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.

[LexBaird]

Well, I'm glad the Rosetta Stone is in London.

If not there, it would have been in France. The Brits seized it, along with many other artifacts, from the French General de Menou, when he surrendered in Egypt. As it turns out, it was a Frenchman who cracked hieroglyphics, using the stone as a key.

Either way, until the French recognized its worth, it had spent centuries langushing in Islamic ruled Egypt, doomed to be used to build a wall with.

[Fred Nerks]

The fact that there were medieval Islamic scholars and philosophers is not even debateable. They existed. I never argued to what level their thought was 'rooted in Islam.'

there's only one level: allah will rule the whole world and mohammad is the last 'prophet'

[ohioWfan]

al Farabi did not accept Islam without question, and al Kindi did not agree with al Farabi.

Your position is that being a Muslim implies blind allegiance to a singular philosophy, and that simply does not line up with the facts.

I am not in any way defending Islam here, but your putting brilliant minds, educated in Greek philosophy and thought, in a tiny little box just doesn't wash.

But, I have no doubt that there is no amount of evidence that will change your mind, so I'll end this now.

[ohioWfan]

btw, look up al Kindi

[Cruising Speed]

So, these 15th century potters were moonlighting as advanced mathematical theorists....riiight.

[El Gato]

LOL, The invention of the razor and depilatory cream allows you to pass as one of us.8-)

Nah, I'm just a naturally less hairy mutant Neanderthal.

[xcamel]

More:
http://www.sciencenews.org/articles/20070224/mathtrek.asp
(more clearly written with examples)

[combat_boots]

Yes, let's give credit where credit is due: http://www.fordham.edu/halsall/med/grabar2.html

highlights inspiration for the work on the Dome of the Rock. Also see history.com for more information about the use of Byzantine craftsmen in the development of "Islamic" architecture.

In Syria, the Athanasian controversy contributed to the iconoclastic argument in the church architecture there.

Or so said the Profs I had years ago.

Now, to say the Hagia Sofia was uniquely Islamic is a lie, as it is a converted cathedral. To say that the Blue Mosque of Isfahan did not inherit the figural patterns of developed through work of the Byzantine craftsmen with the early Umayyads in Syria is also not true. These arch and tile work artisans kept developing after the islamic conquest, but work was both already done, and, apparent prior to it.

[timer]

It was in damascus that Jesus' followers were first called "christians", yes? Then there is the druids, and the samaritans. Their numbers have dwindled to around 500 because of inbreeding/recessive genes. That also is a jewish trait, intermarriage between the 12 tribes. It shows up in the high %age of +AB blood types.

My son was just in istanbul over the christmas holidays. He went to an armenian church service while there. Like jumping back 1000 years in history he said. And some 7 layers of history from roman, crusader, orthodox, turk, etc.

And yet that illustrates the problem thruout the middle east, europe, russia, asia, africa; practically the whole world : people and their culture STUCK in the distant past, living fossils as it were. The US culture is DYNAMIC, language and culture and SCIENCE changing at warp speed.

Analogy : the invention roots may be based in iraq, greece, europe, china, wherever; as the dead core of a tree, WE are the active outer sap layer feeding the growing leaves. Thus the JEALOUSY of all of them towards us. We are to the world what Israel is to the palestinians, a living example of a superior approach to life and its problems.

Thus you have the arab terrorists response of a culture of death and destruction vs our culture of life and creation, which do YOU want to see win in the long run? As for me : GO GWB, stand firm against the forces of evil, both foreign and domestic.

[omnivore]

See _A History of Pi_ by Petr Beckmann, published in 1976. I read it years ago, it's a good history of math. I don't recall the exact method of death penalty used for heretic mathematicians who defied God by using the Satanic symbol of "0", whether it was burning at the stake, breaking on the wheel, tearing off the flesh with red hot pincers, or any of the other routine punishments handed out to heretics, who were the politically incorrect of their day. But they were indeed tortured to death.

What would be revisionism, would be to deny the historical record, that the Church used to torture people to death for various sorts of "heresies" that today are rightly laughed at.

[Radix]

" If you're saying that his stature and credibility were such that later research was stifled if it contradicted Galen...

Yeah, I was saying that, but I completely agree with you. especially when it comes to the Mikolaj Kopernik stuff.

(I had to look up Copernicus real name cuz my memory is out of shape.)

The Galenic methods were radical and astonishing.

Galen did not hold up medical advances himself, but his name is associated with ....for lack of a better word, stagnation.

[Radix]

"...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."

Gosh, I am so completely limited.

I was watching a TV show some while back. The doctor called out...." Give me a high F I O 2...."

I left out some important part of your post that I wanted to quote. Space and all.

The High FiO2 stuff refers to the % of Oxygen inhaled and the context was totally absurd in that fictional circumstance.

I laughed out loud, but then later realized, that, I was likely one of the few viewers who actually got it.. I sort of laughed because it was so meaningless a request to be made in an emergency situation.

