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Old Islamic Tile Patterns Show Modern Math Insight

CowboyNeal posted more than 7 years ago | from the high-tech-tetris dept.

Math 538

arbitraryaardvark writes "Reuters reports that medieval Muslims made a mega math marvel. Tile patterns on middle eastern mosques display a kind of quasicrystalline effect that was unknown in the west until rediscovered by Penrose in the 1970s. '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.' It isn't known if the mosque designers understood the math behind the patterns or not."

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I POST FIRST (-1, Troll)

Anonymous Coward | more than 7 years ago | (#18119816)

YAY ME!

Re:I POST FIRST (0, Offtopic)

Propagandhi (570791) | more than 7 years ago | (#18119950)

How are we supposed to join in your celebrations when you post anonymously? :(

Re:I POST FIRST (-1, Offtopic)

Anonymous Coward | more than 7 years ago | (#18120078)

I'm not. This is my handle, you insensitive clod!

Why wouldn't they? (5, Insightful)

nebaz (453974) | more than 7 years ago | (#18119828)

It seems fairly self important to assume that they didn't understand the math behind the tiles. They generated them, didn't they? Islamic culture was well considered to be centuries ahead of Europe during that time period. They had access to some of the ancient Greek writings that Europe only rediscovered years later. My question is, and I don't mean to troll, what happened? From my perspective, it seems that many people almost disdain the idea of progress in culture and arts now.

Re:Why wouldn't they? (3, Insightful)

kestasjk (933987) | more than 7 years ago | (#18119848)

Well the tiles are just.. tiles. Just because someone uses a curvy shaped dome on top of their mosque doesn't mean they knew how to calculate its surface area or volume using integration.
Maybe they just thought it was a pretty shape?

Re:Why wouldn't they? (5, Funny)

Anonymous Coward | more than 7 years ago | (#18119906)

I'm pretty sure either aliens or reptoids built it, just like with the pyramids.

Re:Why wouldn't they? (3, Insightful)

procrastinx (1000214) | more than 7 years ago | (#18120462)

May be they didnt know the terms 'integration' , 'surface area' and 'volume ' , but they might have understood the real *usefulness* behind those concepts.

"it isn't known if" != "to assume they didn't" (1, Insightful)

Anonymous Coward | more than 7 years ago | (#18119918)

Maybe you'd be less offended by statements if you read them correctly.

Re:Why wouldn't they? (5, Insightful)

grimdawg (954902) | more than 7 years ago | (#18119924)

Most patterns are discovered before the mathematics behind them is fully understood.

A child draws a cube without realising its rotational symmetries are S_4, and draws a circle without knowledge of its useful properties. In the case of decorations, aesthetics tend to come first. When did you first draw a spiral? Did you realise it was fractal?

Hell, most modern mathematics comes from the investigation of an object we thought we knew all about.

It's more than likely the pattern was designed for aesthetic reasons. I'm not trying to run down the guys, but the kind of insight we're talking about here appears at face value to require a long academic tradition. It's not the kind of thing you're likely to stumble on.

Re:Why wouldn't they? (5, Funny)

MicrosoftRepresentit (1002310) | more than 7 years ago | (#18120068)

When I was three I drew the Mandelbrot set in crayons and moments later modelled part of the quaternian Julia set out of plasticine. It wasn't until I was 9 that I understood the maths behind it, which I think proves your point.

Re:Why wouldn't they? (5, Funny)

grimdawg (954902) | more than 7 years ago | (#18120298)

I know the feeling. I proved the Poincare Conjecture when I was 8, using a balloon a stapler. Unfortunately, I assumed it was trivial and never went public.

Re:Why wouldn't they? (4, Funny)

matlhDam (149229) | more than 7 years ago | (#18120322)

I proved the Poincare Conjecture when I was 8, using a balloon a stapler. Unfortunately, I assumed it was trivial and never went public.

Ah, I see. Proof by explosion.

Giving rise to the question: what don't *we* know? (1)

Eternal Vigilance (573501) | more than 7 years ago | (#18120302)

I hope that this link between the aesthetic properties (if not far more) appreciated in the 15th century, and (possibly) greater insight as described by Penrose in the 20th will lead to the consideration that these two aren't endpoints, but merely the first two points in a sequence of understanding.

In other words, a contemplation of the question "Well, they saw the aesthetic properties in the Middle Ages, and they more formally described the mathematical properties in the 1970's. Naturally, after this connection was made, it took only a few years before people recognized the truly world-changing extension to ???."

What might be the "???" ?

Re:Why wouldn't they? (1)

Stooshie (993666) | more than 7 years ago | (#18120478)

... the kind of insight we're talking about here appears at face value to require a long academic tradition.

Which is exactly the kind of tradition that the middle east had at that time (and still do). Well, the parts we haven't bombed back to the stone age at least.

Re:Why wouldn't they? (0)

Anonymous Coward | more than 7 years ago | (#18120484)

a lot of patterns are not "natural". a child drawing a cube most probably does so, because it lives in an environment that provides cubes to its perception. anthropology showed more than once that there are, f.e., tribes in south-east asia that are not even able to draw a straight line, simply because no such thing ever occurs in their world. circles, yes, the sun does that for you.

The Catholic Church happened. (3, Insightful)

Flying pig (925874) | more than 7 years ago | (#18119978)

The last time I suggested white Western civilisation might be less than perfect I got modded to hell, but who cares? It was no less a person than Roger Bacon who said that every educated person needed to know Arabic, but then he was interested in the science and technology of his day, unlike most of the Church. The peak of that Islamic civilisation seems to have been the Kingdom of Granada in Spain, which had an advanced society, religious tolerance (not only were Jews and Christians welcome, but a Hebrew prayer book for women has been discovered there) and advanced technology. There is some evidence that they learned more from the Hindus than the Greeks, as books on the history of numbers point out. There are writings from that society that sound almost modern in outlook.

Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church. For much of recent history, Christian societies have attempted to control and dominate Islamic societies. Since the socially mobile tend to follow the ways of the dominant power, Islam has become increasingly a religion of the poor and ill educated. (I know this is a simplification, but it is a useful simplification.) We are now seeing the effects of creating a society of poor and ill-educated people with ready access to cheap weapons.

On the broader point, I tend to disagree. It is easy to blame television, the movies and the music industry for the destruction of "high" culture, but of course we don't know what "low" culture was like in largely preliterate societies. I suspect the reality is that high culture is more disseminated and understood than ever before, but whereas in the Middle Ages it might have been available to 0.1% of the population, now it is available to, say, 2%. Because mass culture now has access to the media, this fact is concealed in the sheer noise of low culture.

