The Example of the First Circle around the Prophet and Those Who Followed Them

So much so a source of blessings was the Prophet Muhammad, according to the Islamic tradition, that he always had followers who embodied the same spirit and devotion. Those who had the opportunity to be close to the Prophet and witness his person with their eyes and hearts lived in a constant state of rapture with this delight. They walked in his footsteps with the excitement of being imbued with that state, and they always made sure this path that led to him was filled with travelers. Hundreds of thousands have taken wing towards him, their eyes always eagerly fixed on this first “Circle” around the Prophet, and their hearts willing to behold what lies beyond. Watchful for the furthest horizons, they have taught the manners of this journey to those who staggered on their way.

For those who are on this path, faith in God (iman) is a lively source of excitement in hearts. Knowledge (marifa) and love of God (muhabba) are as a sparkling torch in feelings and thoughts. Their eagerness to meet the real owner of everything sheds light on their way as a projector that brightens up the roads extending to eternity. They have walked without falter to the beyond with eagerness for reunion with God (liqa‘ullah), which is a never-fading source of energy in feelings and thoughts; their hearts always beating with the excitement of beholding the very horizons of those in the Circle. They ran in the direction of this Circle without fatigue, but with an insightful perspective of what they saw, with a resolution for journeying in the realms beyond the horizons by means of their mechanism of conscience, their hearts permeated with the awe of this state and the entirety of their physical and spiritual anatomy in full resonance.

Their faith and spiritual knowledge are of the deepest kind. They are thoroughly equipped in both material and spiritual senses, and they entirely leave behind worldliness and materialism. They disregard dirty urges of the carnal soul and its temptations. Though they soar in heavenly realms, their hearts still keep quivering in fear. They keep groaning as if they were the sinful ones in this world. They question themselves with the deepest concerns day and night, and they always have considerations as expressed in:

If the All-Merciful One weighs my sins as they are,
I fear the scales on the Day of Judgment will break.

They keep sighing night and day out of fear, as if they have committed some wrongdoing despite their already glorious spiritual rank. Humility is at the core of their existence. They feel disgusted by receiving appreciation and applause. They hate glory, prestige, and pomp. They always behave as an ordinary person among other people. Acknowledging that all goodness, achievements, and extraordinary qualities come from their Creator, bowing is no more enough for them to show their gratitude, they go down to prostration in reverence.

I am a slave who is not worth all this grace,
I wonder why I am favored so bountifully. (M. Lutfi)

With these feelings, they continue to be relentless in their self-criticism, and are immersed in expressions of humility and self-effacement. They adopt the following important principle of the Qur’an as a part of their character: “(O human being!) Whatever good happens to you, it is from God; and whatever evil befalls you, it is from yourself” (4:79). They do not forget their single mistake or lapse which weighs so heavily on their shoulders, even after many, many years. They forget or disregard the good things that they made or accomplished which may have helped thousands of people. Even if the thought of crediting themselves for a dazzling accomplishment or triumph crosses their minds, they dismiss such thoughts and acknowledge all success to be from God as a grace for people’s collective work and solidarity. These are the character traits of the devoted souls walking on the path of the All-Truthful One, and such is the constant state of monumental personages whose hearts are completely oriented with the ones in the Circle, seeking God’s approval.

Now, with broken statements of mine, I wish to narrate examples of facing oneself from some loyal servants of God, whose eyes and hearts were with the members of the Circle. My words can only represent a few drops from their immense ocean.

As one of the radiant fruits of the blessed tree of the Prophet’s family, Imam Zayn al-Abidin (659-713) was a prominent person of sublime virtues. His father was Husayn (the Prophet’s grandson), his grandmother was Fatima (the Prophet’s daughter), and his grandfather was Ali, the prince of the chivalrous, and his great grandfather was the noble Prophet, peace be upon him. Zayn al-Abidin was a fortunate person who opened his eyes to the world in such a bright ethos and flourished with heavenly water of life, had his heart and spirit always set on God so much so that his path never ever crossed sins even in his dreams. Wherever he turned his eyes, he was enraptured by a view of the Circle. He kept soaring high towards that source of blessed inspiration with a desire and eagerness of reunion with his noble family.

He was always permeated with such feelings and thoughts; he always desired and aimed to be on that blessed course. Yet, he always committed himself to the Divine, assigned no worth to himself, and constantly engaged in self-effacement, a state of being which Seyyid Nigari describes in his own way as follows:

Can one who seeks the Beloved care about his own soul?
Can one seeking to live be concerned for the Beloved?

And thus Zayn al-Abidin kept seeking God and completely closed his eyes to all else, because he was in a state of constant exposure to the Circle, with the sight of both his eyes and heart. His heart would beat with the excitement of being under the same light with them, and he would live with a zest for servanthood to God. Among his prayers constantly offered are the following supplications, which I do my best to convey here, but do so by focusing more on the meaning rather than the exact wording; I do not constrain myself to vocabulary limitations. Instead of rendering all of his supplications here in full, what follow are his heartbreaking cries which I occasionally interpolate with short phrases to offer my personal take on some of his words, so hoping that his inner groans are better internalized first by myself and others like me:

“My God! The wrongs and sins I have been committing have put a mantle of abasement on my soul. By remaining apart from You (O Imam, have your ever been apart? FG) I have found myself in a state of poverty. The gigantic wrongs that I have committed (no way, a hundred thousand times no! FG) have darkened my heart. I seek refuge in You, God Almighty, my only Besought and Beloved! Please accept me as I turn to Your door with serious repentance, and bless me with a fresh revival as if I have been revived after death (if you are not alive, then how should those unfortunate “walking dead” like myself wail? FG). I swear I never knew anyone but You (O God), and in spite of everything, here I submissively expect to be forgiven in Your presence. If you expel this slave of Yours, which door can I ever turn to and with whom can I ever seek refuge? If I am expelled from that door, I will utterly be in a pitiable and shameful condition!”