I left out some of your quote, but my point really is that we are all limited in our knowledge, and the we really, after all in so many ways, stand on the shoulders of a few giants.

I think so.

[Fred Nerks]

http://www.americanthinker.com/2005/08/the_notsogolden_age_of_islamic.html

Why should we care that dhimmi history has convinced most educated people that Christians lost Aristotle and Muslims restored him to them? Why should we care that they believe in a Golden Age of Islamic philosophy that never occurred? We should care because we should care about the truth, but more than that, because these false beliefs are actually quite dangerous, for in the malignant minds of terrorists, they justify murder. Dhimmi history confirms the sense of superiority Islamofascists feel, it sympathizes with their wounded vanity, it shares their enemies, it reminds them of their past glories, it makes them feel unappreciated, it flatters them, it makes them suspect treachery, and it tells them that they are right.

Dhimmi history has the disastrous effect of heightening the 'sense of injur'd merit' that the jihadists feel—along with Milton's Satan. The lies of dhimmi scholars are, like the borders of Islam, bloody.

[Antoninus]

I don't recall the exact method of death penalty used for heretic mathematicians who defied God by using the Satanic symbol of "0", whether it was burning at the stake, breaking on the wheel, tearing off the flesh with red hot pincers, or any of the other routine punishments handed out to heretics, who were the politically incorrect of their day. But they were indeed tortured to death. What would be revisionism, would be to deny the historical record, that the Church used to torture people to death for various sorts of "heresies" that today are rightly laughed at.

Again, prove it. You've cited one book, written in 1976 by an author unknown to me. With the vast resources of the internet at your disposal, you'd think that you could come up with a couple of primary sources (not anti-Papist polemical cr@p from Elizabethan or Cromwellian England) which demonstrated the Catholic Church torturing and killing people for mathematical or scientific ideas.

Just one primary source--that's all I'm asking.

[ohioWfan]

Good grief, Fred! I never said that "Christians lost Aristotle and Muslims restored him to them"......and no one who knows the facts thinks that. Why don't you try discussing the things we are actually discussing and stop handing me refutations of things I have never said, nor even remotely implied?

The problem is that you are denying that Muslims can BE philosophers and can use their God given intellect for anything but slaughter. You are the denying historical reality of Islamic philosophy because there are those in academia who have distorted it into something more than it was.

So it is you who are denying the historic truth, and not I, by your broadbrushing and defending what has not been attacked here.

As I said, you have your template and it will not be cracked. It's no different than discussing the truth with a liberal academic who takes the side of the 'Golden Age of Islamic philosophy,' IMO (with whom I would argue that there was none, incidentally). Your mind is set in concrete and your opinion will not be moved.

Good day, Fred.

[The_Reader_David]

It was in Antioch that the disciples were first called Christians, though you are close: since the forced exchange of populations following the Second Greco-Turkish War, the Patriarch of Antioch has had his seat in exile in Damascus.

Quite frankly I want my religion to be rather static. It's not like there are any new truths about Christ, His Incarnation, Earthly Ministry, Passion, Death, Resurrection, Ascension, and Glorious Second Coming to be discovered (save the date of the last, and that He told us is known only to the Father).
The decrees of the Holy Ecumenical Councils pretty much cover it all.

To the extent that there is anything new to be discovered about living the Christian life, the laboratories are something the Christian Arabs, Greeks, Armenians, Russians, . . . and all the rest who are 'stuck' in the distant past have lots of, while we American have very few of : monasteries.

[omnivore]

It's not my problem if you're not into going to libraries to do your own research. I've given you my source. If _you_ have a problem with it, then I guess _you_ have a problem. So sorry. I'll take Petr Beckmann's word, having read his book and finding it believable, over the word of random people I see posting on the Internet. Contrary to what you may have heard, "primary sources" are generally physical archives, not random drivel on the Internet. I can see this is leading to a Galileo-type situation, where his opponents refused to look through his telescope. In this case, I gave you the reference I got the information from. If you refuse to make any effort to look into it, that is hardly my fault. I'm not the one with a problem, so I don't have the burden of solving or "proving" anything. I've given you what I know. If you don't believe it, that's cool. I don't mind what you believe or don't believe. I'm not trying to cause a beef. I just mentioned something I read in a book, and I still believe. Peace be with you.

[Antoninus]

It's not my problem if you're not into going to libraries to do your own research. I've given you my source. If _you_ have a problem with it, then I guess _you_ have a problem. So sorry. I'll take Petr Beckmann's word, having read his book and finding it believable, over the word of random people I see posting on the Internet.

OK, I just went to the website for the local college library system that I use (Bryn Mawr, Haverford, Swarthmore College) to see if this book was listed. Ta-Da! There it was! Published by Golem Press in 1971. A little more digging revealed that Mr. Beckmann also owned Golem Press. Now, I'm not averse to self-published books in general, but the usual reason for self-publishing scientific books is that you can't be bothered with the peer-review process....

