. The filmmaker behind the film is Cristóbal Vila, who invites you to visit etereaestudios.com for more information about the film.
The film starts out with a view of a chessboard and what appear to be beans arranged on eleven of the board’s squares. This is a reference to the famous “Wheat and Chessboard Problem.” When the creator of the game of chess showed his invention to the ruler of the country, the ruler was so pleased that he gave the inventor the right to name his prize for the invention. The wise man asked the king: for the first square of the chess board, he would receive one grain of wheat (in some tellings, rice), two for the second one, four on the third one, and so forth, doubling the amount each time. The ruler, arithmetically unaware, quickly accepted the inventor’s offer, even getting offended by his perceived notion that the inventor was asking for such a low price. But when the treasurer started doing the calculations, it quickly surfaced that this was an impossible offer to fulfill. Given the request, the final tally would have been 18,446,744,073,709,551,616 2^64 – 1 = 18,446,744,073,709,551,615 grains!
Continuing along, we also see homages to such things as Fermat’s Last Theorem, Leonardo da Vinci’s The Vitruvian Man (Leonardo may have had some help in its creation), Hokusai’s The Great Wave, Jan van Eyck’s The Arnolfini Wedding, Gustav Klimt’s The Kiss (which I saw in person at the Belvedere Palace in Vienna, Austria), and much, much more. In essence, the short film contains a treasure-trove important cultural references. All of the artworks featured in the film may be seen here. All of the math references may be seen here.
If you’re interested in learning more about the creation of the film, take a look at the wireframes below:
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(hat tip: Open Culture)
(Update 3/10/2012: Corrected the count of total grains from 2^64 to 2^64 – 1.)
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The total number of grains on the board would have been 2^64 – 1, or 18,446,744,073,709,551,615.
Good catch, thanks!
…and according to most versions of the story, the king felt humiliated because the inventor had named a reward that would be impossible to grant. And an embarrassed king is a dangerous king, so he had the inventor beheaded on some trumped-up charge…which in turn meant that all his property (including the quintillions of grains of wheat/rice) belonged to the crown. And everything was back to normal, except the king had a cool new game to play.
Love the video!