O dear Imam Abidin, we have studied you and others like you in the literature of the Prophet’s life, and have come to recognize you with your humble face turned down and with your heartfelt supplications. If the cause of your wailing is the temporary fog that occasionally seeps into your imagination during dreams, if this is the factor that triggers your groans, how fortunate you are. And how pitiable are unfortunate ones of our time such as myself who live their entire lives in that fog and smoke, and the so-called theologians who assume themselves to be religious!

Zayn al-Abidin does not suffice with his above prayers. Below he opens another page in his compositions of wails:

“O the Exalted Lord who even forgives the greatest sins and embraces stricken hearts with compassion! I wish and beg You to pardon my disgracing sins and hide away my shameful wrongs and forgive this slave of Yours, in the warm atmosphere of Your forgiveness, along with those whom You saved with Your clemency and mercy.”

I wish it could be possible to find at least a hundredth of these wailings in the spiritual world of those who spend their life in places of worship, who put on airs in Sufi lodges, who waste their lives in nests of heedlessness appearing to be religious schools, and those so-called believers whose faith does not pass beyond imitation and who spend their lives in self-glorification saying “I did this, I did that.”

Zayn al-Abidin continues to open up to God, his yearnings now reaching a peak:

“If repentance and penitence are titles for a heartfelt remorse, so I swear I repent a thousand times for all I committed! If asking forgiveness from You is a means of being absolved from sins, so I cry with truly heartfelt remorse and wish You to forgive this poor servant of Yours!”

With my full respect to him, I skip some of his expressions of sigh and wailing and jump to the following one:

“O God! You are the One who has opened wide the gates of sincere repentance for Your servants and informed us with this glad tidings. You decree “O you who believe! Turn to God in sincere and reforming repentance” (Qur’an 66:8) and thus summon us to the chamber of Your oneness. Those who turn to this door You have opened will hopefully find what they expect, as a result of Your grace. Sins and wrongs certainly are not becoming for servants, but there is no doubt that You are so magnanimous at forgiveness and clemency.

Let us add the following to that:

Bestow on us, O my Sovereign, do not deprive the poor of your bestowals
Is it becoming for the Munificent Bestower to stop bestowing on His slaves? (M. Lutfi)

Yearning souls always presented their petition with this gist of imploring. If it will not be disrespect against the Almighty, I also share these considerations.

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.

December 2, 2015. A mass shooting in San Bernardino, California, following a devastating attack in Paris, France. Anti-Muslim rhetoric mushrooms, but how can I, one person, respond?

December 6, 2015. A hastily arranged interfaith service at Temple Beth Or, Washington Township, New Jersey, is attended by an overflow crowd of almost 400 people. The clergy, representing 18 congregations of the three Abrahamic faiths, walk to their seats as the Woodie Guthrie song, “This Land Is Your Land” is sung. The service gets underway with a call to prayer by a member of the Elzahara Islamic Center of Midland Park, New Jersey, and continues with additional prayers from each of the clergy. One priest from a Catholic Church in Ridgewood, New Jersey, ascends to the podium and asks everyone to take 15 minutes, introduce themselves to someone they don’t know, and “Pass the Peace.” This 15-minute interval turns into a seminal moment for me as “the other” that surrounds me becomes “the individual” – the mother, the student, the neighbor, each concerned about the same issues as I am.

This evening had a profound impact on me, and I still think of it often. It spurred me to approach my Jewish synagogue community and invite them to engage in an outreach program with representatives of the Muslim community. I had no illusions that this would solve the world’s problems, but I hoped it might be a spark to lift a veil in my tiny little corner of New Jersey. And thus began an ongoing journey to take the hand of our Muslim neighbors and turn the unknown and the different into the familiar and the friendly.

Over the ensuing years we have gathered together for various programs. We started with a Friendship Circle to introduce ourselves to one another, watched a documentary movie, BESA – The Promise, and subsequently The Turkish Passport, and discussed what we saw and heard. We invited our Muslim friends to participate in some of our synagogue services, some interfaith and some not. During one Sunday morning Minyan service, two central Jewish life cycle events took place – a baby naming for a newborn girl, and a 13-year-old leading the service one week before his Bar Mitzvah. Questions were casually asked and answered over our bagel breakfast (accompanied by both rugalach and baklava!). This turned into a tour of our sanctuary, led by our Rabbi and accompanied by a number of congregants. The Rabbi took the Torah scroll from the ark so it could be seen up close by everyone. She opened it and chanted that week’s Torah portion, which just happened to be about Hagar and Ishmael! The Rabbi along with our members explained the meaning of the various symbols around the sanctuary – how our prayer books are in both Hebrew and English, what the threads and knots (tzizit) of our prayer shawls represent, why only some of our memorial board lights were lit, etc. The otherness melted away as we engaged one another in vibrant conversation and dialogue.