A genuine example, from the 1500s. A footnote to an edition of Rabelais reveals that at one public fair in France, the prostitutes wanting to operate their trade had to take part at the start of the fair in a naked public footrace. This operates on a number of levels. It would tend to discourage unhealthy or diseased prostitutes. It constituted a form of advertising. And it provided entertainment. But it also shows that, no matter what you think of current entertainment standards, they were just as bad in the 1500s.

Re:The Catholic Church happened. (1)

kripkenstein (913150) | more than 7 years ago | (#18120140)

Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church.
(Honest question, not trolling:) I am curious, where in history do you see this occurring? Enlightenment times? By the British Empire (but they weren't Catholic)? Or later during the 20th century?

Re:The Catholic Church happened. (4, Interesting)

pato101 (851725) | more than 7 years ago | (#18120188)

If I recall correctly (I'm a mess in history and dates, please correct if I'm wrong) Granada was taken by catholics in 1492, the same year America was discovered by Cristobal Colon. The same year Jews were told to leave "Spain" - there was no concept of Spain yet-. Islamic people lived in "Spain" during 8 centuries before 1492, and left a deep footstep in art, language, tradition, diet, ...

Re:The Catholic Church happened. (1)

kripkenstein (913150) | more than 7 years ago | (#18120276)

Yes, that is true (indeed 1492 was an eventful year for that area...). But it only relates to Islam in Spain, not in general. Are there other examples of this?

Re:The Catholic Church happened. (-1, Troll)

Anonymous Coward | more than 7 years ago | (#18120142)

Learn some real history. "Religious tolerance" by islam is a myth.

Thats a curious intepretation of history (0, Flamebait)

Viol8 (599362) | more than 7 years ago | (#18120182)

"Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church."

Umm , actually their civilsation was destroyed by the spanish reclaiming THEIR OWN COUNTRY that had been conquered by the Moors. Highbrow civilisation or otherwise , the Moors were 8th century invaders who outstayed their welcome and were no less barbaric than the vikings when it came to aquiring land. I suggest you go and read some history books then get back to us.

Re:Thats a curious intepretation of history (5, Informative)

pato101 (851725) | more than 7 years ago | (#18120220)

Do you consider a country "own" after 8 century "invasion"?

During those 8 centuries Moors and Christian and Jew people lived together. They had their spaces, but also had interaction, trade, ... . Christian were not obligated to convert to Islam, etc. After Christian re-conquest Moors and Jew were ejected from the territory (or obligated to convert to Christianism- nevertheless I'm not sure they had the same rights than Christians after doing that)

I suggest you go and read some history books

Tell me, who did write those books?

Re:Thats a curious intepretation of history (-1, Flamebait)

Viol8 (599362) | more than 7 years ago | (#18120306)

>Do you consider a country "own" after 8 century "invasion"?

Yes. And obviously the spanish did too.

>During those 8 centuries Moors and Christian and Jew people lived together.

How very cosy and inclusive. You could however say the same about any number of empires down the ages. Perhaps India and half of Africa should still be run by the British? Perhaps Spain itself should still be in charge of Mexicon and central america?

>Tell me, who did write those books?

Are you unable to search Amazon without someone holding your hand? Heres a link for you then:

http://www.amazon.co.uk/s/ref=nb_ss_w_h_/026-23016 89-7838812?url=search-alias%3Daps&field-keywords=m oors+spain&Go.x=0&Go.y=0&Go=Go [amazon.co.uk]

Re:Thats a curious intepretation of history (1)

pato101 (851725) | more than 7 years ago | (#18120394)

Are you unable to search Amazon without someone holding your hand?

good dribbling.

Re:Thats a curious intepretation of history (1)

Viol8 (599362) | more than 7 years ago | (#18120474)

>good dribbling.

I think you'd have made yourself look less foolish if you simply hadn't bothered to reply.

Still , some people just can't admit to themselves that they lost the argument.

Re:Thats a curious intepretation of history (2, Insightful)

Alphager (957739) | more than 7 years ago | (#18120404)

>Do you consider a country "own" after 8 century "invasion"?

Yes. And obviously the spanish did too.
Ah, yes. BTW, i hereby call all native americans to reclaim their country from the US-Invaders!

Re:Thats a curious intepretation of history (1)

Viol8 (599362) | more than 7 years ago | (#18120452)

I suspect given a choice quite a lot of them would love to. Their life isn't exactly a bed of roses is it.

Re:Thats a curious intepretation of history (1)

evilbessie (873633) | more than 7 years ago | (#18120476)

Well they had a flag didn't they? It's how we British took so much of the world...

Please note my tongue is firmly in my my cheek, in case you missed it.

Although I liked Gandhi's answer to what he thought of western civilisation, "I think it would be a good idea"...

Re:Thats a curious intepretation of history (5, Informative)

blictrix (127859) | more than 7 years ago | (#18120460)

So you wouldn't mind if the indians decided to drive the white invaders out of America? After all, the whites have been living as invaders there for less than 5 centuries, much less than the muslims in medieval Spain.

And saying that the spanish wanted them out is misleading, the catholic kings and the church wanted them out, what the people wanted is anybody's guess. Spain didn't exist at that point, the christian part was divided into three parts, the kingdom of Navarra, the kingdom of Castilia and the kingdom of Aragon. And although the Kingdom of Navarra came under the control of the catholic kings (Ferdinand and Isabella) it wasn't until the 19th century it became officially a part of Spain. And when the Moors came to the Iberian peninsula, it was under the control of the Visigoths and they didn't put up much of a fight, so "invasion" is maybe stretching it a bit. Besides, it was at a time when the people of Europe were wildly "invading" each other, none of the nations we know today actually existed at that time. You're obviously prejudiced against the muslims, but the truth is that Al-Andaluz was the most civilized part of Europe at that time.

Re:Thats a curious intepretation of history (1)

Viol8 (599362) | more than 7 years ago | (#18120506)

>So you wouldn't mind if the indians decided to drive the white invaders out of America?

Are there enough indians in america to do that? Unless you mean native americans (given you're being so PC yourself...)
Anyway , wouldn't bother me , I don't live there but AFAIR they spent a long loooong time trying to do just that.

>it was under the control of the Visigoths and they didn't put up much of a fight, so "invasion" is maybe stretching it a bit

So because the gauls were fairly comprehensively defeated by the roman empire the romans didn't invade Gaul? Hmm , interesting bit of revisionism.

