For lust of knowing what should not be known/ We take the Golden Road to Samarkand. [[1]]

The Silk Road has always been known for providing pathways that allow the Far East to exchange goods and ideas with the European West. History often remembers that the Silk Road helped Europe expand and flourish. However, the cities that lived in close proximity to the Silk Road routes also benefited economically and culturally. Samarkand, specifically, became a multi-ethnic city of trade under the leadership of Tamerlane in the 14^th century. According to historian Christopher I. Beckwith, Tamerlane formed Samarkand into a “model city” [[2]]. But was it Tamerlane’s skill as a political leader, or the influence of the trade routes that brought glory to the grand city? While Tamerlane’s empire was vast and incredible, it is impossible to deny that the Silk Road played a larger role in the flourishing of Samarkand due to the market established in the city, as well as its toleration of those with different cultural and religious identities.

Timur the Lame, or Tamerlane, was a successful military and political ruler in the city of Samarkand. As a child, Timur found himself living on the Central Asian steppes where he and his tribe would migrate at the mercy of the seasonal weather [[3]]. However, as he grew older, Timur soon found himself gaining a foothold and conquering tribes, making alliances with other warlords, and looting as a missionary throughout Central Asia [[4]]. One of Timur’s most influential alliances was made with the Balkh warlord Amir Husayn. Throughout the course of the alliance between Timur and Husayn, tensions were high and it eventually disintegrated [[5]]. Despite Timur facing betrayal during his previous experience with Husayn, the two again joined forces to eventually overthrow the Sarbadar government in Samarkand in 1366 [[6]]. While ruling alongside Husayn in Samarkand, Timur gained many followers. Timur was regarded as a brave, intelligent, and generous ruler among his people though it was well known that he was also ruthless to his enemies [[7]]. With his skill to gain followers and prestige all across the Central Asian steppes and cities, Timur was finally able to make his way into the Mongol courts. After Genghis Khan died, Timur was able to cement his control as the sole ruler of the Chagatai territory on April 9, 1370 [[8]].

The ancient city of Samarkand is well known to be a melting pot of people with different races and religions. The Sogdian people are considered to be one of the first to populate the area. In fact, the first traces of the Sogdian people date back to 700 BC. Valerie Hansen of Yale University writes that it is likely that the early Sogdian settlers lived peacefully within the city as merchants, farmers, and servants. She also states that the Sogdians were also able to continue using their native language although it was not the mainstream language of the city [[9]]. However, the Sogdians were not the only people to occupy the city. When Ruiz Gonzales de Clavijo visited the city while on embassy in 1412, he noted that there were people from across the world living in the city. Clavijo wrote:

…The population now of all nationalities gathered together in Samarqand… [Amounting] to about 150,000 souls. Of the nations brought here together there were to be seen Turks, Arabs and Moors of diverse sects, with Christians who were Greeks and Armenians, Catholics, Jacobites, and Nestorians…[[10]]

These different religious and ethnic groups likely lived in peace and toleration of one another and focused on improving commerce within the city.

While Tamerlane was a successful ruler and won the respect and loyalty of his citizens, that alone did not cause the city of Samarkand to become great. Instead, the Silk Road routes are most likely the reason for the city’s strong economy. The Silk Road was a series of trade routes that stretched from China, located in the Far East, to the European West. These dangerous trade routes allowed merchants to not only sell silk, but also chemicals, spices, minerals, leather goods, and paper [[11]]. While China traded with many different countries across the known world, the country mainly focused its trade with Samarkand. The Chinese likely had a special trading partnership established with the Sogdians, who were seen as the “main contributors” to the Silk Roads [[12]]. Hansen refers to the painting that was seen in the Panjikent House. In this painting, a woman is shown who appears to be a deity. The style of art was likely influenced by the Chinese because of their relationship with the city [[13]].

The city of Samarkand also had an elaborate trading marketplace set up with the city itself. Ruiz Gonzalez de Clavijo also mentioned that the city of Samarkand was stocked full of goods and other merchandise from around the world. Some items were even exclusively sold within the city. Spices from India, for example, were “never to be found in the markets of Alexandria.” According to Clavijo, when Timur succeeded in conquering new lands, he would often bring the best craftsmen of the conquered territory to Samarkand. For example, Timur brought weavers from Damascus, gun smiths from Turkey, as well as glassmakers and armorers that were found in other locations [[14]]. Additionally, the fertile soil in the areas surrounding the city helped farmers to harvest wheat, wine, fruit, and cotton. The price of goods was then controlled to prevent inflation from rising too high. Clavijo mentions that the price of a pair of sheep would normally cost a “ducat,” which is equivalent to about six shillings. A person in Samarkand could also pay a “half a real,” equivalent to about three pence, for a bushel and a half of barley [[15]].

Aside from the strong economy and ethnic tolerance in the city, Samarkand is also known for its beauty. On his trip, Clavijo noted that Samarkand was larger than Seville and also noticed surrounding suburbs, orchards, and vineyards outside of the city. It is noted that the “most noble and beautiful houses” are also located among the vineyards, gardens, and farmlands [[16]]. Inside the city, Samarkand also possessed beautiful buildings. Historian Xinru Liu of the College of New Jersey writes that the city’s close proximity to the Silk Roads and the cultural influences from within caused Samarkand to have several different cultural buildings erected from within. For example, Liu mentions that Islamic scholars traveled along the Silk Roads and, eventually, Islamic architectural building and centers sprang up throughout the city [[17]].

Initially, the city of Samarkand was established as a military garrison by the Arabs after defeating the Turks in 712 [[18]]. Overtime, the city became prosperous and a large trading hub where people from across the world could trade for exclusive items. How did the city of Samarkand become such an influential power at this time? Some, including Christopher I. Beckwith, and Clavijo, argue that the rule of Tamerlane is what expanded the city’s influence, wealth, and power. However, it is more plausible that the presence of the Silk Roads and the city’s multi-ethnic identity is what made it great. Today, Samarkand still remains a prosperous city of trade with multi-ethnic identity [[19]].

Bibliography

• Beckwith, Christopher I. Empires of the Silk Road: A History of the Bronze Age to the Present (Princeton: Princeton University Press, 2009).
• de Clavijo, Ruiz Gonzales. “Clavijo’s Embassy to Tamerlane.” University of Washington, http://depts.washington.edu/silkroad/texts/clavijo/cltxt1.html (accessed April 26, 2017).
• Flecker, James Elroy. “The Golden Road to Samarkand.” AllPoetry.com, https://allpoetry.com/The-Golden-Road-to-Samarkand (accessed April 24, 2017).
• Hansen, Valerie. The Silk Road: A New History (Oxford: Oxford University Press, 2012).
• Liu, Xinru. The Silk Road in World History (Oxford: Oxford University Press, 2010).
• Marozzi, Justin. Tamerlane: Sword of Islam, Conqueror of the World (Cambridge: Da Capo  Press, 2004).

Footnotes

[1] James Elroy Flecker, “The Golden Road to Samarkand,” AllPoetry.com, https://allpoetry.com/The-Golden-Road-to-Samarkand (accessed April 24, 2017).

[2] Christopher I. Beckwith, Empires of the Silk Road: A History of Central Eurasia from the Bronze Age to the Present (Princeton: Princeton University Press, 2009), 203.

[3] Justin Marozzi, Tamerlane: Sword of Islam, Conqueror of the World (Cambridge: Da Capo Press, 2004), 28.

[4] Ibid, 30, 40-48.