One of the most moving interactions we experienced was when one of our members, a child survivor of Auschwitz and a longtime Hebrew school teacher, told her emotional story to a Muslim teen group, which left everyone with tears in their eyes. This included a question and answer session that touched everyone who participated. Our membership was invited to an Iftar dinner that year, during which we came to understand the purpose and meaning of the daytime fasting. We were recently invited to visit a local mosque, which was the first time any of us had stepped inside one. We had so many questions, and they were answered beautifully and passionately. We all sat, shoeless, in a circle, and those of us who are Jewish nodded our heads as the number of parallels between our faith practices became apparent. During Ramadan this year, our synagogue hosted an Iftar dinner. Kosher food was graciously brought into our kitchen, and three very dedicated Muslim volunteers spent several hours preparing traditional recipes for our dinner as we chatted and enjoyed each other’s company.

One by one by one, foundational connections have been made between our Jewish congregants and our Muslims friends. We have learned so much about one another: we have talked about our families, showed each other pictures of our children’s weddings, shared our families’ immigration experiences, exchanged phone numbers, and promised to see each other again soon.

The world is a complicated place, and there are no easy answers to the issues that confront us. But we each have the power to step outside our comfort zone, and just decide to take that first leap of faith. The opportunities to engage with one another in a meaningful way are all around us, and the rewards far outweigh the effort. Not only do we reap the benefits ourselves, but we have the potential opportunity to “pay it forward” by sharing our stories of these meaningful and memorable interactions, and maybe, just maybe, inspiring someone else to do the same!

As Jews, one of our overriding objectives is to participate in what is called “Tikkun Olam – Repairing the World.” This implies that while the world is inherently good, there is always room for us to improve it, and I would like to believe that I have contributed, in whatever small way, towards that end. In a world that undoubtedly is in need of a great deal of repair, please join in by taking that first small step alongside me and let us walk together.

“It is He who created the night and the day, and the sun and the moon; all (the celestial bodies) swim along, each in its orbit with its own motion.”  (Quran 21:33)

Almost everyone – depending on his or her age, experience, and education level – is aware of certain facts about nature. We know that the Sun rises in the east and sets in the west; water boils at 100 centigrade; humans have five basic senses; birds can find their way back after migrating thousands of miles; and many more. Likewise, laws of thermodynamics, laws of motion, universal law of gravitation, and laws of planetary motion are among the many tools scientists use to explain how nature and the universe work. In the same context, whether or not we are conscious of it, there is this ubiquitous fact of “revolving, rotating, and circling” in the universe in relation to science, religion, and culture. From the Milky Way, sun, planets, and moons to human eyes, circling is everywhere in the universe. Also, it’s imprinted everywhere in the natural world. Giving examples from scientific, spiritual, and social life, this article aims to inquire the “revolving, rotating, and circling” phenomenon to see if it has any implications for humanity.

Rotation of planets

Earth is one of the eight planets in our solar system, all of which orbit the sun, a giant burning star. We know from astronomy that the sun can fit more than one million Earths inside it. Throughout human history, stargazers have realized that all these planets move in a systematic way. The planets orbit due to the immense gravitational pull generated by the sun. Even though the rate may change, each planet rotates around the sun and on its own axis, an imaginary line running through the center of every planet. Also, there are more than one hundred terrestrial, gas, and dwarf moons that revolve around the planets. Every planet, except Mercury and Venus has at least one moon. For example, the Earth has only one Moon (Luna) which orbits around Earth every 29 days; on the other hand, Jupiter has at least 67 moons such as Ganymede, Callisto, and Europa in orbit around it. In addition, our solar system is swarming with different types of bodies (e.g. comets, meteors, asteroids, and space dust) that rotate around the sun along with Earth. Furthermore, it is believed that the Sun is one of about 200 billion stars (maybe more) just in our galaxy, the Milky Way. Galaxies move and gravitationally pull each other, and they do so while rotating around a center. That is, nothing is truly at rest. (1)

Orbiting an atom

In the 1920s, scientists of quantum mechanics discovered that an atom acts like a small solar system. While planets circle elliptically around the sun, electrons rotate around the atom’s nucleus in diffuse, cloud-like waves; these are known as orbitals since they tell us only the probability of detecting the electron at various places within the atom (Choe 2004). These orbitals can blend together to constitute a clump-like “wave packet” that includes the electrons and does rotate around the nucleus. It looks like this quantum phenomenon seems to support rotation in the universe. (2)

The circulation of blood

Doubtless, the heart is one of the most vital and fascinating organs in the human body. It incessantly pumps fresh blood with necessary nutrients throughout the body so that we can survive. Even though it is as big as your fist, it works like a powerhouse by expanding and contracting 100,000 times each day, pumping approximately five quarts of blood per minute, around 2,000 gallons every day. While the heart beats, it pumps blood through blood vessels in the circulatory system to every area of the human body, which takes about 20 seconds to circulate all over the vascular system. It is reported that the blood travels approximately 12,000 miles per day – nearly half the distance of the Equator (24,902 miles). Blood circulation is vital and fundamental to human life: it not only transfers fresh oxygen and nutrients to organs, but also carries away waste such as carbon dioxide from the organs, which is necessary to maintain a healthy life. (3, 4)