>You're obviously prejudiced against the muslims,

Ah yes , the standard issue "you're a racist" snipe that every right-on adherent has to include in an argument when they have little else to add and hope the other person will become all defensive and give up. Doesn't work with me pal , it just makes me think you're a sad little twat who doesn't really have his own opinions but has to just regurgitate the group-think. Shame , you were doing ok up until then.

Re:The Catholic Church happened. (1)

the_womble (580291) | more than 7 years ago | (#18120194)

The American rights demonization of Islam is ridiculus, but simply producing diametrically opposite propaganda is not any better.

The last time I suggested white Western civilisation might be less than perfect I got modded to hell

Ah yes, but this time you are attacking Christianity so you are right in line with the Slashdot groupthink.

the Kingdom of Granada in Spain

Following an imperialist invasion to found it - not any different from the European empires.

Islam has become increasingly a religion of the poor and ill educated. (I know this is a simplification, but it is a useful simplification.) We are now seeing the effects of creating a society of poor and ill-educated people with ready access to cheap weapons.

So how come these effects are most strongest in places like oil rich Saudi Arabia, rather than very poor countries like Bangaldesh?

There are also plenty of historical precedents for intolerant and repressive Islamic societies - they are not just a modern reaction to some injustice. Consider what happened to Christian communities in the Middle East with the rise of Islam, for example.

Re:The Catholic Church happened. (0)

Anonymous Coward | more than 7 years ago | (#18120250)

Islam has become increasingly a religion of the poor and ill educated. (I know this is a simplification, but it is a useful simplification.) We are now seeing the effects of creating a society of poor and ill-educated people with ready access to cheap weapons.
So how come these effects are most strongest in places like oil rich Saudi Arabia, rather than very poor countries like Bangaldesh?
Because the house of Saud, including every second cousin of a third uncle got rich from their petro-association with the west while the rest of the country hasn't done so well, while in Bangladesh the wealth distribution is both more uniform, the extremes are less in the face of the poor and not so directly based on western money.

Re:The Catholic Church happened. (1)

the_womble (580291) | more than 7 years ago | (#18120482)

The wealth distribution in Bangladesh is hardly uniform [undp.org] .

I would say it is more down to politics and culture.

Re:The Catholic Church happened. (1)

xoyoyo (949672) | more than 7 years ago | (#18120308)

Consider what happened to Christian communities in the Middle East with the rise of Islam, for example.

They were generally tolerated as people of the book, although not accorded the same rights as Muslims - look up Dhimmi in wikipedia; certainly no worse than, and in most cases definitely better than, the position of jews in Christian societies.

Muslim conquerors generally gave the people of newly conquered lands three choices: to be put to the sword, convert or pay indemnity. Very few chose the second, a few chose the middle option and most chose the last option.

By modern standards of course, these are barbarous options, but they are positively courtly compared to the behaviour of the crusaders a few centuries later.

As far as the "Imperialist invasion of spain" theory goes. That too is nonsense. Imperialism is the correct term, but there simply was no "Spain" to be conquered. There was a Roman territory called Hispania, which had collapsed into interfamily and tribal rivalry with the decline of the empire. (Incidentally, many people who fought with the Moors were Jews, fleeing the Church's policy of forced conversion.) The Moors were simply another grouping hoping to take advantage of the chaos.

The Reconquista is a useful national myth for the Spanish, but it doesn't have much basis in fact. The process of the unification of Spain is markedly similar to the process of the unification of England. If the Danes had stood their ground, or the mercians had held out for autonomy the English would have a different national myth, and if the Spanish had failed to retake the south they would have a different story of legitimacy, just as powerful.

Re:The Catholic Church happened. (1)

the_womble (580291) | more than 7 years ago | (#18120358)

By modern standards of course, these are barbarous options, but they are positively courtly compared to the behaviour of the crusaders a few centuries later.

OF course you could compare the crusaders to, say, the Ottoman Turks.

Re:The Catholic Church happened. (1)

xoyoyo (949672) | more than 7 years ago | (#18120442)

You could, but I'm not really willing to get into the kind of "your side did this bad to mine, so when my side does double bad to you it's okay" discussion that bedevils any discussion of the Middle East.

I think it's enough to note that standards have changed in the last thousand years: in mediaeval war it was okay to loot a captured city, for example. Now that's definitely not okay, but destroying the city from space is.

The key point is that the common views, which you cheerfully quote, of the Muslim empire, Granada and the reconquista are wrong because they are based on a narrative that has the Muslims as the intolerant villains and nation states as somehow existing a priori (so that you can reconquer something that never existed).

It's for that reasons like that the ignorant chaps further up there can't believe that Arabs could have come up with aperiodic tiling.

Re:The Catholic Church happened. (4, Informative)

morgdx (688154) | more than 7 years ago | (#18120212)

It is no coincidence that Algebra comes from the "Al-jabr" the Arabic word for reunion, and Algorithm comes from al-Khwarizmi a Persian mathematician living in Baghdad(!). Kind of makes TFA seem a bit patronising.

Re:The Catholic Church happened. (1)

shutdown -p now (807394) | more than 7 years ago | (#18120256)

Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church.
Pray tell, when did that happen? The Crusades were ultimately unsuccessful - Christians were kicked out of the Holy Land and all the way back to Europe, with Ottomans taking all the Balkans soon after, and their advance on Europe only stopped as far back as Vienna - large parts Eastern Europe were under Muslim rule for several centures! When the Ottomans were finally crushed in a series of defeats from European powers in the end of 19th and the beginning of 20th centuries, the Islamic culture of their empire has already been stagnating for the long time (hence the defeat), which also had a chilling effect in development of the Balkans and parts of Eastern Europe under their occupation.

Re:The Catholic Church happened. (0, Offtopic)

pbhj (607776) | more than 7 years ago | (#18120268)

the Koran: sura 9, verse 29 (Ahmed Ali's translation of the Koran, published in 1994 by Princeton University Press)

"Fight those people of the Book [i.e., Jews and Christians] who do not believe in God and the Last Day, who do not prohibit what God and His Apostle [i.e., Muhammad] have forbidden, nor accept divine law, until all of them pay protective tax in submission."

Sounds like that would be just lovely. So tolerant. Why I'm sure that any group of people would love to live under such a tolerant regime. Oh and remember that the followers of Mohammed don't have a new testament telling them that they've misunderstood god and that in fact he rather prefers "treat your neighbours like your self" than "an eye for an eye".

