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Math Science

Old Islamic Tile Patterns Show Modern Math Insight 538

Posted by CowboyNeal
from the high-tech-tetris dept.
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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Old Islamic Tile Patterns Show Modern Math Insight

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  • Tasty thoughts (Score:4, Interesting)

    by tinkertim (918832) * on Friday February 23, 2007 @03:17AM (#18119840) Homepage
    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.
  • by Anonymous Coward on Friday February 23, 2007 @04:32AM (#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.
  • by pato101 (851725) on Friday February 23, 2007 @04:41AM (#18120188) Journal
    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, ...
  • Escher (Score:4, Interesting)

    by Soepkip (1006855) on Friday February 23, 2007 @04:41AM (#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.
  • by denoir (960304) on Friday February 23, 2007 @05:34AM (#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.

  • by wwwrench (464274) on Friday February 23, 2007 @05:35AM (#18120412) Homepage
    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!!
  • Re:Not Surprising (Score:3, Interesting)

    by LordLucless (582312) on Friday February 23, 2007 @06:02AM (#18120524)
    Odd. A document released recently by a Muslim group in Britain said schools shouldn't force Muslims to draw pictures of humans:

    "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 glass, metal/woodwork, landscape drawing, paintings, architectural representations, geometric figures, photography and mosaic art."

    Muslim Council of Britain [mcb.org.uk]
  • by kestasjk (933987) * on Friday February 23, 2007 @06:55AM (#18120784) Homepage
    The number system we use is actually originally derived from Hindu numerals. They were the first to use the number '0' to create a positional number system, which is what put it head and shoulders above the Roman one.. But that's besides the point.

    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."
  • It is little know that Robert Amman co-discovered one of Penroses aperiodic tiles. Amman was am amatuer mathematician in the United States. See his wiki page.

    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
  • by vakibs (1067644) on Friday February 23, 2007 @08:17AM (#18121170) Journal
    Al Ghazali was indeed a very influential philosopher who brought in umpteen damage to the scientific inquiry of the Islamic world. But the real damage was done by another person called Ahmed Sirhindi [wikipedia.org]. In simple words, what he has said was that human brain is futile. Any effort to understand nature/God through reasoning and thought is a waste of time. The only way salvation could be obtained is through studying the Kuran (the unmorphed message from God) and the Hadith (stories about the life of Mohammed). Without the use of Mohammed, man is inherently powerless to understand Nature or God ! In his philosophy, the biggest evil were the Greek & Hindu philosophers. His philosophy sounded the death to the movement of Sufism (mysticism and philosophy) in Islam. At the same time, it put an end to the systematic enquiry of science. Ahmed Sirhindi became the Mujaddid (the equivalent of the pope in Islam) and he convinced the Ottoman empire to use his methods. He convinced the Mughal empire in India to use his methods. Consequently, India and Arabia were mired in dark ages ever since 1000 AD.His influence is strongly felt in the later and the final Mujaddid - Wahhab of Saudi Arabia. The major school of Islam in Pakistan and India is the Deoband school, which is drawn from the ideas of Wahhab & Sirhindi. These are the seeds of Islamic fundamentalism. It is no wonder that all glories of Islamic mathematics, medicine and astronomy were reached before 1000 AD.
  • by Tzinger (550448) on Friday February 23, 2007 @08:24AM (#18121212) Homepage
    The newspaper article hardly tells the story. Here is the abstract from Science

    The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons ("girih tiles") decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.

    If you care to look at the article, it has some very interesting pictures and explanations in the "supplement". Peter Lu, et.al. Science 315, 1106 (2007)
  • by radtea (464814) on Friday February 23, 2007 @08:38AM (#18121308)
    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.

    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 Tiling [uwgb.edu], with its local five-fold symmetry and use of five hexagons to fill out the pattern. I have no idea where Kepler got the idea from--he lived in the 16th century, about a hundred years after the Arab tilings the article talks about.

    In any case, the practical arts routinely outstripped scientific and mathematical understanding until very recently, and even now we do sometimes see science playing catch-up with empirical ability. It is doubtful that anyone at the time understood very much about any of these tilings in the way a modern mathematician would. But by the same token science and mathematics would have a lot less interesting stuff to work with if artisans didn't explore empirical possibilities for their own reasons.
  • by Dr. Manhattan (29720) <.sorceror171. .at. .gmail.com.> on Friday February 23, 2007 @09:17AM (#18121706) Homepage

    Have you actually read al-Ghazali?

    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]".

  • No, Islam happened. (Score:3, Interesting)

    by d3ac0n (715594) on Friday February 23, 2007 @09:41AM (#18121982)

    As to what happened to the high point of Arabic culture, thats easy, we destroyed it in The Crusades.


    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 tribalism for years by that point.

    The only real "advanced" Islam was the one destroyed years earlier in the Grenada area. The only reason they were advanced was their rejection of Fundamentalist Islam, and the creation of a more modern more egalitarian society that viewed Christians and Jews as, if not equals, valuable citizens. Most of the advances IN that society were brought to it by the Jews and Christians living within it. Not the Muslims themselves. Of course, all that was gone by the time of the crusades due to the destruction of that society by greedy Kings using Christianity as an excuse to take land.

    The point is, Islam as we know it today has brought nothing to the table to advance society. While I am all for giving people their due, Modern Islam is owed no credit for any discoveries (unless you consider suicide bombers a discovery), and trying to credit them for this smacks of Political Correctness gone awry.
  • by Anonymous Coward on Friday February 23, 2007 @09:50AM (#18122118)
    Yes I have, what about you? Go and Read Incoherence of the Philosophers where he rebuts reason, and the rationalist philosophers particularly avicenna (ibn e sina). One of the gems of the books (imho) is a passage whereby he describes Fire and how it has no intrinsic property to burn and the only way the burning happens is by the 'direct' intervention of god or his agents (the angels). He goes on to prove this by quoting Abraham walking through fire and how god had not acted preventing the fire from burning him.... He also explicitly rejects all knowledge derived from non muslim sources, a polite way of casting aside the knowledge acquired through the Greek writings (as well as other cultures). The book is available online , google for it and have a read. Truly bone chilling stuff
  • by SatanicPuppy (611928) * <SatanicpuppyNO@SPAMgmail.com> on Friday February 23, 2007 @11:20AM (#18123602) Journal
    In a nutshell, I think that a society that is purely physicalist in its view of living things is...problematical. By those standards stomping on an alarm clock, a flower, and a puppy are all pretty much the same thing, because living things are no different from non-living things.

    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.
  • by t0rkm3 (666910) on Friday February 23, 2007 @02:04PM (#18126028)
    Interesting. As I remember it Muhammed required extra taxes from Christian and Jews (people of the book) when he was feeling merciful, and something less savory when he was not.

    I am an atheist, but it seems odd that a religion whose own founder required the death of unbelievers on several occasions and also had sex with a child is compared to a overall harmless pacifist. It's like comparing Hitler to Gandhi. Seems perverse to me.

    Muhammad was a warlord. A warlord who founded a religion of peace? What need would a warlord have for his people to be pacifistic to his own motivation and conversely hold nothing but mild tolerance or animus for all others?

    As a curiosity, could someone with a deeper knowledge of theology, provide a list of pacifist sects of Islam compared to pacifist sects spawned by Chistianity? Buddhism beats both of the former hands down, more than likely...

    "Muhammad is the Apostle of Allah. Those who follow him are merciful to one another, but ruthless to unbelievers" Sura 48:29. "Kill the Mushrikun (unbelievers) wherever you find them, and capture them and besiege them, and lie in wait for them in each and every ambush..." Sura 9:5
  • by Anonymous Coward on Friday February 23, 2007 @11:22PM (#18131578)
    Europe was hardly mathematically or scientifically inclined till about 1100 A.D.

    People need to stop being so provencial and accept the fact that lots of ideas were thought of before the 21st century.


    You remind me of those people who claim discrimination any time that a minority is questioned or criticised in the least. It's not provencial to suspect that the medieval Arabs didn't understand the finer points of aperiodic tilings.

    Do you think it's provencial when a modern non-western mathematician says he suspects that Fermat didn't really prove his Last Theorem?

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