Five stages in the human life cycle

Similar to the cycle of four seasons (spring, summer, fall, and winter) in a year, the human life cycle has five or six different stages (Birth, infancy, childhood, adolescence, and adulthood). Human life begins as a single tiny cell, not bigger than a mustard seed, in a mother’s womb. After nine months, circa 40 weeks of pregnancy, the mother gives birth to a newborn. During the first year of infancy, the baby is entirely dependent on the parents’ care, but babies develop very quickly to independency. Childhood includes a period from age 4 to 13, when children learn to eat with utensils, dress and undress without assistance, make friends, play with other kids, and other things. Adolescence is the when a child develops into an adult, when teenagers undergo a rapid transformation of their bodies known as puberty. After the age 20, the human body reaches peak fitness and fertility by stopping development and growth. As we age in adulthood, it takes our body a longer time to repair itself and we become less efficient in many skills. (5)

Circling and prayer

It looks like that this one important pillar of Islam reminds us of the spinning motion in the universe, atoms, the circulatory system, and the life cycle. According to Islamic scholars, millions of pilgrims circulating the Holy Ka’ba in Mecca represents the deep reverence in Oneness of Almighty God. It is believed that these seven compulsory circumambulations of the Ka’ba (the most sacred site in Islam) include individual and social meanings like solidarity and maintaining unity. One explanation as to why Muslims circle the Holy Ka’ba seven times, is the Qur’anic verse that describes the sky above as of seven layers:

“The seven heavens and the earth and whatever is in them exalt Him. And there is not a thing except that it exalts [God] by His praise, but you do not understand their [way of] exalting. Indeed, He is ever Forbearing and Forgiving” (Al-Isra17:44).

It is known in Islam that the spiritual part of the human being includes seven different souls known as nafs. Therefore, every circumambulation of the Holy Ka’ba is meant to move from one spiritual level to the next in order to reach and complete the final expectation to turn our self (nafs) from meat and bone into a more delicate, sensitive, and loving form of soul, one even superior to the Angels. This act of circling the House of God, the Holy Ka’ba, shows how man is sincerely, spiritually, and lovingly attached to the divine.

Conclusion

The planets circle the sun, electrons circle the nucleus in an atom, blood circles the human body, pilgrims circumambulate Holy Ka’ba, and seasons and life cycles circle. There are many more examples of circling in the universe. Even though we cannot see all of them with the naked eye, the entire cosmos, ranging from invisible particles to the moons, planets, stars, and galaxies, are in rotation. Remember that all these rotations happen in accordance with the laws that govern the nature. There is no free choice in any of it.

People are members of this infinite universe, and, unlike planets, electrons, flowers, and cells, they can reason and decide, since we are blessed with free will. As Muslims circumambulate the House of God, this pulling motion between the Ka’ba and pilgrims escalates divine love by changing spiritual dimensions in a way similar to moths flying and circling a light source. Without doubt, a visit to the House of God is an obligatory and praised pillar of Islam, but I believe that the Merciful God wants us also to circle many other divine values and social qualities to deserve His love, mercy, and grace. As long as we circumambulate these highly valued vital qualities such as prayer, selflessness, charity, affection, forgiveness, respect, love, truth, compassion, modesty, patience, and all other good qualities, they will pull us closer both to each other and to Almighty God. Ignoring circling these divine and social qualities would be as if Earth left its orbit.

References

• https://spaceplace.nasa.gov/review/dr-marc-space/solar-systems-in-galaxy.html
• “A Tiny Solar System After All,” April 7, 2004. Rev. Focus13, 15. https://physics.aps.org/story/v13/st15
• “Amazing Heart Facts” in Arkansas Heart Hospital. https://www.arheart.com/heart-health/amazing-heart-facts/
• Jody Braverman, “The Human Life Cycle Stages” www.livestrong.com
• “Growing Older,” in Dorling Kindersley, findout!

The heart is the home of God, clean it of others than Him,
So that the All-Merciful may descend into His home at night.

The couplet above, recorded by Ibrahim Haqqi of Erzurum in his Ma’rifetname (Book of Knowledge), expresses the intention of obtaining true love and His pleasure, and tells how to realize it. It concisely describes the way between decision and resolution and from resolution to destination. The only way to obtain peace of mind and be at rest without going to extremes and being exposed to spiritual trouble and pain is to seek the love and pleasure of God, and then order one’s life around this aim. Rumi says:

A heart devoid of the Friend and seeking Him cannot be freed from trouble and pain. [As for] a head in which there is no love of the Friend, do not attempt to find any meaning and value in it, for it consists of bones and skin.

Those who have set their hearts on Him and have decided to reach Him never neglect to follow a way toward Him and to meet the necessities of traveling on it. [1] Even if they turn their eyes from Him for a single moment to look to others, they sigh for a whole lifetime. How unfortunate is the one who lives unaware of a way leading to Him. What a great loss, impossible to compensate, it is to fall and get stuck on the way after taking it.

Decision first appears and develops in the heart, grows firmer and stronger as a feeling, and then becomes a very powerful drive directing one toward his or her destination. In this context, decision signifies an intention and resembles a seed sown in the heart’s soil. If the one who has this intention or seed in his or her heart receives help from God Almighty, the seed germinates and grows into an elaborate, fruitful tree. After a few steps traveled in decision, one finds resolution, which is defined as being determined to do something, steadfast in one’s pursuit, and consciously fulfilling all responsibilities undertaken. Resolution is the first step toward the “heavens” of reliance and surrender. The Qur’an describes this step and the final point to be reached: When you are resolved, rely on (or put your trust in) God (3:159). If this first step can be taken through reliance on and submission to God, then the road becomes level and easy to walk on, and one travels it as if flying through the air.