Re:The Catholic Church happened. (1)

xoyoyo (949672) | more than 7 years ago | (#18120508)

The protective tax system actually led to a rather tolerant Arabic empire - why, there were Christians in Iraq until last year. It's a considerably better lot than say, expulsion. Which is exactly what happened to the Jews when Spanish finally took control of Granada in 1492.

Mod Parent up!! (1, Informative)

Anonymous Coward | more than 7 years ago | (#18120362)

I think this is the first time I have ever seen the original inventor of Science and Technology, Roger Bacon, mentioned on Slashdot. I would expect him to be your Patron Saint!

http://en.wikipedia.org/wiki/Roger_Bacon [wikipedia.org]

For the record, it was not only Arabic that he wanted people to learn, but also Hebrew, so as to translate the Bible correctly. He stressed the revolutionary concept that you got knowledge from provable experiment, not from reading authoratitive books (which was why he was locked up in the March of Ancona for 14 years), and his lectures on the principles of Science (so far as we know he was the first to present these) are so modern in tone that they still bear reading today.

It's a crying shame that, of all the early heros of science, he is probably the most forgotten.

Re:The Catholic Church happened. (5, Interesting)

denoir (960304) | more than 7 years ago | (#18120406)

Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church.
Although the crusades made a deep political impact and united the Muslim world, they managed to self-destruct all by themselves. The reason was the teachings of one al-Ghazali [wikipedia.org] , the most influential thinker in Islamic history. His religious views became law and are still dominant in the Islamic world.

Briefly put, his ideology was that science is intrinsically evil because it proposes that there are natural laws and that would limit the power of God. When an object drops to the floor it doesn't do so because of gravity, but because God wills it. Every event is a singular expression of Gods will and cannot and should not be analyzed and explained.

As you can imagine this did marvels for science in the Islamic world. From being world leader they by their own doing they removed themselves from the game completely. And we have the same view today. In the Muslim world, technology is seen as OK but science as bad. Thanks to that plainly idiotic view they have blocked their own development. There are more books translated in Spain to Spanish than there have in the Arab world translated into Arabic since the 7th century.

Really sad given how great their contributions to early science were. They were centuries ahead of the Europeans but blew it all. It is easy to blame the crusaders but in fact they were only enablers - to kick them out, the Islamic powers all united under one ruler and a single political system.

Re:Why wouldn't they? (1)

wenchmagnet (745079) | more than 7 years ago | (#18119998)

What happened was what happens in most organized religion... in that era, discourse was encouraged and philosophy (and the arts and sciences) flourished. It was not taboo to ask questions and new thoughts and ideas were encouraged.

Then the clergy took over and turned everything on its head. Now the clergy passes fatwas against anything they dont like, and since they are fine with the status quo (it gives them tremendous power and influence), the fatwas come out against anything that even hints at being progressive.

I know I'm over-simplifying but this is it in a nutshell.

Re:Why wouldn't they? (4, Informative)

pfafrich (647460) | more than 7 years ago | (#18120060)

There are basically two forms of tilling patterns [wikipedia.org] , the periodic patterns [wikipedia.org] which have been known for many years, and aperiodic [wikipedia.org] ones, which have only been recently been discovered. For many years it was thought that only the periodic patterns existed, and in particular there were no patterns with five fold symmetry.

The patterns shown in the article are not true penrose patterns, it exhibits two lines of reflection, horizontal and vertical and the pattern does not repeat indefinitely.

Re:Why wouldn't they? (3, Insightful)

Yvanhoe (564877) | more than 7 years ago | (#18120114)

My question is, and I don't mean to troll, what happened? From my perspective, it seems that many people almost disdain the idea of progress in culture and arts now.

The funny thing is that, approx. 1400 years after the death of Jesus we also had our period of intolerance (did you say Inquisition) and of stalling progress. The Renaissance appears to be a flourishing era because of the giant leap that has been made in paintings but in terms of sculpture, architecture or litterature, the trend was to come back to the "classic style" : an aggregation of roman and greek techniques 1000 years old and considered perfect. It is at this time also that we began to see scientists opposing Church dogmas whereas before this time scientists were often also religion scholars.

Re:Why wouldn't they? (1)

Tiro (19535) | more than 7 years ago | (#18120122)

The Islamic civilization is as much a successor to Graeco-Roman Antiquity as Western Christendom. Ayatollah Khomeini's theological doctorate was in -- guess what? -- Aristotelian logic. Where are the glorious cities of Alexandria and the second capital itself, Constantinople? In medieval times these two cities had the population close to one million each; by comparison, Paris had around forty thousand, London had ten thousand.

But of course, being a 'brother' does not mean a twin. The crucial difference between the eastern and western parts of the greater Mediterranean realm was in the patterns of their political economy. In the West, it was serfdom (a part-time and contractual bondage) with peasants subordinated to mostly small and local lords or monasteries -- rather than to a big central government like in the formidable empires of the East. The best book on this subject matter remains to this day Marc Bloch's classic Société féodale, or Feudal society in English translation. This great book gives you a good sense of how the feudal system worked in reality and in its legal theory.

In the more prosperous Eastern Roman Empire, in the much longer established and far longer cultivated (since before the pyramids) Egypt, Fertile Crescent (mostly Syria) and Mesopotamia a different economy endured from one civilization to another, and almost to our days (to the 1950s). It was based on village peasant communities heavily taxed by the central state and where the taxes comfortably sustained the sophisticated urban elite (think Egypt and Alexandria; or Constantinople/Istanbul drawing resources from the rest of Anatolia, the Balkans, and Syria; or Baghdad in the Mesopotamia; or Persepolis and much later the great city of Isfahan in Persia). The land is so fertile, the peasants have nowhere to run, and few resources or opportunities ever to rebel (unless somebody hit from without, like the advancing Muslim armies), and so generation after generation they keep on paying very substantial taxes. Then, the Near East is also a very active commercial zone - think the Silk Road from China to Constantinople, or the Spice and Incense road across Arabia and the Red sea leading to the great bazaars of Alexandria. The trade was predominantly in luxuries, as you see, and guess who consumed those silks, spices, perfumes - and where did they get the money? Remember the "crisis of overaccumulation" and the imperial edifices becoming top-heavy as time went by. Read in Perry Anderson's Passages from Antiquity the very last sections: "Crisis in the East" and "South of the Danube".