[5] According to Justin Marozzi, Timur and Amir Husayn, formed an alliance via a marriage between Timur and Aljai Turkhan-agha, who was Husayn’s sister. The two men went undercover as missionaries when Timur decided that he did not want to submit to Moghul rule. It was even during this time as a missionary that Timur most like injured his leg, which never healed, giving him the nickname “Timur the Lame.” In 1365, the partnership ended when Husayn left Timur on the battlefield after resentment tore the two allies apart. They eventually worked together once more in the battle for Samarkand, but while ruling the city, the alliance once more became strained due to differences in political policies and beliefs. Husayn, reportedly, began to tax Timur and his followers because the two leaders had opposing styles of leadership. The alliance between the two officially ended when Aljai, Timur’s wife and Husayn’s sister, died. In 1370, Timur, backed by the government in Bukhara marched with his followers on Balkh to conquer Husayn’s city. Husayn was captured by one of Timur’s men and reportedly tried to bribe the guard with pearls. He was eventually brought before Timur, surrendered, and then executed.

[6] Ibid, 40.

[7] Beckwith, 197-200.

[8] Beckwith, 198.

[9] Valerie Hansen, The Silk Road: A New History (Oxford: Oxford University Press, 2012), 117, 120.

[10] Ruiz Gonzales de Clavijo, “Clavijo’s Embassy to Tamerlane,” University of Washington, http://depts.washington.edu/silkroad/texts/clavijo/cltxt1.html (accessed April 26, 2017).

[11] Hansen, 5.

[12] Ibid, 4.

[13] Ibid, 126-127.

[14] Ibid.

[15] Clavijo’s Embassy to Tamerlane.

[16] Ibid.

[17] Xinru Liu, The Silk Road in World History (Oxford: Oxford University Press, 2010), 106-107.

[18] Beckwith, 133.

[19] Liu, 66-67.

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
Albert Einstein

I have always been pretty sure that mathematics and science are the best languages to explain the natural phenomena. While for many mathematics is too abstract, for me, it is the beautiful language of the universe.

There is no upper limit to the numerical abilities of humans. First, we discovered fire, to get warm. Then, we needed light, so we invented electricity. When we needed to talk to someone 10,000 miles away, we invented the internet. Behind all these inventions, was mathematics.

Of course, the universe cannot speak or think. However, we, the people, can read the universe. There are many scientifically and mathematically inclined people who can read the universe and find answers and then describe them. We, the normal people, can also use our imagination as an apparatus to read the universe and nature. If we can read, hence, something is written. In order to write, a language is always needed. So, the universe should have a language. The letters are circles, triangles, hexagons, etc.

Everything in life has mathematical patterns. Think of the wild animals with stripes or patterns for the purposes of camouflage. But why does a leopard or cheetah or tiger have a particular design?

The Enigma codebreaker, Alan Turing, had a mathematical theory about leopard’s spots. Turing suggested in his paper “The Chemical Basis of Morphogenesis” (published in 1952) “a mathematical schema for the formation of the patterns found in animals and plants.” This was 60 years ago [1].

Stars have patterns. Astrologists have been looking at the outer space searching for patterns to better understand life. Whatever it may be that they find, it is always about mathematics.

Seasons have patterns. They come and go. And they influence nature: the climate changes, animals migrate north or south, rain comes, snow melts, the earth changes color, etc.… Of course, seasons cannot make these miracles. They can only have mathematical patterns.

Einstein had pondered for years on how mathematics works so perfectly. He knew that mathematics is the bridge or the language that connects humans with the universe. And being a connection between us and the universe makes mathematics the greatest achievement of mankind.

If you take a closer look at the patterns of our world, you will witness the language of mathematics. Let me give you some specific examples.

Fibonacci, the golden ratio, spiral, cabbage…

Our universe is filled with spiral designs. Spirals can be found in the shapes of the DNA double helix, flowers, elephant tusks, sunflowers, hurricanes, draining water, animal horns, a nautilus shell, a snail shell, a pinecone, a cabbage, a fingerprint, algae, galaxies… the list goes on and on. Tons of lifeless and living things have spiral designs. And they are not random spirals. They have something in common: the golden ratio! And surprisingly, “there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time” [2].

All these spirals in nature tell us there are numbers all around us. Let’s observe the numbers of petals on some flowers. When you count the number of petals of the flowers in your garden, you will get the numbers 3, 5, 8, 13, 21, 34, or 55. These numbers are not random numbers. These are very unique numbers; they are part of a sequence developed by Fibonacci, a 13th century mathematician, by adding up the last two numbers starting from 1:

1+1= 2, 1+2= 3, 2+3= 5, 3+5=8 …

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

F_n= F_n-1+F_n-2, F₁=1, F₂=1

But, why are those Fibonacci numbers so important? The key is, the relationship between the progression of growth and the proportion. There is a harmonic proportion hidden in the Fibonacci sequence.

A fact: If you divide one number in the sequence by the previous number, the answers result in or come closer to phi:

For example: 5/3 = 1.6666;

13/8 = 1.6250; 377/233 = 1.61802575; 317811/196418 = 1.618033399

Definition: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities [3].

These numbers can be demonstrated with the spiral of the florets in a sunflower. The florets in a sunflower head also form two spirals. If you count the clockwise and counterclockwise spirals that reach the outer edge, you’ll usually find a pair of numbers from the sequence: 34 and 55. If it is a very large sunflower, you will get 89 and 144 [4].

These spirals are not only in sunflowers. You can see them if you look at a pine cone or a daisy. If you mark the spirals and count them, you will always get a number from the Fibonacci sequence. And if you count in the other direction, this time you will find an adjacent Fibonacci number.

The nautilus shell, the golden mean

What makes the nautilus shell so special for mathematicians? Having the Golden Mean. But how do we know that the nautilus shell has the Golden Mean?

First of all, we will start with drawing a small, one unit square. Then we will draw another square which is larger than the previous one. We need to add in a counterclockwise direction. The length of each square has a value from the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Then we can draw spirals, starting with the smallest one, outward through the largest one. Then the Golden Mean will appear.

Flowers, plants, or objects have no idea about mathematics, yet they manifest the best of mathematical patterns. This marvelous mathematical art has been placed in their nature for us not to be fascinated only but also to explore the mysteries behind it.

Note

1. https://www.bbcearth.com/blog/?article=the-maths-behind-a-leopards-spots
2. https://www.sajs.co.za/article/view/4033
3. http://mathworld.wolfram.com/GoldenRatio.html
4. http://www.sciencemag.org/news/2016/05/sunflowers-show-complex-fibonacci-sequences

In company of al Khadr, plunging into secrets

Brilliant young people with countenances of gold

Surrounded by descending sparkling lights

Enraptured with the heavenly potion imbibed

With eyes revealing the secret attained

Their stormy vigor never exhausted

With hearts of steel, never afraid or shrinking

The entire world knows them, lauding their lands and towns

conquering charm mysteriously marks their faces

Equivalent to a genius, each brilliant mind

Waiting for a blessed dawn,

A dawn whose rooster has crowed

There are many possible explanations for this, not least of which is the presentation of science and the use of reason in Islamic texts, but also sociological factors, such as different economic situations during the Middle Ages, and internal political structures. There is also the fact that the Qur’an simply doesn’t contradict scientific findings .

