It was finally the weekend! After my long mathematics presentation, I came home to watch my favorite tv show, Person of Interest, to de-stress. Surprisingly, the episode was about the most famous mathematical constant, pi (π) which is equal to the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. Mr. Finch (the main character) was acting as a substitute teacher and wrote on the chalkboard 3.1415926535. Then he asked the students, “What does this mean?” I answered the question in my mind, thinking, “If I have a bicycle tire with a diameter of 1, then one full revolution of the bicycle tire would travel the distance pi.” However, in the show, nobody answered. Then Mr. Finch answered the question himself, saying:

Person of Interest, Season 2 Episode 11 “2 Pi R”

“Pi, the ratio of the circumference of a circle to its diameter — 3.1415926535 — is just the beginning. It keeps going forever without ever repeating, which means that contained within this string of decimals is every other number; your birth date, the combination to your locker, your social security number, etc. It’s all in there somewhere. And if you convert these decimals into letters you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, and everything we ever say or do. All of the world’s infinite possibilities rest within this one simple circle. Now what will you do with that information; what it’s good for? Well, that would be up to you…”

Although that scene was actually inaccurate, I loved it. This scene is beautiful because most teachers in the world struggle to be as good and as interesting of a teacher as Mr. Finch is here. His knowledge about the subject expands the discussion beyond the textbooks and keeps the students focused throughout the lecture.

Wikipedia, gif, “Pi Unrolled”

We have all been taught that pi is the ratio of a circle’s circumference to its diameter.

Unfortunately, this is wrong because mathematicians have not proved that pi has the characteristic of “normality” yet. In other words, mathematicians are not sure if pi contains all the finitely long permutations of digits from 0 to 9. They are not sure if every digit continues to be used after a certain amount of time or an unlimited number of times in pi’s decimal representation. Nobody knows what we will find in the digits of pi if we keep going. For instance, when we check the first billion digits of pi, we see that the digit 7 occurs almost 100 million times. This makes pi a nice random number generator. However, after some points, pi may not contain the digit 7 and might instead have a non-repeating number with just two or three digits such as 010203112233000111222333…

For instance, after the first 761 digits of pi, there is a famous mathematical coincidence where six nines occur in a row which is called the Feynman point.

Twitter, Feynman’s Library, “Feynman Point in Pi”

But we are sure that the digits of pi keep going on forever and in a random order. This makes pi interesting because the value of pi is finite; however, its decimal value is infinitely long. This is not a contradiction. Pi is a constant number because it is the ratio of the circumference of a circle and its diameter, which are finite values. Still, we need an approximate value for pi.

In 1768, Johann Lambert proved that the value of pi is an irrational number and it cannot be written as a rational simple fraction. 22/7 is a commonly used approximation but does not contain all of the digits of pi. This is because irrational numbers cannot be written as a ratio of two numbers, such as , because they continue on to infinity and do not follow a pattern. In 1882, Ferdinand Lindemann proved that pi is a transcendental number because it is not algebraic; it is not a non-constant polynomial equation with rational coefficients (“Transcendental number”, Wikipedia).

We can safely say that pi is transcendental because the mathematician Yasumasa Kanada found that the first trillion digits of pi appear to be statistically random. If you check the table below, you see that the event of each digit occurring is independent, and the probability of it is one-tenth of the time (“Kanada Laboratory,” Super Computing)

After many years, Emma Haruko Iwao found 34.1 trillion digits of pi in 2019. It took 121 days for Haruko and his computer, because calculating pi requires a lot of power, even for a computer. You can picture it in your mind like this; if you were to print a billion decimal values of Pi in normal sized, ordinary font, it would stretch from New York to Kansas.

However, 34.1 trillion digits is still not enough to prove whether pi is normal or not (“Pi in the Sky, Google Cloud Blog). Supercomputers are still crunching the numbers. If you check the graph below, you will see the number of known digits of pi, by year, since 250 B.C.

FiveThirtyEight, Graph, “Even After 31 Trillion Digits, We’re Still No Closer To The End Of Pi”

Going back to Mr. Finch, we see that he is not 100% wrong. We can find our birthdays in pi easily. If you go to mypiday.com and type your birthday, it will give you the decimal place in pi. For example, my birthday occurs at the 675,097th decimal place.

If pi is a normal number, then we can say that our whole destiny is encoded in pi. The pictures we are going to take in the future, will be in pi because there are binary numbers behind images. All digital products are in pi. Even this article has been in pi for thousands of years. Furthermore, the DNA of every creature is in pi. Mr. Finch was actually right.

