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Math Science

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."
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Old Islamic Tile Patterns Show Modern Math Insight

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

    by nebaz ( 453974 ) on Friday February 23, 2007 @04:16AM (#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: (Score:3, Insightful)

      by kestasjk ( 933987 ) *
      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?
      • by Anonymous Coward on Friday February 23, 2007 @04:30AM (#18119906)
        I'm pretty sure either aliens or reptoids built it, just like with the pyramids.
      • Re: (Score:3, Insightful)

        May be they didnt know the terms 'integration' , 'surface area' and 'volume ' , but they might have understood the real *usefulness* behind those concepts.
        • by SatanicPuppy ( 611928 ) * <Satanicpuppy AT gmail DOT com> on Friday February 23, 2007 @10:26AM (#18121802) Journal
          They may very well have understood them...You have to remember, the Dark Ages for us was the Enlightenment for them. They were doing a lot of interesting math, and building architecturally advanced structures embodying complex mathematical concepts when we were wallowing around in superstitious ignorance.

          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.
          • by Lord Ender ( 156273 ) on Friday February 23, 2007 @11:20AM (#18122570) Homepage

            A society that doesn't appreciate some form of spirituality is pretty empty

            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.
            • by SatanicPuppy ( 611928 ) * <Satanicpuppy AT gmail DOT com> on Friday February 23, 2007 @12:20PM (#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.
              • Re: (Score:3, Insightful)

                by Lord Ender ( 156273 )
                I realize that without society, my life would be miserable. For that reason, I cherish the things that make society possible and pleasant. This includes valuing human life, science, philosophy, art, economics, law, personal liberties, and many other things.

                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
      • by fub ( 126448 ) on Friday February 23, 2007 @07:02AM (#18120530)
        While the letters we use right now are Latin, the numbers are Arabic. What tells you that about the mathematical abilities of the middle east in those times, compared with the european insight?
        • by kestasjk ( 933987 ) * on Friday February 23, 2007 @07:55AM (#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."
        • Re: (Score:3, Insightful)

          While the letters we use right now are Latin, the numbers are Arabic

          and interestingly, the Arab world now uses indian numbers...

          sometimes a cigar is just a cigar, and sometimes it's a big black d**k
          -george carlin
        • Re: (Score:3, Funny)

          by EatHam ( 597465 )
          That they couldn't do math, and the arabs couldn't write. They got together and made the Reese's Peanut Butter Cup of math and english, which is what the SATs are based on to this day.
      • by Anonymous Coward on Friday February 23, 2007 @10:26AM (#18121804)
        You read the wrong FA. Typical slashdot, using Reuters or the Wall Street Journal or Fox or some such nonsense for a science or mathmatecal FA. Here's [] a FA that actually answers your question and explains why they had to have had advanced math to construct these things.

        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).
    • by grimdawg ( 954902 ) on Friday February 23, 2007 @04:36AM (#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.
      • by MicrosoftRepresentit ( 1002310 ) on Friday February 23, 2007 @05:11AM (#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.
    • 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
      • 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?
        • by pato101 ( 851725 ) on Friday February 23, 2007 @05:41AM (#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, ...
          • 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?
            • by Weedlekin ( 836313 ) on Friday February 23, 2007 @08:38AM (#18120940)
              I think he was referring to Islam in Spain as the civilisation that got destroyed, because Spanish Muslims had diverged significantly from those in Africa and the Middle East (or more correctly, African and Middle Eastern Muslims had diverged from them), so they can justifiably be regarded as a distinct civilisation with a unique culture. Unfortunately for them this meant that they were basically caught between a rock and a hard place, with Catholic Europe on one side who regarded them as enemies, and a stricter, more fundamentalist Islamic culture in Africa (i.e. the other side of Spain) that had also regarded them as enemies since at least the 11th century. What's surprising therefore is not that they ended up getting destroyed, as that was obviously inevitable, but rather that they lasted as long as they did when surrounded by such powerful and fanatical opponents.

              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.
      • 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 th

        • by xoyoyo ( 949672 )

          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

          • 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.

            • by xoyoyo ( 949672 )
              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 empir
      • by morgdx ( 688154 ) on Friday February 23, 2007 @05:48AM (#18120212) Homepage
        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.
        • by TerranFury ( 726743 ) on Friday February 23, 2007 @10:39AM (#18121960)

          >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.

      • 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

      • by denoir ( 960304 ) on Friday February 23, 2007 @06:34AM (#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 [], 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 vakibs ( 1067644 ) on Friday February 23, 2007 @09:17AM (#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 []. 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.
          • Re: (Score:3, Insightful)

            by TubeSteak ( 669689 )

            Consequently, India and Arabia were mired in dark ages ever since 1000 AD.
            It is no wonder that all glories of Islamic mathematics, medicine and astronomy were reached before 1000 AD.
            You should have stopped before saying that.

