New research indicates the mathematical prowess of medieval Islamic architects may have been nearly 500 years more advanced than that of Western mathematicians. By studying the intricate geometric patterns that adorn many Middle Eastern buildings and mosques like the Darb-e Imam in Isfahan, Iran, Harvard University graduate student Peter J. Lu and physicist Paul J. Steinhardt of Princeton University concluded the artisans who developed the patterns had some knowledge of the complex concept of quasi-crystalline geometry.

Unlike simple floor tiles, quasi-crystalline tile patterns include 5 and 10-sided tiles that can extend indefinitely without repeating patterns.

Previously it was thought that the Islamic artisans used straight edges and compasses to draft their complicated star- and polygon-shaped patterns. However Lu and Steinhardt’s findings (published in the journal Science on Feb. 23) state that the artists must have had some understanding of the advanced geometry that Western mathematician Roger Penrose was credited with discovering only in the 1970s.

Using a set of five “girih tiles” as Lu and Steinhardt called them – a rhombus, pentagon, hexagon, decagon, and a bow tie-shaped hexagon – artisans would create two designs, one with the interlocking tiles and another with the line markings atop the tiles. Lu believes this toolbox of tiles allowed medieval artisans to create the enormous tiled motifs that adorn the walls of buildings spread from Bursa, Turkey to Agra, India with few flaws. Without the aid of such tiles Lu said the process would have been painstaking and most likely wrought with mistakes in the line markings.
 As Lu studied the Darb-e Imam (built in 1453) he counted only 11 mismatches in the pattern out of 3,700 Penrose tiles. The mistakes could have been made inadvertently while constructing or repairing a pattern, said Lu. In conjunction with further construction flaws (designs initiated with an arrangement of several large tiles rather than a single girih tile), the small mismatches could also be an indication Islamic designers did not have a full understanding of the quasi-crystalline patterns.

However Lu said, "It shows us a culture that we often don't credit enough was far more advanced than we ever thought.”
Lu believes the girih tiles were being used to trace decorative motifs by 1200 AD and that their use spread across the Islamic world quickly after. The two researchers were able to match the outlines of the tile patterns to the Topkapi scroll, a 15th century scroll held in a museum in Istanbul, Turkey. Lu was first intrigued by the Islamic tiling while on a trip in Uzbekistan. There he noticed the pattern similarity to Penrose tiling and later scoured thousands of photos of Islamic architecture to study the patterns.

"You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex" over time, said Lu as quoted by Reuters.
Jonathan Bloom, co-chair of Boston College’s Islamic and Asian Art program, said that while he is amazed with the mathematics behind the designs he thinks the research has missed an important step. Though Lu’s research focuses on the patterns made with the girih tiles, Bloom said he has not seen actual tiles cut in these shapes.
“From what I see it doesn’t seem to be put together that way,” Bloom said.
Instead Bloom said the mosaics are constructed with simpler tile shapes with the girih tiles as the prominent patterns. In turn this shows that the mathematicians had a high level of knowledge but were possibly unable to articulate it to the craftsmen, essentially leaving a disconnect between those who devised the designs and those who made them.
“It may be revolutionary geometry behind the designs but the actual execution of the design is much more traditional,” Bloom said.

Bloom hopes that Lu and Steinhart’s research, in which Bloom is noted, will intrigue others to study the mosaics for further clues about their actual construction. Aside from the Topkapi scroll, Bloom said there is no other evidence to give clues as to how the artisans made the mosaics.

U.S. interest in bio-fuels on the rise
Valentina Pasquali – Washington Prism

While American consumers are just beginning to wean themselves away from gas-guzzling SUVs and move toward more fuel-efficient options, Pete Rasmussen has been pursuing an environmentally sustainable life for some time.  With a degree in environmental studies and a focus in sustainable food systems, Rasmussen began experimenting with bio-fuels three years ago in an effort to power his 1982 diesel engine truck.

“Once I made a batch of bio-fuel with three friends in a garage,” he recalled. “We had collected the used vegetable oil from a local Thai restaurant the day before, nearly 55 gallons.” A few days later Rasmussen’s truck was running on the home-made fuel when as he was driving to school he felt overcome by hunger. “I rolled down the windows, squinted my eyes, furrowed my brows and sniffed the air: Thai food. I craved spring rolls, pad Thai.” After the initial surprise, Rasmussen realized it was the bio-fuel that triggered the cravings. “This is the danger to using bio-fuel; the hunger factor from the exhaust. At least I wasn't craving French fries or doughnuts.”

The idea of powering vehicles with bio-fuels is not a new one. Robert Diesel debuted his invention, the diesel engine, at the World Exhibition in Paris in 1900 and ran it off peanut oil. The father of the modern automobile, Henry Ford, built ethanol plants in the Midwest in the early 1900s because he was convinced that as a renewable resource, bio-fuels would be vital to the automotive industry. By the early 1920’s about 25 percent of all fuel sales were bio-fuel. In the 1940s however, petroleum companies had undercut the bio-fuel industries and they were left mostly forgotten except by a small minority of environmental activists. Yet recently the use of bio-fuels has jumped to the forefront of the public debate.

