Islam

By Mina Teicher 

Leonardo da Vinci’s Vitruvian Man, ca. 1487

It is known that mathematicians see beauty in mathematics. Many mathematicians are motivated to find the most beautiful proof, and often they refer to mathematics as a form of art. They are apt to say “What a beautiful theorem,” “Such an elegant proof.” In this article, I will not elaborate on the beauty of mathematics, but rather the mathematics of beauty, i.e., the mathematics behind beauty, and how mathematical notions can be used to express beauty—the beauty of manmade creations, as well as the beauty of nature.

I will give four examples of beautiful objects and will discuss the mathematics behind them. Can the beautiful object be created as a solution of a mathematical formula or question? Moreover, I shall explore the general question of whether visual experience and beauty can be formulated with mathematical notions.

I will start with a classical example from architecture dating back to the Renaissance, move to mosaic art, then to crystals in nature, then to an example from my line of research on braids, and conclude with the essence of visual experience.

The shape of a perfect room was defined by the architects of the Renaissance to be a rectangular-shaped room that has a certain ratio among its walls—they called it the “golden section.” A rectangular room with the golden-section ratio also has the property that the ratio between the sum of the lengths of its two walls (the longer one and the shorter one) to the length of its longer wall is also the golden section, 1 plus the square root of 5 over 2. Architects today still believe that the most harmonious rooms have a golden-section ratio. This number appears in many mathematical phenomena and constructions (e.g., the limit of the Fibonacci sequence). Leonardo da Vinci observed the golden section in well-proportioned human bodies and faces—
in Western culture and in some other civilizations the golden-section ratio of a well-proportioned human body resides between the upper part (above the navel) and the lower part (below the navel).

By Oleg Grabar 

Oleg Grabar (back row, second from right) with the 1969 staff of his archaeological team in Syria excavating a site known as Qasr al-Hayr

It has been nearly sixty years that I have been engaged in an active scholarly life. My first article came out fifty-eight years ago, and there are still now two or three studies in the process of being printed or ready to appear on the Internet. In between lie some twenty books, several of which were translated into at least seven languages, and over one hundred and twenty more or less significant articles.

This considerable production can easily be divided into three groups, whose chronology raises interesting conclusions about the path of research traveled by a historian of the arts of the Islamic world who came into academic existence in the middle of the twentieth century. Whether this path is unique or typical is for others to decide.

The first group consists of traditional research based on the publication of documents, the excavation of new documents, and the significance of these documents within relatively strict chronological and spatial limits. Scholarship of this type is for the most part restricted in its interest and usefulness to other scholars of the same vintage, and it dominates the first half of my creative years. The number of works of this type that would have been initiated by me has clearly diminished with time, even though their scientific quality (or weakness) tends to remain steady over the years.

By Mohamed Nachi 

Protests in Tunisia culminated when Zine el-Abidine Ben Ali, who had ruled for twenty-three years, fled on January 14, 2011.

The Tunisian revolution of 2011 (al-thawra al-tunisiya) was the result of a series of protests and insurrectional demonstrations, which started in December 2010 and reached culmination on January 14, 2011, with the flight of Zine el-Abidine Ben Ali, the dictator who had held power for twenty-three years. It did not occur in a manner com­parable to other revolutions. The army, for instance, did not intervene, nor were there actions of an organized rebellious faction. The demonstrations were peaceful, although the police used live ammunition, bringing the death toll to more than one hundred.

The demonstrations began in the town of Sidi Bouzid, west of the country’s geographical center. On December 17, 2010, a young street vendor set himself on fire following the confiscation of his wares (fruits and vegetables) by the police. Mohamed Bouazizi was twenty-six, and he succumbed to his burns on January 4. The next day, five thousand people attended his funeral. He became the symbol of the liberation of the Tunisian people from the despotic rule of the Ben Ali regime. The population, and predominantly the youth, began to demonstrate with calm determination, in order to demand the right to work and the right to free expression.

