Hi Bernard

I read this article to the end as requested and I was not impressed by the Spanish author’s experience he had obviously never walked in the courtyards of the Alhambra, nor had he visited Cordoba , Seville, Toledo or Malaga nor had he done the least rudimentary research into his own country’s history, how had he missed the splendours of Moorish Spain?

My view is that he chose to miss the splendours of Moorish Spain because he wanted to make a narrow bigoted point in a piece that Goebbels himself would be proud of.

“And under the pretence of tolerance, and because we wanted to prove to ourselves that we were cured of the disease of racism, we opened our gates to 20 million Muslims, who brought us stupidity and ignorance, religious extremism and lack of tolerance, crime and poverty, due to an unwillingness to work and support their families with pride. They have blown up our trains and turned our beautiful Spanish cities into the third world, drowning in filth and crime.”

These people are poor economic migrants who chose to come to Spain. (Spain has a direct border with Morocco from its territories in North Africa) to better themselves, do all of them not work? Do all of them plan to blow-up the Spanish state? Or do many of them work and lead normal lives, pay their taxes, educate their children and have the same dreams as we do to live in peace and harmony and carve out a peaceful and fulfilling future for their children?

I suspect the latter, they have the same fears and dreams for their children as we do, they gaze at the same stars and wonder the same thoughts, and to yoke them to filth and crime as the author does in his article quoted above is a Goebbelesque construct.

And you are propagating this rubbish, you fought to end bigoted Nazism and all Goebbels stood for, you once quoted a short inscription that was printed in servicemen’s pay books that summed up what you were fighting for in the Second World War. I cannot remember it exactly but it had nothing to do with bigotry and sectarianism but on the contrary extolled freedom, democracy and tolerance.

I would be grateful if you could append that inscription to this note because it will remind people on this auspicious day of what you and countless others fought for.

The Nobel Prizes

This again is a cheap shot by our bigoted author The Nobel Foundation was founded as a private organisation on 29 June 1900, this was at the heyday of imperialism, European countries were subjugating the world in the their dash for land and much of the Arab lands were brought under European control and this state of affairs only came to a close with the French loss of Algeria in the 1960’s . So it’s unlikely that many noble prizes would be issued to Muslim scholars as very few were issued to Chinese scholars during this period and the world’s Chinese population is probably nearing 2 billion, nor did many Indians receive the noble prize and the population of India is 1 billion.

But wait and see, my view is that lots of future Noble prizes will be issued to scientists and scholars in the BRIC countries. . In my opinion the noble prizes follow economic activity and rewards excellence in the humanities and sciences so as the economic dominance of populace countries like Brazil, Russia India and China increases the prizes will follow.

However, it is in the development of mathematics that primarily Arab cultures have aided the development of the world by developing and advancing the only universal human language; the language of mathematics… see my researches below:

So, Bernard I think you will agree that a minutes thought and research on the subject raised by our bigoted Spanish polemist doesn’t bear scrutiny.

In my view we all live and die in the blink of a celestial eye and during our short time on this earth we should try and improve things by seeking the truth in all matters and by fighting ignorance, injustice, intolerance and bigotry wherever it raises its head irrespective of race, culture and religion.

Best Regards

Joe Rice 11/11/11 A date that makes you think of what is important and what we owe

My own 5 minute internet research:

Arab Mathematics

I suppose the major influence of arab culture is in the field of mathematics: The background to the mathematical developments which began in Baghdad around 800 is not well understood. Certainly there was an important influence which came from the Hindu mathematicians whose earlier development of the decimal system and numerals was important. There began a remarkable period of mathematical progress with al-Khwarizmi’s work and the translations of Greek texts.

This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty, whose reign began in 786. He encouraged scholarship and the first translations of Greek texts into Arabic, such as Euclid’s Elements by al-Hajjaj, were made during al-Rashid’s reign. The next Caliph, al-Ma’mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of of research. Al-Kindi (born 801) and the three Banu Musa brothers worked there, as did the famous translator Hunayn ibn Ishaq.

We should emphasise that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realise that the translating was not done for its own sake, but was done as part of the current research effort.

The most important Greek mathematical texts which were translated are listed in [17]:-

Of Euclid’s works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes’ works only two – Sphere and Cylinder and Measurement of the Circle – are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apollonius’s works were translated, and of Diophantus and Menelaus one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of Ptolemy’s Almagest furnished important astronomical material.

The more minor Greek mathematical texts which were translated are also given in [17]:-

… Diocles’ treatise on mirrors, Theodosius’s Spherics, Pappus’s work on mechanics, Ptolemy’s Planisphaerium, and Hypsicles’ treatises on regular polyhedra (the so-called Books XIV and XV of Euclid’s Elements) …

Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as “algebraic objects”. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. As Rashed writes in [11] (see also [10]):-

Al-Khwarizmi’s successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.