There is an interesting and artistic way to show the randomness of pi. Some scientists might be happy with their tedious scatter plots, but there are some artists who use colors for data visualization to communicate with the public. Martin Krzywinski is one such artist, who found beauty and artistry in the randomness of Pi. He took the digits of pi and gave each digit a different color. For instance, he gave 3 the color orange, 1 as red, 4 as yellow, and so on. Then he made a beautiful poster. And if you look at it carefully, you do not see any particular pattern to the colors.

Science Art by Martin Krzywinski

Should we stop working on pi? Or should we continue looking for a better approximation? Is assuming pi as equal to 3.14 good enough? Or is it enough to use 40 digits of pi to find the circumference of the Milky Way galaxy to an error less than the size of a proton (JPL NASA)? Are the first 152 digits enough to find the circumference of the observable universe at 93 billion light-years (WIRED)? There are hundreds of mathematicians who have been trying to figure out more digits of pi for years. It is like trying to get to the moon and then to the next planet, and so on…

But why? Why do mathematicians bother calculating any more digits? Why aren’t 34.1 trillion digits of pi enough? Is it because pi lurks in every circle?

The logical reason seems cryptic: is it because pi is a beautiful source to generate random numbers? Or is it that countries can show off their technology to other countries, because calculating trillions of digits of pi requires a very powerful computer? For instance, in the Star Trek episode “Wolf in the Fold,” Spock foils the evil computer by commanding it to “compute to last digit of the value of pi.” So asking a computer to compute pi is called “a stress test” and may make it crash.

On the other hand, we humans are just weird. Staying at home and drinking tea is a beautiful activity, but when we get bored, we try to climb the highest of mountains, befriend a tiger, or try to memorize the digits of pi, like Chao Lu, who correctly memorized the first 67,890 digits of pi. We will keep doing these things because we like to understand the world around us.

We are inevitably connected to the past, and pi is a thread that’s gone through all of human history. That’s why we can say that as long as there are people, there’s always going to be somebody who wonders what’s next. And I assure you that somewhere in the world there is a mathematician or scientist using pi for something important, because pi is still the mysterious constant of nature.

Finding Pi

The previous statement is utterly true: there has always been someone who works on pi. Math is as old as civilization. Pi has been studied by the human race for almost 4000 years. When the last mammoths were going extinct, people were studying Pi. As far as we know, Archimedes was one of the first humans who calculated pi. He was most likely helping wheel makers. But how did he estimate the value of pi?

Firstly, he saw that all polygons are a circle. According to Archimedes, if you keep increasing the number of the sides of a polygon, you get closer to the perfect circle. In other words, a pentagon is more circle than a square, but a hexagon is more circle than a pentagon, and so on… Thus, more than two thousand years ago, he defined a circle as a regular polygon with an extremely large number of sides.

His definition is useful because measuring a curved surface was hard to do accurately. He found a way to find the circumference of a circle. First, he drew a square with its corners touching the perimeter of a circle and found the perimeter of the inscribed square. Secondly, he drew another square with its sides also touching the perimeter of the circle and found the perimeter of the circumscribed square. He came to the conclusion that the circumference of the circle had to lie somewhere between the value of those two perimeters of squares.

Using this method, however, the difference between those two values was pretty big. So, he drew pentagons to see the upper and lower bounds of the circumference of the circle. This gave him a smaller range of bounds. He kept increasing the number of faces of the polygon that he was drawing inside and outside the circle. Each time he did this, his estimation was getting more accurate. Archimedes got up to a 96 sided regular polygon [called an enneacontahexagon] until he grew exhausted. The lower and upper bound that he found were 3.1408 and 3.1429. Thus, he calculated π to two decimal places.

Archimedes’ method needed improvement because his life span was not going to be long enough to find the other digits of pi by hand. Mathematicians needed to discover more efficient formulas and new techniques.

Before they could do this, they needed to discover algebra. Its discovery by the great mathematicians inspired a whole new way of looking at the world.

The next great jump in calculating pi was the invention of calculus. After that, mathematicians started working on infinite series. An infinite series is an expression with numbers added together until infinity; sometimes these infinite series converge to a particular value.

There are many methods available now to calculate pi. Gottfried Leibniz found pi in infinity. James Gregory was working on one of the astonishing infinite series for the inverse tangent function below. He added infinitely many small numbers together and found pi.

He put x = 1 into the inverse-tangent series. He showed us the further we go, the closer to the estimation of pi we get. However, in order to get 10 digits of pi, we need to write about 5 billion fractions.

After that, another great mathematician, Leonhard Euler – who officially adopted the Greek letter “π” as a symbol to represent the value – found a more efficient equation for pi, when he was only 28. The symbol became iconic. Euler’s Pi equation calculates an infinite sum. The Basel Problem was named after him.

