Mediaeval Muslims made stunning math breakthrough

Scotsman ^ | 22-Feb-07 | Will Dunham

[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.

[paulat]

I bow to your superior intellect, paulat. ;)

...nice of you to say...just looking for a kindred spirit...LOL!

[Ramius]

Even though Galen did certain radical things in surgery back in the 2nd century or so, he still, effectively held back medical progress for more than a thousand years.

How so? I'm not questioning your basis, I'm curious what you mean. I'm aware of Galen, and his (for then) breakthroughs in treatments. But how did that hold back further advance? If you're saying that his stature and credibility were such that later research was stifled if it contradicted Galen... well, that's probably true, but it's not the fault of Galen, it's the nature of the scientific community. Anybody that questions the conventional wisdom in science is suppressed until they can no longer be ignored, if they're right.

I'm not even admitting that it necessarily a bad thing. It's just the way scientific thought works.

Isn't that sortof like saying that Copernicus delayed the advent of more modern astronomy? That's not a fair accusation. It's just the natural story of the progress of science.

[omnivore]

"Why do you suppose this article was written?"

I'm sure a big part of it is that it refers to a "pre-discovery" of something Penrose discovered more recently. Penrose may not be a familiar name to non-scientists, but he's a really major British physicist. Check out his lastest book _The Road To Reality_, it's excellent. So just finding anything that was done a long time ago, that looks like something Penrose has done, even a superficial resemblance, will get articles and headlines in the scientific media. Penrose is that famous.

[Antoninus]

You are right, and even the math and science they get credited for is mostly just Greek learning which they copied. They should get credit only for maintaining the magnificent works of the ancients, but very little was invented by them.

They didn't always preserve, either. They pretty much destroyed all representational art they found in the conquered provinces of the East. And their record of preserving the writings of the ancient past is dismal compared to the West.

[Antoninus]

Just for the record.....al Farabi, Avicenna

Both of those fellows appear to be Persians, not Arabs.

Now, if you're going to tell me that Persia had a great heritage of science and philosophy, then let's talk. But it goes WAY back beyond the Muslim conquest.

[Antoninus]

Napoleon's soldiers blew up part of the Parthenon.

No, they were Venetians. And they blew it up because the Turks were storing gun-powder there. Sound familiar?

[Antoninus]

Good luck pushing anti-bigotry on FR. A majority of posters seem to think that Arabs and Muslims are subhuman.

There's a difference between exposing half-truth propaganda and bigotry. Muslims are not sub-human. At the same time, their achievements have been vastly over rated--particularly considering most of them were the products of their conquered populations which they subsequently exterminated in many cases.

[SierraWasp]

I was kind of wondering if it wasn't part of the Muslim CAIR public relations/propoganda program to actually try to convince the free world that we really would be better off under the tyranny of Muslim fundamentalism after all, so that we could at least continue to live with a live head on our shoulders and continue using it to literally think with... Just wondering...

Sounds like that Penrose dude's got the world on a string, wrapped around his finger... "pre-discovery?" Does that prove, once again that there's nothing new under the sun? The Muslim fundamentalists can no longer find anything new under the moon!!!

[LexBaird]

btw, I'm an aussie, I have no idea who Adam Sandler is.

And your life is richer for the ignorance. Trust me. Would that some Aussie had warned me about Yahoo Serious.

[philetus]

this is real history, and arabic math predates mo-ham-head by at least 500 years"

If it's "Real History" and predates Muhammad, why does it say
Mediaeval Muslims made stunning math breakthrough?

[Free Vulcan]

"While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century"

Dark Ages? Byzantine Empire anyone?

[The_Reader_David]

More or less so.

Any finite tiling involving principally five or ten sides shapes will look a bit like part of a Penrose tiling.

During the times and places when and where the local imams or mullahs too the Koranic prohibition on images as forbidding representational art, there wasn't much for an artist to do but fancy Arabic caligraphy and trying out different geometric patterns.

[jordan8]

Wowee, quasicrystalline Islamic tilings! We should throw open our borders! And . . . it is unclear whether the mediaeval Islamic artisans fully understood the mathematical properties of the patterns they were making. Really desperate multiculti propaganda.

[Ramius]

...it would have neither beginning nor end: it would simply be. What place, then, for a creator?

As the old joke goes... God created time merely to keep everything from happening at once. :-)

But this business of timelessness is a problem for us, and I suspect it has much to do with our own limitations as time-dependent beings. If we stretch our imaginations we often entertain the idea of existence without end. That's not so hard, since we imagine the same self in perpetuity.

But it really fouls our senses to consider the concept of existence without a beginning. Mostly, I suppose, because we're so aware of our own beginning. Everything has to start someplace, or rather somewhen. Existence ~apart~ from time is a tough nut for us to crack. It's entirely possible that it is not something we are capable of describing.

[Antoninus]

I'm curious as to your response to post 86...

[montag813]

"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."