Some sort of a crisis (climate catastrophe) unsettled the power arrangements and thus security in Arabia a generation before the Prophet. Any economy directly dependent on the yield from plants and animals would be vulnerable to climate fluctuations, wouldn't it? Remember the concept of "carrying capacity": how many humans could be sustained in a given ecological niche? Then, of course, politics is how people negotiate their problems, sometimes very violently. Pay attention to the special role played by Mecca once the region was engulfed in feuds and how from this role flowed the special peace-making role of the Prophet himself: his adoption of radical monotheism (one God for all humans to worship), the idea of salvation (it has to be one's own moral responsibility to behave properly in this life in order to be saved, and thus following the Law of much higher order than tribal adat or king's law), the sense of brotherhood of all believers, the obligation to defend all fellow Muslims as if they were one's family, and the idea of social justice -- the rich must share with the poor by give away and charities.

Cavalry played a very big role in the military victories of Muslim Arab armies. I have spent a lot of time on that, and McNeill has an excellent discussion in this regard, and Perry Anderson wrote a whole section on "The Nomadic Brake". But beware! It is not cavalry alone - the Zoroastrian (flame-worshipping) Persia (Iran) under the Sassanian dynasty was based on an even better cavalry, yet it collapsed before the advancing Arabs with an astonishing speed. The reason must be the legalism of Islamic religion: it strictly limited how much one could tax the peasants and the merchants. In fact, among the earliest Islamic legal scholars perhaps as many as forty per cent were merchants from the towns like Basra! That's pretty different from Christianity (or Buddhism for that matter) whose codification was performed by either the monks turning their backs on the sinful world, or the high priests (bishops etc.) at the handsomely paid service of empire. Islam is not only a very simple, very rational and legalistic religion, with an extraordinary sense of internal solidarity and mutual help among the faithful, it is perhaps not too wrong to say that Islam is also the most worldly of religions. Merchants and soldiers could be priests (mufti -- simply the member of congregation who knows the Holy Writ and can lead the prayer); and those priests not just performed rituals, they had to argue their cases pretty much like modern lawyers and judges (Islamic judge is called kadi or qadi), by Aristotelian logic and precedents (haditha means stories) from the lifetime of the Prophet!

Try to imagine yourselves in the situation of those Egyptian or Syrian peasants who paid taxes to sustain the consumption of towns, who spoke some sort of Semitic language related to Arabic but unrelated to Greek, and who were literally treated like dirt, merely the human accessory to the rich land exploited by the foreign-imposed urban elites. Can you now guess why the avalanche-like spread of Islam across the whole Middle East and North Africa was not due to cavalry alone? Recall the legal system accessible to all, the regulation of taxes, the defense of fellow Muslims, and all that Michael Mann calls "normative pacification".

Max Weber was the great classical sociologist who wrote a century ago the famous essay on "Protestant Ethics and the Spirit of Capitalism". Randall Collins, himself a leading Weberian scholar today, set out to correct the great dead German: yes, religion of salvation mattered because it made one's earthly behavior strongly linked to afterlife. But it is not Protestantism alone, it is rather the material organization of production first pioneered by the monasteries. And which is the other religion of salvation with a highly-developed institution of monasticism? Buddhism, of course. Could it be that Max Weber also went badly wrong in his assessment of Chinese civilization (which he saw as ritualistic and basically static)? Evidently, Weber was reading the wrong books (but were there correct books on China in Europe a century ago?) and moreover he followed the colonial prejudice of his epoch: in the 1900s German navy was occupying, permanently as they thought, the Tsingtao peninsula (remember the brand of Chinese beer? Ever wondered where from did they get the brewery?)

The second and very big problem is for you to realize just how difficult was the birth of capitalist economy. So many factors had to be overcome! I just warn you: that's the corner of the world of major importance today and for the rest of your life. As Americans are getting obsessed with Islam and the Middle East, quite possibly the East Asian countries are right now obtaining their geopolitical opportunity to rise. None of what I teach you is ancient history.

--Georgi Derluguian

What went wrong was the crisis of overaccumulation, as described above, combined with the military expansion of Europe. It is quite like the example of Spain v. Netherlands/Britain. Spain had a crisis of overaccumulation, mining American gold [linear/flat growth], while Netherlands/Britain grew [exponential economic growth]. The Arabs were dominated quite harshly by the Europeans, so no wonder some of them are hostile to the US led liberal economic order!

Re:Why wouldn't they? (1)

WheelDweller (108946) | more than 7 years ago | (#18120126)

Sure! The invented zero, for example. Back in the day, the Arab world was something special. In fact while 'wandering' in the desert, one of the first places they came to, thinking they'd DIE in the desert, was a huge, lush compound owned by Ishmael. Now that the populace is starving, poor, and unhappy, they've gone into the bomb-making business, as if that's going to change anything. 10% of their population makes the 1% of the evangelical-wackos look like kids on a field trip. They kill at random (Like in Bali) and disturb the chances to EVER get their communal lives back to normal, like it was once before. It's a shame what the oil money did to them. ...more reason to get off the oil standard, ASAP. :(

Re:Why wouldn't they? (1)

bheer (633842) | more than 7 years ago | (#18120168)

They invented a lot of things, but not zero. There's quite a bit of evidence that the Arabs got that from the Indians.

Re:Why wouldn't they? (1)

WheelDweller (108946) | more than 7 years ago | (#18120202)

Is that so? Well how cool is that? Good to know.

Re:Why wouldn't they? (1)

Hal_Porter (817932) | more than 7 years ago | (#18120310)

It's a relative thing. Medieval Islamic societies had more scientists than medieval societies in the west. But that's like saying you have more scientists than the Taliban, quite literally. It's important to note that medieval islam was by no means enlightened by todays's standards. It was still possible in those societies to get killed for blasphemy, or just for displeasing the Caliph. Then in the west the enlightenment totally reformatted society - it was suddenly possible for people to ignore religion without fear of getting killed. Nothing like that happened in the Islamic world, in fact the fundamentalists and secular dictators have managed to roll back what civilisation existed there. And the roots of the enlightenment, a powerful middle class that demands a law based society still don't exist in the Islamic world now.

You can see in Iraq for example, that there isn't sufficient domestic pressure to sustain a liberal democracy after the US/UK leave. It will go back to being a tyranny, and most people will see that as being preferable to civil war.

Re:Why wouldn't they? (1)

David_Shultz (750615) | more than 7 years ago | (#18120472)

It seems fairly self important to assume that they didn't understand the math behind the tiles. They generated them, didn't they? Islamic culture was well considered to be centuries ahead of Europe during that time period. They had access to some of the ancient Greek writings that Europe only rediscovered years later. My question is, and I don't mean to troll, what happened? From my perspective, it seems that many people almost disdain the idea of progress in culture and arts now.
Since depictions of the prophet are forbidden, Islamic art focuses of patterns and designs. It is therefore not "self important", as you describe it, to presume that perhaps their art was simply art, without mathematical justification.

