Posted on 02/22/2007 6:15:51 PM PST by xcamel
WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in mediaeval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.
By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasicrystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.
Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.
"Oh, it's absolutely stunning," Lu said in an interview. "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years."
Lu and Steinhardt in particular cite designs on the Darb-i Imam shrine in Isfahan, Iran, built in 1453.
Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns.
The walls of many mediaeval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs.
"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, Lu added.
ISLAMIC ACHIEVEMENTS
While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas.
Lu said the new revelations suggest Islamic culture was even more advanced than previously thought.
While travelling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasicrystalline Islamic tilings.
The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide.
Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasicrystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran.
Joshua Socolar, a Duke university physicist, said it is unclear whether the mediaeval Islamic artisans fully understood the mathematical properties of the patterns they were making.
"It leads you to wonder whether they kind of got lucky," Socolar said in an interview. "But the fact remains that the patterns are tantalizingly close to having the structure that Penrose discovered in the mid-70s."
"And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show," Socolar said.
No doubt there's often a correlation between musical and mathematical talent, at least when it comes to Western music and it's unique interplay of harmony and counterpoint. However, the mathematics of string theory is equally unlikely to suddenly surface in the medieval Germany of Bach as is Roger Penrose's mathematics in 15th century Iran. The title of the original article, "Mediaeval Muslims made stunning math breakthrough", is just the kind of fluff which underlies the bigotry of low expectations one expects from contemporary 'liberals'.
Indeed.
Thread is a more accurate term.
Your statement may sound educated, but you are about 300 years off in your attribution of Bach to medieval Germany.
1685- 1750......Baroque. His music is far more advanced than you may know. Have you ever analyzed a Bach fugue? Sheer genius.
I thought it was somebody else, but it's of no matter.
Had the Romans (and others) not burned the library at Alexandria (several times), we'd know a hell of a lot more about what the world knew and didn't know before Mohammed showed up.
I'd vote for that as possibly the single greatest crime in the history of the world. A tremendous setback. It's completely imponderable what things had to be re-discovered perhaps centuries later. Perhaps some things that haven't yet been re-discovered. Who knows?
I suppose that it's likely a moot point. If it hadn't already been burned, Mohammed might likely have been the one to do it anyway. :-)
Medieval or not, Bach still didn't have the education nor the tools to formally understand the math which may underlie his beautiful music. Under different circumstances, he might have been a brilliant mathematician, no doubt.
"There are something like ten million million million million million million million million million million million million million million (1 with eighty zeroes after it) particles in the region of the universe that we can observe. Where did they all come from? The answer is that, in quantum theory, particles can be created out of energy in the form of particle/antiparticle parts. But that just raises the question of where the energy came from. The answer is that the total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity.
"Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.
"Now twice zero is also zero. Thus the universe can double the amount of positive matter energy and also double the negative gravitational energy without violation of the conservation of energy.
"It is said that there's no such thing as a free lunch. But the universe is the ultimate free lunch."
--Stephen Hawking
Sad isn't it. Using that logic, we might as well write off German innovation in the sciences and arts because of the Nazis, Chinese inventions and culture because of Mao or even American culture and ingenuity because of Adam Sandler.
It just supports the old story that if you put an infinite number om monkeys in a room with an infinite number of typewriters they will eventually type in every geat work of literature every written.
Well here are the monkeys.
I see............sort of like you have no 'formal' understanding about Bach.
Was that just by accident, or did you do it on purpose?
Hitler and Mao were in power for a very short time - whereas mohammad, to muslims, rules from the 7th century until forever. The koran and hadith have ruled every thought and action of muslims for 1400 years. Germany and China regressed under Hitler and Mao, but it was a temporary regression. Islam is permanently regressive. btw, I'm an aussie, I have no idea who Adam Sandler is.
Are you kidding?!? Every news article posted here that states medieval Islamic scientists contributed anything to Western civilization is met with comments like that or just short of it. I've seen worse, even been directed to a site or two that was junk revisionist history if not flat out racism
The subject at hand here, mathematics, is by definition about formalisms.
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