Decision and resolution are two important dimensions or functions of willpower. Every traveler who intends to make a long journey must stop at the station of decision and resolution to receive the permit or visa, given by God, in order to progress to higher stations. Only after this does the journey truly begin. One who has taken the wings of decision and resolution feels attracted toward the goal and, no longer advancing by his or her own power, is taken to it. A friend of God says: Whoever overflows with the desire to meet with God, despite his inability to fulfill the requirements of the way leading to his goal, God Himself comes to him. God then becomes his or her eyes with which to see, ears with which to hear, and tongue with which to speak.

For the traveler who flies along on the wings of decision and resolution, meeting with God means finding subsistence in or through annihilation. For those with whom God wills and desires to meet, it means subsistence within subsistence, [2] and they suffer no trouble or pain in the “virtuous circle,” [3] where they encounter good after good. In this circle pain changes into pleasure, and wrath or chastisement are manifested as favors. One who has reached this point always utters in pleasure: Whatever comes from You, whether it be a favor or punishment, is good. With a cup of resignation in one’s hand, he or she sips whatever comes from God, the Truth, as if it were the water of Paradise.

Notes

1. There is more than one way to God. It is said that there are as many ways or paths to God as there are breaths of people. Such a statement is said to express the differences in people’s temperaments and moods. In addition, spiritual orders use different rituals to help their initiates make progress on the spiritual path.
2. This phrase denotes the concept of compound subsistence, defined as a “firmer subsistence” and as “being well-versed or grounded in subsistence.”
3. This is the opposite of the “vicious circle” that so many people encounter in their daily lives.

It was 3 o’clock in the morning. The rain outside beat on the windows and the loud thunder ripped through the night. A loud knock on the door startled the boy. All alone in the mansion, he was not really expecting anyone this late. But the stranger insistently knocked on the door. The boy got up hesitantly and grabbed the doorknob with shaking hands… Flash forward. He woke up with a scream, drenched in a pool of sweat. “Thank God, it was all a dream.”

I turned off the TV, feeling a mix of boredom and hunger gnawing hunger at the pit of my stomach. I headed down to the kitchen to grab a bite.

The world is full of wonders. We are amazed at how fish swim or how birds fly; by imitating their systems, we attempt to swim or fly. One of our most precious attributes is curiosity. Once I attended an exhibition associated with a popular movie. I was amazed at the power of human imagination and the dreams it can conjure, turning them into reality. The props and costumes used in this movie were displayed lavishly for the curious eyes of the fans and the flash of the cameras. We, as human beings, were being entertained with the products of the human imagination. Even the flow of events that happened at the exhibition, the flashing cameras, the décor and costumes, which seemed so important at that time, were all a design of the human imagination; they were not real. As the actors and actresses took on the personalities of their characters, they not only assumed the role of a movie character, but also became a player in a man-made dream world. We followed the entertainment with curiosity and interest. The characters, the story, the costumes, the light, and sound: all this captivated our attention. As the glow of the entertainment slowly faded off, I began to feel that this popular movie and even the exhibition itself existed within another movie… a more real movie in which we all played our roles.

My favorite pieces in the exhibition were the “magically alive” animated portraits. I couldn’t help but smile when I saw the people in the portraits applauding us, as if we had accomplished some feat. I liked the idea of animated portraits and photos. A picture is ultimately just a 2D image, but an animated image encompasses a third dimension: time. A movie’s ability to capture the charm of time is what appeals to us and captivates our attention.

Early in the morning, I glanced out my window and noticed the autumn leaves falling from the tree in my back yard. About two or three weeks ago they were all green, but now the scene had completely changed. Tinted with different shades of orange, yellow, red and purple, the leaves ruffled on their branches with the whoosh of the light breeze.

I imagined that my window was an animated picture inside my home. There was someone insistently striking His brush against my easel, coloring this picture day by day, moment by moment, and giving it motion for me, making me feel the changes He brought about. Filled with these wondrous thoughts, words fell out of my mouth: “He is truly a magnificent artist.” At the moment, I recalled what the lead character in a movie had said as he looked, bewildered at the harmony of colors in the sky during sunset: “God must have been an artist.”

In order to make an animated picture or create a video sequence, the consecutive pictures or “frames” of a scene must be joined together. If the difference between the capture times of two consecutive frames is too long, the video will not run smoothly, stuttering like an old silent film, with intermittent flickers. Modern day movies use a larger number of frames per unit of time. The greater the number of frames, the smoother the images will appear. When I focused my attention on this outside “movie,” a movie in which I was an actress along with the rest of humanity, I couldn’t help but wonder what the number of frames was. Since we are living in a “perfect” movie, the movie of our world that we see through our eyes everyday must have an infinite number of frames. I contently followed the descent of a snowflake onto my hand. It made me admit once again that we’re part of a great cinematography and screenplay. The producer is not only an artist who covertly paints the pictures with His gentle brush strokes, but is also someone who strings an infinite number of picture frames with great skill and attention to detail, creating the perfect animation of “life.”

Imagine the animation of a falling bird feather; one would need to perform an enormous number of calculations between the sequences of frames. It would be necessary to run many computers in parallel to be able to process such animation in real time. Then I used this same information and applied it to the scene of the falling snowflake. Contemplating the details of each moment within that scenario and considering each moment to be a single frame helps you appreciate the complicated task of stringing these frames together in real time.

When you see a man inscribing circles with a light source you actually see a circle of a light. In fact, you perceive it as a circle because of the speed and the continuity of the motion. Life is analogous to that imaginary circle; it exists because of the continuity of the artist’s efforts. Yes, life as a “perfect” movie is similar to the continuity of this circle of light, because the artist’s magnificent skills continuously color and illuminate each picture frame, stringing them together in a perfect fashion.

