Medieval Muslims made stunning math breakthrough

 

By Will Dunham

Fri Feb 23, 6:32 AM ET

WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.

 By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be “quasicrystalline” designs, Harvard University’s Peter Lu and Princeton University’s Paul Steinhardt wrote in the journal Science.

Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. 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.

“Oh, it’s absolutely stunning,” Lu said in an interview. “They made tilings that reflect mathematics that were so sophisticated that we didn’t figure it out until the last 20 or 30 years.”

Lu and Steinhardt in particular cite designs on the Darb-i Imam shrine in Isfan Iran, built in 1453.

Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns.

The walls of many medieval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs.

“You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex” over time, Lu added.

ISLAMIC ACHIEVEMENTS

While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas.

Lu said the new revelations suggest Islamic culture was even more advanced than previously thought.

While traveling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasicrystalline Islamic tilings.

The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide.

Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasicrystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran.

Joshua Socolar, a Duke university physicist, said it is unclear whether the medieval Islamic artisans fully understood the mathematical properties of the patterns they were making.

“It leads you to wonder whether they kind of got lucky,” Socolar said in an interview. “But the fact remains that the patterns are tantalizingly close to having the structure that Penrose discovered in the mid-70s.”

“And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show,” Socolar said.

New Favorite Blogger

MYSPEAK from Denmark offers excellent commentary regarding current events, and also writes poems.

His commentary of Tony Blair’s announcement to start withdrawing troops from Iraq is great! I couldn’t help but paste some of his words here.

Rats Leaving Sinking Iraq

[...] 

As for the neo-Cons’ fantasies about the American troops eventually returning home victorious and with honor, having liberated Iraq, defended the world, and made America a safer place - words fail me, they really do…. As they did recently when GWB said on a TV show that “the Iraqis owe the Americans a huge debt of gratitude”. Almost like saying to some hapless victim whose good legs you just deliberately amputated: We did this out of compassion and because we are super compassionate we will give you a free pair of artificial legs.

But the nightmare-scenario often referred to by many American politicians, that “If we do not finish the job [whatever that may mean] the terrorists [whatever that may mean] will follow us home”, is highly likely to materialise - and who could blame them, after the unspeakable death and destruction you brought to Iraq?? Should they follow you home, it would be a perfectly normal, healthy human reaction, and I for one hope that they will and they do, and wish them every possible success in their endeavours which, as opposed to what you did to Iraq (and to Afghanistan, Lebanon and Palestine, and to Islam in general), would be both wholly justified and richly deserved.

Somali Resistance Picks Up

 

At least 18 people died and 50 injured as hundreds more fled the city on Monday as the city of Mogadishu sees its bloodiest day so far.

Heavy fighting erupted after dark, as gunmen pounded the sea port, the presidential palace and two army bases with mortars and hand grenades causing unknown casualties to the Ethiopian and “government” forces stationed there, this assault led to a vicious retaliation by the enemy forces as they used heavy artillery rounds (picture) to pound many parts of the city for hours causing mass panic and casualties.

After day break medics started to collect the dead and injured as the fighting took a break, most of the hospitals were filled by many seriously wounded people, others started to gather their belongings and started to flee the city trying to find refuge in their clan based regions outside the capital, almost 1000 people have fled the city due to the last two weeks of fighting. Many residents blame the Ethiopians for being cowardly and not fighting the resistance in hand to hand combat. KC has also been informed that some warlords and resistance groups have combined forces to route the “government” since most of the warlords have been denied positions in the new government, neither the prime minister nor the president have not set foot in the capital for the last 2 weeks fearing the bombardment and the plotting by the resistance, choosing to stay in Baidoa instead.

In Jowhar the city has fallen to a ruins, many people in authority fled the city and left the former warlord’s gunmen now part of the army to loot houses and shops since most of them did not get paid by the “government”.

Many people in the country are predicting a quick Collapse of the government and puppet authority once the Ethiopians leave the cities, in Baidoa around 150 warlord’s gunmen entered the city after increase of insecurity in the area, Maxamed Ibraahim “Xaabsade” a warlord belonging to the Baidoa region entered parts of the city after many residents lost hope in the security provided by whats left of the “government” forces in the town, “Xaabsade” is a known ally of the former parliamentary speaker Shariif Hassan and a pro Islamic warlord government minister.

Many clans in the south of the country are angry at the warlord president Abdullahi Yusuf who comes from the Puntland region in the north which is Relatively a peace full and commercially developing region accusing him of trying the keep the south poor and underdeveloped with continuing clan violence, the former puppet army commander general Naji who led the war on the Islamic courts now appointed ambassador to Oman publicly announced in an interview that the Hawiye clan in the south would never accept a president from the Darood clan in the north, that’s why there will be resistance until the “president” goes.