By Glen W. Bowersock 

The negus Kaleb celebrated his campaign in Arabia with an inscription set up in Axum. The text is in classical Ethiopic but written in South Arabian script (right to left). Note the cross at the left end of the first line.

In these turbulent times in the Middle East, I have found myself working on the rise and fall of a late antique Jewish kingdom along the Red Sea in the Arabian peninsula. Friends and colleagues alike have reacted with amazement and disbelief when I have told them about the history I have been looking at. In the southwestern part of Arabia, known in antiquity as Himyar and corresponding today approximately with Yemen, the local population converted to Judaism at some point in the late fourth century, and by about 425 a Jewish kingdom had already taken shape. For just over a century after that, its kings ruled, with one brief interruption, over a religious state that was explicitly dedicated to the observance of Judaism and the persecu­tion of its Christ­ian population. The record sur­vived over many centuries in Arabic historical writings, as well as in Greek and Syriac accounts of martyred Christians, but incredulous scholars had long been inclined to see little more than a local monotheism overlaid with language and features borrowed from Jews who had settled in the area. It is only within recent decades that enough inscribed stones have turned up to prove definitively the veracity of these surprising accounts. We can now say that an entire nation of ethnic Arabs in southwestern Arabia had converted to Judaism and imposed it as the state religion.

This bizarre but militant kingdom in Himyar was eventually overthrown by an invasion of forces from Christian Ethiopia, across the Red Sea. They set sail from East Africa, where they were joined by reinforcements from the Christian emperor in Constantinople. In the territory of Himyar, they engaged and destroyed the armies of the Jewish king and finally brought an end to what was arguably the most improbable, yet portentous, upheaval in the history of pre-Islamic Arabia. Few scholars, apart from specialists in ancient South Arabia or early Christian Ethiopia, have been aware of these events. A vigorous team led by Christian Julien Robin in Paris has pioneered research on the Jewish kingdom in Himyar, and one of the Institute’s former Members, Andrei Korotayev, a Russian scholar who has worked in Yemen and was at the Institute in 2003–04, has also contributed to recovering this lost chapter of late antique Middle Eastern history.

By Stelios Michalopoulos 

Stelios Michalopoulos, the Deutsche Bank Member (2010–11) in the School of Social Science, proposes that geography and trade opportunities forged the Islamic economic doctrine, which in turn influenced the economic performance of the Muslim world in the preindustrial era.

Karl Marx linked the structure of production to the formation of institutions. According to Marx, religion is like any other social institution in that it is dependent upon the economic realities of a given society, i.e., it is an outcome of its productive forces. In contrast, Max Weber highlighted the independent effect of religious affiliation on economic behavior. Weaving these insights together, my research with Alireza Naghavi and Giovanni Prarolo of the University of Bologna proposes that geography and trade opportunities forged the Islamic economic doctrine, which in turn influenced the economic performance of the Muslim world in the preindustrial era. Since Islam emerged in the Arabian peninsula when land dictated productive decisions, the arrangement of Islamic institutions had to be compatible with the conflicting interests of groups residing along regions characterized by a highly unequal distribution of agricultural potential.

In particular, we argue that the unequal distribution of land endowments conferred differential gains from trade across regions. In such an environment, it was mutually beneficial to establish an economic system that dictated both static and dynamic income redistribution. The latter was implemented by enforcing an equitable inheritance system, increasing the costs of physical capital accumulation, and rendering investments in public goods, through religious endowments, increasingly attractive. These Islamic economic principles allowed Muslim lands to flourish in the preindustrial world but limited the potential for growth in the eve of large-scale shipping trade and industrialization. In a stage of development when land attributes determine productive capabilities, regional agricultural suitability plays a fundamental role in shaping the potential of a region to produce a surplus and thus engage in and profit from trade. Based on this idea, we combined detailed data on the distribution of regional land quality and proximity to pre-Islamic trade routes with information on Muslim adherence across local populations.