Wait, wait, it doesn’t end here. I close my eyes; it is easy for me to see things that happened years ago in all their details. The time I dropped my ice cream on my favorite shirt when I was five, the gift that my brother gave me on my thirteenth birthday, the day I graduated from college… like a movie, I can watch all these whenever I like. This illustrates another issue in video processing, storing the videos, in other words, the frames, in an efficient way so that they can be accessed promptly when needed. I already have a good technique to store the story of my life in my memories. Moreover, in order to remember any sequence, all I need to do is just remember a small detail of the time, an event, or a memento. This is the fastest content-based image retrieval system I have ever seen! No moment of life is wasted and all is saved somewhere, providing relief for the human heart, which is helplessly attracted to eternity. Any art necessitates an exhibition and an audience. Then there must be a place and a time in which the whole movie will be watched again by the audience.

My brain not only stores my memories as videos, but also creates videos as I dream. These are mostly movies in the making; because I can do everything in my dreams, they do not need to be logical. I heard the phrase “Dream Theater” and I smiled. What else can one call a dream other than a grand theater full of surprises? Moreover, although the length of time that a dream takes up is not that long, it still contains a sizeable story that takes up days of real life. It’s one rabbit warren inside another.

As the rain hits the Boston ground, I look outside my window at my moving picture. Through this open window, I also hear the pitter-patter of the falling rain. The smell of wet soil seeps into my room. I shut my eyes and I can repaint the entire picture, using nothing but sounds and smell. What kind of magic is this? I cannot stop myself as I think about Him, the Producer of the real movie of my very existence. After all, I know that He loves me. No matter how busy I am watching man-made movies inside the real movie, I feel the presence of the true artist always with me and the imprint of His ever-lasting art in every moment of my life.

“What would you do if you were told you had only 72 hours to live?” was the theme we announced in the last year’s essay contest. The winner of this contest is Joseph Salter, who participated from behind bars. Yes, this is true. He is the author of five unpublished novels he has written during his term in jail. Read what this talented author, who is serving jail-time for a period unknown to us, has to say about if he were told he only had three days remaining to live. We will continue to publish other interesting essays submitted for the contest in following issues. Each of them responds to this question – which is somewhat distressing for many – with unique content, revealing unaccomplished dreams, regrets, and thankfulness.

We would like your attention and participation as we announce a new initiative that our magazine is introducing: The Fountain Talks. Organized by The Fountain and other participating organizations, The Fountain Talks is the name for locally organized seminars in which we will discuss any of the essays published in our most recent issue or any of those themes we generally stress in our publication. The first of such events took place on February 20 in Ohio in cooperation with TASCO, which featured Dr. Nuh Aydin, who made a presentation on his book review published in the previous issue. The Fountain Talks will be held very soon in Singapore, Australia, Indonesia, and Malaysia in the form of a series of panels starting from March 29. TCC in New York will host Julie Ann Cunningham who will speak on her “Music of the Spheres” article (issue 76) March 31. Please contact your local representative for The Fountain to learn about the details.

“Philosophy considers force to be the point of support in social life, and life as the realization of self-interest (as its goal) and conflict (as its principle).”1 When Said Nursi wrote this sentence in The Words, he was looking at the Cyclops-like aspect of the European philosophy of his time, which totally excluded spirituality from the interpretation of the relationship between humans and the universe. There was only one eye on that face which concentrated solely on the materialist side of the creation. Said Nursi called this face “philosophy”; he was opposed to nineteenth century materialist philosophy, but rather favored one that was open to metaphysics and the spiritual as well as to the rational, an approach that he would later call “the marriage of the mind and the heart.”

This materialist philosophy, which considers “power” to be the point of support in social life, actually shaped the social and political movements of the twentieth century. Those individuals who were empowered with personal and financial resources built production facilities and had the less powerful individuals in society work for them in exchange for little remuneration. Capital thus quickly accumulated in the hands of an increasingly prosperous minority, whereas the majority of the members of the “developing” society were barely able to make a living. Mercy seldom descended from the narrow top of the pyramid to the base-and envy and resentment rose in dark clouds from the wide base to the top. Power became the main determining effect in social life, as individuals or groups tried to realize their self-interests to the degree that their “power” allowed them to.

When there was a conflict between interests, might was used as the arbitrator. Revolutions simply shifted the building blocks of the pyramid, but the shape of the pyramid always remained the same. “Natural selection,” a misconception thought to be observed in nature, became the very basis of civilizations. The political arena always had its actors whose pockets were full and waves of ordinary people were merely directed, explicitly or implicitly, in what they should do with their lives. Nations with less economic power became oppressed, their lands and resources were looted, and their futures were thrown into a deep, dark well of uncertainty. The world saw the bloodiest wars of all times as humanity descended to the lowest of the lowest, “asfal al-safilin.”