Source: KC

If Americans Knew

Five minute video. Check it out.

Video of U.S. Chinook / Sea Knight Shot Down in Iraq

 

THE VIDEO IS AT THE BOTTOM OF THE POST

The aircraft was the 7th shot down in 15 days killing all seven onboard.
The following report is from The Islamic State in Iraq and the video that follows was produced by them:

The Islamic State of Iraq / Downing a crusaders aircraft in al-Karma side

In the name of Allah the most Gracious the most Merciful

All Praise and thanks are Allah’s, the Lord of all that exists. And peace be upon our prophet Muhammad, his family and companions in entirety.

On Wednesday morning, February 7, 2007, the Mujahedeen “by the grace of Allah” downed a crusaders “Chinook” aircraft in al-Karma side included in al-Anbar province which caused its destruction completely and killing all its crew, the operation was filmed and will be presented soon, all praise and gratitude be to Allah .

Those operations are included in “al-Karama (dignity) plan”, declared by al-Sheikh Abu Omar al-Baghdadi , leader of the Islamic State of Iraq “may Allah protect him” .

Allah is great.

“Honor, power and glory belong to Allah, to his messenger, and to the believers, but the hypocrites know not.”

The Islamic State of Iraq/Go ahead in your plan it will only be defeat and disappointment for you

In the name of Allah the most Gracious the most Merciful

All Praise and thanks are Allah’s, the Lord of all that exists. And peace be upon our prophet Muhammad, his family and companions in entirety.

As for what follows;

It had been days and days and the whole world waiting for the birth of the new security plan for the American administration in Iraq however no work on it , it is apparent that the enemy feels shy and afraid from putting forth its new plan after the repeated failure of its predecessors , otherwise where all their promises to eliminate the Mujahedeen and to protect their followers from Shiites and apostates!! Let them go on their plan , we have prepared for them what will be sufficient to bury it alive “by Allah’s will”.

We don’t miss to inform about what the apostate “Tarek Al Hashimi” said about the necessity of hurrying up in implementing the new plan , and that the cause of failure of the previous plans was the low numbers of the crusader soldiers , we say to him and who still stand up for this so-named “Islamic party Iraquian” we say to him (Here is the secretary-general of this party calling for help from his crusader masters for eliminating Mujahedeen who fight for sake of Allah , is there any more obvious picture of supporting and sponsorship that this picture !!! O Allah we are innocent from this party and we bear witness that Tareq Al Hashimi has waged war against your soldiers ,O Allah restrain him from us by the manner you see ).

We say to our sunni people in Iraq and specially in Baghdad “Know that the first aim of this plan is to annihilate you , for this , show Allah the good from your selves , persevere in patience and constancy , mingle with your Mujahedeen , we swear by Allah that no body cares for you after Allah except them “.

We say to the Mujahedeen of the Islamic State of Iraq what our commander “Abu Omar Al Baghdadi “ said in his last talk ,(Keep in mind the mutilated bodies of children ,the cries of widows and the moans of the elderly , explode the anger volcano , burn the ground underneath the Jews feet and their allies , annihilate their army , destroy their machines , down their aircrafts and don’t leave them one way out , ambush them in houses, in valleys and turns , be Covered by the night and turn their light into fire , Know that your grandfather “Ubada ibnul samet” said to “Jabala Ebnul Ayham” ( O Jabala , have not you know how Allah defeated you and granted us victory and your idol escaped!! And the rest of your troops is easy for us to handle with , and we are not afraid of those who attack us from your forces , for we tasted bloods and we find out the Roman blood as the most sweet , don’t miss it because the enemy will withdraw very soon then you will regret .

O Mujahedeen of the Islamic State , Grill their flesh with explosions , tear into pieces their bodies with bombs , extract their hearts of panic and fright and Know that the best means defeat is to attack , and do never put down your weapon until the war lays down its burdens.

Allah the Al mighty says “And slacken not in following up the enemy: If you are suffering hardships, they are suffering similar hardships; but you have hope from Allah, while they have not. And Allah is full of knowledge and wisdom” Al nisaa 104, and Know that victory comes with patience , “So lose not heart, nor fall into despair: For you must gain mastery if you are true in Faith.” Al Emran 139, and Know that Allah drew you the morals of war when He The Al mighty said : “O you who believe! When you meet a force, be firm, and call Allah in remembrance much (and often); that you may prosper: And obey Allah and His Messenger. and fall into no disputes, lest ye lose heart and your power depart; and be patient and persevering: For Allah is with those who patiently persevere:” Al anfal 46.

Let it be your banner and your cheer in the battle “Allahu Akbar (Allah is the greatest)” , “Deenul-lahi ghaleb( Allah’s religion is the victor )” raise your voices with it and keep alive its meanings in your consciousness and hearts , our war is not nationalist ,but our war is for the Word of Allah is exalted to be the heights)

And Allah has full power and control over His Affairs, but most of human know not.