In answer to the question of "what happened" to islamic culture, the answer is "religion happened". Anti-intellectualism swept their culture clean of vile rationality.

It's a pattern? (1)

senatorpjt (709879) | more than 7 years ago | (#18119838)

The article doesn't really say anything other than it's a pattern. It just looks like random dots. Maybe like the yellow circles on money?

Re:It's a pattern? (5, Informative)

Scarblac (122480) | more than 7 years ago | (#18119952)

See Penrose tiling [wikipedia.org] on Wikipedia.

They really have cool properties - you can tile an infinite plane with just two different tiles, in such a way that the pattern never repeats; the ratio of the frequencies of both types is exactly the golden ratio. There's a lot more, see the article.

Apparently they found actual Penrose tiles, hundreds of years old.

Re:It's a pattern? (1)

joh (27088) | more than 7 years ago | (#18120206)

See Penrose tiling on Wikipedia.

They really have cool properties - you can tile an infinite plane with just two different tiles, in such a way that the pattern never repeats; the ratio of the frequencies of both types is exactly the golden ratio. There's a lot more, see the article.

Apparently they found actual Penrose tiles, hundreds of years old.


From the the Wikipedia arcticle: "Pentaplex Ltd., a company in Yorkshire, England controlled by Penrose, owns the licensing rights to Penrose tilings."

This culture will go under, no doubt, and we all know why.

Re:It's a pattern? (1)

2Bits (167227) | more than 7 years ago | (#18120340)

I can't access Wikipedia from China, you insentive clod!

Re:It's a pattern? (0)

Anonymous Coward | more than 7 years ago | (#18119976)

The article doesn't really say anything other than it's a pattern. It just looks like random dots. Maybe like the yellow circles on money?

I guess I a weird. I see a pattern.

Re:It's a pattern? (1)

gdav (2540) | more than 7 years ago | (#18120090)

The dots on money [wikipedia.org] aren't random either.

Tasty thoughts (3, Interesting)

tinkertim (918832) | more than 7 years ago | (#18119840)

Since it isn't known (as TFA points out) if they fully understood the mathematics behind the designs, we could have a bit of fun speculating, yes?

I am no expert on Islam but I really like to read and study up on various forms of encryption. I'm not a crypto genius by any means, I don't endeavour to break codes, I just like to be able to recognize them.

If I am not mistaken (flog me if I am), the mural depicted could in effect be a key to a cipher, and one's starting point applying that mural as a key would be very important. In fact, perhaps a key with infinite grooves and landings that fits a lock with only a few tumblers.

Now, if that structure was destoryed during war (many were), and that key easily re-created from mathematical notes, that would be something. The notes themselves would be useless to pretty much anyone else at the time.

I don't think they understood the math behind it was we do (or better wording would be the significance of the math beyond their application of it) but I do think they understood quite a bit more about cryptography than we previously thought.

Of course, it could just be that the design held some spiritual significance. A lot of trouble to go through, however.

Re:Tasty thoughts (2, Funny)

networkzombie (921324) | more than 7 years ago | (#18119904)

Oooh, look. That looks like a watch. There must be a watchmaker.

Re:Tasty thoughts (1)

mrbobjoe (830606) | more than 7 years ago | (#18119982)

Sounds like an excerpt from some Islamic Da Vinci Code, maybe Contact, maybe even Stargate. Clearly encoded in these tiles is the plan for an interstellar transport system of some sort.

Re:Tasty thoughts (1)

tinkertim (918832) | more than 7 years ago | (#18120030)

Sounds like an excerpt from some Islamic Da Vinci Code, maybe Contact, maybe even Stargate. Clearly encoded in these tiles is the plan for an interstellar transport system of some sort.


Or a way from keeping invading armies from stealing precious culture and a well developed body of knowledge. Not everything is trivial simply because it resembles contemporary fiction.

Of course, you're welcome to ask Dan Brown what he thinks.

Re:Tasty thoughts (1)

Beryllium Sphere(tm) (193358) | more than 7 years ago | (#18120072)

>Of course, it could just be that the design held some spiritual significance. A lot of trouble to go through, however.

There are cathedrals that took centuries to build. Don't underestimate what people will invest in religious expression.

Re:Tasty thoughts (1)

tinkertim (918832) | more than 7 years ago | (#18120356)

There are cathedrals that took centuries to build. Don't underestimate what people will invest in religious expression.


Church also stood for governance, still does to a degree. I am still in awe when I drive through downtown DC (or really any other capitol in the world). Its not *just* religious expression that they are investing their time and resources in building.

Did not mean to minimize it, however :) It just seems a little too intentional to be unintentional. Someone else alluded to "I see a watch, there must be a watchmaker" .. I'm more .. "I see a watch, there could be a watchmaker".

Not suggesting this become the foundation for the next slaughter of millions of innocent trees, just tossing it out as a possibility.

Re:Tasty thoughts (3, Funny)

larry bagina (561269) | more than 7 years ago | (#18120106)

Just add a harvard symbologist, a beautiful egyption female mathematician, and a one-armed assassin for the plot of a Dan Brown book.

Re:Tasty thoughts (1)

Kredal (566494) | more than 7 years ago | (#18120344)

... or a joke on Family Guy.

Not Surprising (1)

gbulmash (688770) | more than 7 years ago | (#18119850)

IIRC, the concept of zero has Arabic roots, and prior to the crusades, there were some pretty bad-ass universities (for the time) in Arabic lands. Between Mongols (let's not forget that the "white man" can't be held responsible for *all* the destruction of art and culture across Europe, Asia, and the Middle East) and European crusaders, a lot of impressive cultural development was trashed across the Islamic world.

- Greg

Re:Not Surprising (0)

Anonymous Coward | more than 7 years ago | (#18119958)

I hate that myth; zero has a history far predating islam [wikipedia.org] .

for example, Zero is also known as 'nil' from the Latin.

Re:Not Surprising (1)

jez9999 (618189) | more than 7 years ago | (#18120342)

You can't really predate something that claims to be the truth from the beginning of the world.

Re:Not Surprising (4, Informative)

anaesthetica (596507) | more than 7 years ago | (#18119960)

The Arabs got zero from the Indians through their trading contacts actually. See the Wikipedia entry: History of Zero [wikipedia.org] .