The Middle Ages (or the Dark Ages as they used to be known) of European civilisation extended between the 5th and 16th centuries, encapsulating the Islamic Golden Age spanning the 7th to 16th centuries. It was once thought that Islamic science during this time was little more than a translation of Greek conclusions, however there is now sufficient evidence to suggest that this was a scientific revolution in its own right, and it contributed greatly to the basis of modern scientific thought. Part of the reason science played such a key role in the Golden Age of Islam is surely because of the importance placed on it in Islamic texts. There are hundreds of references in the Qur’an related to human knowledge and contemplation, including the first command of God, instructing humanity to “read.” The hadith also contains hundreds of references the Prophet made to seek knowledge, including one instance of the him saying, “Seek for science, even in China” ; the significance of China being that it is the furthest known country to the Muslim Empire. There is a moral obligation for Muslims to seek knowledge; in fact, learning is often seen as a form of worship and a quest for spiritual perfection through knowledge. This surely acted as an incentive that enabled them to become the great scientific civilization they were during the Golden Age. The Renaissance, which followed the Middle Ages, could be described as the Western equivalent

There is nothing in the Bible to discredit specific scientific discoveries, though it also doesn’t encourage the scientific pursuit in the same manner as the Qur’an. The Bible does convey an ordered world in which science is not only possible but should tend towards the truth, but any such scientific commendation can also be levelled at the Qur’an.

What’s unique about the Qur’an, however, is that it is not as susceptible to the human fallibility excuse, in that it was written immediately after the Archangel Gabriel imparted the Revelation to Muhammad, it was arranged by Muhammad himself, and has remained unchanged since, at least when speaking of the original Arabic and not a translation. The areas of science explored in the Qur’an range greatly from astronomy to physics to biology, and all seem to be in well keeping with modern scientific findings.

Perhaps not surprisingly, the Qur’an does not contain any hardline indisputable science, however. The meanings of many of the Arabic words are subtle and open to interpretation, and different interpretations of the same passages have been used to support different scientific enquiries at different times.

The rapid expansion of the Muslim empire beginning in the 7th century brought great wealth and security, and this naturally led to great advancements in science and technology, similar to the Greek and Roman empires before them. Once an empire establishes itself and can comfortably support its population in terms of food and security, it can turn sights on its lesser problems, and attempt to solve them using its ingenuity, thus making great strides in science and technology. The West had, as already noted, become stagnant in these fields following the collapse of the Roman Empire. Europe was unified once more under the Catholic Church, but there was much animosity between the destitute working class and the self-interested ruling class. It was a time of prosperity for few, and the Muslim empire attracted great minds and became the hub of scientific achievement. Viewed in this context, the Islamic Golden Age is not so much a religious achievement as it is a cultural achievement of a burgeoning civilisation.

The contrast with the Western Renaissance is clear. Galileo, a friend of the pope and of the church, is the most famous example. Upon expressing his approval of Copernican theories, he was incarcerated for heresy. The pope famously rebutted Galileo’s arguments by stating that Galileo could not assert a scientific theory that contradicted the scripture unless it could be shown that God, in his infinite power, could not have brought it about that all the evidence in support of the theory existed and the theory itself not be true. This is of course an impossibly high standard of truth for science to achieve, and furthermore put in jeopardy all scientific knowledge. Galileo was, however, purposefully antagonistic towards the church, and may have done more harm, especially for the relationship between religion and science, than he is usually given credit for. Rene Descartes was on the verge of publishing a similar paper in support of Copernicus, but suppressed it upon seeing the treatment that Galileo received. During this time, it was required that all work be approved by representatives of the church before it was published in order to avoid the publication of any heretical material. This was catastrophic for any scientific theory that may have contradicted the interpretation of the scripture as advocated by the Church. Islamic science avoided this problem. While the Church, as a figure of authority, advocated a particular interpretation of the scriptures and had in the past exercised this authority with punitive measures such as excommunication and incarceration, Islam had no centralised authority with the same level of control. The closest analogous administration is the caliphate, whose role has changed over time, but never gained the overarching power of the Christian church. This could well be due to the Muslim Empire being founded by many small tribes with Bedouin roots, and city states, who had no history of being subject to a greater authority. Also, due to their disparate nature, both culturally and geographically, such an overarching authority was a logistical impossibility. Furthermore, the legitimacy of any one caliph was always controversial; the most divisive split of course being between Sunni and Shi’a Muslims, the former believing Abu Bakr, Muhammad’s father-in-law, was his rightful successor, while the latter preferring his cousin and son-in-law Ali ibn Abi Talib. Such disagreement continued and constantly threatened the supreme power of the caliphate, despite Muhammad’s assertion that Muslims should fulfil oath of allegiance to only one caliph. This disagreement in turn led to a lack of a single ruling authority, and a lack of one single interpretation being enforced across the empire. Often, the interpretation of the Islamic texts varied from community to community. Further supporting a lack of enforcement was the Qur’an. “There is no compulsion in religion” can be interpreted both as a decree of tolerance to other religions, and also a decree of tolerance within Islam itself. This aspect of religious tolerance must surely have played some part in the ability of Muslims to abide alternate interpretations of their text, and also rationalise discrepancies between the text and the constantly evolving hypotheses of science. Without an authority to push an anti-scientific agenda, the Muslim Empire became a hub of scientific enquiry which, along with an unusual tolerance for religion, attracted scientific minds from across the entire region.

There is another hypothesis that should be noted, which is that the view of Christianity and science being in direct opposition to each other is unwarranted. After all, modern scientific prosperity grew out of the Christian West, and it can also be argued that without the fundamental view that nature is uniform and has an observable order and organisation, provided initially only by religion, science would never have even had a grounding on which to start. Perhaps religion and science are not as diametrically opposed as they seem, and their previous confrontations have been due to misunderstandings that are not fundamental to their positions. While it is undoubtedly true that Christianity and science have in the past had a tolerant, if not a symbiotic, relationship, it is nevertheless the case that for quite some time the two held hostile policies in regard to each other, and these policies have resulted in animosity that exists even to this day. This animosity is not a necessity, however, as demonstrated by Islam.

It seems it can then be concluded that the roots of the Islamic propensity for science are a product of both Islamic texts and sociological factors, such as a lack of a centralised authority pushing a particular interpretation of the text. The search for knowledge which the Qur’an advocates must surely have helped initiate this scientific resurgence, but it was also the ability of the Muslim population to interpret the findings of the scientific community (and it should be noted that Muslim and scientific groups were by no means mutually exclusive) in a way that didn’t conflict with their theological beliefs which allowed science to flourish. The Golden Age of the Muslim Empire should stand as an example to all cultures that science and religion can coexist, and not just tenuously, but harmoniously.

Stephen Pant is a freelance writer in Australia. He has a degree in philosophy and history from Monash University, Melbourne.

Notes

1. H.R. Turner. 1997. Science in Medieval Islam: An Illustrated Introduction, Austin: University of Texas Press, pp. 5-9.

2. George Saliba. 2007. Arabic Islamic Science and the Making of the European Renaissance, Cambridge, Mass. MIT Press.

3. A.H. Syed, Islam and Science, New Delhi, 2003, p. 111.

4. Ibid.

5. Maurice Bucaille. 1978. The Bible, the Qur’an and Science: The Holy Scriptures Examined in the Light of Modern Knowledge. Indianapolis, p. 92.