Let us follow the development of algebra for a moment and look at al-Khwarizmi’s successors. About forty years after al-Khwarizmi is the work of al-Mahani (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu Kamil (born 850) forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as xn.xm = xm+n. Let us remark that symbols did not appear in Arabic mathematics until much later. Ibn al-Banna and al-Qalasadi used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least a century before this.

Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x2, x3, … and 1/x, 1/x2, 1/x3, … and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years. Al-Samawal, nearly 200 years later, was an important member of al-Karaji’s school. Al-Samawal (born 1130) was the first to give the new topic of algebra a precise description when he wrote that it was concerned:-

… with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.

Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work [18]:-

If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared.

Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karaji’s school of algebra but rather follows Khayyam’s application of algebra to geometry. He wrote a treatise on cubic equations, which [11]:-

… represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry.

Let us give other examples of the development of Arabic mathematics. Returning to the House of Wisdom in Baghdad in the 9th century, one mathematician who was educated there by the Banu Musa brothers was Thabit ibn Qurra (born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory. He discovered a beautiful theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other. Al-Baghdadi (born 980) looked at a slight variant of Thabit ibn Qurra’s theorem, while al-Haytham (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form 2k-1(2k – 1) where 2k – 1 is prime.

Al-Haytham, is also the first person that we know to state Wilson’s theorem, namely that if p is prime then 1+(p-1)! is divisible by p. It is unclear whether he knew how to prove this result. It is called Wilson’s theorem because of a comment made by Waring in 1770 that John Wilson had noticed the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Lagrange gave the first proof in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this

achievement of Arabic mathematics.

Continuing the story of amicable numbers, from which we have taken a diversion, it is worth noting that they play a large role in Arabic mathematics. Al-Farisi (born 1260) gave a new proof of Thabit ibn Qurra’s theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 17296, 18416 which have been attributed to Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 still many years before Euler’s contribution.

Let us turn to the different systems of counting which were in use around the 10th century in Arabic countries. There were three different types of arithmetic used around this period and, by the end of the 10th century, authors such as al-Baghdadi were writing texts comparing the three systems.

1. Finger-reckoning arithmetic.

This system derived from counting on the fingers with the numerals written entirely in words; this finger-reckoning arithmetic was the system used by the business community. Mathematicians such as Abu’l-Wafa (born 940) wrote several treatises using this system. Abu’l-Wafa himself was an expert in the use of Indian numerals but these:-

… did not find application in business circles and among the population of the Eastern Caliphate for a long time.

Hence he wrote his text using finger-reckoning arithmetic since this was the system used by the business community.

2. Sexagesimal system.

The second of the three systems was the sexagesimal system, with numerals denoted by letters of the Arabic alphabet. It came originally from the Babylonians and was most frequently used by the Arabic mathematicians in astronomical work.

3. Indian numeral system.

The third system was the arithmetic of the Indian numerals and fractions with the decimal place-value system. The numerals used were taken over from India, but there was not a standard set of symbols. Different parts of the Arabic world used slightly different forms of the numerals. At first the Indian methods were used by the Arabs with a dust board. A dust board was needed because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this to be done in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, al-Uqlidisi (born 920) showed how to modify the methods for pen and paper use. Al-Baghdadi also contributed to improvements in the decimal system.

It was this third system of calculating which allowed most of the advances in numerical methods by the Arabs. It allowed the extraction of roots by mathematicians such as Abu’l-Wafa and Omar Khayyam (born 1048). The discovery of the binomial theorem for integer exponents by al-Karaji (born 953) was a major factor in the development of numerical analysis based on the decimal system. Al-Kashi (born 1380) contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as π. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner.

Although the Arabic mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy. Ibrahim ibn Sinan (born 908), who introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. These mathematicians, and in particular al-Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. Omar Khayyam combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means.

Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. For example Ibrahim ibn Sinan and his grandfather Thabit ibn Qurra both studied curves required in the construction of sundials. Abu’l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan. Al-Biruni (born 973) used the sin formula in both astronomy and in the calculation of longitudes and latitudes of many cities. Again both astronomy and geography motivated al-Biruni’s extensive studies of projecting a hemisphere onto the plane.

Thabit ibn Qurra undertook both theoretical and observational work in astronomy. Al-Battani (born 850) made accurate observations which allowed him to improve on Ptolemy’s data for the sun and the moon. Nasir al-Din al-Tusi (born 1201), like many other Arabic mathematicians, based his theoretical astronomy on Ptolemy’s work but al-Tusi made the most significant development of Ptolemy’s model of the planetary system up to the development of the heliocentric model in the time of Copernicus.