Euler also used pi to write another beautiful equation, Euler’s Identity.

Thanks to the Indian mathematician Ramanujan’s obsession with pi, we have many new formulas to find pi. When he arrived at Cambridge from India, he brought with him a notebook in which there were 400 pages of formulas to find pi.

After the invention of mechanical computers, mathematicians used Leibniz’s, Euler’s, and Ramanujan’s infinite series to calculate a trillion decimal digits of pi (Stanford Cryptography Group). Without a supercomputer, finding this many digits of pi would be difficult. For example, the mathematician William Shanks managed to calculate the first 707 digits of pi by hand but unfortunately, he had made a mistake after the 527th place.

Pi is everywhere

Children start learning about pi when they are in 7th grade and use it until they graduate from college. Even after that, most people use pi again when their children go to school. Pi appears everywhere in the universe. It is literally woven into our universe: the orbits of planets, electromagnetic waves, rivers, the colors of auroras, the structure of DNA, the Great Pyramid of Giza… If a scientist wants to describe the structure of the universe or find the relationship between planets, he/she definitely needs to use pi: anything involving a circle or a sphere is about pi. Circles appear throughout the natural world, whether they’re a soap bubble or the moon in the night sky.

 A Gif showing the clever play on the letters “pi”

Sinuosity of rivers

Pi has a direct relationship with rivers. But how? To figure this out, we need to measure the length of a river in two different ways. Assume that we know the starting and ending point of the river. First, we need the actual length to see how bendy the river is. In other words, the distance that you need to swim from the beginning point to the ending point. This whole length will be “L”. Second, we need to find a straight length. In other words, this time we need to fly from the beginning to the end. And this direct route will be a lowercase “l”. Now we can write the formula for the sinuosity by dividing L by l. The sinuosity is a ratio and measures how bendy the river is.

What is important here is there’s no limit to how high sinuosity can be. Rivers can be really bendy. However, Hans-Henrik Stølum proved that theaverage sinuosity of rivers around the world is pi. If you find the sinuosity of all the rivers and take the average sinuosity of them, you should get pi (Meandering River).

There is another interesting fact about sinuosity. Rivers can be very bendy at some points. But suddenly, those rivers become straight and make the sinuosity around pi. So, it is hard to find the sinuosity of a river equal to 7 because of fluid dynamics. Mathematicians found the highest sinuosity to be around 3.5 and the lowest sinuosity around 2.7.

At the extremely bendy point, rivers cut off after the bend point and make a shortcut to become straight again. This phenomenon is known as an oxbow lake, which controls the sinuosity of rivers. This keeps the sinuosity of a river around Pi.

Pi in Space

There is a mathematical order inherent in our universe. For instance, to understand our solar system, we need pi. We know that our planet moves in front of its host star. And the light comes from host stars. To talk about that light, we need to know how big the host star is. In other words, we need the surface area of the host star. The formula for the surface area of a sphere is 4πr², with r being the star’s radius. The size of a planet also helps scientists to guess whether it is habitable or not.

Another good example to show the relationship between pi and the universe is electrostatic force, which is the force between two electric charges. An electron exerts a force in all directions and forms a sphere field. Electrons also interact with each other on an electric field. To figure out that interaction, we need to find the surface area of spheres, where again pi comes up.

There is also a connection between pi and gravity. If you have had a chance to see Einstein’s field equations, you might notice that pi is there also:

The formula above calculates how objects with a large mass, such as stars and galaxies, can curve space and time with their gravity. Einstein said that, just like a ball sitting on a bedsheet, any form of momentum and energy can also curve space-time around it. In words, the formula is saying:

Gravity = 8 x π x Energy & Momentum

Lastly, if you take the square root of Earth’s gravity, you almost get pi.

Pi Day

After so many years studying pi, people decided to organize an official celebration of pi on March 14th. Since 1988, people have celebrated this magical constant. Coincidentally, Albert Einstein was born on pi day – March 14, 1879. Einstein also published his theory of general relativity on pi day.

The Google logos for Pi Day.

The year 1492 has long been a historical landmark: the Americans recently celebrated the 500th anniversary of Columbus’s ‘discovery’ of the new continent. But there was another 500th anniversary to be marked in 1992. Although this event was also of momentous importance for the history of mankind, it has attracted much less attention. The event we are referring to was the fall of the last Muslim city left in Spain: Granada. The date was the second day of 1492 when the Catholic king of Castile captured the city which had been governed for nearly eight centuries by Muslims.