6. Syed. 2003. p. 116.

7. Syed. 2003. p. 115.

8. F. M. Donner. 1981. The Early Arab Conquests. Retrieved 16/5/2009 from http://www.fordham.edu/halsall/med/donner.html

9. John Cottingham. 1991. The Philosophical Writings of Descartes. Cambridge: CUP, pp. xi–xiii.

10. Sachiko Murata, William Chittick. 1994. The Vision of Islam. New York, p. xxiv.

11. A. H. Siddiqui. Translation of Sahih Muslim. 2007, 20:4543.

12. Qur’an 2:256.

13. Syed. 2003. p. 112–113.

Today, those who have made it their business to identify and cure these feelings of emptiness and the consequent loneliness that is experienced by the human self have presented panoply of solutions, usually gift-wrapped in various intellectual discourses. People struggle with each discourse, hoping that maybe one will, after all, be their stamped pass through the golden gateways of enlightenment. Time unwraps each solution and lays its contents bare. History stands as a graveyard, giving testimony to the inadequacy of the philosophical critiques and theoretical discourses of modernity and post-modernity. The world is still in a state of chaos and, within this existentialist milieu, human beings still question their solitary existence.

It seems that history has selected a fistful of people who deem themselves destined to step into the arena of intellectual combat, jumping to the rescue of humankind. The common man finds themselves in a literary laboratory where they are left to experiment with the latest medicines that have been prescribed for their affliction. In a desperate attempt to break free from the onslaught of isms hurled at us by the age of modernity and post-modernity, the intellectuals of our age have come up with a new literary concoction. The era of isms has ended. It is now the age of paradoxes. There is an increasing trend of juxtaposing ironies in the guise of facts and universal truths. Language is the best-seller in the market for dressing-up contradictions with such frills; one is often left so dazzled by the linguistic niceties that they are unable to detect any lacuna in the logic presented. People develop unique dictionaries for each of these. The logic presented for this discrepancy in the repertoire of every person is simple: each person’s world is made up of their distinct life experiences, their memories of the past and their imagination of the future, as well as their comprehension of the now and their plans of action for grappling with the present. Thus, the language one employs and the peculiar meaning it entails is contingent upon one’s very own, individual privé monad. It is these self-concocted dictionaries, composed of their distinct vernacular along with their numerous subtleties, which form one’s individual mental architecture by which the affairs of one’s life are orchestrated.

This novel concept of individual dictionaries rotates round and round the dining tables of the most “progressive” of humankind. People prize themselves as being part of what is now being hailed as a grand intellectual revolution. This revolution, it is believed, gives one the ability to guard one’s pristine exclusivity. Inherent within this exclusiveness of the individual self from the “other” is the championing of the self, and a sense of security prevails, giving humankind the assurance that the esoteric nature of our pristine binaries of right and wrong, true and false, beautiful and ugly make all that we do and say a private matter. And, some like to believe, within this privacy, within this unique sphere of personal space lays the epitome of freedom that humanity has ever been able to reach.

It is within this multiplicity of one’s private, peculiar lingua franca that they are able to ascribe meaning to their very existence. One’s conceptualization of the self and one’s ferocious defense of this newly-acquired perception of freedom are what form the basis of one’s interaction with those around them and the world that they live in. This sense of exclusivity leads to what Habermas has called a breakdown in “communicative action”-the absence of common relatable backgrounds to the extent that no one can any longer imagine being in another’s shoes. Without this mutual taking of perspective, the very precious element of human emotional intelligence that is known as “empathy” is automatically removed from many people’s dictionaries. Empathy is the same trait that makes a child burst into tears when another one cries in front of them, thinking that the pain is not the other’s but their own. This quality of being able to relate to, to actually understand and feel not only the other’s pain, but also their happiness, is what forms the main spring of the concept of rescue, a concept upon which entire literary laboratories have been established. If it were not for empathy, the demarcation between the self and the other would make it unimaginable for anyone to surmount those towering walls to rescue another; this would have been a thing of fairy tales and folklore. This is the point when an eagerly embracing the age of private dictionaries, with their golden masquerade of personal freedom, draws one actively into an intellectual maelstrom against the “other,” and against tolerance.

Confronted by such tempestuous times, when I look upon the glorious pasts of our ancestors in an attempt to find some point of reference that could aid in navigating, one string of events presents some relevant points to my argument. While growing up, my life, just as that of any other child who was growing up at the same time, was colored by numerous stories and legends. Over time, I managed to dust off images of flying horses and heroic men coming to the rescue of people who were being tortured by brutal potentates. But the more human memories have remained with me to this day. As a young child, I often saw my grandmother leave the house and walk over the next-door neighbors’ house with some delicious dish she had prepared. The visits had an almost ritualistic feel to them, since every single time some delectable dish was cooked and brought over to our house; I knew some of this would find its way to our house. On the occasions when I was allowed to accompany my grandmother on these visits, I would witness her place the dish on the table, and then either herself or the recipient would divulge some important piece of news, each launching off into a torrent of complaints and remarks about this, that and the other. On one such occasion, the meeting took a sudden unpleasant twist. I remember quite vividly that my grandmother severely rebuked one of our neighbors, a regular receiver of sweets and meals. The hot halawa lay on the table in front of her, sending off sweet enticing whiffs while both grownups were engaged in a heated verbal brawl. The point of contention was indecipherable to me, as grown-ups at that time had a way of skillfully employing a code language in front of children; perhaps this was part of an attempt to protect our innocence from being tarnished by the realities of adulthood. At the end of the quarrel, my grandmother apparently had the last word and made her way home with the hot dish of sweet-smelling food still sitting on the neighbor’s table. From that time onwards, there was a continuation of exchanges of harsh words over hot delicious meals or sweet mouth-watering delicacies. My young mind was at first befuddled and later exasperated by the on-going quarrel, the continuation of which was clearly contingent on the exchange of meals. I knew that all the trouble would effortlessly come to a halt if neither lady were to cross the fence that demarcated their house from the other. No ties of blood bound them and the cessation of any contact whatsoever would not have disrupted the routine of our lives. It was as simple as that.

What left my young mind baffled in the past was the persistence of my grandmother and our neighbor to maintain contact, despite the conflict; however, this makes sense to me now. People in the past had a more wholesome experience of life because it was framed within a sense of collectivity. Their dictionaries were not discrepant from others and they spoke a common language based on a certainty that their essence was unique to them not as individuals, but as an individual human race. It was their recognition of the unity of essence, shrouded within a multiplicity of existence, which enabled them to forge ties that were so tenacious. This notion of being united in essence, in their human proclivity to do good and believe in the Absolute Truth, was translated into their relationships and their persistent efforts to maintain relationships that had been forged willingly. The entire saga of my grandmother’s quarrels with the neighbor is intelligible to me now as a part of ongoing effort to remind her friend not to detract from this natural inclination towards goodness that was rooted within her very makeup as a human being. The whiffs of sweet-smelling treats were left as a message that her act of reprimanding her friend did not spring from a desire to claim a higher moral ground based on her own personalized set of rights or wrongs, but rather from an active concern for the community that she perceived herself to be a part of. The fact that the neighbor welcomed her at the door each time before the drama took place relates the moral pattern of people at that time, or at least within the confines of such interactions. It reflects a broad moral consensus of the entire neighborhood; they were actively involved in saving not just the one who was being wronged, but also the one who was doing wrong. Each person comprehended the fact that the underlying reason for the argument between the two found its source in the legacy of mutual concern, handed down to them from their elders. An active sense of empathy, of the fear that the wrong that was being committed today could be committed by them tomorrow, the fear that if it was not ended it would form a part of the legacy of their children, existed among these neighbors.

Today, people find a false sense of security in the notion of privacy and personal space. A sense of relief is felt that no busybody from the neighboring apartment will come knocking on the door, with the sense that the gift of a sole meal or a plate of sweets grants them the moral right to correct one’s wrongs or to criticize acts. One finds themselves comfortably ensconced in this preservation of private space and thus fails to recognize that the so-called privacy that is so aggressively guarded is actually shrinking with every passing day. In the past, at least one was able to walk down a street without having some person or another trying to sell them expensive means to look socially acceptable. But the case today is the total opposite of this. The alienation that is a direct cause of protecting what we now term “personal space” has curtailed our freedom to guard our natural proclivity towards goodness which connects us with humanity. The percolating sense of otherness and spreading intolerance are just two sides of the same coin.

