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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
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?
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.
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
Start a happiness pandemic
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.
How are we supposed to join in your celebrations when you post anonymously? :(
The article (which extends to 3 pages) is long on talk and pityfully short on actual examples. The one image shown is a nice mosaic, no doubt about that and has an obvious five-sided theme to it. However that's all we see. If they don't have any examples other than this, then the editor needs to be sacked. This looks to me like a small local story being talked up to a level of importance it simply doesn't warrant in order to make the author seem more important or insightful.
politicians are like babies' nappies: they should both be changed regularly and for the same reasons
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.
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.
---
Pre-Roman Crystalline Structure Dance
Ace
I seem to recall Roger Penrose has a patent or copyright on the pattern that bears his name.
Perhaps this constitutes prior art or shows that he does not actually own a copyright to it.
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.
"Unfortunately their civilisation was destroyed by a European power under the aegis of the Catholic Church."
Umm , actually their civilsation was destroyed by the spanish reclaiming THEIR OWN COUNTRY that had been conquered by the Moors. Highbrow civilisation or otherwise , the Moors were 8th century invaders who outstayed their welcome and were no less barbaric than the vikings when it came to aquiring land. I suggest you go and read some history books then get back to us.
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.
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"
Of course they understood what they were designing. Just because they had not developped the sophicticated mathematics that we did right now does not mean that they were unaware of what they were doing.
Math is just projecting some kind of light to nature, and wait for its reflection to understand and appreciate nature. Sometimes, the beauty or the simple truth might be equally clear to the naked eye.
Therefore, it is really irrelevant to ask whether they could mathematically show what they did. They designed something that is visible to us by another means.
There's plenty of room at the bottom! Richard P. Feynmann
People tend to believe that just because a design used by
s _Cube and
2 620286523&q=sacred+geometry9 066334035&q=sacred+geometry
. shtml
a certain religious group that it was created or at least
understood by that group. There is undoubtedly depth and
ancient knowledge _in the works_ from which for example
islamic, christian or jewish scriptures are _edited from_,
but you will need prior knowledge to actually point it out.
Take Christianity for an example here for it was far from
the exception. You will find in many of the older churches in
Europe displays of zodiacs and other graphics depicting
astrological concepts - even though Christians are forbidden
to engage in astrological practices.
Exploring this further you will find many temples throughout the
world are chock full of fascinating mathematical artefacts. Take
for example the Seed of Life http://en.wikipedia.org/wiki/Seed_of_Life
design which can be arranged into the Flower Of Life design
http://en.wikipedia.org/wiki/Flower_of_Life from which in turn
Metatron's Cube is derived http://en.wikipedia.org/wiki/Metatron#Metatron.27
from which in turn you can finally derive the Five Platonic Solids
from http://en.wikipedia.org/wiki/Platonic_Solids.
If you're interested in this there is a good presentation albeit
lengthy demonstration of sacred geometry on Google Video
http://video.google.com/videoplay?docid=867372331
(part 1) and http://video.google.com/videoplay?docid=-62179233
(part 2)
Lastly sacred geometry not only appears in mosques or other temples but
also in crop circles http://www.lucypringle.co.uk/photos/2004/uk2004cf
and that makes you think doesn't it.
I hope that this link between the aesthetic properties (if not far more) appreciated in the 15th century, and (possibly) greater insight as described by Penrose in the 20th will lead to the consideration that these two aren't endpoints, but merely the first two points in a sequence of understanding.
In other words, a contemplation of the question "Well, they saw the aesthetic properties in the Middle Ages, and they more formally described the mathematical properties in the 1970's. Naturally, after this connection was made, it took only a few years before people recognized the truly world-changing extension to ???."
What might be the "???" ?
