IMPOSSIBLE XMAS TREE

 

 Let me post my Christmas tree here, it's not a new work, it was already here on the Utis Blog a few years ago, but not many people commented then. Yesterday I posted it on theFacebook, where it got over 500 likes and 22 shares in one day. I didn't look at how many times the shares were re-shared and how many times they were liked, but one thing caught my eye. The page named after Escher has 1.3 K likes and 767 shares (on Christmas Day morning). Since the uploader did not name the author (me), the more uninformed viewer is entitled to believe it is the work of M. C. Escher. In fact, Escher also dealt with probably the best known and simplest example of "impossible objects", the "tribad", more "scientifically" known as the Penrose triangle. It has been used so much in the visual arts, design, advertising and even psychology, and has become such a well-known symbol in the 20th century, that we hardly even think about questioning its origins. The curious triangle is called the Penrose triangle because it was first published in 1958 in an English psychology journal by the later renowned mathematician Roger Penrose, who won the Nobel Prize last year. But he was far from "discovering it". In Sweden, a young man called Oscar Reutersvärd had invented it decades earlier and drawn it.  "In Latin class (in 1934), I drew some sketches in the margin of a grammar book. I tried to edit the 4,5,6,7 and 8-pointed asterisks as accurately as possible. One day, I was drawing a six-pointed star with cubes on the sides. I got a surprisingly interesting shape. I added three more cubes to make a triangle. I immediately realized that what I had in front of me was a paradox."  The above recollection is from a letter Reuterswärdnak wrote to his friend, the Dutch mathematician Hans de Rijk, who, under the pen name Bruno Ernst, wrote the best books on visual paradoxes, and his compatriot Escher. From him we learn that Reuterswärd, having become familiar with Escher's increasingly popular oeuvre, including some Penrose triangle paraphrase, tried to contact him by letter, mentioning that he himself was experimenting with similar 'impossibilities', but received no reply from Escher. Yes, even the greatest people can have their moments of weakness. Whether the 'tribad' was drawn by someone before Reuterswärd, I don't know, but I wouldn't be surprised if it appeared in the sketches of, say, Armand Thiéry, Louis Albert Necker or Henrich Schröder, since it already appears in Giovanni Battista Piranesi's Prison Sculptures of the mid-1700s, even if it is not easy to pick out among the architectural elements that are so proliferating. But there it is!