O Allah , defeat the spiteful Rawafeds (Shiites) and the Zionist Crusaders and their allies..
O Allah , make them with their equipments a booty for the Muslims..
O Allah destroy them ..
O Allah , the sky is yours, the earth is yours, the sea is yours, O Allah , drop all their forces in sky, destroy all their forces in earth and sink all their forces in sea..
O Allah, retaliate upon them, afflict them like you did to Pharaoh and his nation , O Allah afflict their country with flood , make them in need of money and food and persons ..
O Allah defeat them , destroy them O the All-Strong, the All-Mighty .

Allah is great.

“Honor, power and glory belong to Allah, to his messenger, and to the believers, but the hypocrites know not.”

The Pendleton 8 Murderers

Where are all of those sick supporters of these murderers? The ones camped outside of the gates of Camp Pendleton demanding that these criminals be released. The ones that said they are only innocent good ole boys. The ones that sent thousands of dollars for their defense. Where is the disgraced syndicated radio host Michael Savage that swore these guys are innocent and the Iraqi victims are “lying terrorists”? Where are all of these people now that the murderers have confessed their crimes?

Take a look at these people:

Marine ‘Congratulated’ men for murder of Iraqi civilian: Witness

CAMP PENDLETON - A US Marine squad leader congratulated soldiers “for getting away with murder” after an Iraqi civilian was bound and shot dead at point-blank range, a military court has heard.

Sergeant Lawrence Hutchins, who will stand trial for murder next month, made the comments after the abduction and killing of 52-year-old Hashim Ibrahim Award in Hamdania outside Baghdad last April, a witness testified.

Navy medic Melson Bacos, who was jailed for one year last September for his role in Awad’s killing, recounted Hutchins’ comments while giving evidence at a sentencing hearing for another Marine, Trent Thomas.

Bacos said that after Awad had been shot in a roadside hole, squad members had to work quickly to remove “zip ties” used to bind his hands and feet.

The squad wanted to make it look like they had just come upon the victim, when in fact they had dragged him from his home, Bacos said.

“When all was cleaned up, Hutchins said, ‘Congratulations. We just got away with murder, gents,’” Bacos told the hearing at the Marines’ Camp Pendleton base outside of San Diego.

Prosecutors say Hutchins, who is to stand trial on March 19, was the ringleader of the plot to kill Awad.

A hearing is ongoing to determine a sentence for Thomas, who pleaded guilty to unpremeditated murder last month in connection with the case. Thomas had earlier denied murder charges.

Thomas’s sentencing hearing will continue on Thursday.

Five of the eight servicemen implicated in the killing have now admitted to charges connected to Awad’s death, one of a string of incidents that has tarnished the reputation of US forces in Iraq.

Other witnesses involved in the case have testified that Awad was killed after the squad of soldiers failed to locate a suspected insurgent operating in the area west of Baghdad.

Awad was allegedly taken from his home and frog-marched to a hole, which Marines had dug to look like a roadside bomb crater.

He was then bound before being shot three times in the head. An AK-47 rifle was then left beside his body to create the impression he had been an insurgent planting a bomb.

Video of Apache The Fourth U.S. Helicopter to be Shot Down in Two Weeks

February 3, 2007

by Bassem Mroue

Associated Press

BAGHDAD, Iraq — A U.S. Army helicopter crashed Friday in a hail of gunfire north of Baghdad, police and witnesses said — the fourth lost in Iraq in the last two weeks. The U.S. command said two crew members were killed, and the top U.S. general conceded that insurgent ground fire has become more effective.

A brief U.S. military statement gave no reason for the crash and did not identify the type of aircraft. A Pentagon official said it was an Apache attack helicopter, which carries two crew members.

Iraqi police and witnesses said the latest crash occurred about 7:30 a.m. as two Apaches were flying along a well-established air route near Taji, a major U.S. base about 12 miles north of Baghdad. One helicopter was struck by heavy machine gunfire but continued flying, the witnesses said. The other helicopter banked sharply and flew back toward the source of fire, apparently to attack the target.

But that helicopter was also struck by ground fire, exploded in a ball of fire and crashed, the witnesses said. The other helicopter flew away, they said. The witnesses spoke on condition of anonymity, fearing for their own safety.

The Islamic State of Iraq claimed on Friday that it shot down the Apache near Taji in a statement posted on a Web site. “We tell the enemies of God that the airspace of the Islamic State in Iraq is prohibited to your aircraft just like its lands are,” the statement said. “God has granted new ways for the soldiers of the State of Iraq to confront your aircraft.”

The video of the 5th helicopter (chinook, sea stallion) to be shot down in 15 days is here.

Below is the 4th: