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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
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?
Maybe you'd be less offended by statements if you read them correctly.
Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church. For much of recent history, Christian societies have attempted to control and dominate Islamic societies. Since the socially mobile tend to follow the ways of the dominant power, Islam has become increasingly a religion of the poor and ill educated. (I know this is a simplification, but it is a useful simplification.) We are now seeing the effects of creating a society of poor and ill-educated people with ready access to cheap weapons.
On the broader point, I tend to disagree. It is easy to blame television, the movies and the music industry for the destruction of "high" culture, but of course we don't know what "low" culture was like in largely preliterate societies. I suspect the reality is that high culture is more disseminated and understood than ever before, but whereas in the Middle Ages it might have been available to 0.1% of the population, now it is available to, say, 2%. Because mass culture now has access to the media, this fact is concealed in the sheer noise of low culture.
A genuine example, from the 1500s. A footnote to an edition of Rabelais reveals that at one public fair in France, the prostitutes wanting to operate their trade had to take part at the start of the fair in a naked public footrace. This operates on a number of levels. It would tend to discourage unhealthy or diseased prostitutes. It constituted a form of advertising. And it provided entertainment. But it also shows that, no matter what you think of current entertainment standards, they were just as bad in the 1500s.
Pining for the fjords
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.
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Pre-Roman Crystalline Structure Dance
Ace
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.
Just because you're paranoid doesn't mean there isn't an invisible demon about to eat your face
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.
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"
Yes. And obviously the spanish did too.
Ah, yes. BTW, i hereby call all native americans to reclaim their country from the US-Invaders!
Their life is that way because of their own choices. Sure you can go back a hundred years or so and say this or that happened. But today, they have the same opertunities as anyone else. Even moreso then most, especialy the iner-city folks we refere to as the welfare clans. (notice, I'm not refering to blacks, hispanics or anyone because of race. You will always have poor people living next to poor people in some of the worst neighborhoods availible).
While there has been challenges in the past, the bigest limiting factor is a culture that refuses to be part of the success around it. And this goes to the inner-city clans too. Far too many people fail to shine because it just isn't hip! Those who do succed get ignored while everyone concentrates on those losing at life (and no i didn't call anyone a "loser" I said they weren't succeeding). But thats what happens when the government "keeps" people dependent on them, too few look at taking care of themselves.
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.
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:
S
LS
LSL
LSLLS
LSLLSLSL
LSLLSLSLLSLLS
LSLLSLSLLSLLSLSLLSLSL
etc...
You can go at infinity with this. You won't find periodicity or a pattern that repeat itself. Now to the point: does this means that you take the two segments and you put them together randomly you get the F. sequence? No, by any chance. The rules are simple (and the Fibonacci sequence is old (~1200), so I would not be surprised if the Islamic mathematicians were aware of it, so they "ported" it in 2D (the Penrose tiling is the 2D version of the F. sequence).
By the way the story goes even back in time further: the ratio between the number of L and S for a significantly large sequence, is tau, the golden mean (again the same is true for the Penrose tiling). The golden mean was a key number (sqrt5+1)/2~1.6... in the greek world, where it was used as a proportion standard to build building and temples. It's also a key element in fractal growth, in key dimensions of our body, etc.
So the Islamic artists (scientists?) of the time were a bit like today's scientists. they gathered previous studies and assembled together using some new insights.
Why don't give them credits for it, instead of stupidly saying: "well they just got lucky?".
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.
[Fuck Beta]
o0t!