A little more web searching on Beckmann indicates that in one of his other self-published books, he declares that he's debunked Einstein's Theory of Relativity. He also seems to be a favorite of objectivists, which explains his antipathy toward Christianity and Catholicism in particular.

I've known lots of people like Mr. Beckmann who are brilliant in one extraordinarily complex field of study like mathematics or physics and somehow think that gives them free reign to pontificate about all other realms of knowledge where they are not expert. It doesn't. When, in this case, they blather on about the wicked Catholic Church, they end up sounding like ill-informed cranks.

I've given you what I know. If you don't believe it, that's cool. I don't mind what you believe or don't believe. I'm not trying to cause a beef. I just mentioned something I read in a book, and I still believe. Peace be with you.

Actually, you're telling me what you think you know. I'm telling you that what you think you know is seriously out-of-whack with reality. That's why I'm encouraging you to actually find some primary sources which prove your point:

"I don't recall the exact method of death penalty used for heretic mathematicians who defied God by using the Satanic symbol of "0", whether it was burning at the stake, breaking on the wheel, tearing off the flesh with red hot pincers, or any of the other routine punishments handed out to heretics, who were the politically incorrect of their day. But they were indeed tortured to death."

If you're going to make a claim like that, you should be prepared to back it up. I recommend something a bit more significant than the self-published work of a author with an obvious axe to grind.

Try this book:



Is it biased in the other direction? Sure. But it's written by an author who knows his stuff--and goes out of his way to build his case based on the works of scholars who are otherwise harshly critical of the Catholic Church.

[timer]

Monestaries...MONE(y)...STAR...IES(word play). Medieval monestary orders(dominican, francisan, others)began as praying orders, devout/poverty ridden. As the generations went by they became more worldly and MONEY oriented. Ye cannot serve god and mammon(money)saith the lord, yes?

So this duality has always been with us : essenes and many other monastic orders in ALL religions. On the one hand : PRAY, on the other hand : PAY. This is why the rise of science in the past 300 years. Religion wasn't advancing the human physical condition one whit, look at all SCIENCE has done to improve everyone's lives. It's a sure bet that YOU wouldn't even be alive w/o medical SCIENCE.

As to the "stasis" of old time religion, a scientific pin to prick your balloon : Jesus was an in vitro implant into the host mother Mary by intelligent aliens(nordics probably). He was a missionary from a cosmic PETA group to save a few from the cosmic battleline that will sweep across the solar system/earth shortly. A "dances with wolves" advance scout to warn the local indians of what's coming.

Arthur Clarke's Third Law : a sufficiently advanced technoloy will seem like MAGIC to a less advanced technology. The feeding of the 5000 : know what a xerox machine is? If you see someone on their knees in front of a xerox machine, is it in prayerful AWE of 5000 copies being cranked out, or just replenishing the stack of paper and bottle of toner?

Thus, are you so self-centered/full of hubris to think that the EARTH was the first place in the UNIVERSE that the xerox machine was invented? Or the slice-by-slice CAT SCAN machine? Can it DAWN on you that an advanced version of the xerox machine was banging out 5000 fish and loaves of bread on the mount when jesus was giving his sermon? No, it was located on an orbiting spaceship and the UPS delivery service was almost instantaneous(see what competition between UPS and FEDEX eventually brings?).

Or the tansfiguration on the mount, again, the same whole body record(clone in the machine)as a record to return HIS body to in the resurrection. His corpse was slam frozen to 0 deg K with a su-co ring in the horizontal plane, defining the xy plane, the excess heat was radiated up/down(+z/-z)as a gamma ray burst, making the scorch-image on the shroud of turin.

But the atoms still had residual gyroscopic precession, thus small CONES of radiation = nose in focus, neck(further away) is fuzzier. Thus when in this su-mo state the death-damage is repaired/returned to the volumetric clone record. But it was TOTAL, he had no brain memory of the past 2 years. This is why he called Mary Magdelene "woman", he ddn't know who she was! It took awhile for his BRAIN memory to catch up to his SPIRITUAL memory.

This may come as a shock at first, but be not afraid. I could tell you MUCH more about Jesus' secrets, how this whole biblical story is about alien/advanced technology, from the distant past and far into the future. But know this, GOD loves us ANIMALS("apes with guns" as the aliens call us), he sent JESUS as his son to bootstrap us into the future.

There is obviously a cosmic chess game going on, played by RULES we only dimly percieve. To wit, WHY is satan let out on parole after 1000 years of Jesus' rule? The next few years should be "interesting times"...

[Dr. Frank fan]

This is stupid. Let me explain this: what they "discovered" was tiling a floor. The fact is that Penrose's stuff was only remarkable in its mathematical rigor. It's nothing innovative. The Greeks did similar stuff.

Thank you. Referring to this sort of thing as a "math breakthrough" because it's an instance of whatever type of tiling Penrose identified and classified is like saying that whoever first drew a circle actually discovered the number pi. The headline's writer seems to understand neither math, nor breakthroughs.