The decisive factor in the above discussion is that no time is in and of itself golden. It is the people who are living at that time who cast it in varying hues, hues by which the future generations will remember them. Only if people could burst their own bubble which divides them from the other and embrace the unified proclivity towards Good and Absolute that is part of their human makeup, will they be able to live up to the moral responsibility that they have, not only towards themselves and their contemporaries, but also towards their future progeny. In this hour of need what we need is not another so-called glamorized intellectual revolution, but rather a grand intellectual revival of the human estimation of one’s own self. In my opinion, expensive intellectual laboratories and large think-tanks can help, but a revolutionary revivalism of that which can help us find a positive continuity with the past and a beneficial connection to the future could play a small start. The muddy hand of a child is enough to hold up a mirror to each and every one of us, shattering any claims of uniqueness or separateness. This brief muddy treasure will remind us of what we are made of and of what we mean to one another. Within this humbling realization, I believe, flickers a great hope.

Raaza Jamshed Butt has an MA degree in international relations from the International Islamic University, Malaysia.

One category of galaxies is the spiral; this is dependent on the galaxies’ appearance. The magnetic field of the Sun is also a spiral. Among many things that have a spiral form are the cochlea inside our ears, our navel cord, our fingerprints, the teeth of mammoths, elephant trunks, some spider webs, the horns of some goats, cluster of sunflowers, thousands of types of mollusks, the pattern in which subatomic particles move, plus many more examples. Grapevine shoots, ivy, some microorganisms, and the positioning of some leaves around their branches are in the form of a helix. Nature displays brilliant examples of spiral and helix forms over a wide spectrum, ranging from fossils to galaxies. Below we will discuss some of them:

The Archimedean spiral

Named after its discoverer, this spiral is the geometrical location of a point which moves across a line turning around a fixed point at the speed of q and with a straight angle (Figure 1). The equation for the polar coordinates is p=aq. The distances between the curves are equal. A good example of this type of spiral is the spider web constructed with equal distances from the center.

The Equiangular (Logarithmic) spiral

This spiral type was defined by Descartes in 1638. In an equiangular spiral, any line that crosses the center cuts through all coils of the curve (Figure 2). The equation for polar coordinates is Inr=a.q or r=ea.q. Sea shells and the shells of snails are formed with this spiral.

Fibonacci Numbers and the Golden Ratio

The following numbers, the sequence of which is made by adding the last two numbers together, are known as Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … In other words, each number is the sum of the preceding two numbers. Let us divide each number with the preceding one and write down the quotients:

1/1=1; 2/1=2; 3/2=1.5; 5/3=1.666…; 8/5=1.6; 13/8=1.625; 21/13=1.615…; 34/21=1.619…; 55/34=1.6176…; 89/55=1.618…

If we continue to divide in this way, we will reach a mathematical constant, i.e., 1,618034, which is known as the golden ratio (φ).

Let us now draw a new geometrical shape with the Fibonacci numbers. Next to a 1-unit side square put another square that has equal dimensions. Then add another square, this time equaling the sum of the sides of the previous two (2 units). As we continue to add new squares with double the units of the previous two we get what is called the Fibonacci or golden rectangle. When we draw an arc from one corner of this rectangle to an opposite corner and continue drawing through neighboring squares, as in Figure 3, we will get a spiral. A good example of this is the nautilus shell. The golden rectangle and the spiral is frequently used in fine arts, architecture, and technology.

The Helix

The space curves that coil around a cylinder and cut through its main axis at a right angle is called a cylindrical helix (Figure 4). An ivy plant climbs a tree in a helix, and a helix is the shortest distance to a certain height. The Selimiye Mosque, Edirne, Turkey, features one of the best examples of helices in architecture. The architect Sinan designed the minarets of this mosque with three balconies, which are reached via different stairs that have no connections between them.

The 3D Archimedean spiral and the Logarithmic spiral (Helico spirals)

Conical helices are the space curves that coil around a right cone and cut through its main axis at a right angle. Sea snails, or limpets, have this spiral shape (Figure 5).

Galaxies and hurricanes

Galaxies and hurricanes are also spiral in shape and they have some similar features. Sharing the Stamp of Unity, the law of which governs the entire universe, both galaxies and hurricanes are affected by major forces, like the force of gravity, angular momentum or rotation.

Spiral galaxies are divided into two categories: elliptical and barred spiral galaxies. Barred spiral galaxies have arms that extend away from the main core (Figure 6).

(As evidence for a people open to belief) We have assuredly set in the heaven great constellations, and We have made it (the heaven) beautiful for those beholding. (Hijr 15:16)

The Nautilus: A wonder of creation

The hard shell of the nautilus has a beautiful logarithmic spiral shape. Each coil is at a distance from the next at an increasing proportional distance, each coil is multiplied by a constant. The chambers in the shell are similar, but they widen in a geometric sequence. It is amazing that calcium carbonate, the material that makes up the shell, can accumulate in such a way so as to comply with this geometrical pattern. In this pattern, the nautilus occupies the least space that is possible, thus losing as little heat as possible. Architects have been inspired by the nautilus to produce designs to use the smallest possible space to contain the most possible room.

The Cochlea

The cochlea in our ears is like a double-ramp tunnel coiled upon itself. Etymologically, the word cochlea comes from a Greek word that means snail. The spiral shape of the cochlea reminds one of sea shells.

Horns

Horns of the sheep and goats have the shape logarithmic spiral; they grow in the form of helicoids, as if coiling around a cone.

The Rose

The leaves of a rose are lined up and shoot out in a spiral shape.

Spirals open for us gateways to thought in our efforts to explore the wisdom and beauty that have been set in motion in the universe and are constantly maintained. Spirals, like other living or non-living objects or beings around us, are exquisite works of art that point to the fact that nothing exists from coincidence. Looking through a telescope to a marvelous galaxy in outer space or examining a sea shell on the beach or holding a rose in the spring may become a rewarding act if we contemplate on their Fashioner, for such “contemplation for an hour is worth voluntary prayer for a year.”

Educators who see the beauty at the center of mathematics and can make their students see it that way, are more likely to be able to get their students’ attention and teach them more effectively. Also, as well as facilitating the study of sophisticated mathematics, this puts mathematics in its proper place so as better to understand the value of what it has to say to human beings. To see the beauty and the pleasure in mathematics can change the negative attitudes of some students and help educators in teaching mathematics.

Often it seems that we pursue mathematics education from either a structural or an applications point of view. From a structural point of view, we insist on building up all of the tools one may need in a sequential, logical order, because an educator will need the students to know all of the smaller pieces before they can build any of the larger ideas. An analogy for this would be if we forced somebody to study all of the nails, screws, bolts, and tools to build a house before we let them even see the plans for the house. This is one of the main reasons that most people who study mathematics in their school years think that it is a pointless exercise in playing with formulas and has no significance in real life. For these people, mathematics might be helpful only in keeping track of their checkbooks after graduation. Some students think that they can calculate whatever they need using computers, but sometimes this is not very effective because students may not understand the logic behind the problems and the results do not mean anything to them or they are unable to detect errors.

