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Old Islamic Tile Patterns Show Modern Math Insight
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."
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.
Rhymes that keep their secrets will unfold behind the clouds.There upon the rainbow is the answer to a neverending story
See Penrose tiling on Wikipedia.
They really have cool properties - you can tile an infinite plane with just two different tiles, in such a way that the pattern never repeats; the ratio of the frequencies of both types is exactly the golden ratio. There's a lot more, see the article.
Apparently they found actual Penrose tiles, hundreds of years old.
I believe posters are recognized by their sig. So I made one.
The Arabs got zero from the Indians through their trading contacts actually. See the Wikipedia entry: History of Zero.
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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.
The Arabs got zero from the Indians through their trading contacts actually. See the Wikipedia entry: History of Zero.
Nah, that was just one of the first examples of outsourcing.
A more interesting link.
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, ...
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.
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.
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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"
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?
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.
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!!
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So you wouldn't mind if the indians decided to drive the white invaders out of America? After all, the whites have been living as invaders there for less than 5 centuries, much less than the muslims in medieval Spain.
And saying that the spanish wanted them out is misleading, the catholic kings and the church wanted them out, what the people wanted is anybody's guess. Spain didn't exist at that point, the christian part was divided into three parts, the kingdom of Navarra, the kingdom of Castilia and the kingdom of Aragon. And although the Kingdom of Navarra came under the control of the catholic kings (Ferdinand and Isabella) it wasn't until the 19th century it became officially a part of Spain. And when the Moors came to the Iberian peninsula, it was under the control of the Visigoths and they didn't put up much of a fight, so "invasion" is maybe stretching it a bit. Besides, it was at a time when the people of Europe were wildly "invading" each other, none of the nations we know today actually existed at that time. You're obviously prejudiced against the muslims, but the truth is that Al-Andaluz was the most civilized part of Europe at that time.
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.
Quidnam Latine loqui modo coepi?
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
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
Nobody knows, but the step after that will be Profit!
Free as in mason.
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.
I'm not going to change your sheets again, Mr. Hastings.
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.
"If we generalize this to the field of anthropology, it might explain our modern astonishment at finding more evidence of intelligence and intention in our ancestors the closer we look... The Ice-Man's tattoo of acupuncture therapy is one example."
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.
I'm not going to change your sheets again, Mr. Hastings.
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:
You are in a maze of twisty little passages, all alike.
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.
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No, but the quotes I've seen 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".
PHEM - party like it's 1997-2003!
>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.
The first usage of zero as an actual numerical quantity occurred in the Mayan vigesimal numbering system around 36 BCE. (see the Wikipedia article on Mayan numerals ) Some people postulate, although, that this was derived from the older Olmec numbering system, which could have gone as far back as 1200 BCE. If this is true, then it means that the Olmecs discovered zero 1828 years before Brahmagupta re-discovered and formalized it in 628 CE in India. jdb2