I think this is the first time I have ever seen the original inventor of Science and Technology, Roger Bacon, mentioned on Slashdot. I would expect him to be your Patron Saint!
http://en.wikipedia.org/wiki/Roger_Bacon
For the record, it was not only Arabic that he wanted people to learn, but also Hebrew, so as to translate the Bible correctly. He stressed the revolutionary concept that you got knowledge from provable experiment, not from reading authoratitive books (which was why he was locked up in the March of Ancona for 14 years), and his lectures on the principles of Science (so far as we know he was the first to present these) are so modern in tone that they still bear reading today.
It's a crying shame that, of all the early heros of science, he is probably the most forgotten.
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!!
Deconstruct the State
Allahu Akbar!
This must be the work of the Mad Arab Abdul Alhazred! He did this to praise the Old Ones, no doubt.
"Words of wisdom: drop that zero and get with the hero" -- Vanilla Ice
However keep in mind that muslims conquering generally let the elite of a society (ie. architects) intact.
So most mosques were actually designed by non-muslims. E.g. the blue mosque in Istambul was constructed by a Christian architect, who was trained by another Christian architect, the "best ottoman architect ever", by the name of Sinan.
Did muslims understand the maths necessary to construct large domes in the 11th century ? No.
But Byzantine Christians did. As did Moroccan Jews.
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?
OLD!
and you'll see the pattern. If you squint with your left eye just a little more than with your right eye, you'll see it in 3D.
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
Please quit worshiping the "middle ages middle east" astronomers. I personally re-discovered these so-called tiles and spent my life up to about 30 examining the "mathematics" which gave them credit for the infinite universe or at least pi, oh and everything else too. Bullshit. Learn some physics. Then never comment, until you're 50+.
Nobody knows, but the step after that will be Profit!
Free as in mason.
Just not in the last 1000 years...
Short answer? Religion happened.n _the_Islamic_World#Decay_of_Islamic_science
= Session%202 n ce.php
http://en.wikipedia.org/wiki/History_of_science_i
Long answer (do you have two hours?):
http://beyondbelief2006.org/Watch/watch.php?Video
http://research.amnh.org/~tyson/PerimeterOfIgnora
The misunderstanding of Islam is just plain dangerous. Many old ladies proudly display pictures of their favourite grandchildren wearing Ayatollah kit - the black adab - because Moslem's started the European academic tradition. The quads and cloisters at Oxford and Cambridge recreate the Andalusian universities, where they made sense. Academic citation recreates Muslim chains of transmission - roughly the equivalent of the Christian apostolic succession. Mathematicians chase "x" because Europeans didn't recognise "shai", the Arabic for "that which is sought", but Greek "chi" sounded similar and they wrote that instead. Chi Anglicized is "x" of course. Europeans got the point of algebra and algorithms, but alchemy - the art of transforming the operator and seeing things differently - was just too epistomoligically advanced and got converted by Chinese Whispers into wrong chemistry. With the exception of rare cases like Roger Bacon and Isaac Newton, most Europeans are still unable to get the point of alchemy. Many stars have funny sounding names because they are Arabic. "Doctor Mirabilis" by James Blish is a very good intro to this stuff. All this because while the Hebrews say the material world was created as a wind-up, and the Christians say it is a trick, and the Buddhists say it doesn't exist at all, Islam says it is the work of God, and it is our spiritual duty to study it. These days some people look at the primitive state of many Moslems and imagine that they were all sitting around going "More tea Vicar?" before Mohammad came along, and then they all went mad. Nothing could be further from the truth. Apart from the Arabic language, the Arabs had absolutely nothing before Mohammad. Their entire society and culture comes from the genius of one man, who they believe was divinely inspired. That is in large part why they are so sensitive about his memory - they all know exactly what he did for them. Badmouthing Mohammad is like badmouthing Jesus, Washington, Lincon, Bacon and Thomas Crapper in one go. Interestingly, the so-called militant Islam is always strongest in populations where Western values have been or have become dominant - the Taleban were created and funded by the West, also look at Turkey and Saudi Arabia. Iran's still dealing with the backlash against the Shah. Turkey actually has more crazy Creationists than the USA: http://www.newscientist.com/data/images/archive/25 65/25653701.jpg And anyone who thinks the Taleban's mockery of Islam has a monopoly on lunacy hasn't been following the news: http://www.kxxv.com/Global/story.asp?S=5785699 http://www.bi-valley.com/Articles/GovernmentTerroi smAgainstPhysicians.htm http://www.villagevoice.com/news/0345,owen,48381,1 .html
Of course, the child probably wouldn't care that you call it S_4, so that's irrelevant. Understanding does not mean "sharing our understanding". In the case of Mosques, Islamic artists might well have understood (yes, understood) it as a beautiful spiritual pattern, without ever codifying (or caring to codify) that understanding it in what we would call the "modern" way. A number of "modern" people might even agree with them.