The Muslim conquest of the Iberian Peninsula, which marked one of the most magnificent and glorious periods in Islamic history began with an invitation from one side of a civil war then raging in Visigothic Spain in 711. Musa Ibn Nusayr, the Umayyad governor of North Africa, was asked to help the rival of a Visigoth king. Thereupon, Nusayr ordered his general Tariq Ibn Ziyad to aid these people with an army of 7,000. In the following years he himself went to Spain. Within seven years the Muslims took control of the whole of the Peninsula, except for Galicia and Austuria. Muslim rule was accepted voluntarily by many Spaniards and over time some of them accepted Islam. The Andalusian Muslims did little to disturb the natives and allowed them to perform their religions and customs. After the dissolution of the central Umayyad government between 1009 and 1031 as a result of uprisings and a succession of weak rulers, a number of independent petty kingdoms (in Arabic mutluk al-tawaif and in Spanish taifa) became established. In spite of the fact that these little kingdoms were weaker than the former Umayyad state, an astonishing flowering of arts and learning took place during the taifa period. One reason for this outstanding development was that each ruler patronized artists, scholars and scientists to gain more prestige than the others. Eventually, the absence of a centrally organized state led to the end of Muslims’ power in the Peninsula. They lost considerable areas of territory to the Christian kingdoms that were reasserting themselves in the north. The petty kingdoms of Al-Andalus asked Yusuf Ibn Tashufin, the Almoravid (in Arabic al-Murabitun) ruler in Morocco, to intervene. They got the help they needed, but in 1090, the Almovarids left the country to its own destiny. This time the taifa kingdoms asked the Almohads (in Arabic al-Muwahhidun) for help. The Almohads willingly accepted and for a period of time they won some success in Spain. Nevertheless, in 1212 at the battle of al-Iqab they were defeated and within a few decades the Almohads were forced back across the Strait of Gibraltar. Muslim cities fell one after another until 1260, when only the kingdom of Granada remained. Granada survived for another two centuries. By the end of 1491, the armies of Ferdinand and Isabella were at the gates of the city. There remained only one final act to be played out on January 2nd, 1492 by which Muslim political sovereignty in Spain came to an end. In 1500, Spanish Muslims were presented with a terrible choice–either to convert to Catholicism or be expelled from Spain. Some did convert, others continued to practice their faith in secret and the rest chose exile.

It is a fact that the Andulusians developed a uniquely plural society whose main features were freedom, tolerance and lack of assimilation–Arabs, Christians, Jews and other immigrants lived side by side in peace for about eight centuries. Cordoba, the capital city of Al-Andalus, was the centre of a sophisticated and rich Islamic-Hispanic civilisation. In its heyday, Cordoba was famous for its intellectually advanced culture, its centres of learning and its great libraries. In those years, there were about one million people, 200,000 houses, 60 palaces, 600 mosques, 700 baths, 17 universities and 70 public libraries in the city. The biggest central library of Cordoba had 400,000 hand-written books and the catalogues which included only the names of the books consisted of 44 volumes. The famous orientalist, Dozy, stated that nearly all the people in Cordoba could read and write.

Gebert of Aurillac, the French monk, later to become Pope Sylvester II, was the first European scholar of importance to study Arabic sciences. He was also responsible for sending many teams of students into Al-Andalus during the closing years of the 10th century. By the end of that century, the various schools in Cordoba employed hundreds of students as translators and just as many copyists working closely to interpret and translate hundreds, perhaps thousands, of manuscripts from Baghdad and Cairo. Through these translations, philosophical and scientific thought from the Greek, Roman and Arab worlds, preserved and expanded upon by Muslim scholars, passed into European consciousness to fuel both the Renaissance and the Age of Enlightenment. Western Europe, in general, owes a great debt to this enormously long and rich intellectual flow from Al-Andalus.

Islamic Spain was an immensely fertile ground for learning, producing a long series of intellectual, aesthetic and scientific advances attributable to Muslim, Christian and Jewish thinkers and the ethos they created. This blossoming was due in part to the spirit of tolerance that prevailed for much of the history of Al-Andalus.

In literature, Ibn Hazm (died in 1013) expanded traditional romantic poetry with his Tawq al-Hamamah (Dove’s necklace). This form of poetry passed from Al-Andalus into North Africa. Islamic literature in Andalus, however, reached its peak during the taifa era when the poet-king of Seville, Al-Mutamid, established an academy of letters, and Ibn Darraj al-Qastalli wrote a series of qasaid (poems) of unequalled beauty.

By the end of 11th century, Al-Andalus was at the forefront of European sciences. The Andalusians excelled in astronomy, both theoretical and practical, perfecting their tables and the precision of their astronomical instruments. Toledo astronomer Al-Zargali, (d. 1087), simplified the Hellenic astrolabe; his version, known as the saphea azarchelis, remained in use until the 16th century. He also anticipated the 17th century German astronomer Johannes Kepler in suggesting that the orbits of the planets are not circular but elliptical.

