2 Paintings by Picasso Stolen

Pablo Picasso's "Portrait of Jacqueline," left, and "Maya with Doll."
Image from NY Times.

Two paintings by Picasso, worthy $66 million were stolen by some professionals. The left oil, “Portrait of Jacqueline”, was done in 1961 and it is a vivid Cubist work of of Picasso's second wife, Jacqueline Rogue.
Once again, the theft raised the question: who should own and make profit from the great work of these great artists who have passed way? The whole society or their descendants?

Matuse

Matuse, Japan. Image from NY Times.

Since there is no snow at all in Chengdu, this picture of Matuse, famous for castles, appears right for this moment, the Chinese new year. In my memory for the past Spring festivals at younger ages, the village is almost covered with white snow. Sometimes, it is bitter cold, but it makes the holiday full of festival atomosphere. The sound from stamping feet on the paritally frozen snow is so delicate. Esp. during the nights when I return to the bedroom, the sound breaks the blue/white silence and it seems like there is a spirit accompanying me. Snow also makes a good time to catch sparrow, fish or weasel...

Matuse is known for castles. The story in the NY Times is about Lafcadio Hearn, a Greek-Irish writer who stayed in Japan in the time at the turn of 1900's. Hearn, who married a local Japanese woman, played a similar role of a foreign observer as Edgar Snow who interviewed Mao and many other leaders of the Chinese Communist Party. In contrast to the revolutionary Yan'an, Matuse is a "fairland", a "crimeless Utopian society". Hearn wrote down local folk tales in English told to him by his wife. Then his English stories were translated back to Japanese. They were very popular for a time.. Interestingly, many stories recorded by Hearn are ghost stories. That does not make Matuse a fairland, instead a frighten place. It seems that is quite a part of Japanese culture.

Last day of 2006

After finishing the problem set for N and stuffing the stomach with some food, took a walk in the streets. The weather was nice, at least there was sun in the sky, which is rarely seen in Chengdu. The temperature was warm, and many plants along the streets are blooming. There were not so many people in the streets though. Most of people are celebrating the Chinese new year at home. Buying a ticket of 5 RMB, I was able to get into the culture garden, which is ususally free of admission. It was said a flower show is going on. There are actually not many.. There are many Camilia trees along the streets and in the garden and it is high time for them to bloom. I started to miss Dresden and the story about Camilia..

It is almost 11 pm now. There are fireworks here and there and the firecracks from near and far.. The new year is full of good wishes, isn't it?

Rhombi Tiling

The graph is about rhombi tiling an octagon shape, created by R. Kenyon and A. Okounkov. Finally, I figured out how to read the graph.
The graph is planar 2-D shape. But there are three possible orientations for a rhombi, straight up, left and right. These three orientations are painted by three different colors. As a result, if you pick the color properly, the graph looks like a 3-D one (block buildings). The genius thing here is that the third coordinate does not come in a natural sense (for example, directly proportional to color or some other parameter). Rather it seems a visual effect only without deep meaning. They further proved that for the random tiling, the 3D graph shows some patterns: The borders of the 3-D building approaches to some functions. The idea seems crazy at its first sight. However, it works very beautifully. The understanding of the deeper connection seems not easy though.

Euler Characteristic

Königsberg City Map and 7 Bridges
(Königsberg is a city of Prussia where Goldbach (Yes, the Goldbach Conjecture!) is born.)





The Swiss mathematician Leonhard Euler is one of the great mathematicians of all times. He used to live in a city called, Königsberg, which is a city divided into a few islands by several rivers. See the picture. It was at there that he put forward the Königsberg bridges problem (i.e. the sales man problem): One cannot cross all seven bridges just once for each.
TWF also made up a story for Euler to find the Euler characteristic formula, V - E - F. It goes like this... There used to be an isolated island in the city and there was no brige connecting it with the rest of the city. But one day, the city finally decided to build a brige to the island and Euler saw the construction. Then he thought, the number of the isolated islands is decreased by one due to the new bridge. Everybody can see this... Well, Euler did one step further: The bridge was acting as a negtive bridge. So, # islands - # bridges. One can another step further.. If there is a dock builded between the two bridges, the dock is then acting as a negative bridge, i.e. a positive island, # islands - # bridges + # docks. So comes the Euler characteristic V - E - F, where V stands for the number of vertices of a polyhedra, E stands for the edge (connecting vertices) and F for the face (connecting edges). Well, the story does not stop here if you imagine a higher dimensional world than 3-D. You may add some structure to connect two faces in a 4-D world and the formula repeats the alternative sigh pattern. The Euler characteristic is applied into counting the size of categories...
Just like this idea. Simple and clear.