We should give them the honor doing this, why you probably ask?
very simple! because I've tried to remember what they have done recently and the only thing I could come up with was mIRC... so please people... give them the honor of inventing these tiles, they desperately need it!
funny thought, lol.
didn't you know there's people that speak other languages to you? clue: christopher columbus was not a WASP
my password really is 'stinkypants'
I've always liked Penrose tilings - and this reminded me. There's a small patch under my washbasin that would benefit from some decorative tiling. Does anywhere sell sets of Penrose tiles, ready to lay?
Otherwise I can tell I'm going to need to fire some myself, dammit!
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.
Can someone explain how something can be said to be a pattern and yet never repeat? Isn't there some sort of semantic contradiction here?
The newspaper article hardly tells the story. Here is the abstract from Science
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)
"If all the American people want is security, let them live in prisons." Eisenhower
What I'd like to see is an explanation for why the Muslim Arab cultures were at the cutting edge of technology and science until what, the 11th, 12th century? And then for some reason, they have subsequently failed to advance technologically or culturally since then.
-Styopa
Yes, Hindus are a big part of the puzzle here, but please remember there is no such thing as Hindus. Muslim technology, mathematics and concepts was most probably derived more from India and the countries surrounding India, and more specifically from the Vedic Scriptures. India was once the greatest super-power in Asia, but then Buddha came along and taught people to have peace and tranquility. People misunderstood his message, and tore down the armies and development, so India became a back-water country.
Before Hinduism was invented, people in India just lived the Vedic knowledge, in all its diversity. Then came Europeans and started branding this way of living for "Hinduism", and people got an identity. However, there is no general principles concerning "Hinduism", thus it is an artificial concept, and has brought alot of conflict and confusion.
About "Hinduism" and Vedic Knowledge (Sanskrit)
Vedic Knowledge on the other hand is a scientific knowledge, which includes western medicine and is all-encompassing. It deals with medicine, herbs, effects of sounds, way to make instruments, technology, materials and their properties, etc, etc. SO MUCH of it has been lost in time. It is said that to study it all would require life-times. So nobody has really studied all of vedic litterature (which is vast!). In its whole form, the Vedas will encompass the whole universe, but it is unknown wether this form has yet existed on our planet, but certainly you will still find many texts about different dimensions and different universes, as well as subtle energy centers in our own body, which science will have to admit are there pretty soon.
It is in many ways more advanced than Western thought, philosphy and principles. It was Vedic Knowledge from India that spurred Greek philosophy and Chinese medicine (Ayurveda has the original form of acupuncure, acupressue, Feng Shui called Vastu etc). The Vedas are really the root of many of the advanced mathematics, medicine and science today. Its application on the psyche far surpasses todays psychology.
The Vedas even describes how to make space-ships, has manuals for controlling space-ships, how fast they are moving, the age of the current universe-cycle, and much more. Alas, much of the originals are lost and many believe those texts are remainders of more advanced civilizations, so it is hard to study the fragmented remains.
I can only recommend to open up your mind and study what the Vedas can do for you. It is amazing it has been forgotten by people outside India.
http://www.debunkingskeptics.com/
This is embarrasing,unintentionally condescending,patronizing,and hilarious. Sitting under the desert sun,eating dried camel dung Omar discovers Fractals,begins doing integral calculus in the sand. Perhaps the chimpanzee with his bush baby chop stick demonstrates a sophisticated understanding of aerodynmics and ancient Chinese traditions? In other news, prehistoric men taught anatomy and physiology in Cave Art Schools. Credit Reuters for mentioning "Images" were banned by God,so art/design was forced into the abstract.But, along with these idiot academics,they do not even realise they are looking down thier noses,by being amazed that the people of the time did something interesting. It is completely over the top,a pathetic effort to say merely hey people, in spite of all the evidence, Muslims once had a clue.
"....My question is, and I don't mean to troll, what happened?..."
Being a Muslim myself I really wanted to know "What the hell happened to Islam and Muslim?". Mulsim's were philosopher and thinkers, had scientist in all wake of life.
I did some research and discovered what happened?
Center of the Islamic civilization was Baghdad, when Mongols came to Baghdad, they burned all the libraries and every single book. Although they later converted to Islam, they took it back by centuries. Mongols were a race of warriors, modern day Islam is influenced by Mongols. All the thinkers and educators were lost when Mongols invaded various lands.
So over a very short period, Islam turned into a religion of warriors instead of thinkers.
Now, why haven't we recovered after so many years, well we can thank the present day Saudi Arabia for that (IMHO). Their flavor of Islam is that of the "word" written in Quran as opposed to the spirit of that word. Unfortunately, with their wealth and large reserve of oils, they get to influence a lot of people. Modern day al-qaeda is a direct result of "Wahabi Islam", the flavor of Islam followed by Saudi Arabia. I had the fortune of living in Saudi Arabia as my dad worked for consulting company there. The screwed up religious police you to beat kids if they were caught playing during prayer times. Its easy to see the unfortunate events of 9/11 are a direct off shoot of this thinking. Beat the damn kid if he doesn't follow Islam.
Thats what happened to Islam.
Mu 0.02$
it was also discovered that these ancient muslims also developed something thought to be a modern invention: Beheading infidels.
This Christian-superior-over-others argument is laughable. Such narrow-mindedness in the western societies shows exactly that no people in one country is born better human than in another, the opposite of what the GP implies.
People who dislike China tend to mention Tiananmen Square a lot, but they always forget the Tank Man is also a Chinese.
Never mind that the Arabic/Persian world completely ignored the Renaissance, the Enlightenment and the Industrial Revolution. I'm sure and my Marxist teachers in college swear on a stack of Howard Zinn's that it's some white imperialist capitalist Zionist nation's fault. It always is.
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.
My! Medieval Muslims were mind-bendingly magnificent in their mathematical mastery! Makes many a man marvel.
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.
Official Heretic from the "Church of Global Warming". Proven right thanks to whistle blowers. AGW = Flat Earth Theory
The word ``pattern'' has analgous usages. It can mean a repeating order. It can also be used to describe something that is an ordered design. Not all ordered designs repeat.
Very subtle. I think I love you.
What do YOU know about Bali, punk ? I don't like these extremists as much as you do, but Bali bombing stinks of conspiracy like somebody farting just in front of your nose after he gulped 5 cans of baked beans.
In indonesian media, just after the bombing, there were a LOT of news about how strange the police is handling it, and how the Australian and other foreign officials are tampering with the investigation.
We may not be a Dutch colony anymore, but instead the Australian officials can easily kidnap a key witness, and then returned her dead - already cremated too.
Not only that, several police officers reported detection of C4 traces in the scene. They were silenced after.
Then even after the police failed to find conclusive proof, they still jailed Abu Bakar Ba'asyir anyway.
Yes, there are a LOT that YOUR media did NOT report.
And you're wondering why people from so many countries hate America, huh ?
If your western government keep on bullying others like these, it's YOU, the people, that will suffer the retaliation. Bush? Howard? They'll have Secret Service covering and licking their asses 24x7.
this is all well and good, but any of those camel jockeys come near my property i'm still gonna give em both barrels worth
I think the question itself reflects the drive to categorize people as "us" and "others". We are human kind, with all the positives and negatives. We created the Giza pyramids, poetry as well as holocaust and weapons of mass desruction. To categorize people according to their race, culture or religion is a primitive motive. Therefore, we built the mosques with those tiles back in time and we rediscovered them recently. The rest is politics.
That's not very surprising when you think about the roots of modern math: Islamist mathematicians during Europe's middle Ages... Europe wasn't always that mighty thing that it is now you know... In fact Europe got out of that period because of the insights and knowledge they "acquired" from Muslims during the "Crusades"...
Norman Cantor covered this in his book "The Civilization of the Middle Ages," which is a very good general resource (although it does have a few inaccuracies regarding arms and armour).
In Muslim society up to the 12th century, the scholars and scientists tended to be secular, without an attachment to the organized Muslim faith (meaning that they weren't imams). The religious leaders were either fundamentalists and religious legalists or mystics - and they had never tried to reconcile their theology and scientific thought.
Around the end of the 12th century, as Europe was seeing the intellectual impact of the Twelfth Century Renaissance through the transmission of Greek thought via Spain and Sicily (not the Holy Land, though - that was actually considered to be an intellectual backwater even before the First Crusade), the religious section of Muslim society across the board decided that scientific thought was a threat to the traditional faith, and managed to enlist the help of the state. As Cantor put it, "after 1200 scientific thought in the Islamic world was dead."
Frankly, it was a tragedy, and not only did it bring an end to the Muslim golden age, but I don't think Islam ever recovered.
(I don't think the Crusades really had anything to do with this, though - as I said, the Holy Land was considered a backwater, to the point that when Jerusalem fell, some Muslims took up protesting in mosques to make authorities at least notice that it had fallen. I think this religious movement happened on its own, and we do have similar movements in Christianity in the Western World - think of the Intelligent Design controversy, for example.)
Robert B. Marks
Author, Demonsbane in Diablo Archive
When you see how those islamic terrorists started their plans to conquer us mathematically several hundred years ago it is obvious how important it is to bomb the crap out of all muslims !
(Since Americans might read this it is probably best to add that this was a joke.)
Yeah. Here's a small list of wars during islamic kingdoms. You may notice that there is not a single 3-year period without a major war :
s pain4.htm
http://historymedren.about.com/library/text/bltxt
Tolerance was non-existant under muslims of the caliphate, and thousands of christians and jews were brutally slaughtered. Just as the byzantine christians were slaughtered and, more recently the christian armenians fell under the ottoman turks when the ottoman empire had just lost its fight with the west.
The Moors killed quite a few Christians during the period in which they ruled Spain, beginning with their conquest. Christians were essentially second class citizens and conversion from Islam was a capital offense. When a European Christian coalition of the willing reconquered the area, they gave resident Muslims a choice between expulsion or conversion. The difference in persecution was one of extent, not of kind. Instead of constant pressure to convert to gain full rights as a citizen, the choice was more black and white. Convert if you want to be any kind of citizen. While the Caliphate of Cordoba was more tolerant than the King Ferdinand, neither was anywhere near as tolerant as the Romans (both eastern and western) were for most of their imperial eras.
And to be fair, most of the difference stems from political norms not religious norms. The Moors were heavily influenced by the Roman, Byzantine, and Persian style of imperial rule which took more of a conglomerate approach (local chieftains left in place subservient to the overarching monarch) while western Europe was trending towards more of an absolute monarchy. This has less to do with religion than with the struggles of the dark ages in western Europe and the sorts of political regimes that made it possible to rise out of chaos and re-establish the rule of law.
I think calling them Arabs would be more correct. There are Muslims in other places also.
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...
"The last time I suggested white Western civilisation might be less than perfect I got modded to hell"
I didn't mod you to hell, but only for lack of mod points. If I had some now you'd be getting overrated, and here's why.
Regardless of the clear revisionist history that has been spread by "white Western" civilization, there is no reason to engage in re-revisionist history as you have.
