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."
Why wouldn't they? (Score:5, Insightful)
Re:Why wouldn't they? (Score:3, Insightful)
Maybe they just thought it was a pretty shape?
Close, but no cigar? (Score:2, Insightful)
"it isn't known if" != "to assume they didn't" (Score:1, Insightful)
Re:Why wouldn't they? (Score:5, Insightful)
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.
The Catholic Church happened. (Score:3, Insightful)
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.
Re:Why wouldn't they? (Score:4, Insightful)
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.
Tells us almost nothing. (Score:3, Insightful)
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 [douginadress.com]
Not Surprising (Score:4, Insightful)
Interesting definition of "rediscovered" (Score:3, Insightful)
Nice Work - but NO evidence of mathematics (Score:5, Insightful)
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"
Re:Thats a curious intepretation of history (Score:3, Insightful)
Yes. And obviously the spanish did too.
Re:Why wouldn't they? (Score:3, Insightful)
Re:Why wouldn't they? (Score:5, Insightful)
Re:Why wouldn't they? (Score:1, Insightful)
Re:The Catholic Church happened. (Score:5, Insightful)
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.
Re:The Catholic Church happened. (Score:5, Insightful)
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:Why wouldn't they? (Score:3, Insightful)
and interestingly, the Arab world now uses indian numbers...
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sometimes a cigar is just a cigar, and sometimes it's a big black d**k
-george carlin
Re:Thats a curious intepretation of history (Score:3, Insightful)
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.
Re:Why wouldn't they? (Score:5, Insightful)
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.
Geometric Analysis (Score:3, Insightful)
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.
Re:The Catholic Church happened. (Score:5, Insightful)
>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.
Re:Why wouldn't they? (Score:0, Insightful)
I'm not sure that's true. Religion has a way of focusing the mind. Think of it like a drug. Say religion is like coffee. You drink a cup and you can read and think a bit faster. Drink a keg and you've lost your mind. Just like many things, moderation is the key.
Re:Why wouldn't they? (Score:4, Insightful)
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.
Re:Why wouldn't they? (Score:2, Insightful)
Re:Why wouldn't they? (Score:3, Insightful)
Personally, I think that a society who follows those tenets because they believe them to be right, rather than because that's what their god supposedly wants, is a more enlightened society.
The perfect example: the Fibonacci sequence (Score:3, Insightful)
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?".
Re:Al Ghazali & Ahmed Sirhindi (Score:3, Insightful)
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.
Re:Why wouldn't they? (Score:5, Insightful)
And he is right indeed. But he cheated you a bit. He didn't told you *why* it's more difficult.
I'll do: it's more difficult because we are intelligent beings and irrationalism is against our highest nature. In other words: it's difficult because it's stupid, and being conciously stupid it's hard.
Re:Why wouldn't they? (Score:3, Insightful)
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 spirituality makes society whole. I think social values make society whole. Unless you mean to say "all social values are a form of spirituality," which is an unusual definition of the term, then I just don't think your view is well supported.