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."
Why wouldn't they? (Score:5, Insightful)
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Maybe they just thought it was a pretty shape?
Re:Why wouldn't they? (Score:5, Funny)
Re:Why wouldn't they? (Score:5, Funny)
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Re:Why wouldn't they? (Score:5, Insightful)
Just because things have swung back the other way today, doesn't mean they won't swing back again tomorrow...That's the real lesson to learn from all the fundamentalist chrsitian movements...A society that doesn't appreciate some form of spirituality is pretty empty, but a society to embraces spirituality above all other things is hardly removed from barbarism.
Re:Why wouldn't they? (Score:4, Insightful)
What is your definition of "empty?" I'm sincerely curious. For that matter, what do you mean by "spirituality?"
Would you describe the Star Trek society (secular, cosmopolitan, humanist) as "empty?" Humans don't believe in any sorts of spirits or other supernatural creatures in Roddenberry's vision of an ideal society.
Re:Why wouldn't they? (Score:4, Interesting)
Now Star Trek is an interesting case (despite what others seem to think) because they embrace some of what I would think of as "the divinity of man"...They have very strong beliefs about not only the intrinsic value of life, but also the value of things like art, literature, science, and the uplifting of the human condition, as well as a sophisticated value system dealing with the sort of things that are ethically "desirable" in an individual.
So, when I say, "Spirituality" I'm definitely not talking about anything supernatural per se, but more about an appreciation of the value of things beyond the actual physical substance of the world. Religion is a form of spiritualism, though not one that appeals to me personally because I feel it often misses the point, and because it tends toward anti-intellectualism.
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The reasons I cherish these things have nothing to do with spirits, magic, gods, auras, karma, superstitions, or other spiritual concepts. A society composed of people with these values would flourish and be far from "empty."
So I really don't agree that s
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Personally, I think that a society who follows those tenets because they believe them to be right, rather than because that's what their god supposedly wants, is a more enlightened society.
Re:Why wouldn't they? (Score:5, Insightful)
And he is right indeed. But he cheated you a bit. He didn't told you *why* it's more difficult.
I'll do: it's more difficult because we are intelligent beings and irrationalism is against our highest nature. In other words: it's difficult because it's stupid, and being conciously stupid it's hard.
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Re:Why wouldn't they? (Score:5, Insightful)
Re:Why wouldn't they? (Score:5, Interesting)
I'm not saying Muslim nations weren't, in many respects (especially maths and astronomy), the most advanced nations around at the time. What I am saying is that it's a bit of a leap from "they used this shape" to "they knew all the advanced mathematics that can be derived from studying this shape."
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)
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and interestingly, the Arab world now uses indian numbers...
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sometimes a cigar is just a cigar, and sometimes it's a big black d**k
-george carlin
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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:Why wouldn't they? (Score:5, Insightful)
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? (Score:5, Funny)
Re:Why wouldn't they? (Score:5, Funny)
Re:Why wouldn't they? (Score:4, Funny)
Ah, I see. Proof by explosion.
Re:Why wouldn't they? (Score:5, Funny)
Re:Giving rise to the question: what don't *we* kn (Score:5, Funny)
Nobody knows, but the step after that will be Profit!
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.
I wouldn't be so sure. (Score:3, Informative)
The Catholic Church happened. (Score:3, Insightful)
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Re:The Catholic Church happened. (Score:4, Interesting)
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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.
No, Islam happened. (Score:3, Interesting)
Except for one fact: Europe LOST the crusades. Yes, they held an area of land approximately equivalent to modern day Israel for a short period of time, but most of Arabia was still dominated by Islam. Yes, "The Caliphate" as Mohammad's original empire was known was gone, but it had been in serious decline for some time due to internal strife, the slow march towards religious extremism and traditional trib
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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 w
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The American rights demonization of Islam is ridiculus, but simply producing diametrically opposite propaganda is not any better.
Ah yes, but this time you are attacking Christianity so you are right in line with the Slashdot groupthink.
Following an imperialist invasion to found it - not any different from the European empires.
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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 barb
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OF course you could compare the crusaders to, say, the Ottoman Turks.
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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 empir
Re:The Catholic Church happened. (Score:5, Insightful)
It's not so much astonishment, but an ingrained prejudice that renders many people incapable of accepting the fact that ancient peoples were _not_ less intelligent than us. It's therefore easier for them to believe that Atlanteans (who are inevitably portrayed as being white!) or aliens were responsible for gigantic and impressive structures from thousands of years ago than what they think of as "a bunch of ignorant wogs who didn't have TV and cars". Furthermore, the fact that (for example) the ruins of ancient Zimbabwe were attributed to Phoenicians, Hebrews, lost tribes of white men, etc., etc., because "darkies" were incapable of such architectural feats shows that archaeologists and anthropologists haven't always been immune to cultural prejudices.
