The Kurdish people compose one of the ancient nations of the Middle East. Kurdistan, the land of the Kurds, is spread among several modern states: northwestern Iran, northern Iraq, northeastern Syria, southeastern Turkey, and small parts of Armenia.
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.
It's also not even true. It's like saying that because the Egyptians knew that there were right triangles with sides of lengths 3, 4 and 5, they knew the Pythagorean theorem, in the sense of knowing it in full generality with a proof, centuries before Pythagoras. I've heard that claptrap spouted by 'multiculturalists' who want to claim with no basis that the Greeks got their culture from Africa.
What is true is that the Muslims, by conquering both the southern provinces of the Christian Roman Empire that had preserved classical Greek learning, including mathematics, and India, where the Hindus had made different advances in mathematics, were able to make a few advances, all of which were fairly obvious once one had digested both of the conquered cultures' mathematics.
As I pointed out in my last post, any finite tiling using 5 or 10 sided regular figures as major tiles will look a bit like a Penrose tiling. Claiming a 'mathematical breakthrough' on this basis is like equating a 3,4,5 right triangle with the Pythagorean theorem. Find a medieval Arabic text explaining how a pattern with local 5-fold symmetries can be extended without repetition to an arbitarily large region, and you can claim they beat Penrose by 500 year. A bit of flooring or wall tiles with pentagons or decagons is a doodle, not a mathematical breakthrough.
whoops! sorry...
Simplistic misconception.
The "prohibition" depends on which Muslims, where, and during what time period.
I've seen stunningly beautiful collections very old Islamic glass animal and bird figures in musseums. Corning Museum of Glass has one such collection.
Anyone can find examples of Muslim figural art if they just bother to search.
Gee, and not one mention of the fact that the people in question were in fact Greco/Roman 700AD.
That's the great lie--Gibbon, wanting to claim Romanitas for the 'Enlightenment' against Christianity, and all the Muslim apologists now, all want us to forget that there was a Christian civilization that was never overrun by Germanic barbarians, from which the Muslims took most of their learning, from which they copied such civilized ways as they adopted, and which in the end they destroyed.
The name 'Byzantine Empire' is itself part of the lie.
It was the Roman Empire, its capital moved to Constantinople, New Rome, by Constantine, and it preserved classical learning, mathematics included, until its fall. The Caliph of Damascus once offered a great sum of money to the Emperor to let one Leo the Mathematician visit his court--the Emperor declined. Its scholars fleeing the advance of the Muslims, and settling in the most Roman regions of Italy--not Rome itself, but the Veneto--were the trigger for the Rennaisance.
In practical Roman fashion, the few advances in mathematics made during the Christian era in the Roman Empire were related to engineering: Anthemius of Tralles, one of the architects of Justinian's Hagia Sophia, wrote treatises on conic sections, giving some advances on Apollonius and Archimedes, including describing the focal properties of the parabola, and developing the method of drawing ellipses with two pins and a loops of string.
Of course, no one goes on about the advances of 'Byzantine mathematics' (and rightly so, just as with the Muslims, there really weren't very many), and its history is largely forgotten except among us Orthodox, and quirky academic 'Byzantinists' (a lot of whom eventually convert to Orthodoxy).
That's a really interesting letter. Did you write it?
90% The Copts holding out in their ancient homeland are still 9% of the population, with other Christians (mostly Greek Orthodox Patriarchate of Alexandria) constituting another 1%.
Don't overstate the success of the minions of the false prophet Mohammed.
Yes, should they actually succeed in taking over the globe, they will bring themselves down in debauchery and ruin.
From sacred geometry we see a lot of math developing from geometric construction. "Square root" for example, and such things as the square root of 3 found in the vesica pisces, a symbol of Christ. We also have Pythagoras and his "unutterable" numbers, which we call irrational. Pythagoras definitely knew quite a bit of the math involved and we know he knew.
That the geometry is connected to math and/or math derived from geometry construction we know from the writing and history. We lack this in the case of these Islamic constructions. So it's, so far, a leap to say they had the math figured out, when the designs can be explained by geometric construction (they also knew Euclid) based on the beginning polygon.
Or, as the article states:
"Some scientists are skeptical. Craig Kaplan, a computer scientist who studies star patterns made by Islamic architects, says that it has not yet been proven that medieval artisans understood the mathematics of their intricate designs."
Thanks for the post, it's an interesting subject.
No. It was written by Peter Betbasoo. Look here:
http://www.aina.org/aol/peter/brief.htm
superb. Thanks.
How does the history of Assyrians then mesh with that of the Kurds? Seems (to my uneducated eye) to be pretty much the same territory?
The Kurdish people compose one of the ancient nations of the Middle East. Kurdistan, the land of the Kurds, is spread among several modern states: northwestern Iran, northern Iraq, northeastern Syria, southeastern Turkey, and small parts of Armenia.
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