To simplify, the fact that so many people kissed up to "white Western" civilization is not a good justification for you and those like you kissing up to other civilizations now. Which, if you didn't realize it, is exactly what you're doing. History is a slippery thing, and many of us are tired of people like you disregarding some parts of history in an effort to raise one society over another. Islam did some good things. Islam did some bad things. Watching you slurp Islam like you did sickens me, if only for the intentional obfuscation of the bad things for no reason other than to discredit "white Western" history.
And before you lamely try to object, you yourself admit what you did (albeit, in an understated fashion) when you say "The last time I suggested white Western civilisation might be less than perfect I got modded to hell"
So you earned your mods. I hope you realize why (and no, it's NOT because you dared to discredit "white Western" civilization, so save that crap).
They cry when their stomach is empty! Does that mean they know 0? Or (shudder...) maybe they know 0- !! ... and for the math fan boys - that they cry when they start feeling hungry is greater knowledge than 0!!
We tend to see history in all the perspective that time in between gives us. We wont know unless we get into their shoes (or sheep skins). But the point is we dont need to - it does not matter. As this comment does not matter - nothing really does.
Sent from my desktop computer
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
I am an atheist, but I live in a predominantly Christian country. If I invent something, it does NOT belong to Christianity. It belongs to me, an individual.
I wrote my first program at the age of six, and I still can't work out how this website works.
What drove you to that conclusion?
Here's a translation of the verse in Question (I also read it in the original Arabic): "It is not fitting for a Believer, man or woman, when a matter has been decided by Allah and His Messenger to have any option about their decision: if any one disobeys Allah and His Messenger, he is indeed on a clearly wrong Path"
It roughly means "believers are not to disobey Allah or his prophet". Why does that makes you think it prohibits independent thinking?
There are may verses of the Quran and many quotes of the prophet that encourage thinking and reasoning (for example Quran verses 4:82, 47:24, 16:11 to 16:13).
In fact, a complete branch of Islamic studies is called Ijtihad, which is all about independent thought.
to quote an online Islamic site: "A scientific approach has been encouraged in the Qur'an with the objective of ascertaining its truthfulness. It provides man with a chance to verify its authenticity." so in Islam, independent thinking is in fact an essential part of the religion.
Were there any bomb instructions or directions to behead infidels who don't convert to Islam, as stated in the Quran?
I'm trying to imagine symmetry that doesn't repeat. .taeper t'nseod taht yrtemmys enigami ot gniyrt m'I
I thought algebra was originally from Mesopotamia and Egypt. I never heard the India theory until reading this story today, you are the second person to mention it. Where did you get this idea from?
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
But the coastal Arabs had such an enviable setup the Romans called it "Happy Arabia."
By the way, I got the translation to the sura's mentioned from here
It's worth noting that a translation isn't equivalent to the original Quran (considered to be Allah's literal words), but rather an interpretation that has been translated, and thus a translation may not be 100% accurate.
This appears to be a case where Prior Art really is Prior Art. How can you copyright something that's already 500+ years old?
"It's the height of ridiculousness to say for those 9 lines you get hundreds of millions."
You take the tiles and you randomly try to tile your space, and I garantee you (actually you can demonstrate it) that you can't cover all the space, you will have blanks. There are specific "combining rules" to be followed to be able to form those nice and ordered patterns. Having a pretty geometry has nothing to do with it.
Read my post carefully, what I said was in fact that human nature was not very different from country to country, religion to religion. I did not attack or praise either religion. So stop using your bias to interpret my intelligence.
Post #18120990 quoted some bad law in contemporary Saudi Arabia in support of the poster's speculation about the converted ancient architect's intention, with which he/she would implie Christians' superiority over Muslims. Reading the post in context, I don't think I've been unfair on this. Note post #18120500 was by the same poster and expressed such a view quite explicitly.
You know what, I think you just said enough about yourself in your post. Haha!
People who dislike China tend to mention Tiananmen Square a lot, but they always forget the Tank Man is also a Chinese.