Re:The Catholic Church happened. (Score:4, Informative)
Re:The Catholic Church happened. (Score:5, Insightful)
>Algebra comes from the "Al-jabr" the Arabic word for reunion
IIRC, algebra was like the 'Arabic numerals' (which other posters have mentioned) in that it came to the Arabs through trade with India.
Then, thanks to the Arabs, algebra was developed and preserved, and then communicated to the West. Then, when the British colonized India, they presumably set up schools that taught the subject... (Funny, these circles).
Algebra survived because the societies that understood it stayed in contact with one another; this was necessary in order for it to spread. Knowledge get passed around -- and each society that holds the baton for a bit tends to add something useful to it.
Moral of the story: extroverted societies learn more; xenophobia hurts knowledge.
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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
Re:The Catholic Church happened. (Score:5, Interesting)
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.
Al Ghazali & Ahmed Sirhindi (Score:5, Interesting)
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If you had RTFA, you'd have noted that these Penrose patterns showed up after 1000 AD and over the next several hundred years, became more and more elaborate.
Re:The Catholic Church happened. (Score:5, Interesting)
No, but the quotes I've seen [wikipedia.org]don't really support scientific inquiry very well: "...our opponent claims that the agent of the burning is the fire exclusively;' this is a natural, not a voluntary agent, and cannot abstain from what is in its nature when it is brought into contact with a receptive substratum. This we deny, saying: The agent of the burning is God, through His creating the black in the cotton and the disconnexion of its parts, and it is God who made the cotton burn and made it ashes either through the intermediation of angels or without intermediation. For fire is a dead body which has no action, and what is the proof that it is the agent? Indeed, the philosophers have no other proof than the observation of the occurrence of the burning, when there is contact with fire, but observation proves only a simultaneity, not a causation, and, in reality, there is no other cause but God."
This is called "Occasionalism [wikipedia.org]".
Re:The Catholic Church happened. (Score:5, Insightful)
Also on a note Europe and western powers made a rise because of their highly organized states and armies, more evolved banking and finance sectors, appraisal for knowledge and education and on a later date ability harness finance&scientific knowledge to serve industrialization. This was which raised western civilization from the drain. You also note that christian societies have attempted to control and dominate Islamic societies, but you forget that in 19th and 20th century the focus of European imperial powers was to control and dominate the whole world, not just Muslims. And before that if you make a note about crusades, you should understand that crusades were an attempt to take back old christian lands from Muslim conquers. In the view of these, there isn't any grand christian plot to suppress Muslims as you try to suggest.
Also on a note when you say that the socially mobile tend to follow the ways of a dominant power, you should also understand than in previous times there were no immigration. When Europe and west started to raise, that didn't succumb able part of other cultures to Europe because there still was religion, language and ethnic barriers. What we have seen in Islamic societies in middle east, in last 1000 years are the effects on what it does when the leading elite doesn't embrace trade, banking, formal organization of government, formalization of armies, science, knowledge and education of masses. What happened to Islamic civilization was not that it failed in absolute terms, it just didn't keep up with the rest and thus in 18th and 19th centuries was very much behind western world.
Just to give you example on what I am discussing in practical terms. In example in Finland Mikael Agricola, a priest, formed the Finnish written language in 16th century which teaching was started even to the simple masses. Of course the literature rate didn't rise quickly, but in time of several centuries it made quite big part of Finnish able to read and write, which in turn made possible to further educate more and more people. Also in western Europe kings and nobles started to understand the practically of stable banking and finance sectors and in time became more tolerant and took more responsibilities to pay their debts and not just wipe out debts to bankers. The fact that western civilization got first to industrial revolution and later on became first modern and birth cradle for global civilization is nothing to do with suppressing or exploiting other civilizations, it's everything to do on using own strengths and continues building and evolution of everything in societies.
Re:The Catholic Church happened. (Score:4, Funny)
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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?
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Yes. And obviously the spanish did too.
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While there has been challenges in the past, the bigest li
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.
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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: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.
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Even the fact of local five-fold symmetry is interesting, although I agree these are not true Penrose tiles, which typically use only two shapes (I count at least three or four in the picture) each of which have a reflection symmetry but no rotation symmetry.
The tiling shown in the picture with the article looks quite a lot like a Kepler T [uwgb.edu]
Re:Why wouldn't they? (Score:4, Insightful)
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.
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Since depictions of the pro
It's a pattern? (Score:2)
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.