Many of the Arabic mathematicians produced tables of trigonometric functions as part of their studies of astronomy. These include Ulugh Beg (born 1393) and al-Kashi. The construction of astronomical instruments such as the astrolabe was also a speciality of the Arabs. Al-Mahani used an astrolabe while Ahmed (born 835), al-Khazin (born 900), Ibrahim ibn Sinan, al-Quhi, Abu Nasr Mansur (born 965), al-Biruni, and others, all wrote important treatises on the astrolabe. Sharaf al-Din al-Tusi (born 1201) invented the linear astrolabe. The importance of the Arabic mathematicians in the development of the astrolabe is described in [17]:-

The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medievals. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and al-Biruni invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Shatir (1305-75), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways.

Moorish Spain

The Alhambra’s Moorish palaces were built for the last Muslim Emirs in Spain and its court, of the Nasrid dynasty. After the Reconquista (reconquest) by the Reyes Católicos (“Catholic Monarchs”) in 1492, some portions were used by the Christian rulers. The Palace of Charles V, built by Charles V, Holy Roman Emperor in 1527, was inserted in the Alhambra within the Nasrid fortifications. After being allowed to fall into disrepair for centuries, the Alhambra was “discovered” in the 19th century by European scholars and travelers, with restorations commencing. It is now one of Spain’s major tourist attractions, exhibiting the country’s most significant and well known Islamic architecture, together with 16th-century and later Christian building and garden interventions. The Alhambra is a UNESCO World Heritage Site, and the inspiration for many songs and stories.

Moorish Spain’s Golden Age

The Different Periods of Moorish Rule 711 to 1492 AD

The Dependent Emirate (711 to 756 AD)

The Independent Emirate (756 to 929 AD)

The Caliphate (929 to 1031 AD)

The Almoravid Era (1031 to 1130 AD)

Decline (1130 to 1492 AD)

________________________________________

Simultaneously, (because of continuous extension of the Islamic Empire) Europe became isolated, evolving into The Middle Ages. European Medieval Times perspective was steeped with illogical reasoning and irrational beliefs. Barbarity and illiteracy were commonplace. Squalor was ubiquitous.

________________________________________

Emir Abd-al-Rahman 1

The sole Umayyad heir was well accepted by the Iberian Muslims. He was half-Syrian and half-Berber (a direct bloodline from his mother).

The Iberians called the Moors = Moors because they were largely Berbers and were black. Berbers were a major part of the invasion-force.

The ruling Arabs sustained a sense of racial superiority and purity of faith over the Berbers. Many Berbers were either of a pagan background or had been converted to Byzantine-Christianity.

First Islamic Monument on Iberian Soil

It was Emir Abd-al-Rahman 1 who introduced islamic art and architecture during the construction of the first Islamic monument built in the al-Andalus. The famed Cordoba Mosque (Aljama Mezquita) incorporated much of Umayyan Mezquita History heritage, combining local techniques of Hispano Art and Architecture, all of which evolved in creating, the unique features of the Cordovan Mosque.

Work commenced on Cordoba’s Mosque in 785 AD. It was finalized – over two hundred years later.

A Major Element to Muslim Successes

The Art of Papermaking.

The Chinese had developed a cotton-paper. The paper-making secrets were extracted from Chinese prisoners – after the battle of Tallas 751 AD.

Written documents were first preserved on Clay Tablets and Papyrus. As proven with the Phoenicians: Papyrus documents perished. Parchment was extremely expensive.

• Paper documents preserved excellently and could be copied extensively

• The secret of paper-manufacture catapulted Islam’s first directive: education

• Translation, copying and reproducing of the collective wisdom of the pre-Islamic societies began – both in Baghadad and in Cordova

• Baghdad created the “House of Wisdom”: It was a literary society and was an outstanding library

• An inherent love of language and elegant Arabic poetry became a focal point to the educated al-Andaluz

• Calligraphy was highly regarded

The Art of Paper-Making

Polishing Paper with Hard Stone

The Excellence of Caligraphy

• Education became Universal. Literacy existed in every Social Class – meanwhile (in comparison), 99% of Christian Europe was illiterate

• Vast Libraries

• Widespread amount of Schools

• Universities: Cordoba, Sevilla, Valencia, Málaga, Granada

Cordoba was the Connecting Point

• The Arabs Translated and studied the Ancient Masterpiece Works of: Aristotle, Archimedes, Apollonius, Euclid, Hipoocrates and Galen

• The philosophy of these works became the stimulating-point for the revival of European Civilizations

• Thousands of bookstores opened in Moorish Spain

Islamic Architectural Influences

Spectacular Islamic Architecture expressed revered worship of Islam, to the Caliph and to God. Moorish Spain’s architecture symbolized the Caliph’s or Emir’s power.