There has not been any single event in the course of social history which has not been motivated by a system of thought. The intellectuals of the last century tended to strip human beings of their inner dimensions and consider them as a piece of walking/talking machinery. This machine was supposed to produce goods constantly in order to satisfy the increasing needs of mankind. Simultaneously, the circle of the needs extended itself to the farthest point of the imagination, until there was no way that circle could be encompassed. Most of these needs took the shape of carnal desires, and the machine became dedicated to gratifying these desires. Relations between individuals and their families, in neighborhoods and within countries, started to deteriorate. Divorce, domestic violence, deceit, murder, and other crimes-enough to make anyone with a heart grow mute-began to seem and sound normal to the general public. Thus, the machine began to annihilate itself and its surroundings. Bediuzzaman Said Nursi brought the matter to public attention at that time with the following words: “Force calls up aggression, seeking self-interest causes battles over material resources, and conflict brings strife.”2

Since life was considered to be the realization of self-interest, the self became the center of all interests. Individualism was raised as the banner of victory, while the bonds that connected selves together began to disappear. “Country, religion, family, ideas of civilization, all the sentimental and historical forces that stood between cosmic infinity and the individual, providing some notion of place within the whole, have been rationalized and have lost their compelling force.”3

Contrary to accepting power as the fabric of social life, such as it has been in the past two centuries, the Holy Qur’an accepts “rights” to be the constant point of support in social life. The first Caliph of Islam after the Prophet Muhammad, peace be upon him, the honorable Abu Bakr, stated this Qur’anic approach in his first speech to the public: “The weakest among you is the strongest in my eyes until his rights have been delivered to him, and God willing I will accomplish that; and the strongest among you is the weakest in my sight until he delivers the rights to their real owner, and God willing I will pursue that.”4

One of the five pillars in Islam is the prescribed alms, zakat. According to the Qur’an, every Muslim with adequate financial resources is obligated to give one-fortieth of his wealth to people in need. This portion of the wealth of the rich is considered a right that is given to the poor from God. This is a very interesting point, because the Qur’an draws a circle around the rights of the powerless within the circle of the powerful. In so doing, the Qur’an effectively silences brute force and allows “rights” to speak instead. Thus, the Qur’an teaches and commands believers to practice “giving precedence to the common interests of the community over one’s own interests.” The fact is that all unrest in human social life proceeds from two sources or attitudes: “Once my stomach is full, what do I care if others die of hunger?” and “You work, I will eat.”5 These statements symbolize a world where labor and capital confront each other and zakat, as a moral imperative, is abandoned; yet mankind has been advised to use charity as a form of purifying alms that is essential to the establishment of social welfare and order.

Human rights, huquq al-ibad, are a very important issue in the Qur’an. A devout believer who has pursued a virtuous life in this life may be pardoned for all their sins. However, the violation of the rights of others is excluded from this pardon, for such a violation must be resolved between the person who violated the rights and the one whose rights has been violated. The “others” here can be Muslims or non-Muslims and they can be of any race, ethnicity, belief, or worldview, in fact, anybody whom God has created. An anecdote from the time of the third Caliph, Umar is noteworthy here. It occurred in the city of Hims (Syria) in 635. The Muslim army was in retreat and leaving the city at the approach of a huge Roman army. The commander of the Muslim army ordered his men to reimburse the people of the city for the taxes that had been collected. The tax collectors told the Christian population of the city that the Muslim army would not be able to protect the city against the Roman army, and that since the taxes had been collected in payment for the protection of the city, the army no longer had any right to keep the taxes.6

The Qur’an does not leave the individual by themselves in the universe. “Does man think that he will be left uncontrolled (without purpose)?” (Qiyama 75:36). Human beings have the willpower and determination to choose between evil and good. Humans are responsible for their choices as well as their actions, and they will be held accountable for every deed they commit. This very fact should urge everyone who hears this message to adjust their standing within the community. The Qur’an commands each soul to uphold righteousness and forbid evil. This command is not limited only to the person’s interactions with the rest of the society. Rather, each person is also responsible for their own physical and psychological being. Nobody can commit suicide, harm their own body, or fall into despair or cut themselves off from society.

From a Muslim’s point of view the holy books that preceded the Qur’an also hold “rights” to be paramount within the community for the establishment of justice and harmony; the Qur’an states, “And we have sent down to you (O Muhammad) the Book (the Qur’an) in truth confirming the Scripture that came before it” (Maida 5:52). If we want to live in a safer and a happier world, where every human being’s rights are secured, the followers of the Holy Scriptures should refer to the enlightening realm of the revelation, advocating “right” rather than “might” as the criteria for any decision that affects the destiny of humanity. Rights have to be promoted at every level of society, and this cannot be done without taking the metaphysical dimensions of the individual into consideration. Looking at how people all around the globe are returning to the warm home of religion and how members of different faiths are striving to understand each other, one can hear the joyful celebration of the marriage between the mind and the heart and can see rights sitting on their throne supported on the shoulders of might.

Notes

1. Nursi, Said, The Words, The Light, Inc., NJ: 2005 p. 146-7.

2. ibid. p. 146-7.

3. Bloom, Allan, The Closing of the American Mind, Simon & Schuster Inc., 1988, p.85

4. Hz. Muhammed (s.a.s.) ve Hayati (Prophet Muhammad and His Life), Diyanet Yayinlari, Ankara: 1996, p. 435, Turkish Religious Council Publications, p. 435

5. Nursi, Said, The Letters, 22nd Letter, Truestar, London: 1995, p. 74.

6. Belazuri, Futuhu’l-Buldan, Beirut, 1987, p. 187.

A major achievement in the computation of π was made around 250 BC. Archimedes of Syracuse (287-212 BC) had the brilliant idea to approximate π by using inscribed and circumscribed polygons that approached a circle (see the figure). The circumference of a circle of diameter 1 is π. He inscribed a polygon of n-side and computed its circumference.