That is utter nonsense. I have read books from the 1940's discussing the rotational patterns of these tiles and the ones at the Alhambra in Spain. As far as the canard that "Europeans didn't show such sophisticated tiles for 500 years"...the Euros didn't bother with such trivialities. They were busy painting frescoes and icons and beautiful religious artwork--all things expressly FORBIDDEN in Islam.

Above: The "Gero Cross", in the Cologne Cathedral (Cologne, Germany) was sculpted and painted in the year 976.

The painted or sculpted representation of the human form itself was not permitted, so the Muslims had tons of time to play with geometry. And let's not forget that much of what they did in geometry was influenced by the Greek Pythagoras. It is amazing how people are willing to distort history just to put Islam in a good light.

[Fred Nerks]

"The overt racism and ignorance on this kind of thread is appalling."


http://www.americanthinker.com/2005/07/hyping_islam_s_role_in_the_his.html

The American Association for the Advancement of Science (AAAS) claims for its journal Science

'the largest paid circulation of any peer—reviewed general science journal in the world, with an estimated total readership of one million.'

Thus when it publishes a politically correct history of the relationship between science and Islam, as filled with errors as a garbage can left too long in the sun is filled with maggots, its falsehoods enter credulous and influential minds on every continent, including Antarctica.

'Science in the Arab World: Vision of Glories Beyond' by Wasim Maziak in the June 3, 2005, issue of Science, cites as its sole source for Islamic history 'the historian James Burke.' Burke has written that the invention of lens—grinding lathes led to hairdressing, that Mozart's Marriage of Figaro brought about the development of the stealth fighter jet, and that the Boston Tea Party caused the invention of contact lenses. One can easily and quickly verify that Mr. Burke is no historian, but a television star, by pulling up information about him on Amazon.com, where even his admirers admit to his "snarkiness."

Rather than refuting all of the snarky errors in this snarky history, I will focus on a single snarky paragraph:

Of equal importance to the Arab—Islamic scientific discoveries on the European Renaissance was the reintroduction of ancient Greece's natural philosophy by way of translations by Islamic scholars. The historian James Burke identifies several knowledge shocks that ignited the Renaissance. One was delivered by Ibn—Sina (Avicenna, 980 to 1037), whose Kitab Al—Shifa ('The Book of Healing') introduced medieval Europe to the principles of logic and their use to gain knowledge and understanding of the universe. Another major shock was delivered by Ibn—Rushd (Averroes, 1126 to 1198), whose writings and commentaries reintroduced to medieval Europe the Aristotelian approach to studying nature by observation and reasoning.

The 'Islamic scholars' who translated 'ancient Greece's natural philosophy' were a curious group of Muslims, since all or almost all of the translators from Greek to Arabic were Christians or Jews, as were the translators from Arabic to Latin. Consider the astonishing statement of Bernard Lewis in The Muslim Discovery of Europe:

We know of no Muslim scholar or man of letters before the eighteenth century who sought to learn a western language, still less of any attempt to produce grammars, dictionaries, or other language tools. Translations are few and far between. Those that are known are works chosen for practical purposes [philosophy being considered a practical discipline] and the translations are made by converts [who knew western languages before conversion] or non—Muslims.

According to Franz Rosenthal in The Classical Heritage in Islam,

'Almost all of the translators [from Greek into Syriac or Hebrew or from Greek, Syriac, or Hebrew into Arabic] were Christians.'

One possible exception is Masarjawaih, who may have been a Jew. Another is Thabit b. Qurrah (ca. 834—901 A.D.), a 'heathen' Sabian from Harran.

Similarly, 'Aristoteles latinus' by Bernard Dod, a chapter of The Cambridge History of Later Medieval Philosophy, provides a comprehensive list of medieval translations of Aristotle from Arabic into Latin, none by Islamic scholars—unless by 'Islamic' one means 'Christian or Jewish.'

But if Islamic scholars did not actually translate ancient Greece's natural philosophy from Greek into Arabic and from Arabic into Latin, didn't they at least preserve these works? Didn't they rescue Plato and Aristotle from oblivion? They 'ignited the Renaissance.' Didn't they?

No, they did not. Plato did not make the long journey from Greek to Syriac or Hebrew to Arabic to Latin, and Western Europeans preferred [surprise!] translations of Aristotle directly from the Greek, which were not only superior but also more readily available.

According to Charles Burnett in 'Arabic into Latin,' a chapter of The Cambridge Companion to Arabic Philosophy,

'The Republic of Plato, though translated into Arabic, was not subsequently translated into Latin.'

Thus, the only work of Plato translated into Arabic did not make its way back to the West.

In A History of Philosophy, Frederick Copleston says that

'it is a mistake to imagine that the Latin scholastics were entirely dependent upon translations from Arabic or even that translation from the Arabic always preceded translation from the Greek.'

