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."
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.
Patent or Copyright Implications? (Score:1, Interesting)
Perhaps this constitutes prior art or shows that he does not actually own a copyright to it.
Re:The Catholic Church happened. (Score:4, Interesting)
Escher (Score:4, Interesting)
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.
Prior art in Kleenex patent dispute?? (Score:5, Interesting)
Re:Not Surprising (Score:3, Interesting)
"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]
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."
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
Al Ghazali & Ahmed Sirhindi (Score:5, Interesting)
from the original journal (Score:2, Interesting)
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)
Re:Why wouldn't they? (Score:3, Interesting)
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.
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]".
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 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.
Re:The Catholic Church happened. (Score:1, Interesting)
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.
Re:The Catholic Church happened. (Score:2, Interesting)
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
Re:Why wouldn't they? (Score:1, Interesting)
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?