The applications point of view leads to making up “word problems” that appear to be about the real world, but everyone knows that they are highly artificial. It also leads to focusing at higher levels on only the applications. Hence, for instance, in calculus we spend a lot of time plodding through various physical applications, without letting students see the bigger picture. Or we spend time in liberal arts mathematics talking about things such as modeling and linear programming, which yield great applications, but are generally tedious and do not give most students much appreciation for mathematics. If we see the beauty at the center of mathematics, as well as introducing ideas that may have application or may build some tools, we can bring students to have a much bigger picture of mathematics at a much earlier stage in their mathematical development.

Educators can include some fun topics in courses that they teach. For instance, they can encourage students to discover the amazing number patterns in nature, such as the Fibonacci sequence in pine cone spirals, pineapples, and cauliflowers, in which the number of pieces increases in the following manner: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … (add the last two numbers to get the next). Another example is the “golden ratio.” In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is a mathematical constant, approximately equal to 1.6180339887 and recent research shows that people think that the shapes and figures in this ratio are more interesting and aesthetically pleasing to the human eye.

Sometimes, even a small algebra trick can miraculously bring students to love mathematics and be more focused, and then more interested in the deeper aspects later on. Take a look at this symmetry:

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321.

Here are a few more examples showing the beauty of mathematics visually with numbers:

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10 = 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888.

Students’ minds can be broadened by seeing the surprising differences that arise when we move to non-Euclidean geometry. Fractal shape examples in nature, such as snow crystals, and things like the Mandelbrot set, which is a set of points in the complex plane the boundary of which forms a fractal, can be introduced with a background and give rise to amazingly beautiful images and ideas. Even such deep and thought-provoking ideas as these can be understood by students when they have curiosity, creativity, and an open mind.

All these examples and others like them can inspire people to see the beauty of mathematics and give them a better understanding and a sense of the expanse of mathematics. With a little more discovery of and exposure to the more beautiful aspects of mathematics, students are much less likely to feel any hatred for mathematics and may develop a much greater appreciation for the creation of the universe.

Ali Kemal Unver is a postdoctoral scholar at the University of California, Los Angeles.

Note

* The golden ratio can be derived by the quadratic formula, by starting with the first number as 1, then solving for the 2nd number x, where the ratio [x+1]/x = x/1 or (multiplying by x) yields: x+1 = x2, or a quadratic equation: x2-x-1=0. Then, by the quadratic formula, for positive x = [-b + sqrt(b2-4ac)]/2a with a=1, b=-1, c=-1, the solution for x is: [-(-1) + sqrt([-1]2 -4*1*-1)]/2*1 or [1 + sqrt(5) ]/2. See the second reference for details.

References

1. http://users.forthnet.gr/ath/kimon/
2. Green, Thomas M. “The Pentagram and the Golden Ratio.” http://www.contracosta.cc.ca.us/math/pentagrm.htm.

Roughly speaking, the bulk of Central Eurasia consists of Central Asia and the Caucasus but also stretches to such regions as Turkey, the Turkic/Muslim regions of southern Russia, northern Afghanistan, southern Siberia, Tibet and Mongolia.[1] Largely due to Turkic influence, shaped historically by a tolerant understanding of co-existence as enjoined in Islam, this region has won prestige internationally for its peaceful efforts in this diverse geographical area.

Such leading U.S. universities as Harvard University, the University of Wisconsin at Madison, the University of California in Los Angeles, and the University of Indiana in Bloomington offer graduate courses on Central Eurasian studies and languages. The notion of a “clash of civilizations” promoted by Huntington[2] in the era of globalization has never been accepted by many people throughout Central Eurasia in their rich historical experiences of living in “mosaic societies.”

Pluralistic Islam at the heart of Eurasia

Unfortunately, for last couple of decades the experience of the diverse pluralistic Islam of Central Eurasia has been obscured by the political trends of Islam in the Middle East. The latter, rather than the former, has become the focus of most academic scholars of social sciences and humanities and media. Historically, while Turkey formed the western boundary of the Muslim world, Central Eurasia has largely represented the northern and north-eastern boundaries of the classical Islamic world. Islam in Central Eurasia emerged mainly through remarkable Sufi masters like Ahmet Yassavi, Korkyt Ata, Mevlana Rumi, and Baba Tukes. The merchant caravanserais of the Silk Road that traversed vast areas between the Middle East and China came into existence through peaceful means, and new Muslims in this area were very tolerant toward the many religions and cultures of their neighbors. Although the revelation of the Qur’an started in Arabia, most of its scholarly interpretations and the hadith compilations were compiled in Central Asia.[3] The greatest contributions to almost all areas of religious and positive sciences, engineering, art and culture were witnessed in this part of the world between the ninth and fourteenth centuries ce. The works of such outstanding intellectual figures as Ibn Sina (Avicenna), Al-Farabi (Alfarabius), Al-Khwarizmi still benefit

people all over the world. The largest library in the world in the thirteenth century ce was in Otrar (a city in present-day southern Kazakhstan), which was later totally demolished by Genghis Khan during Mongol invasion.

In the period between the seventh and thirteenth centuriesce, the Muslim world was ruled predominantly by Arab caliphs of the Umayyad and Abbasid dynasties. However, starting from the twelfth century up until the beginning of the twentieth century, Muslims of Central Eurasia of predominantly Turkic origin became the foremost rulers of the Muslim nations. Among them were the famous states administered by the Seljuks in Central Asia, the Golden Horde in Russia, the Baburides on the Indian subcontinent, the Mamluks in Egypt, and the Ottomans in Eastern Europe, North Africa and the Middle East.

The Golden Horde’s legacy of tolerance toward Christian, Jewish and Buddhist communities laid the foundation for the flourishing of Moscow and the Russian

Empire, which became heir to the Golden Horde’s legacy.[4] Saray, which was the capital of the Golden Horde from thirteen to fifteen centuries, and which was located very close to the border of modern-day southern Russia and western Kazakhstan, became a center of intercontinental diplomacy as envoys and ambassadors representing princes and popes sought audiences with the Muslim khans of the Golden Horde.[5]

Dialogue between world religions in Central Eurasia in the modern secular context

After more than two hundred years of Czarist rule, the ex-Soviet Central Asian republic of Kazakhstan, being one of the most diverse countries in the world, the home of 120 ethnic groups and many world religious communities for the last seventeen years became the active initiator of peace, dialogue, integration and reconciliation initiatives across not just the Eurasian states of the former Soviet Union, but also the larger international community. After independence, to ease tension among superpowers Kazakhstan’s government decided unilaterally to dismantle the huge nuclear arsenal left as the Soviet legacy of the cold war. Following the breakup of the USSR, Kazakhstan’s President Nursultan Nazarbaev’s proposal to form a “Eurasian Union” was praised by many leaders across Russia and the ex-Soviet republics. The late pope John Paul II met Nazarbaev in Astana on September 11, 2001.

Muslim–Jewish dialogue in Central Eurasia

In 2002 Kazakhstan served as the facilitator of Islamic– Jewish dialogue in Eurasia, an event which took place in the new capital, Astana. At the conference, thirty rabbis from various countries noted that the only way forward in the relationship between Muslims and Jews is through constructive dialogue. They also expressed their wish to see Kazakhstan as a center of Muslim–Jewish dialogue.[6] The fact that the headquarters of the Euro-Asian Jewish Congress (EAJC) was placed in Almaty, the largest city in Muslim Kazakhstan, at a time when there is growing instability in the Middle East, is a sign of the huge potential of the mutual trust between Muslim and Jewish communities in Eurasia.[7] Alexander Mashkevich, the head of the EAJC, considers Kazakhstan a unique example of cooperation and peaceful coexistence between various peoples and religions. He also noted that the largest synagogue in Central Asia, which was opened in Astana, best characterizes Muslim Kazakhstan as the land of inter-ethnic peace and inter-confessional harmony.The latest phase of this dialogue at the First International Conference of Peace and Accord was held in Almaty the previous year. Presidents of the leading Jewish organizations of the United States, leaders and plenipotentiaries of the states of Central Asia, Azerbaijan and Turkey, and members of the leadership and the Council of Rabbis and Central Asian Muslim leaders condemned terrorism and declared that there are no antagonistic contradictions between Judaism and Islam.

