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.

[toddlintown]

They had zero inventions.
I hope you are being WONDERFULLY ironic...

---

I was wondering the same thing. Double entendre or coincidence?

[paulat]

I am better for it

More (if you really WANT to make yourself crazy...best when read in context of above, however):

"The idea that space and time may form a closed surface without boundary also has profound implications for the role of God in the affairs of the universe. With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break these laws. However, the laws do not tell us what the universe should have looked like when it started - it would still be up to God to wind up the clockwood and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundaries or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?

So...from zero...God creating a perpetual motion machine that has no creator.

My head hurts....

[ohioWfan]

So facts can be wrong as long as formalisms are given?

(You'll have to excuse me. I'm a musician, but I'm used to dealing in historical facts).

[omnivore]

"... in the 1400s, China under the Ming Dynasty stopped their seafaring to foreign places shortly after a few excursions to Arabian areas.
The "civilized" culture was possibly revolted by backward Islamics, and then decided to lay low and back away from the Troglodytes."

I've read elsewhere that these Chinese expeditions were discontinued mainly because they never made a profit. The Chinese ships that arrived in Arabia and East Africa couldn't find any civilizations advanced enough to sustain trade with on economically favorable terms.

As a general note, I recall the Arabs and Persians also had some knowledge of anatomy and surgery that was pretty advanced by the 1400's (although acquired through some pretty gruesome methods involving the disassembly of living slaves).

The Islamic culture is given a great deal of credit for forwarding the concept of "zero" from the Hindu culture, not only because they developed the first algebra using it ("algebra" is another word borrowed from Arabic, al gebra), but because it was in contrast with the Christian church (Western Catholic church of the dark ages) which insisted on Roman Numerals. Using zero or "cyphering" as it was called, was of course using demonic symbology. The only people who would do that were considered heretics, suitable for non-anatomically-instructive disassembly with red hot pincers under the auspices of people who knew "zero" about math, but were Theologically Correct.

But the Church's Roman numerals totally sucked for algebra and higher math. Also for simple long division. Mathematicians remembered this hostility to logically superior methods for a good long time. Which is probably why the Islamics get more mileage out of their mathematical contributions than would otherwise be warranted.

What lesson do we take away from this? Don't oppose progress, especially don't oppose it for theologically based reasons. Progress is inevitable, and those who stand in its way will be judged pretty harshly in the histories of those who actually accomplish the progress. And if the opposition to the progress was theologically based, don't look for any sympathy for that brand of theology in the long term, once the obstacles have been bypassed and that theology has been left in the dust by progress, the way Islam has.

[ohioWfan]

I wasn't kidding, bill, but it was more or less rhetorical.

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

It makes intelligent discussion of the subject nearly impossible, don't you think?

[paulat]

It makes intelligent discussion of the subject nearly impossible, don't you think?

No...you haven't read my posts, LOL!!!

[Aikonaa]

So facts can be wrong as long as formalisms are given? (You'll have to excuse me. I'm a musician, but I'm used to dealing in historical facts).

There are no historical facts presented in the article to support the fantastic headline.

[LexBaird]

Napoleon's soldiers blew up part of the Parthenon.

Ahh, no. That would be the Ottoman Turks, who sited a powder magazine there, which blew up during a siege by the Venetians. Napoleon was never in Greece.

[ohioWfan]

I was referring to your lack of factual, historical, analytical understanding of Bach.

You're the one who brought him up on this thread. I'm sorry I bothered you with correct details about his life and his music.

Carry on.....

[ohioWfan]

I just read your Stephen Hawking quote and I didn't understand a single word of it.

I bow to your superior intellect, paulat. ;)

[bboop]

The point being???? It was 500 years ago -- where are the fruits of those centuries??? One Big Deal. I am so sick of this stuff.

[SierraWasp]

Why do you suppose this article was written?

What inspired you to post it here?

What type of reaction were you hoping to generate?

I other words... what good does this article do???

[omnivore]

"Can you recognize the humility in me that I got from that silly Astronomy Course?"

Yes, I recognize the humility, I had a similar experience, with a different course. Perterbation Methods, a graduate level math course. What I learned, aside from not nearly enough from the course, was that everybody has their limits, as to what level of abstraction they can handle. I'm glad I found mine. When I talk to people, much more important than knowing what their limits of understanding are, is finding out if they even comprehend or will admit that there are limits to their understanding.

Note that this type of thing, finding one's limits of understanding in terms of level of abstraction, finding that one has such limits, is much more concrete in the hard sciences, than it is in the arts and humanities. This is why so many people who come from the humanities side of the educational spectrum (cough ... lawyers ... cough) are either unaware of their own limits of understanding, or are even unaware that they even have limits to their own understanding. So instead they try to contort every description of reality into something they can comprehend, without realizing they are doing so. And this leads them into talking about versions of reality (as if they were real) which are weirdly alien to everybody else on the planet. I don't think this is good for the human race. So I commend you on your discussion of human limits to understanding.

[Aikonaa]

I was referring to your lack of factual, historical, analytical understanding of Bach. You're the one who brought him up on this thread. I'm sorry I bothered you with correct details about his life and his music.

I mistakenly used medieval instead of baroque - thank you for correcting me on this. But I don't still don't understand what's your problem with my overall argument - that the article, and especially the headline, is very much a piece of propaganda.

[LexBaird]

I think you're thinking of the Great Sphinx, which Napoleon's soldiers used for target practice.

Also false. Napoleon shipped a lot of Egyptian artifacts back to France, and started a fashion craze, but his soldiers did not shoot at the sphinx. The nose was lost in antiquity, but British propaganda blamed it on French vandalism. In fact, he had an archaeologist with him that laid the foundation for much of Egyptology as we know it, including rescuing the Rosetta stone from being used as rubble fill for a fort. Then, the British seized it from the French and shipped it off to the British Museum, much as Lord Elgin did with the sculpture from the Parthenon.

[Antoninus]

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.

Uh, that's exactly the time immediately after the Arabs conquered most of the Greek East. And as we know, the Greeks were magnificently sophisticated when it came to mathematics. I'd like to see proof that Arabic math was anywhere near as sophisticated before they conquered most of the Greek East.

[omnivore]

Perturbation methods. Can't even get the darned name of it right after all these years.

[Antoninus]

They had craftsmen and tradesmen doing tilings for centuries. They were interested in it -- as a trade.

And during the middle ages, most of those artisans doing tile work were ... Greeks.

[Antoninus]

By hiring and working alongside Byzanitine designers and craftsmen.

You forgot "enslaving" but you're on the right track.

[little jeremiah]

Arabs learned geometry and other mathematics from India. So-called Arabic numerals are originally Sanksrit. Sanksrit numerals also have zero, and descriptions of various geometrical formulas are in Vedic shastras describing how to build altars.