Re:Not Surprising (4, Funny)

value_added (719364) | more than 7 years ago | (#18120028)

The Arabs got zero from the Indians through their trading contacts actually. See the Wikipedia entry: History of Zero.

Nah, that was just one of the first examples of outsourcing.

A more interesting link [wikipedia.org] .

Re:Not Surprising (1)

KDR_11k (778916) | more than 7 years ago | (#18120160)

That article sucks, it doesn't even mention how Zero dies in every second game.

Re:Not Surprising (0)

Anonymous Coward | more than 7 years ago | (#18120012)

As far as I recall, zero as a concept originates from India,
and yes, the Arabic world have an impressive cultural development,
and our number system originates from there.

Re:Not Surprising (1)

Filip22012005 (852281) | more than 7 years ago | (#18120016)

Both 'algebra' and 'algorithm' are derived from Arabic words. Also, we inherited out left-to-right number system from Arabian math.

Re:Not Surprising (1)

Filip22012005 (852281) | more than 7 years ago | (#18120368)

Obvisouly I meant right-to-left...

Re:Not Surprising (1)

Beryllium Sphere(tm) (193358) | more than 7 years ago | (#18120082)

Also, it's interesting to look up the etymology of "algebra" and "algorithm".

Re:Not Surprising (1)

myowntrueself (607117) | more than 7 years ago | (#18120166)

Also, it's interesting to look up the etymology of "algebra" and "algorithm".

Alcohol as well, though in todays climate and Islamic political correctness, that may not go down so well...

(IIRC the Koran refers specificaly to prohibition of date wine so theoretically other alcoholic beverages *should* be fine)

Re:Not Surprising (0)

Anonymous Coward | more than 7 years ago | (#18120222)

Well I dont remember the complete phrase but it says more along the line "any substance that intoxicates is illegal"

Re:Not Surprising (0)

Anonymous Coward | more than 7 years ago | (#18120134)

Zero was introduced by the Indians, not the Arab.

Close, but no cigar? (2, Insightful)

glittalogik (837604) | more than 7 years ago | (#18119862)

Well it's pretty, I'll give it that. TFA's a bit light on details though, and "tantalizingly close to having the structure that Penrose discovered in the mid-70s" isn't exactly awe-inspiring; maybe a few more examples would have been in order before they published?

headline (5, Funny)

Anonymous Coward | more than 7 years ago | (#18119864)

medieval Muslims made a mega math marvel
Asinine alliterations alienate audience

What a complete non-story (1)

petes_PoV (912422) | more than 7 years ago | (#18119956)

The article (which extends to 3 pages) is long on talk and pityfully short on actual examples. The one image shown is a nice mosaic, no doubt about that and has an obvious five-sided theme to it. However that's all we see. If they don't have any examples other than this, then the editor needs to be sacked. This looks to me like a small local story being talked up to a level of importance it simply doesn't warrant in order to make the author seem more important or insightful.

Re:What a complete non-story (1)

Derling Whirvish (636322) | more than 7 years ago | (#18120172)

This looks to me like a small local story being talked up to a level of importance it simply doesn't warrant in order to make the author seem more important or insightful.

This follows on the exhibition of "1001 Inventions [aljazeera.com] " that toured the UK last year which claimed such 'Islamic inventions' as "flying with wings and rocket flying." It's part of a drive to show Islam as a progressive force.

Another Islamic math-art mystery (5, Informative)

sky7i (1067592) | more than 7 years ago | (#18119970)

The recent documentary by Oxford historian Brittany Hughes, When the Moors Ruled in Europe [google.com] , revealed (among many other very surprising findings) that the strikingly gorgeous Alhambra Palace also contains a very interesting mathematical curiousity within the design of all of its walls and floor patterns. (I won't spoil it for people who want to watch the documentary, which is available in its entirety on Google Video.) Also, many more Islamic patterns [flickr.com] from throughout the Muslim world are available on flickr's Muslim Cultures group [flickr.com] for those intrigued by the sort of artwork mentioned in the article.

Re:Another Islamic math-art mystery (1)

oZZoZZ (627043) | more than 7 years ago | (#18120420)

"When the Moors Ruled in Europe" I think you mean "Moops"

Obl. Seinfeld (1)

$pearhead (1021201) | more than 7 years ago | (#18120446)

When the Moors Ruled in Europe
Moops! [wikipedia.org]

Tells us almost nothing. (2, Insightful)

Ace905 (163071) | more than 7 years ago | (#18120120)

It would be nice if the article actually identified why these patterns have to be based on a complicated mathematical principle, and if they're not - how they could have been made and still represent that mathematical principle. According to the article, the patterns aren't even exact but quasi-crystalline-structures.

I can do a quasi-fractal-pattern by accident if I have enough time to create random patterns, like say an entire country's worth of structures covered in patterns.

Can some statistics-guru figure out the odds of this being a random accident, considering how few examples they have, and how the examples aren't even exact representations of the mysterious mathematical formula(s) they mention? I really don't get why this is believable based on the article.

---
Pre-Roman Crystalline Structure Dance [douginadress.com]

Re:Tells us almost nothing. (2, Informative)

Napoleon The Pig (228548) | more than 7 years ago | (#18120314)

The whole reason these patterns are attracting so much attention is because they don't explicitly repeat themselves yet they still show a rotational symmetry. Making crystaline structures isn't very difficult mathematically. Crystals are very ordered and neat, repeating themselves ad infinitum. Quasicrystals on the other hand are very complex mathematically because of their aperiodic structure.

The patterns found on the structures would be even more incredible if they were just random accidents. The pattern on the shrine mentioned in the article is a near perfect match to the mathematical model, the chances of that happening are very very slim. I'm not saying that this proves they knew the math behind the patterns, I'm just saying that they deliberately created the patterns in such a way that we can't rule out that they didn't.

Check out http://intendo.net/penrose/info.html [intendo.net] for more on the math behind the patterns.

Patent or Copyright Implications? (1, Interesting)

Anonymous Coward | more than 7 years ago | (#18120156)

I seem to recall Roger Penrose has a patent or copyright on the pattern that bears his name.

Perhaps this constitutes prior art or shows that he does not actually own a copyright to it.

Not Surprising (3, Insightful)

LordLucless (582312) | more than 7 years ago | (#18120164)

I suppose it's not really surprising that Muslim architecture is going to uncover these sorts of complex patterns. As I recall, the Quran prohibits art depicting humans (or possibly anything created by Allah, I can't recall exactly), and as a result, Islamic art tends to the more abstract. Without the devotion to realism that characterised Western art through much of history, it makes sense that they'd develop the more abstract art to a greater complexity.