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Tasty thoughts (Score:4, Interesting)
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.
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There are cathedrals that took centuries to build. Don't underestimate what people will invest in religious expression.
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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.
:) It just seems a little too intentional to be unintentional. Someone else alluded to "I see a watch, th
Did not mean to minimize it, however
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Re:Tasty thoughts (Score:5, Funny)
Youssef Abu Sufah, a British scholar of 12th century Muslim architecture and amateur mathematician summed up the almost unanimous response of the scientific, mathematical, and historical communities with the following observation:
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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.
Not Surprising (Score:2)
- Greg
Re:Not Surprising (Score:5, Informative)
Re:Not Surprising (Score:5, Funny)
Nah, that was just one of the first examples of outsourcing.
A more interesting link [wikipedia.org].
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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)
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Close, but no cigar? (Score:2, Insightful)
headline (Score:5, Funny)
Another Islamic math-art mystery (Score:5, Informative)
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Tells us almost nothing. (Score:3, Insightful)
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]
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The patterns found on the structures would be even more incredible if they were just random accidents. The pat
Not Surprising (Score:4, Insightful)
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"In Islam the creation of three dimensional figurative imagery of humans is generally regarded as unacceptable because of the risk of idolatress practices and some pupils and parents may raise objections to this. The school should avoid encouraging Muslim pupils from producing three dimensional imagery of humans and focus on other forms of art, calligraphy, textile art, ceramic gl
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.
Interesting definition of "rediscovered" (Score:3, Insightful)
Escher (Score:4, Interesting)
Nice Work - but NO evidence of mathematics (Score:5, Insightful)
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"
Prior art in Kleenex patent dispute?? (Score:5, Interesting)
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.
Penrose was a the CO-discoverer of aperiodic tiles (Score:5, Interesting)
http://en.wikipedia.org/wiki/Robert_Ammann [wikipedia.org]
I knew Bob Amman. I shared an office with him in my first job out of college. He was doing minor programming work for a small network/modem company in the early 80s. His white board always had tiled diagrams on it. I graduated from MIT but he was probably the best example I knew of a prodigy.
The curious thing about Amman was how poorly he dealt with life. A man of his genius should not have ended up at the post office.
I never knew he was famous until years later when something must have happen to Penrose (quasicrystals?) and Amman was in the local paper. I couldn't believe the guy I worked with traveled in these circles. One of the scientists I worked with at Kodak had a book on tiles. I checked the index, Amman was all over it, using cited by other mathematicians "unpublished personal correspondence."
It makes one wonder what other geniuses are out there sorting mail.
Paul
Geometric Analysis (Score:3, Insightful)
Don't miss Granada's Alhambra, a breath-taking treasure and not just for the intricate artwork.
There are a number of books, I'll let you browse Amazon at your leisure, on the beauty of Islamic art. One I purchased explores the mathematics behind the designs, Keith Critchlow's "Islamic Patterns: An Analytical and Cosmological Approach". It explains how patterns emerge from arcs and intersections of polygons. Further, Critchlow argues that for the Muslim these patterns displayed a spiritual aspect, that the wonder experienced at looking at these patterns pales in comparison to the complex thoughts behind their creation.
Alas, if only there were more hours in the day I'd try reproducing them via Java2D or OpenGL. Fascinating stuff.
Oh, please... (Score:3, Funny)
The perfect example: the Fibonacci sequence (Score:3, Insightful)
1. at every S you change it with a L
2. at every L you change it with LS
so you build the different generations of the sequence as follow:
S
LS
LSL
LSLLS
LSLLSLSL
LSLLSLSLLSLLS
LSLLSLSLLSLLSLSLLSLSL
etc...
You can go at infinity with this. You won't find periodicity or a pattern that repeat itself. Now to the point: does this means that you take the two segments and you put them together randomly you get the F. sequence? No, by any chance. The rules are simple (and the Fibonacci sequence is old (~1200), so I would not be surprised if the Islamic mathematicians were aware of it, so they "ported" it in 2D (the Penrose tiling is the 2D version of the F. sequence).
By the way the story goes even back in time further: the ratio between the number of L and S for a significantly large sequence, is tau, the golden mean (again the same is true for the Penrose tiling). The golden mean was a key number (sqrt5+1)/2~1.6... in the greek world, where it was used as a proportion standard to build building and temples. It's also a key element in fractal growth, in key dimensions of our body, etc.
So the Islamic artists (scientists?) of the time were a bit like today's scientists. they gathered previous studies and assembled together using some new insights.
Why don't give them credits for it, instead of stupidly saying: "well they just got lucky?".
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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.
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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 require