In medicine, Al-Andalus produced scholars like Al-Zahrawi (d. 1013), who wrote extensively on surgery, pharmacology, medical ethics and the doctor-patient relationship. Ibn Zuhr (known in the west as Avenzoar), a century and a half later, was an advocate of clinical research and practical experimentation. The first medical school in Europe was built in Salerno by Andalusians.

Abdullah Ibn Abdulaziz was one of the best-known geographers and renowned for his great work Al-Masalik wa’l-Mamalik (Roads and Countries). Another important geographer was Al-Idrisi who was educated in Cordoba and wrote Kitab al-Rujari (Roger’s Book) under the patronage of the King of Sicily, Roger II. In this book he divided the world into seven different climatic regions and each region into ten parts. He illustrated his book with some outstanding maps remarkable (and unique) for their accuracy.

Andalusians were also very successful in mathematics, especially geometry. They used the number ‘0’ for the first time in Europe. Among the well-known philosophers who lived in Andalus were Ibn Bajja, Ibn Tufayl and Ibn Rushd all of whom influenced European thought very profoundly. Abu Bakr Ibn Umar, Abu Marwan, Ibn Fradi were particularly famous in historical studies.

Although, over the years, the lost splendour of Al-Andalus has been much idealized in the Islamic world, there remains an appreciation of the factors behind its downfall. Some of these were external, such as the unification and expansion of the Christian kingdoms of Spain and the geographic and political isolation of Al-Andalus from the rest of the Muslim world. There were also internal factors that contributed to the decline of Al-Andalus particularly the rivalries that weakened and divided Muslim Spain, the greed and self-indulgence that gripped its elites, and the loss of inner religious dynamic.

Surely every person at some time looks up at the sun and moon and the brilliant stars and asks, who positioned all these so perfectly on the face of the sky’?

People have always marvelled at the stars and planets. But they have not always realized that there is a harmony in their positions and movements, a law and order, as indeed in the whole universe. For example, seen from the perspective of the ancient Greek astronomers, celestial bodies in the universe are aimless objects. That seems to be the implication of the term ‘planet’ which means ‘wandering’. The Greeks may have thought the ‘wandering stars’ or ‘planets’ moved in unstable orbits, more or less randomly.

The ancient astronomers’ judgement was not founded upon the Oneness of the Creator Who orders everything in the universe. Inevitably they did not have a clear grasp of the orderliness of the macro-cosmos and did not seek it.

The Qur’an revealed many centuries ago that it is Allah who created the heavenly bodies and put them into their peculiar orbits. There is nothing in the Islamic teachings that argues the view that phenomena or events are random.

Do they not look at the sky above them, how We have built it and adorned , and there are no flaws in it. (50.6)

We have built above you seven strong (heavens) and placed therein a blazing lamp. (78.12)

The ‘blazing lamp’ referred to is the sun.

People have always been fascinated by the thousands of gleaming lights sprinkled across the night sky. Today many enjoy looking into the heavens and learning about the patterns and positions of the stars, and discovering what stars can tell us about our universe as a whole. From our planet, if very high buildings and city lights permit, we can see about 6,000 stars with the naked eye. They change in colour, size, and brilliance.

We are near enough to one particular star, the sun, to find out many details about what these celestial bodies are made of and how they function. A star is composed of gases and other substances compressed together under the force of gravity. The pressure at the core of a forming star is sufficiently intense to initiate nuclear reactions that begin generating energy. During this process, matter is converted into energy, releasing large quantities of heat and light.

The sun may not catch up the moon, nor may the night outstrip the day. Each one is moving smoothly in its own orbit ( 36.40). Here an essential fact is clearly stated, namely the existence of the solar and lunar orbits. At the time of the Revelation, it was generally believed that the sun orbited a motionless earth. This, the geocentric system, had held sway from the early second century (the time of Ptolemy). It continued to do so until the sixteenth century. Fourteen centuries ago, the Qur’an directed the inhabitants of the Arabian Peninsula and, through them, all of mankind, towards the truth. The demonstration of the existence and details of the solar and lunar orbits is one of the recent achievements of modern astronomy.

Those who do not believe in One Creator maintain that everything comes about by chance. They do not realize that every creature in motion, from minute particles to the planets, displays on itself the stamp of the Eternal and of His Unity. Also, by reason of its movement, each of them, in some sense, takes possession of all the places in which it travels in the name of Unity, thus including them in the property of its Owner. As for those creatures not in motion, each of them, from plants to the fixed stars, is like a seal of Unity that shows the place in which it is situated to be the letter of its Maker. That is to say, each flower and fruit is a stamp and seal of unity that demonstrates, in the name of Unity, that its habitat and native place is the letter of its Maker. What all that inter-connectednes means is that one who does not have all the stars within his command does not have command over a single small particle either.