Re:Not Surprising (1, Informative)

Anonymous Coward | more than 7 years ago | (#18120436)

Wiki:

"Contrary to a common belief, Islamic art does include representations of humans, of animals, and even of the Prophet himself: these were banned only in religious sites and works (mosques, madrasas, and Qu'rans), and even there exceptions may be found."

http://en.wikipedia.org/wiki/Islamic_art [wikipedia.org]

Interesting definition of "rediscovered" (2, Insightful)

Viol8 (599362) | more than 7 years ago | (#18120170)

Presumably in this case it actually means resdiscovered-by-western-academics since presumably these patterns have been looked at by thousands of people everyday for hundreds of years as they went to pray. I can't think of any other reason why despite millions of arabs looking at these patterns over the years they were considered "lost" to mankind until "rediscovered" by an english professor.

Escher (4, Interesting)

Soepkip (1006855) | more than 7 years ago | (#18120190)

Recently I visited the Escher museum (http://www.escherinhetpaleis.nl/) in The Hague. They have a statement of Escher on the wall in which he expresses his he expresses his sadness that Islam didnt allow depiction of anything else other than abstract patterns. Apparently Escher works of interlocking creatures were inspired by his visits to the mosques in Spain (?)... Guess Penrose wasn't the only one in "the west" to have discovered those mathematical qualities.

Nice Work - but NO evidence of mathematics (5, Insightful)

hackershandbook (963811) | more than 7 years ago | (#18120218)

I have an ongoing debate with a friend who is both a philosopher of science and a mathematics teacher.

Suffice it to say that I wish he had taugh me mathematics (and algebra, geometry, calculus) rather than the teachers I had ..

One of the things that come up in our discussions is the idea the the Ancient Egyptians knew about PHI and PI - as can be seen from the structure of their architecture - and that the builders of Stonehenge also had working knowledge of trigonometry.

But as a mathematician - he denies that the there was any knowledge of "mathematics" because the principles were never described "mathematically" - just used in an "intuitive way".

"Without the maths", he said, "You can't argue that they understood the maths" and, he continued, "if they never expressed their finding in mathematical terms (i.e. in formulas with proofs) - then it isn't maths anyway - its just architecture"

Re:Nice Work - but NO evidence of mathematics (0)

Anonymous Coward | more than 7 years ago | (#18120290)

Well there was a book Written by Al-Khawrazmi called Algab-o-wal-Muqabila. I have read the English Translation from my college lib and there this fellow
talks about how to solve Quadratic Equations. So it's not a bad idea to assume that they knew what they were doing. And Arabs had awesome universities before Bghdad got ruined by Mongols. Why did that happen? I have been told many reason I like to believe two
1-You cant stay on the top for ever. Romans went away... Greeks had to fall why not Muslims .........
2-Muslim gave up all the traits that made them great in that time. so they started to decline and now they are technologically/scientifically worthless and politically as well

The math behind... (1)

kyc (984418) | more than 7 years ago | (#18120258)

Of course they understood what they were designing. Just because they had not developped the sophicticated mathematics that we did right now does not mean that they were unaware of what they were doing.

Math is just projecting some kind of light to nature, and wait for its reflection to understand and appreciate nature. Sometimes, the beauty or the simple truth might be equally clear to the naked eye.

Therefore, it is really irrelevant to ask whether they could mathematically show what they did. They designed something that is visible to us by another means.

These mysteries have survived millenia.. (1)

gd23ka (324741) | more than 7 years ago | (#18120292)

People tend to believe that just because a design used by
a certain religious group that it was created or at least
understood by that group. There is undoubtedly depth and
ancient knowledge _in the works_ from which for example
islamic, christian or jewish scriptures are _edited from_,
but you will need prior knowledge to actually point it out.

Take Christianity for an example here for it was far from
the exception. You will find in many of the older churches in
Europe displays of zodiacs and other graphics depicting
astrological concepts - even though Christians are forbidden
to engage in astrological practices.

Exploring this further you will find many temples throughout the
world are chock full of fascinating mathematical artefacts. Take
for example the Seed of Life http://en.wikipedia.org/wiki/Seed_of_Life [wikipedia.org]
design which can be arranged into the Flower Of Life design
http://en.wikipedia.org/wiki/Flower_of_Life [wikipedia.org] from which in turn
Metatron's Cube is derived http://en.wikipedia.org/wiki/Metatron#Metatron.27s _Cube [wikipedia.org] and
from which in turn you can finally derive the Five Platonic Solids
from http://en.wikipedia.org/wiki/Platonic_Solids [wikipedia.org] .

If you're interested in this there is a good presentation albeit
lengthy demonstration of sacred geometry on Google Video
http://video.google.com/videoplay?docid=8673723312 620286523&q=sacred+geometry [google.com]
(part 1) and http://video.google.com/videoplay?docid=-621792339 066334035&q=sacred+geometry [google.com]
(part 2)

Lastly sacred geometry not only appears in mosques or other temples but
also in crop circles http://www.lucypringle.co.uk/photos/2004/uk2004cf. shtml [lucypringle.co.uk]
and that makes you think doesn't it.

Prior art in Kleenex patent dispute?? (4, Interesting)

wwwrench (464274) | more than 7 years ago | (#18120412)

Mmmh, if this is true, maybe it counts as prior art in his patent dispute with the makers of Kleenex. [gwu.edu] They were using Penrose tiles because the quasi-periodic structure makes it less likely that the overlapping of the pattern will cause ridges to form. Math patents!!

Strap A Bomb to That Kid! (0)

Anonymous Coward | more than 7 years ago | (#18120422)

Allahu Akbar!

Abdul Alhazred (1)

metroplex (883298) | more than 7 years ago | (#18120424)

This must be the work of the Mad Arab Abdul Alhazred! He did this to praise the Old Ones, no doubt.

If they actually did it, great for them (1)

OeLeWaPpErKe (412765) | more than 7 years ago | (#18120500)

However keep in mind that muslims conquering generally let the elite of a society (ie. architects) intact.

So most mosques were actually designed by non-muslims. E.g. the blue mosque in Istambul was constructed by a Christian architect, who was trained by another Christian architect, the "best ottoman architect ever", by the name of Sinan.

Did muslims understand the maths necessary to construct large domes in the 11th century ? No.

But Byzantine Christians did. As did Moroccan Jews.
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