Indeed, 'translation from the Greek generally preceded translation from the Arabic.' This view is confirmed by Peter Dronke in A History of Twelfth—Century Western Philosophy:

Note that Latin versions of a number of learned Greek works (Euclid, Ptolemy) came through translations from the Arabic; most of the works of Aristotle, however, were translated directly from the Greek, and only exceptionally by way of an Arabic intermediary...translations from the Arabic must be given their full importance, but not more. Another confirmation comes from Dod, according to whom the following were first translated from Greek: Categories, De interpretatione, Prior Analytics, Posterior Analytics, Topics, Sophistici elenchi, Physics, De generatione et corruptione, Meteorologica (Book IV), De anima, De sensu, De memoria, De somno, De longitudine, De inventute, De respiratione, De morte, De animalibus (De progressu, De motu), Metaphysics, Nicomachean Ethics, Eudemian Ethics, Politics, Oeconomica, Rhetoric, Rhetorica ad Alexandrum, and Poetics. Only the following were first translated from Arabic: De caelo, Meteorologica (Books I—III), and De animalibus (Historia, De partibus, De generatione).

So the great rescue of Greek philosophy by translation into Arabic turns out to mean no rescue of Plato and the transmission of Latin translations of Arabic translations of Greek texts of Aristotle, either directly or more often via Syriac or Hebrew, to a Christendom that already had the Greek texts and had already translated most of them into Latin, with almost all of the work of translation from any of these languages into any other having been done by Christians and Jews and none of it by Muslims.

But if Islamic scholars did not actually translate ancient Greece's natural philosophy from Greek into Arabic and from Arabic into Latin, did not actually rescue Plato and Aristotle from oblivion, and did not actually ignite the Renaissance with them, didn't they create a vibrant and superior philosophy?

Were not Avicenna and Averroes great? Great they were, and philosophers too, but not exactly Islamic ones.

Islamic philosophy is a misnomer; at least, what we in the West think of as Islamic philosophy is. It is not Islamic in the sense of being rooted in Islam or even in the weaker sense of being melded to it. It is based rather on those vaunted translations from Greek and has a higher allegiance to Neoplatonism than to Islam. It considered philosophy the highest expression of truth, available only to the wisest, and Islam a lower expression suitable for the masses. It believed that the Koran is temporal, not eternal, and that God knows only universals, not particulars. In short, it was in opposition to what we and most Muslims think of as Islam.

In A History of Islamic Societies (Cambridge University Press, 2002), Ira M. Lapidus, Professor Emeritus at Berkeley, a mild and genial apologist for Islam, admits that

[Islamic] philosophers did not truly reconcile Greek thought to Islam; rather, they tried to rationalize their acceptance of Greek philosophy in terms of Islam. Their metaphysical and religious mentality was based on Greek opinions rather than Quranic tradition. Philosophy, they thought, was a higher vision, superior to the revealed but inferior version of truth known as Islam.

They were 'remote from the mainstream of Islamic religious and cultural trends.'

If we want to find Islamic philosophy that is characteristically Islamic, we have to leave Avicenna and Averroes behind and enter a realm that not even James Burke, Wasim Maziak and the American Association for the Advancement of Science can claim had anything to do with the Renaissance or the Scientific Revolution. Instead, they swirl around in an eddy outside of the main current of Islamic thought.

To elevate Islam, Maziak even caricatures medieval Christianity. In Science he writes that Avicenna

'introduced medieval Europe to the principles of logic and their use to gain knowledge and understanding of the universe';

and Averroes

'reintroduced to medieval Europe the Aristotelian approach to studying nature by observation and reasoning.'

The caption of a picture of Avicenna in the article in Science says that he helped bring about the Renaissance by

'advocating the use of reason and logic as the way to gain knowledge.'

If this means that Avicenna believed that reason and logic were the way to gain knowledge, he was not a Muslim. If he believed that they were a way to knowledge, with whom was he arguing?

To whom was it necessary to advocate the use of reason and logic? All of the vast resources of the American Association for the Advancement of Science will not suffice to answer that question. All the king's horses and all the king's men cannot find a medieval Christian scholar who denied 'the principles of logic and their use to gain knowledge and understanding of the universe' or the study of 'nature by observation and reasoning.'

[LibWhacker]

LOL, most historians? That's like saying most communists. I do not care what the entire history department at Columbia University is saying. First, they know nothing about mathematics, and second, their only agenda is to tear down western civilization.

The fact is (and if you wish to dispute this, I challenge YOU to cite original scientific works produced by arabs), islamo-arabic "civilization" is a bloody militaristic, parasitic culture that would've died out centuries ago if it hadn't fed on the industry and accomplishments of better people it enslaved.

If the flea and the tick and the mosquito and the leech had the ability to steal our language, I'm sure they would claim that they invented blood. But that doesn't make it so even if the POS historians at Columbia agree.

[Fred Nerks]

LOL! What an odd creature he was/is.

[Fred Nerks]

LOL! What an odd creature he was/is.