There are two other verses in the Qur’an about the sun and the moon and their usefulness to human beings, not only as light, but also as points of reference for space and time:

Allah subjected the night and the day for you, the sun and the moon. The stars are in subjection to His Command. Verily in this are signs for people who are wise. (16.12)

Allah is the One Who made the sun a lamp and the moon a light and ordained for it mansions, so that you might know the number of years and the reckoning (of the time).

Allah created this in truth. He explains the signs in detail for people who know (10.5)

The solar system comprises the sun and the nine planets that orbit it. The closest to the sun is the planet Mercury, at an average distance of 58 million km; the farthest, Pluto, is 5,900 million km from the sun. The closer a planet is to the sun, the shorter the time taken to complete its orbit. Thus, Mercury takes only 88 earth days to go round it, while Pluto orbits the sun only once in 248 earth years. Absolute time and distance are nowadays both measured in terms of light speed–a metre, for example, can be defined as the distance the light travels in a certain ‘space’ of time, in fact, 0.000000003335640952 seconds.

It is hard to think of the sun as a passing event. Nevertheless, its ‘term’ is fixed–the Qur’an is explicit on this point: And the sun runs its course for a period fixed for it (36.38). So, how long has the sun left to run? Astronomers nowadays calculate about 4.5 billion more years in its present state. It will still have nearly the same surface temperature (6.000 °C) and yellowish colour that it has now but it will appear about twice as bright because it will be about 60 percent bigger. Its next 4.5 billion years will have begun to take their toll on the sun’s nuclear fuel supply. What then? We don’t really know. Any calculations we make can only be made on the basis of theory.

The sun is full of gases composed of two thousand trillion tons (2×103 kg) of matter,

with the remains of other elements. For every million atoms of hydrogen there are about 85,000 helium atoms and only about 1,000 of any other kind. Pressure from all that mass compressing into the centre of the sun is high enough for the hydrogen atoms to fuse in the core to form helium. This simultaneously creates new energy which keeps the sun from collapsing further and provides the energy that allows it to (or makes it) shine. A series of nuclear fusion reactions, whose end result is the conversion of hydrogen to helium, happen on a vast scale and release very great amounts of energy in the form of heat, light, X-rays and so on. A part of this reaction must be the release of so-called neutrinos. Neutrinos are particles that interact so little with other matter that they can probably float through entire galaxies without being affected. They exist but have no mass nor any other physical property, which is like saying that they simultaneously exist and do not exist: we know they must be around by the way the movement of other (‘real’) particles is affected. If the theory about the way that the sun shines is correct, the sun should be producing about 180×1036 neutrinos each second. Obviously, only a small portion of these neutrinos will come in the earth’s direction.

The sun generates magnetic fields deep in its interior. Through mechanisms not yet fully understood, some of these fields erupt periodically through the sun’s surface, the photosphere. The high temperature and structure of the corona are produced by energy pumped from the photosphere up into the outer layer of the sun’s atmosphere along these magnetic fields.

The sun has been fusing hydrogen into helium throughout its present lifetime of 4.5 billion years, using up less than half of the available hydrogen in its core. By another 4.5 billion years, 90 percent of the available hydrogen in the core will have been converted into helium. Serious questions about the fusion rate in the sun still remain, but according to one theory, the humans of the future will face a sun that is running out of core hydrogen.

When that happens, the gas temperature and pressure will drop and the interior of the sun will collapse under the weight of the surrounding mass. The pressure in the collapsing gas will build up sufficiently for a rind of hydrogen to start burning around the core, now helium. This fusion will provide an outward force on the outermost layers of the sun, pushing them farther out than they are now. The surface of the sun will expand outward until it reaches the orbit of Venus.

Finally, this hydrogen outside the core will run out. The core of the sun will continue to contract, trying to replace the heat no longer generated by hydrogen burning. When the internal temperatures reach 100 million Kelvins, the helium (generated by the hydrogen burning) will itself start to burn. This will happen quickly, forming a carbon-rich core. Around this burned-out core, helium burning will start, and then the rind of hydrogen also will start to burn. The vast energy released by both rinds will push the sun’s outer layers further out until they reach the orbit of Jupiter. Earth will then be ‘inside’ the sun. The temperature on the surface of earth, around 6.5 billion years from now, will be around 30,000 Kelvins, and everything organic will be burned to a crisp.

