Times Online UK: Amazing maths of the mosaic makers

Author: Mark Henderson, Science Editor
Date: February 23, 2007
Times Online UK

Medieval Islamic artists produced intricate decorative patterns using geometrical techniques that were not understood by Western mathematics until the 20th century, scientists have discovered.

The combinations of ornate stars and polygons that have adorned mosques and palaces since the 15th century were created using a set of just five template tiles, which could generate patterns with a kind of symmetry that eluded formal mathematical description for another 500 years.

The discovery, by Peter Lu, of Harvard University, published in the journal Science, suggests that the Islamic artisans who created these typical girih designs had an intuitive understanding of highly complex mathematical concepts, even if they had not worked out the underlying theory. “We can’t say for sure what it means,” said Mr Lu, who is studying for a PhD in physics. “It could be proof of a major role of mathematics in medieval Islamic art or it could have been just a way for artisans to construct their art more easily.

“It would be incredible if it were all coincidence. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we thought.”

Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines. It had been assumed that straightedge rulers and compasses were used to create them — an exceptionally difficult process as each shape must be precisely drawn.

From the 15th century, however, some of these designs are symmetrical in a way known today as “quasicrystalline”. Such forms have either fivefold or tenfold rotational symmetry — meaning they can be rotated to either five or ten positions that look the same — and their patterns can be infinitely extended without repetition. The principles behind quasicrystalline symmetry were calculated by the mathemetician Roger Penrose in the 1970s, but it is now clear that Islamic artists were creating them more than 500 years earlier.

Mr Lu, who designs physics experiments for the International Space Station, began wondering whether there were quasicrystalline forms in Islamic art after seeing decagonal artworks in Uzbekistan, which he visited after a trip to a space facility in Turkmenistan.

On returning to Harvard, he started searching the university’s vast library of Islamic art for quasicrystalline designs. He found several, as well as architectural scrolls that contained the outlines of five polygon templates — a ten-sided decagon, a hexagon, a pentagon, a rhombus and a bow-tie shape — that can be combined and overlaid to create such patterns.

There is no evidence that the template tiles were themselves attached to surfaces to create mosaics. Artists probably used holes in the templates to trace a design on to a surface, which would be made into a mosaic.

West’s Six Killer Apps

The Harvard historian Niall Ferguson, who has just written a book, Civilization: The West and the Rest, puts things in historical context: “For 500 years the West patented six killer applications that set it apart. The first to download them was Japan. Over the last century, one Asian country after another has downloaded these killer apps — competition, modern science, the rule of law and private property rights, modern medicine, the consumer society and the work ethic. Those six things are the secret sauce of Western civilization.”

Read more at: http://www.time.com/time/nation/article/0,8599,2056610,00.html#ixzz1G5PGRGwT

Population Hysteria

The Guardian Article: Why population hysteria is more damaging than it seems

Following are some excerpts from the article:

The core problem is not how many of us there are, but how we use the planet and share its resources.

Seven billion is a big number. It doesn’t seem quite so big, however, if you think that 7 billion of us could fit into the state of Texas and live there with a population density enjoyed by the residents of New York City.

What the more alarmist news reports often fail to mention is that since the 1970s fertility has been declining in almost all nations and that once the trend to smaller family size begins it is hard to reverse – as policy makers in Japan, Korea and Italy have found.

And this is where an almighty hole appears in the argument of those who suggest that if we care about climate change we should worry about women having lots of children in the countries with high fertility rates.

The reason is simple: so unequal are global consumption levels that one European or North American may be responsible for more emissions than an entire village of Africans.

Population is certainly a multiplier, but that does not make it the cause of the problem. As the Australian writer Simon Butler puts it: “People are not pollution. Blaming too many people for driving climate change is like blaming too many trees for causing bushfires.”

Industrialized countries with 20% of the world’s population are responsible for 80% of the accumulated carbon dioxide in the atmosphere.

The world is already growing enough grain to feed a population of 10 billion on a vegetarian diet. (Source: Fred Pearce, Peoplequake, 2010)