Old Islamic Tile Patterns Show Modern Math Insight 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."
Re:It's a pattern? (Score:5, Informative)
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:Not Surprising (Score:5, Informative)
Another Islamic math-art mystery (Score:5, Informative)
Re:Why wouldn't they? (Score:5, Informative)
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:The Catholic Church happened. (Score:4, Informative)
Re:Thats a curious intepretation of history (Score:5, Informative)
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)
Tell me, who did write those books?
Re:Tells us almost nothing. (Score:2, Informative)
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.
Mod Parent up!! (Score:1, Informative)
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:Not Surprising (Score:1, Informative)
"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]
Re:Thats a curious intepretation of history (Score:5, Informative)
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.
Almost needs a "patents" tag (Score:4, Informative)
But I suppose "tantalisingly close" isn't enough to prove prior art on Penrose's U.S. Patent 4133152.
If I recall correctly, the proof that Penrose tiling is aperiodic depends on projection of a line marked out in intervals representing an irrational number onto a line marked out in uniform intervals. According to Wikipedia [wikipedia.org] (hey, this isn't an academic paper, so I can cite Wikipedia, right?) the first reference for irrational numbers was in the Indian Sulba Sutras composed between 800-500 BC, so the fundamental knowledge was available in plenty of time for these tilings. And because irrational numbers were arrived at geometrically I can imagine that the ancients could indeed have understood the math.
There's more information about the ancient tilings here [sciencenews.org], which shows that the Islamic tilings break down into five basic tiles, and that each of those five tiles can be broken down into Penrose tiles. So it looks as if they beat the first modern aperiodic tiling, Berger's initial one, which needed 20426 tiles, but didn't get as far as cutting it down to Penrose's two.
Re:The Catholic Church happened. (Score:2, Informative)
Baghdad was much larger and wealthier than any other city in the Middle East, in Europe, or in Africa. It was almost completely destroyed by the Mongol army.
Re:The Catholic Church happened. (Score:5, Informative)
NB: although it ended up being Christian rulers who destroyed the Spanish Muslim civilisation, the original poster's claim that this was done "under the Aegis of the Catholic Church" is unjust. As has often been the case, the Catholic Kings used religion as a political and propaganda tool very effectively, but the conquest of the Muslim kingdoms in Spain was really about territory, and their subsequent persecution of Jews and Muslims had a lot more to do with eliminating possible sources of dissent together with jealousy (jews in particular occupied important administrative positions that Spanish nobles wanted for themselves) than real religious differences. There's no better evidence of this than the fact that many Spanish Jews fled to Catholic Italy, home of The Vatican, where they not only managed to live without many problems (i.e. some people had personal prejudices against them, but there was ittle if any persecution by either the Italian political authorities or the Church), but were also able to obtain important administrative posts and teach in universities, where their translation of ancient Greek works that had been preserved by Spanish Muslims into Latin became a key factor in the subsequent European Renaissance.
Re:Prior art in Kleenex patent dispute?? (Score:2, Informative)
Re:Why wouldn't they? (Score:5, Informative)
there are rules (now) that Steinhardt and his colleagues (including my wife...which is why I know something here...heh) have developed which can tell you what shape should come next to prevent backing yourself into the corner, but they have taken years to develop -- not because they're mathematically complex, but just because it takes a looooong time to try all the possible combinations, and then recognize what happened at each vertex.
my assumption is the same as the parent's -- that the Muslim artists simply "brute forced" these -- that is to say, put down random tiles, took them back up when they created bad spots, and patted themselves on the back when it all worked and looked pretty -- and then jotted down what the pattern looked like. having helped my wife do the same thing early in her thesis work -- let me tell you, it's a pain in the arse with these shapes -- but by no means impossible, and the results are always impressive.
Re:If they actually did it, great for them (Score:3, Informative)
Your argument was that Muslim architecture was in most part due to their policy of leaving societal elites in place, including architects, during the conquest. You go on to support this argument by pointing to the careers of two Ottoman architects Sinan and Mehmet Aga, and claiming that most of the mosques in Istanbul were built therefore by Christians. From this you draw the conclusion that muslims in the 11th century did not have the mathematical skills required to build large domes in the 11th century.