Intelligent beings on earth 5 or 6 billion years from now, if any, would face the pressure to leave earth and, indeed, the solar system. They would need to have colonized planets around younger (therefore more stable) stars in order to survive. It is likely that humans in the near future will move off the earth in search of mineralogical and economic gain, whereas the future beings of our speculation will move off in order to save the species. The ageing sun will give future life a focus and a goal. And then, if we may be permitted to use the expression, a sort of Doomsday will have happened: certainly, the sun will have run to the end of its appointed (muslaqarr) time.

SOURCES

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• Astronomy January 1992: March 1993.
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• NURSI, S. (1987) The Thirty-Second Word from the Risale-Nur Collection.
• NURBAKI, H. (1989) Verses from the Glorious Qur’an and the Facts of Science T.D.V.. Ankara

The Ottoman treasury had a surplus of revenue coming in from the booty of wars, as well as from taxes collected from Muslims and non-Muslims. This revenue was disbursed in expenditure on large and extensive public works on local amenities such as inns, hospitals, schools and places of worship, and on infrastructural projects such as bridges, roads, canals, and so on, in the conquered territories. The Ottomans aim was not to expropriate the wealth of these lands in the form of raw materials or slave labour, as the Western powers did in the lands they conquered. Rather, their aim was to spread Islam and thereby spread civilization and justice. There are a considerable number of historical buildings, bridges, inns, schools, etc., in Europe, Asia and Africa, which date from this period, some of them still in use even now. Thus, the milieu in which Sinan was born and grew to manhood was conducive to the discovery and development of his extraordinary genius. Today the works of Sinan the Architect can be found, and are admired, on three continents. The son of one Abdulmennan Efendi, Sinan was born in a small village called Agirnas in Kayseri in 1490, where he spent his childhood. In 1512 he was selected and brought to Istanbul as a recruit to the Janissary division. His life changed completely as a result of this move, new horizons opened up before him. He took part with the army in the Chaldiran campaign in 1514. Two years later, he again campaigned with the Ottoman army in Egypt under the leadership of Yavuz Sultan Selim during the years 1516-1520. During these campaigns, he saw and studied the arts of Anatolia, Persia and Egypt. In 1520 he joined the service of Sultan Suleiman the Magnificent and began his university education the same year. He served as a zemberekcibasi in the battles of Rhodes, Belgrade and Mohac. Here too his mind was busy, now picking up the styles and techniques peculiar to Western architecture. He went even to Baghdad and Persia during the campaigns there, in 1529 and 1536 respectively.

In that last campaign the army had to take Van Castle situated on the shore of Van Lake, the biggest in Turkey. Sinan was commissioned to design and build three galleys which the Army needed in order to conquer the Castle. He completed this task so successfully that he was given command of the galleys. On his return to Istanbul, he became the haseki or personal bodyguard of the Sultan. In 1537, he prepared the navy for a jihad to Italy. After two years, he was appointed super-intendent of police.

As the reader will have gathered, already at the age of 49, Sinan had yet to embark upon the career that was to make him world-famous. The duties given to Sinan so far had nothing directly to do with architecture. However, when in 1539 he was put in charge of the Ministry of Public Works his life and work changed dramatically. From 1539 until he passed away, he worked continuously constructing a seemingly endless series of the most remarkable and magnificent monuments from Bosnia to Makka.

Beginning in the West, according to historical documents, Sinan organized and supervised the construction of some public building on behalf of Sokullu Mehmet Pasha in Bosnia. The most important work of Sinan’s, in what is now misnamed Yugoslavia, is the 180-metre long Sokullu Mehmet Pasha Bridge on the Drina river. In Greece too there is a Sinan-designed mosque, built for Osman Pasha. In Budin, the capital city of Hungary at the time, Sinan built another mosque, this one financed by Sokullu Mustafa Pasha.

In the Eastern part of the Empire, there is a mosque and tekke (lodge) named the Qanuni Sultan Suleiman Mosque in Syria which was built by Sinan. The second of his major works was the Husrev Pasha Mosque in Halep. We can see another of his mosques in the Crimea built on behalf of Devlet Giray Khan I of Crimea. In Makka, the House of Allah was enlarged by Sinan: first of all the pillars were put in place and later minarets. In the city centre, there were a number of buildings, including Turkish baths and a university, attributed to Sinan. However, today, none of these have been conserved because of misguided Saudi hostility towards their Ottoman heritage.

Naturally, Sinan paid special attention to Istanbul as the Imperial capital. He solved its drinking water and transportation problems, as well as designing the city’s sewage system. He constructed roads and bridges; he established its navy and navy buildings; he also restored or renovated castles; he built public watertraps, dykes and waterways; and he built inns, schools, hospitals, dormitories, and so on. He restored the Aya Sophia Mosque and deserved, in every respect that his name be inscribed on the golden pages of Ottoman history and Islamic civilization. It was by his help that Constantinople, the centre of the Eastern Roman Empire, was converted into a great Islamic city, Istanbul, and the capital and centre of Islam.

Three of his monumental works are generally accepted as representing the three stages of his work. The first, the Shehzadbasi Mosque, is referred to as his apprentice work. The second, the splendid Suleymaniye Mosque is described as his master-craftsman work. Finally the Selimiye Mosque is said to be Sinan’s supreme masterpiece, the most sublime of his extraordinary achievements.

Among the fascinating innovative features of these mosques are, in the Suleymaniye mosque, 64 large earthenware jars, 50cm in length placed upside-down, which function superbly as resonating chambers for the recitation of the imam. There is also a small chamber just above the main entrance which accumulates the soot emanating from the huge candles and oil filters. The soot is carried through by means of a very soft breeze circulating inside the mosque. The black powder collected in the chamber was the best raw material available at the time to make the fine inks used during the Ottoman Empire. The mosque is situated in a compound of 700,000 square metres, housing, as well as the mosque itself, four schools, a faculty of medicine, a library, an inn, a primary school, private premises for those studying the sciences of hadith and kalam, a big bazaar and, finally accommodation facilities for the staff. The construction took seven years during which 164 account books were kept to certify where each of the 996,300 gold coins allocated to the whole project were spent.

As for the Selimiye mosque, the great man himself judged it to be his masterpiece and believed that with the construction of this mosque, Islamic sacred architecture gained an unequivocal victory over Christian sacred architecture. He himself wrote of the Selimiye:’I concentrated the whole of my powers on the Selimiye mosque. I meant to put on show the whole of my talent [so that] even if all architects and construction engineers were to come together and do their best, they would not be able to build such a masterpiece of art.’ The two minarets of the mosque are utterly stunning: although there are three winding stairways leading to each landing (sherefe), a person climbing up to any of the landings cannot, from any point during his ascent, see anyone else climbing the other. The stairways are so delicately twisted that mathematicians with very powerful modern computers have difficulty calculating the linear formulas needed. The subtlety of Sinan’s use of colour to match and vary the lines of the stairways will be clear from the photograph.

Sinan built the dome of such awesome dimensions deliberately to exceed those of the Aya Sophia: it is roughly 5 metres higher and 3.5 metres deeper. The simple reason for this rivalry was that some arrogant architects among the Christians had claimed that a dome could not be raised in the Islamic world as large as the one they had put up in the Aya Sophia. They were proud of what they had achieved to the point of claiming that such a dome would be virtually impossible to build again. In the end, Sinan more than matched what had been achieved before him: he exceeded it by a substantial margin in both engineering and artistic terms: The radius of the dome of the Selimiye mosque is 31.5 metres, while its weight is 2,000 tons.

By the time the Selimiye was completed, 400 master craftsmen and 14,000 workers had laboured on it day and night for seven years. In all, 28,000 purses of gold were spent on the project. The famous German architect and historian Professor Ernst Dier said of it: ‘…the Selimiye is above all architectural monuments in the world from the point of view of size, height, unity and brightness.’ Another European commentator expressed his admiration in these words: ‘This is not a man-made building rather it is a place for divine worship descended from heaven.’

Frank Lloyd Wright, one of the best-known architects of our time wrote in his book: ‘Two architects have come on earth. The first one is the Ottoman architect Sinan and the other one is myself. Sinan was a contemporary of both Italian Michelangelo and British Christopher Wren. While the cracks on the dome.., built by Michelangelo are being repaired by iron hoops by the blacksmiths of Rome. Sinan’s temples will stand until Doomsday.’

Sinan served four Sultans and was profoundly admired and appreciated by all of them. He had 77 properties, 40 of which were shops, inns, Turkish baths. Before he died, he established and funded a waqf (charity trust) and specified in his will that the house he resided in be made into a school, with six akche a day (old currency) to be allocated for the teachers of that school, and that orphans and widows be given clothes, and wood and coal for heating. Only a small percentage of the income of the trust was given to his family in accordance with the will. He also wished that one-thirtieth of the Qur’an be recited for his soul’s sake and one akche be given for this. As we learn from the biographies written of him, he was a very generous man. Every day and evening, some twenty to thirty people used to come and eat at his expense.

We should also record that he gave away not only his personal wealth for charitable purposes for the benefit of his fellow-men, he also passed on all his knowledge to hundreds of architects and thousands of master-craftsmen.