• Umayyan-styled Caliphal Architecture

• Evolved leading to the wonders of the Rich Islamic Architecture – of the Alhambra Granada Spain

• It was the (refugee) Artisans of Granada who planned, constructed and embellished the magnificent Alhambra Granada

Spain Palaces.

• What was so special about the Architecture? Alhambra Granada Spain 1

• Significances of Sacred Geometric patterns in islamic art and architecture 1

• Alhambra Granada Generalife: The Generalife’s summer palace

• Alhambra Granada Spain Water Technology

• Alhambra Granada Palaces Gems: The Magical Artistic Corners of the Alhambra and its Political Intrigues…

• The Downfall of the Alhambra Spain

• Boabdil and the surrender of the Alhambra Spain 1492 to the Christians

The Moors Reintroduced:

• Art

• Astronomy

• Mathematics

• Philosophy

• Physics

• Science

• Chemistry

Luna Mora

________________________________________

The Luna Mora Festival evokes how street lighting was done during the Moorish Spain epoch. One of the evening’s highlights is the themed backkground of arabigo-andalusi, flamenco and sefardi, music and dance.

Over twenty-thousand candles illuminate Guaro during Luna Mora.

________________________________________

Cordova’s Lifestyle

• Cordoba had illuminated-paved streets with pedestrian sidewalks – several hundred years before London or Paris could boast of such amenities

• Lusterware: losa dorada, expensive gold-glazed ceramics

Moorish Agriculture

• Muslims perfected ancient and new techniques of raising river-water for irrigating fields

• The use of the Noria/water-wheel was introduced from the East

• In 961 AD, the Cordova Calender was published. Agricultural Exact Observations: soil-analysis, when to plough, when to irrigate and the correct times for planting or harvesting

• The importance of Moorish flour mills and their passage in history: Andalucia Travel Costa del Sol

• A meticulous approach to crop rotations and varied types of manure according to each soil-type

• Famous Moorish Water Gardens were created

• Harvest preservation methods

• “The Green Revolution” was the cornerstone of the wealth and success of the Cordovan Caliphate

• See: the History of Spanish Food

• New Plants – such as cotton – were introduced to the Iberian Peninsula which led to…

Specialities of al-Andalus handicraftsman

• The al-Andalus became a major manufacturer of Silk, especially in the Alpujaras

• Silk and cotton weaving

• The softest Merino Wool and its products

• Tanneries, especially in Cordoba Leather

• Taracea Craftsmanship (beautiful inlaid wood decoration – unique to Granada)

Tracing the Doctrine of Revered Moorish Scholars

o Averroes

o Avempace

o Avicenna

o Abulcasis

Advances in Moorish Medicine

Moorish Medicine Education, New surgical techniques, Moorish Medicine Health Care new medical instruments, improvement in paediatrics, obstetrics, ophthalmology, anatomy

o Hospitals with running water

o The use of Latrines

o City Sewerage systems

o A Widespread Construction and Use of Public Baths

o The Distillation and popular use of Floral Essences

Metalwork

Excellence in intricate Gold and Silver Handicraftsmanship

Spain possessed a huge mineral wealth: copper, gold, tin, silver, lead, iron, mercury and alum were extensively mined

Spanish Perfumery

originates from Moorish Spain

Toledo sword blades were considered the best in Europe

Murcian Brass and Iron factories produced first-class work

Gunpowder was introduced to Europe by the Arabs

Cordoba under Abd-ar-Rahman 111 became the prime metropolitan-based economy of Europe. It was renowned for prosperous buisnesses such as silver-smithing. Local currency was Cordobes Gold.

During this period the largest European urban concentration, was in the al-Andalus capital Cordova, Moorish Spain.

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]]>Included in the letter I received was a statement “Muslims must ask ‘what can they do for humankind’ before they demand that humankind respects them!!”. It was probably that which set me off and made me take this really really REALLY stupid letter to heart.

Following is a link to a website with a commemoration to a dear friend and colleague. A Somali [Muslim] who could have left Mogadishu anytime he wanted, but chose to stay and work towards peace. Assassinated in 2007 for his activism.

http://www.hiiraan.com/op2/2007/july/commemoration_of_a_somali_peace_activist_abdulkadir_yahya_ali.aspx

Many thanks for your comments on that letter, Mr. Ebersole.

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