            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.
      • by Iloinen Lohikrme ( 880747 ) on Friday February 23, 2007 @09:32AM (#18121274)
        Others have already posted to your comment so I will keep it short. First of all, no civilization was wiped out when Moors where removed from Spain, what happened was the removal of governing Muslim elite and replacing it with a christian king and nobles. What stayed the same were the peoples, their language and their habits and culture which in any case were there before Moor conquers. It should be noted that civilization, religion, nation, language i.e. don't mean the same thing. Civilization [] can be mix of many religions, nations, languages i.e. that are bond together. In Spain, the majority of people where Christians, they spoke the same language and had similar habits, which in later terms made them a nation that can be counted to western civilization.

        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: (Score:3, Informative)

        by SengirV ( 203400 )
        You can also point to Al-Ghazali - [] - as the destroyer of the enlightened Islamic dynasty as it was known. 100 years before Roger Bacon's time, Al-Ghazali lead a "Cultural Revolution" in islam which forbad any and all thought that men determined their own fate. All actions were a direct act of God and free will was non-existent. Thus, any teachings of Aristotle, Plato, etc... were heresy. Islam turned from a pinnacle of intellectualism to a parasite living off
    • by pfafrich ( 647460 ) <rich@sing s u> on Friday February 23, 2007 @05:08AM (#18120060) Homepage
      There are basically two forms of tilling patterns [], the periodic patterns [] which have been known for many years, and aperiodic [] 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: (Score:3, Interesting)

        by radtea ( 464814 )
        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 T []
    • by Yvanhoe ( 564877 ) on Friday February 23, 2007 @05:19AM (#18120114) Journal
      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.
    • by Tiro ( 19535 )

      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 be

    • 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
    • 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 pro
  • 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?

  • Tasty thoughts (Score:4, Interesting)

    by tinkertim ( 918832 ) * on Friday February 23, 2007 @04:17AM (#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.
    • Re: (Score:2, Funny)

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

    • Re: (Score:3, Funny)

      Just add a harvard symbologist, a beautiful egyption female mathematician, and a one-armed assassin for the plot of a Dan Brown book.
    • by ConceptJunkie ( 24823 ) * on Friday February 23, 2007 @09:31AM (#18121266) Homepage Journal
      After decades of arduous archaeological work, months of supercomputer time (including hundreds of CPU years using a popular new BOINC module) and the lifetime work of more than a dozen mathematicians, cryptologists, experts in medieval Arabic and early second millenium Muslim culture (which in many ways led the world in science, math, astronomy and philosophy), the incredible Mosque mosaics were finally decoded:

      Don't forget to drink your Ovaltine.

      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:

      Son of a bitch!

  • 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
  • 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 (Score:5, Funny)

    by Anonymous Coward on Friday February 23, 2007 @04:23AM (#18119864)

    medieval Muslims made a mega math marvel
    Asinine alliterations alienate audience
  • by sky7i ( 1067592 ) on Friday February 23, 2007 @04:44AM (#18119970)
    The recent documentary by Oxford historian Brittany Hughes, When the Moors Ruled in Europe [] , 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 [] from throughout the Muslim world are available on flickr's Muslim Cultures group [] for those intrigued by the sort of artwork mentioned in the article.
  • by Ace905 ( 163071 ) on Friday February 23, 2007 @05:19AM (#18120120) Homepage
    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 []
    • Re: (Score:2, Informative)

      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 pat
  • Not Surprising (Score:4, Insightful)

    by LordLucless ( 582312 ) on Friday February 23, 2007 @05:33AM (#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.
  • by Viol8 ( 599362 ) on Friday February 23, 2007 @05:35AM (#18120170) Homepage
    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 (Score:4, Interesting)

    by Soepkip ( 1006855 ) on Friday February 23, 2007 @05:41AM (#18120190)
    Recently I visited the Escher museum ( 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 hackershandbook ( 963811 ) on Friday February 23, 2007 @05:50AM (#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"
  • by wwwrench ( 464274 ) on Friday February 23, 2007 @06:35AM (#18120412) Homepage
    Mmmh, if this is true, maybe it counts as prior art in his patent dispute with the makers of Kleenex. [] 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!!
  • by digitig ( 1056110 ) on Friday February 23, 2007 @07:25AM (#18120634)

    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 [] (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 [], 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.

  • 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. []

    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.

  • Geometric Analysis (Score:3, Insightful)

    by ChunderDownunder ( 709234 ) on Friday February 23, 2007 @10:37AM (#18121942)
    I haven't visited the Arabic world but my encounters with Moorish craftsmanship in Spain have been awe-inspiring.

    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.
  • by Venik ( 915777 ) on Friday February 23, 2007 @11:23AM (#18122636)
    We all know it's pure chance they stumbled into these mathematical patterns. What can Arabs possibly know about algebra and numbers in general? Oh, wait...
  • by feranick ( 858651 ) on Friday February 23, 2007 @01:51PM (#18124914)
    People say that it's a coincidence. What Lu and Steinhardt are demonstrating is deep knowledge of advanced math. The best example of quasiperiodic tiling (as they are called), is the Fibonacci sequence. To build it you need to differnet tiles (say a long segment "L" and a short segment "S") and two combining rules:

    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:


    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?".

God made machine language; all the rest is the work of man.