On his trip to through Latin America in March, U.S. President George W. Bush struck a deal with Brazilian President Luis Inacio Lula da Silva to further develop alternative energy resources. Under Bush’s 20/10 program he has proposed that the United States reduce its gasoline dependence by 20 percent in the next 10 years. In his last State of the Union Address, Bush listed the environment as the third national priority for 2007. “Our third goal is to promote energy independence for our country, while dramatically improving the environment,” Bush said.

After being ignored for so long, the sudden interest in bio-fuels has risen as a way to cut American dependence on the import of foreign oil, a problem made more worrisome by the deteriorating situation in the Middle East.

Increasing the production of American-born ethanol, a clean-burning alternative to gasoline produced from renewable sources, is the solution called for by Congress as well.

Supporters point to the advantages of this clean, renewable fuel made from vegetable crops; lower emissions, greater engine longevity and improved performance.

In a phone interview, Rich Carter, spokesman for Rep. Don Manzullo (R-IL) said, “Ethanol and bio-diesel are American made, we do not need to rely on foreign government for their supply, they are renewable, good for the environment, and for us in Northern Illinois – where we have large production of both corn and soybeans – they also represent an important new market for our farmers.”

A growing consensus in Washington sees bio-fuels as the solution to the nation’s energy needs.

However, skeptics point to the fact that most of the ethanol produced is corn-based. They contend that corn-based ethanol is not an energy efficient raw material, or feedstock. “Out of every one unit of energy that is put into its production, only a maximum of 1.3 new units is obtained,” said Janet Larsen, director of research at the Earth Policy Institute (EPI), a think tank in Washington, D.C. devoted to environmental issues.

Also, if the United States increases its consumption of ethanol, the related spike in the demand for corn is bound to drive up the price of the crop. This trend is already taking place, as reported by the Wall Street Journal. At $4.05 a bushel, the price of corn as traded on the Chicago Board of Trade, an exchange for commodities, is almost twice as much as it was last year.

The rise in the price of corn is also likely to cause the prices of many other commodities to rise. Refrigerators in the United States are filled with corn, contained as a sweetener in drinks or breakfast cereals, but also found in milk, eggs, cheese, ham, ground beef, ice cream, and yogurt.

Concerns are also spreading abroad. Corn importers like Japan, Egypt, and Mexico are worried that a reduction in American corn exports, driven by an increase in local consumption, will threaten their livestock and poultry industries. In sub-Saharan Africa and in Mexico, additionally, corn is the staple food for the population.

So can the United States produce enough corn for both food and fuel? Lester Brown, president of the EPI, writes; “In looking forward to 2007, first we need a rise of 73 million tons just to overcome the 2006 production shortfall. Beyond that we will need 24 million tons of additional output to cover the estimated annual growth in food and feed needs. If we then add 39 million additional tons to supply the new distilleries for ethanol, for the United States alone we are looking at a growth in demand of 136 million tons of additional grain from the 2007 harvest.”

However, the average global growth in the grain harvest has only been around 20 million tons per year since 2000, the EPI found. The chances that the American corn industry might provide such a huge jump in the harvest next year are not good, even with the stimulus of high grain prices.

As Bush advocates for ethanol as a viable alternative to fossil fuel, the time seems to have come to start thinking about alternatives to the alternative.

Other countries have already successfully experimented with different feedstocks. “In Brazil they produce ethanol from sugar cane, in a way that seems much more efficient,” Larsen said. “Especially because they produce the ethanol from the sugar part of the plant but they also use the leftovers, such as the woody cane, to power their boilers.”
Larson added that France, on its part, uses sugar beats quite efficiently. 

In the United States, ethanol is still almost entirely made out of corn, partially because the country does not produce other feedstock as well. “It is also true that the corn growers’ lobby is quite influential and it has successfully pushed for the use of corn in producing ethanol,” Larsen said. 
Nevertheless, experts are evaluating the potential of other materials as feedstock.
Switchgrass, a summer perennial grass that is native to North America, could be promising.  Switchgrass is resistant to pests and plant diseases, and it can produce high yields with very little fertilizer. It is also very tolerant of poor soils, flooding and drought.
Hemp could be another possibility since, thanks to a relatively short growth cycle of 100-120 days, it is an efficient economical to grow. Although the use of hemp is legal, its use is complicated by legal issues due to the plant’s association with marijuana. Hemp and marijuana come from different breeds of the same plant, Cannabis sativa. “I hear hemp is a great feedstock for ethanol, but it is such a politically charged issue in this country,” Larsen said. “It seems that in other places they are making much better use of it.”

A growing number of activists are attracted to the potential of algae. “In my opinion, algae is the answer. It can be grown on marginalized lands where nothing else lives and it thrives on agricultural runoff and other brackish water, as such it is not a sink for precious fresh water,” said Sonia Rani, an account coordinator with Antenna Group, a public relations firm that works with renewable energy start-up companies. “Some algae actually physically leak hydrocarbons and many varieties double in population every day, making it possible to get many harvests in one season.” However, research on algae is still in the initial phase and will take time before it becomes commercially viable.
 
While debates rage over which feedstock will provide the best bio-fuel, a much more simple answer to American energy needs may have been lost in the squabbling. As Larson pointed out; “One easy way to address our dependence on foreign oil, environmental issues, and the problems related to corn-base ethanol, is to increase the fuel efficiency of our vehicles.”