Arabs invented the current numeric system we all use How hard would it be to believe they also understood mathamatics? If you were told that Aristotle had invented a never repeating pattern and made a building roof out of it no big deal but if Muslims or Arabs, well .... it has to be an accident.
Arabs over the ages have given the world numerous concepts and technologies
Check it out if you care
http://www.adc.org/index.php?id=247
On a side note, the Quran (The Muslims bible)
Has accurately described the early development of the fetus
The Speed of light and many many more
http://www.speed-light.info/
Then again, maybe the Quran was written by aliens.
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.
Yeah, that would be like ending up a patent clerk.
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?".
You can use brute force to form pseudo quasiperiodic tilings. However they are not really quasiperiodic, they are "approximants". So if are patient enough you can get to a point where you have a large pattern, but not necessarily being quasiperiodic. So to a degree of trial and error the Islamic artists must have developed a degree of knowledge which you seem to underestimate. point in case: the Fibonacci sequence and the golden mean. Simple mathematical rules at the base, not impossible to grasp with the arabic knowledge of math of the time. The 2D mapping may just have been their "next step". There have been long speculation of the fact that Islamic art was for long considered just a coincidence. The article here present the prove that this may indeed be not true. Disclaimer: I (not my wife) did my PhD in quasicrystal tiling.
You'll only need one hand.
The Rabelais footnote is a really interesting example of culture.
Could you provide a more complete citation?
early glide path calculations for crashing a jet into a tower...
...through modern western lens.
News at 11.
Since Mexicans are reclaming what used to be ours first.
The native population can send their representatives can negotiate with us one the US is an hispanic country (not that they will be very lucky, they should look at native people in Mexico itself for a clue about how bad they could be treated).
And although you jest, the only fair thing to do would to give to those people at least part of their *good* land back as a very small token of compensation.
But as your attitude points out, the legitimization of forceful removal of entire populations by force is a human trait that we may never manage to extirpate from our humanity.
IANAL but write like a drunk one.
Figure 17 is particularly interesting.
Not everyone wants fame and glory. Some people are content to live their lives out simply and in relative obscurity, doing menial jobs, without the headache of building and maintaining a reputation, only assisting when asked but rarely otherwise.
Bruce Lee once touched hands with a waiter at a restaurant (friendly, I suppose, though I doubt anyone will ever know for sure). Afterwards, he lamented that there are many unknown kung fu masters out there waiting on tables.
I see the same thing here.
"If a nation expects to be ignorant and free in a state of civilization, it expects what never was and never will be."
What say you on this guy's post? How long can you cling to your "they are just here to jobs Americans won't do" mantra?
"They will have to deal with us first.
Since Mexicans are reclaming what used to be ours first.
The native population can send their representatives can negotiate with us one the US is an hispanic country"
Who cares?
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)
I'm sorry to tell you that Christians and Jews were indeed forced to convert to Islam (or die or go into exile). Now, Moorish Spain was not one state, so conditions varied over time, and at times conditions were quite liveable (although Christians and Jews did have to pay special taxes, wear distinctive clothes etc). But tolerant, the Moors were not. I could list events of forced conversions and expulsions by the Moors against Jews and Christians, but you would do better actually reading some history books. Yes, really. (But consider: Where was Maimonides born? When and why did he leave that city? Just to put a human face to historical events.)
The golden age of Al-Andalus is a European 19th century orientalism fantasy. It became popular with West European Jews who wanted to paint a contrast to the intolerant European society of the day. But it is nevertheless a fantasy. The Jewish nostalgia for Al-Andalus is of course the large cultural heritage in terms of philosophy, science and literature that was produced in Spain. This has little to do with any tolerance on the part of the Moors though, and more todo with the fact that 80% of the world Jewry lived in Spain at the time. After the dispersion of the Spanish Jewry it would take three hundred years until a similar center of Jewish learning (and demography) arised.
Grovel before an imaginary dictator in the sky five times a day!
Oppress "your" women, make them dress like Darth Vader, walk 10 paces behind you, and stone them to death for "immorality."