Dialogue between world and traditional religions at the heart of Eurasia

At a time when some dark forces are trying to bring about a clash of world religions and civilizations, Central Eurasia offered an unprecedented challenge to these dangerous trends by initiating a series of high profile civic activities bringing together members of the clergy of world and traditional religions in the heartof Eurasia in Kazakhstan’s capital Astana in 2003 and 2006.[8] A unique role model for intercultural communication and dialogue, Kazakhstan, with a number of other countries of Central Eurasia, showed the whole world that traditional values can be reconciled with liberal norms in the formation of a successful, peace-loving, civil, mosaic society. Leading Turkish Islamic scholar Fethullah Gulen, active promoter of interfaith and intercultural dialogue, valued this significant interfaith event in Eurasia highly and said, “The only way for humankind to solve its problems is by way of dialogue: meeting, learning and talking to each other…With all my heart I state that all these initiatives done out of pure intentions will serve to establish peace and stability in the region, to improve relationships among nations and also to build lasting peace on the whole planet.”[9]

Dialogue Eurasia: “DA”

A number of Turkish people are working to pave the way for dialogue in the Eurasia region.[10], [11] Diyalog Avrasya (Dialogue Eurasia), a publication of the Dialogue Eurasia Platform, has been the voice of common sense in seventeen countries, from Moldavia to Mongolia, since its founding in 2000. A bilingual quarterly published in Turkish and Russian, DA adopts an approach to conflict with reconciliation, using the slogan, “Dialogue starts with ‘DA’” (“Da” in Russian means “yes” in English). DA representatives recently gathered in Istanbul and discussed the latest developments in the Eurasia region. DA stressed that its ideology is knowledge and love, and that convergence, compromise and understanding constitute the backbone of their policy. Renowned Kyrgyz writer Chingiz Aytmatov, who passed away recently, also served on the journal’s advisory board; he described DA as “the business card of Eurasia.” Garnering great interest in the countries where it is published, DA also brings together Eurasia’s famous writers, intellectuals and civil society volunteers. In addition, opinions and essays of leading politicians frequently appear in the journal.

Interestingly, present and past dialogue efforts in Central Eurasia go hand in hand with positive trends in education, which for the last decade or so, has experienced quite a renaissance.[12] Hopefully, dialogue efforts combined with excellence in education will yield great fruits in the future in this important region of the world, which will benefit the whole of humanity again as during the region’s golden ages between the ninth and fourteenth centuries. There is hope that the dynamism of inter-cultural diversity which has prevailed for centuries on the Eurasian continent with its multi-ethnic, multi-linguistic and multi-religious characteristics will gain momentum in future again.

Dr. Zhandos Utegulov is researcher at University of Nebraska–Lincoln.

Notes

1. http://cesww.fas.harvard.edu/

2. Huntington, Samuel P. 1993. “The Clash of Civilizations?” Foreign Affairs 72(3): 22-49.

3. Ali Unal, Alphonse Williams eds. Advocate of Dialogue: Fethullah Gulen, 2000, The Fountain Publications.

4. http://www.accd.edu/sac/history/keller/Mongols/states3.html

5. Janet Martin. Medieval Russia, 980-1584, CUP, 2008.

6. http://www.jewishsf.com/content/2-0-/module/displaystory/story_id/19476/edition_id/395/format/html/displaystory.html

7. http://www.eajc.org/publish_gen_e.php?rowid=40

8. http://www.religionscongress.org

9. Interview with Fethullah Gulen in Kazahstanskaya Pravda, Sept 15, 2006.

10. http://www.zaman.com/?bl=culture&alt=&trh=20061206&hn=38940

11. http://www.interfaithathens.org/article/art/10081.asp

12. Ismail Demirkan, Aksar Beketov. “Islam, Science, and Free and Open Inquiry,” Physics Today, January 2008, p. 11.

The appeal of the Golden Ratio to the human eye and brain has been scientifically tested. When subjects are presented with a range of rectangles, people invariably pick out as most pleasing ones those whose sides are of the Golden Ratio. This golden number is the basic number at work in aesthetics; there are even claims that the Golden Ratio was used by Leonardo da Vinci when painting the Mona Lisa, and by the Greeks in building the Parthenon. But the surprising thing is that a number deemed aesthetically pleasing by human beings also crops up in nature and science. In a newly published article in Physical Review B, it is stated that the Golden Ratio appears in the structures of some metals. The Golden Ratio is seen in the arrangement of seeds on flower heads, in the spirals of sea shells and galaxies, even in black holes. This ratio can be found almost everywhere in the universe.

Although the Greek mathematician Euclid first defined the Golden Ratio in around 300 BC, the followers of Pythagoras probably knew of it two centuries earlier. Euclid defined it as a line that can be divided into two unequal parts (Figure 1), where the ratio of the smaller part of the line to the longer part is the same as the ratio of the longer part to the whole. This ratio is 1.6180339887…, the Golden Number.

What makes the Golden Ratio special is the number of mathematical properties it possesses. The Golden Ratio is the only number whose square can be produced simply by adding 1 and the reciprocal of which can be arrived at by subtracting 1. If you take a Golden Rectangle – that is a rectangle where the length-to-breadth ratio is equal to the Golden Ratio, and take out a square, what remains is another, smaller Golden Rectangle. Also, think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. If you start with 7 and 11, then what you have is:

7, 11, 18, 29, 47, 76… When you have written down approximately 20 numbers, calculate the ratio of the last to the penultimate: the answer should approximate the Golden Number.

In mathematical terminology it is (an/an-1) equals to the Golden Ratio.

Another example of the Golden Ratio is the Fibonacci Numbers, that is a number series where each number is simply the sum of the previous two numbers. These numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… The ratio between any two successive Fibonacci numbers approaches the Golden Ratio as the numbers get larger. We can find the Fibonacci series particularly in the spirals of sea shells and in the arrangement of seeds on sunflower heads.

It was the elusive nature of the Golden Ratio that led the Italian friar and mathematician Luca Pacioli to equate it with the incomprehensibility of God. In the 15th century, he wrote a three-volume treatise, Divina Proportione (Divine Proportion), that was crucial in the dissemination of the Golden Ratio beyond the world of mathematics. After him, many artists, architects, and musicians used the Golden Ratio in their works; for example, musicians such as Debussy and Bartok and the architect Le Corbusier.

Let’s examine the arrangement of leaves on the stem of the plant Phyllotaxis. As each new leaf grows, it does so at an angle offset from the leaf below. The most common angle between successive leaves is 137.5 degrees – the Golden Angle; 137.5=3d 360-360/G, where G is the Golden Ratio. Why does the Golden Ratio play a role in the arrangement of leaves? It is all down to the irrationality of the number. A new leaf must collect sunlight without throwing too much of a shadow on the leaves below. A plant must arrange its leaves in such a way that the greatest number can spiral around the stem before a new leaf can sprout immediately above a lower one – that is at 360 degrees. If the leaves were arranged at an angle of 120 degrees, then the leaves would grow as 3 separate columns with large gaps between them. This would effectively block out the sunlight to the lower leaves. If the angle were 50 degrees, then there would be spaces between the leaves. But, with an angle of 137.5, the maximum amount of leaves can be arranged with a minimum of space being left between the leaves.