Your argument fails in a number of respects:
* The architects you reference flourished some 700 years after the first Muslim empire
* They were both active in a country that was not part of the Muslim Empire
* The Ottoman empire had been established for 200 years by the time of Sinan's birth, so he was not conquered
* Both architects were trained by the Ottoman army, so their skills were not acquired before a Muslim conquest
* Both architects were converts to Islam, not Christian as you state.
In addition, Islamic mathematicians were intrigued by the properties of Spheres, see, for example the work of Al Sijzi, who was active in exactly the time frame you claim Muslims were mathematically ignorant: http://www-groups.dcs.st-and.ac.uk/~history/Biogr
Re:Why wouldn't they? (Score:5, Informative)
The dome shape was explained in (of all places) an undergraduate art history class I took thirty years ago. Those domes are imposible to construct without advanced geometry (and other advanced disciplines as well).
Re:The Catholic Church happened. (Score:3, Informative)
Re:Why wouldn't they? (Score:4, Informative)
Persian mathematicians invented Spherical Trig, etc.
Persian architects built the Taj Mahal for Shah Jahan.
Persian astronomers developed the systems and observations of Indians and extrapolated complete mathematical systems, that were the basis for both Newton and Leibnitz.
Actually the Mayans did this first. (Score:5, Informative)
Islam and independent thinking (Score:4, Informative)
What drove you to that conclusion?
Here's a translation of the verse in Question (I also read it in the original Arabic): "It is not fitting for a Believer, man or woman, when a matter has been decided by Allah and His Messenger to have any option about their decision: if any one disobeys Allah and His Messenger, he is indeed on a clearly wrong Path"
It roughly means "believers are not to disobey Allah or his prophet". Why does that makes you think it prohibits independent thinking?
There are may verses of the Quran and many quotes of the prophet that encourage thinking and reasoning (for example Quran verses 4:82, 47:24, 16:11 to 16:13).
In fact, a complete branch of Islamic studies is called Ijtihad, which is all about independent thought.
to quote [islamicity.com] an online Islamic site: "A scientific approach has been encouraged in the Qur'an with the objective of ascertaining its truthfulness. It provides man with a chance to verify its authenticity." so in Islam, independent thinking is in fact an essential part of the religion.
Re:No, Islam happened. (Score:3, Informative)
You're either misinformed or lying. I'm going to assume you're misinformed. Here are some quotes from the Koran to help enlighten you.
"The punishment of those who wage war against Allah and his messenger and strive after corruption in the land will be to be killed or crucified, or to have their hands and feet chopped off on opposite sides, or to be expelled out of the land. Such will be their humiliation in the world, and in the next world they will face an awful horror." (Koran, 5:33-34)
"When we decide to destroy a population, we send a definite order to them who have the good things in life and yet sin. So that Allah's word is proven true against them, then we destroy them utterly." (Koran, 17:16-17)
"Remember Allah inspired the angels: I am with you. Give firmness to the believers. I will instill terror into the hearts of the unbelievers: you smite them above their necks and smite all their fingertips off of them." (Koran, 8:12)
While it's also true that you can find commands from God to kill people in the Bible, all of those quotes are in the Old Testament. The New Testament does not contain any commands to kill, though it does give warnings to people who reject God. But their punishment will be meted out by God in the next life, at no point are Christians told to exact that punishment themselves. In fact, they're specifically told not to do it.
Re:Why wouldn't they? (Score:2, Informative)
Read here: http://en.wikipedia.org/wiki/Algorithm#Etymology [wikipedia.org]
http://en.wikipedia.org/wiki/Muhammad_ibn_M%C5%AB
And then, after you read where the source is, maybe it would be time to know where Algebra came from:
http://en.wikipedia.org/wiki/Algebra [wikipedia.org]
Some architecture info can be found here: http://www.islamicarchitecture.org/architecture/i
Pretty shape!!!
I wouldn't be so sure. (Score:3, Informative)