Fast pointlessly for a month a year!
Amputate the limbs of suspected thieves with no anasthetic and unsterilized tools!
Blow up innocent infidels in the name of god!
Come to Mecca and be trampled to death in a stampede!
Abstain from alcohol and pork but cultivate opium poppies to sell to the junkie infidel!
Call Jews pigs and deny the Holocaust!
Call for Israel to be wiped from the face of Allah's earth (why he can't do it himself is another matter)...
...and you too can be very, very good at geometry!!!
It sure looks like it repeats to me. I saw it!
simple, fast homepage with your links: http://www.ngumbi.com/
Apparently the Penrose tile has a trademark which prevented a generic company from printing the pattern on toilet tissue. I suppose that since the photograph of arabic medieval art looks spot on to the penrose trademark, is this an example of "prior art" and thus Penrose tile can't make a valid claim of discovery?
Allah and Muhamed (PBUH) is Wise and Merciful enough to give subtle clues that only he Enlightened can comprehend. Dirty Infidel Pig Scum cannot. Hence 9/11 and Penrose took hundred mores of years to figure tiles. Pray or I blow you infidel pig-brain out. You let woman face in public.
The Catholics like to make statues of various figures, so they split up the paragraphs so that the "graven images" bit doesn't get its own number, and coveting your neighbor's wife and you're neighbors other stuff get numbered separately. So for them it's three commandments about Gods and seven about dealing with other people.
By the way, if you look at how the Bush Administration's doing with the 10 commandments, they're not doing very well. Putting up statues of the 10 commandments at courthouses violates the graven-images bit, using religion as a justification for rabid right-wing politics violates #3, lying about weapons of mass destruction as an excuse for a war gets #6 and #9, having a war because you want to steal peoples' oil pretty much covers #8 and #10, and Republican politicians seem to get caught cheating on their wives about as much as Democrats do, even if they don't get impeached about it. But I guess they sometimes take Sunday off, except down at Guantanamo.
Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
Do you know what drove him? Why did he do this. Why did he drop out of everything. More importantly, why did he find this branch of mathematics to be fascinating? Was there any philosophy behind it?
Please tell us what you know about him personally, it is infuriating that little or nothing is known of such people. It is also a matter that affects me personally, so your reply is much appreciated...
The Harvard Gazette article is original, I think, rather than just being a regurgitation of Reuters and/or New Scientist.
The core claim seems to be that the ancient Moslems discovered a set of patterns that interlocked in a very practical way.
Now let's go to Wikipedia. Scroll down and look at the how-to pictures, and note the references to the Golden Mean. I don't see anything there that couldn't have been discovered by the Greeks or their successors.
Finally, let's go to common sense. I don't know the history of how Penrose discovered these tilings, but two main avenues come to mind:
1. Dumb luck/trial and error/general geometric insight.
2. Symmetry groups (the analysis of rotational symmetries via the abstract algebra concept of "groups", something any computer science graduate is somewhat familiar with).
Well, if it's #1, then of course somebody ancient could have done it too. And if it's #2 -- well, a lot of ruler/compass constructions were done by the ancients, long before Galois proved they were better analyzed via group theory.
So yes -- it's easy to imagine, given the evidence, that somebody figured this out 500-1,000 years ago. True, it's almost impossible to imagine that they understood it in the same way that Penrose did -- but there's a whole lot of physical evidence that, at some level, they understood it just fine.
To err is human. To forgive is good system design.
Did they know at least the basic equations behind it and that said equations never repeated, or at least not within the amount they could calculate? Probably. Did they know WHY the equations behaved that way or even related to real world crystals? Probably not.
You've come to the right place. Over 70 % of the slashdot demographic is composed of unappreciated geniuses. Just post the question and one of us will provide a brilliant answer that will be sadly misunderstood and languish in obscurity. Besides, we like sorting mail.
The Chinese translation for "code" is "ma".
The term "luan ma" is normally used to refer to text displayed in a wrong encoding (so the viewer will see a bunch of weird characters).