The Golden Ratio also crops up in hard sciences. Let’s take a look at the growth of “quasi-crystals.” These maintain a five-fold symmetry, which means that they make a pattern that looks the same when rotated by multiples of one-fifth of 360 degrees. Since the time when these crystals were discovered in 1984, many physicists have been researching their properties. In Brookhaven National Lab in New York State, Tanhong Cai imaged the microscopic terrain of the surface of such crystals made from alloys of aluminum-copper-iron and aluminum-palladium-manganese. It is found that flat terraces are punctuated by abrupt vertical steps. The steps come in two predominant sizes, with the ratio of the heights of these two steps being the Golden Ratio. This fact was discovered in 2002.

The most surprising place where the Golden Ratio appears is in black holes, a discovery made by Paul Davies of the University of Adelaide in 1989. Black holes and other self-gravitating bodies, such as the sun, have a negative specific heat. This means that they get hotter as they lose heat. In a spinning black hole there is an outward centrifugal force acting to prevent any shrinkage of the hole. The force depends on how fast the black hole is spinning. It turns out that at a critical value of the spin (when the ratio between the square root of the mass value and the square root of the spinning parameter is equal to the golden ratio), a black hole flips from having negative to positive specific heat. In other words, the Golden Ratio determines the character of the black hole.

Figure 2 shows the finger bones of a hand. The ratio of each bone at the top of the hand to the bones at the bottom of the fingers is the Golden Ratio. Pine-cones show the Golden Ratio spiral clearly (Figure 3). If one looks carefully at an ordinary cauliflower, one can see a center point where the florets are smallest, and the florets are organized in spirals around this center in both directions (Figure 4). The flower, Echinacea Purpura, has the same spirals (Figure 5).

With the help of developing science, new examples of the Golden Ratio are waiting to be discovered in the universe. The latest discoveries demonstrate that by using this ratio in technology, new products which make our lives easier will soon be available to all. This mystery that is spread throughout the universe may be an opportunity to renew and change our points of view on life.

Reference

• Chown, Marcus, “Why Should Nature Have a Favorite Number,” New Scientist, 21-28 December 2002, 55-56.

Nowadays, children and parents are estranged, employees and employers are continuously at odds, the government is deaf to the public and the public seems to be unaware of the government, the teacher and the pupil no longer talk the same language; these phenomena can all be explained when we realize the serious lack of communication that we are facing. What has gone wrong?

The reason that we are removed from one another in terms of communication, despite physical distances having been lessened, is that we either are unaware of that important component of human communication, empathy, or we are not giving it due consideration. There are many definitions of empathy; a brief definition is that it is the ability to recognize and understand another person’s perceptions and feelings and to accurately convey that understanding through a com- passionate response. In other words, it means understanding another person so well that you feel as he/she does. Native Americans expressed this as walking a mile in another person’s moccasins. It is being able to listen so intently and to identify so closely with another that you experience that person’s situation, thoughts and emotions. Empathy has many different descriptions, but they all narrow down to the same thing: developing the ability to see the world from another’s point of view without judging. Being empathetic is a bit like being an anthropologist; when an anthropologist goes to study a different people or tribe, there is no judgment or criticism involved, the anthropologist just accepts and describes the way of life, the way of seeing things. One must develop the ability to put oneself in another’s shoes, to see the world as they see it, without judgment or criticism or over-identification and agreement. Good therapists are said to do this; the same can be said for good friends. It is only with empathy that we can understand each other thoroughly and proceed to build close and reliable relationships.

Empathy acts as an inhibitor of aggression and violence. A person with greater empathy tends to act in pro-social ways simply because such a person is able to identify and recognize the plight of others. On the other hand, people acting in antisocial ways are likely to lay the foundations for violent and aggressive patterns. In this respect we can say that there is a strong relationship between empathy and morality. Morality can be explained as a set of principles or ideals that help an individual distinguish right from wrong. It is a term used to cover those practices and activities that are considered significantly right or wrong, the rules that govern these activities and the values that are embedded, fostered or pursued by these activities and practices. It would be correct to say that a man of high moral values is at the same time highly empathetic. This is true because the ability to see the world from another person’s point of view without personal biases or judgments usually leads one to a correct understanding of the situation and therefore assists one in making a correct decision. An empathetic person always places him/herself in the place of the people with whom he/she is in contact, looks at events from their perspective and thereby is able to attain a deep understanding of the situation. When it comes to making comments about the situation, such a person still assumes that he/she is still in the other person’s place and talks as if he/she is not talking to somebody else, but to him/herself. The result of such behavior is perfect comprehension and a correct evaluation of the situation.

To be empathetic in this way is a difficult human relations skill to gain. It would be relatively easier if there were only few people with whom one is in contact. At least then one would know each of these people’s characteristics and could understand each of their situations more easily. But what if there are many people with whom one is in contact, each having his/her own personal differences? Now it is that communicational ability arises and that one must be able to adapt to each situation, without being self-centered. This can only be achieved by a skill that has been fostered by high moral values. A person who has such skills is one that creates a feeling of intimacy and well-deserved trust in others. Such a person becomes someone to whom a story can always be told in confidence, and such a person may even understand a situation better than the person involved.

This is how the Almighty Creator wants us to be and how he expects us to be. This reality is evident in the religions that God has sent to us with His messengers. What is called The Golden Rule is a prevalent idea of Christianity. The golden rule is best interpreted as saying: Do unto others as you would have others do unto you. To use this rule, one must imagine oneself to be in exactly the same place of the person who is involved in the action. If we act in a given way toward another person, yet are unwilling to be treated that way ourselves under the same circumstances, then we have violated this rule. To apply the golden rule adequately, we need both knowledge and imagination. We need to know what effect our actions will have on the lives of others. And we need to be able to imagine ourselves, vividly and accurately, in another person’s place in a given situation. With knowledge, imagination, and by applying the golden rule, we can progress far in our moral thinking.

The golden rule is best seen as a principle of consistency. It does not replace regular moral norms. It is not an infallible guide by which to judge the correctness of an action; it does not provide all the answers. It only prescribes consistency – that is that we not let our actions (toward another person) be out of harmony with our desires. It tests our moral coherence. If we violate the golden rule, then we are violating the spirit of fairness and compassion that lies at the heart of morality.

Moreover, Prophet Muhammad, upon him be peace and blessings, the Messenger of Islam, says He who does not feel the hunger of his neighbor when he goes to sleep in his comfortable bed cannot in any way share our values. It is of utmost importance to put effort in empathizing with another’s circumstances and to understand other people well. Islam actually states that the most important of all the divine characteristics that a person should have is their personal relations with other people. That is the only thing for which God, the All Merciful, will not directly show His compassion when the time comes to account for our sins after death. In other words, suppose that you have mistreated somebody in this world; God will first ask the person who has been mistreated whether you are to be forgiven. This is God’s absolute justice, an important part of His character.

There is no doubt that God gives particular importance to communication among people and to their understanding of one another. Taking into consideration the scientific finding that almost 90 percent of human communication is comprised of non-verbal elements, empathy plays a great role in the part of good communication. In the history of humanity so much has changed, but the main component of communication, empathy, has maintained its place as before. It is the invisible bridge that connects our hearts to one another through which we understand and feel one another, a bridge that God wants us to construct to span our hearts, a bridge via which God’s love can be acquired.