Month: March 2017

Stanze al Genio – Private Collection of Sicilian Tiles

Stanze el Genio in Palermo, Sicily   http://www.stanzealgenio.it/

This private collection of Sicilian tiles is absolutely a hidden gem.The collection has more than 2300 tiles from sixteenth to early twentieth century. The owner started collecting tiles on the streets as a child, and now he has probably the largest tile collection in the world.

Stanze el Genio is not easy to find, but well worth the effort. The collection is located in a private apartment, with a tiny entrance on a sketchy street corner. It took quite a bit of courage to ring the bell.

I don’t think I can describe the tiles better than the pictures, so…

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Henry Billingsley’s First English Translation of Euclid’s Elements

For a class project, this week I had the opportunity to view an original copy of Henry Billingsley’s first English translation (1570) of Euclid’s Elements (~300 BCE). This edition was printed very finely, and it even included foldable pop-up geometric diagrams! I wish all geometry textbooks could be up to this standard.

Billingsley Elements

Foldable pop-ups in the eleventh book.

Euclid’s Elements has a pretty interesting history of transmission. The original Greek manuscript of Elements was lost to Western Europe in the Middle Ages. In 8th century, Elements was translated into Arabic and became known to Byzantine scholars. From the Arabic version, English monk Adelard of Bath produced the first Latin translation in 12th century. The Latin translation of Elements was first set in type in Venice in 1482 under the title Elementa Geometriae. Later in 1533, a Greek edition by Theon of Alexandria was fortunately recovered, and Billingsley’s first English edition was translated from the Greek edition in 1570. It’s really fascinating to think that we are still able to read something from more than two thousand years ago.

Billingsley Elements (1)

The handsome woodcut title page shows Billingsley’s ideal of the beauty of mathematics.

Billingsley Elements (2)

An example of complicated geometric figures in the book.

The Muslim East in Mozart’s Opera ‘Abduction From the Seraglio’

In a strange coincidence with current politics, LA Opera’s production of Mozart’s The Abduction From The Seraglio was premiered on January 28. On the same day of the premiere, Donald Trump closed America’s borders to refugees and immigrants from seven Muslim-majority countries. In the opera, the hero Belmonte travels from Paris to Istanbul to rescue his fiancee from the Ottoman ruler Pasha Selim. When the Christian West meets the Muslim East through the Orient Express, the two cultures collide in a series of comedic episodes. The setting of the opera on a moving train symbolizes the changing interactions between the East and the West.

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The Turkish monarch Pasha Selim and his servant Osmin are perhaps the most interesting pair of characters. Somewhat surprisingly, Pasha Selim, the central ‘villain’ of the story, is a spoken role without any singing parts. With Mozart’s genius design, Pasha’s character is developed by the others’ musical response to him, rather than by his own voice. Meanwhile, Bass Morris Robinson’s sonorous and resonant voice suits Osmin’s vulgar personality very well. Morris Robinson is one the most sought after basses performing today, with acclaimed appearance in The Magic Flute, Don Giovanni, Madama Butterfly, Salome, and others. His voice is a highlight of LA Opera’s production of The Abduction From The Seraglio.

Although the opera as a whole is under the influence of 18th-century Orientalism, Pasha and Osmin are far more complex than conventional stereotypes. Despite being in a powerful position, Pasha is determined to win the love of his abducted woman Konstanze (Belmonte’s fiancee) without force by being a gentleman. It is very natural for the audience to sympathize with the soft-hearted Pasha, who perhaps represents Mozart’s humanist vision of the Muslim West. Meanwhile, his servant Osmin is a barbaric terrorist who tortures Belmonte and teases Konstanze’s maid, but a funny terrorist, not a scary one. Mozart presents the conflicts between the East and the West lightheartedly with comedy, sending a message that humor transcends the difference between the two cultures. At the end of the opera, Pasha forgives Belmonte with his genuine benevolence and lets go of the family feud. There is a lesson of Islamic compassion in the happy ending, which might be too good to be true for our current affairs today.

Patching a Hole in Escher’s Artwork with Conformal Geometry

Last December, I happened to be in Milan just in time for a major Escher exhibition at Palazzo Reale. The Metamorphosis series was my all-time favorite, and I really liked his non-mathematical early works of Italian scenery, but I’d like to share something else in this post.

In “Print Gallery” (1956), Escher left a hole in the center of the lithograph because he did not know how to complete the picture consistently. This is a beautifully done paradox of looking at pictures in a print gallery while being in a picture.

print-gallery

In 2002, number theorist Hendrik Lenstra from Universiteit Leiden found a way to describe the geometry in “Print Gallery” by a complex exponential function. Using conformal mappings, the Leiden group generated a new rendition of “Print Gallery” with the hole filled in.

You can play around with the computer program and zoom in at the project website: http://escherdroste.math.leidenuniv.nl/index.php?menu=im&sub=main&view=2

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Picasso Lithographs: Looking inside the Artist’s Mind

By recording intermediate states of artworks, lithography provides a rare opportunity for the viewer to see inside artists’ minds. To make a lithograph, the artist draws the image on a limestone plate with a special ink, and the image is printed to paper from the stone. It is very convenient for the artist to modify the image by adding or subtracting ink on the same stone. By printing each intermediate state to paper, the artist can easily keep a history of his creative process.

The Norton Simon Museum has a long history of collecting Picasso prints. Norton Simon, the museum’s namesake, purchased 850 Picasso prints in 1977 from the collection of Fernand Mourlot. More than 80 Picasso prints were on view last month at the Norton Simon Museum, including “The Bull” and “Long-Haired Young Girl”.

Not many artists valued the intermediate steps of the artistic creation process as much as Picasso did. He was interested in investigating his own thought process, and consciously wanted to document his “states of mind”. Since he met the French lithographer Mourlot Frères in 1945, Picasso produced 185 lithography plates in the next three years, and more than 400 plates by the end of the 1960s.

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“The Bull” is one of the most famous lithographs by Picasso. The full transition from a realistic behemoth to a simple outline demonstrates how the artist searched for the spirit of the bull in the process of abstraction. From the first plate to the second plate, Picasso bulks up the bull to make the image more powerful. Starting from Plate 3, the bull is dissected by muscle and skeleton contours as if in a butcher shop. As the simplification process continued, the image lightens with a more elegant sense of balance. In particular, the head shrinks, the front sharpens, and a tail appears. In Plate 10, the bull is reduced to a line drawing – except that the bull’s reproductive organ remains shaded to indicate its gender. With all the careful consideration in each step, Picasso shows us in the final plate what he considers to be the absolute essence of the bull.