This circumference is clearly less than π. Similarly, he circumscribed another polygon of n-side and computed its circumference. This time the circumference of the polygon is greater than the circumference of the circle which is π. So, he arrived at the inequality 3 < π

In the following centuries, some people used Archimedes’ technique, using polygons with more sides, and arrived at more accurate estimates for π. Ptolemy (c. 150 AD) found the value up to 4 places, Zu Chongzhi (c. 500) 6 places, al-Khwarizmi (c. 800) 4 places, al-Kashi (c. 1430) 14 places, Roomen (c. 1580) 17 places, while Van Ceulen (c. 1600) arrived at 35 places.

Unfortunately, Archimedes’ idea was the only mathematically significant approach for almost 2,000 years. The second major step in this direction came with the Renaissance. The general progress in theoretical mathematics gave a great push to the computation of π. With the aid of calculus and infinite series Gregory found the following formula: arctan(x) = 1- x/3 + x3/5 – x5/7 +… He then plugged in x=1, arriving at π/4 = 1- 1/3 + 1/5 – 1/7 +…

This formula looks very nice to begin with, but unfortunately it is not very useful for the computation of π. To get the first 4 places right, we need 10,000 terms of the series, making it very untidy. This formula was considerably improved later by others, and went on to become very useful for computation. By using trigonometry, Machin found the following formula for π: π/4 = 4arctan(1/5) – arctan(1/239).

With Gregory’s expression for arctangent, this formula became so powerful that one could arrive at 5 places of π in just 6 terms. Again, with such a formula, the only problem left is that the computation is quite tedious. In the 18th and 19th centuries, Machin, Rutherford, Shanks, and others improved the calculation of π to 700 digits.

On the other hand, amazing facts were discovered about the nature of π. In 1761, Lindemann was the first to show that π is irrational, which means that it cannot be written as the ratio of two integers, like 22/7, 353/113, etc. Then he proved that it is transcendental, or “very irrational,” i.e. it cannot be a root of any integer coefficient polynomial. In other words, it cannot be A10,A2 + A3, 3A29, etc. These facts imply that π is a very irregular number, that there is no pattern in its decimal places, and that one cannot express π in a simple algebraic way.

So, by the beginning of 20th century, we were able to compute only 700 digits of π. In the first quarter of the last century, the brilliant Indian mathematician Ramanujan accomplished the third great theoretical leap in or the computation of π, and came out with many impressive infinite series. He arrived at sound algebraic expressions which are very close to π.

In the second quarter of the last century, computers came onto the scene. With the arrival of computers, pen and paper calculations were rendered obsolete. After Ramanujan’s time, the people calculating π became programmers rather than mathematicians. In 1955, more than 3,000 digits were calculated at the Naval Ordnance Research Center in only 13 minutes, almost 500 times faster than the ENIAC only 6 years later. In 1959 an IBM 704 calculated more than 16,000 digits of π. In 1961 an IBM 7090 calculated over 100,000 digits of π in around 9 hours, in 1966 an IBM 7030 calculated 250,000 digits of π, while a year later a CDC 6600 calculated 500,000 digits and in 1973 a CDC 7600 calculated 1,000,000 digits of π in 23 hours.

However, the techniques for calculating π were still using arctangents which have a quadratic growth rate. In 1976 Eugene Salamin rediscovered a formula developed by Gauss. It was calculation intensive in Gauss’ time, but well suited for modern super computers the size of the Whitehouse and had a much lower growth rate than the arctangents formulas did. In 1982, a HITAC M-280H calculated 16 million digits of π in 30 hours, in 1988 a Hitachi S-820 calculated 201 million digits in 6 hours, while in 1989 both the 500 million and 1 billion π calculation records were broken. In 1995, 6 billion digits were calculated, in 1996, 8 billion, and finally in 1997 a Hitachi SR2201 calculated 51 billion digits of π in 29 hours. This Hitachi machine had 1,024 processors and 212 gigabytes of RAM. However, in September of 1999 a new record of 206,158,430,000 was announced. The calculation was set by Yasumasa Kanada and the University of Tokyo. The calculations took over 37 hours, with 43 hours more needed to verify them. The machine used contained 817GB of main memory and consisted of 128 Hitachi SR8000 processors.

So, we can see that this mysterious number has attracted the attention of many people for centuries; it seems set to continue to do so. It might not seem very interesting to compute billions of digits of one transcendental number, and it might even seem pointless. The real point here is not the billionth digit of the number, but the excitement and the beauty of the problem, and the challenge to human intelligence, like with so many other mathematical problems.

References

• J. J. O’Connor and E. F. Robertson, www.gap.dcs.stand.ac.uk/history/HistTopics /Pi_through_the_ages.html
• D. Hazeghi, www.myownlittleworld.com/pi /history.html
• D. H. Bailey, J. M. Borwein and P. B. Borwein, www.cecm.sfu.ca/organics/papers/borwein /paper/html/paper.html
• Lazarus Mudehwe, www.geocities.com/CapeCanaveral /Lab/3550/pi.htm
• www gap.dcs.stand.ac.uk/history/HistTopics/Pi_chronology.html

In a book that deals with questions of logic, when we see numbers written in succession, such as 5, 15, 25; then we are able to discover the relation between these numbers, to predict the next number and to realize that this pattern was made by somebody. However, if we were to be told that these figures indicate the distance covered in equal segments of time by a pebble that has been dropped from a certain height, most of us would not think about the One Who made this general rule.

Or for example, the equation 11.111.111 x 111.111.111 = 12.345.678.987.654.321 may be as amazing to some people as the verses of a beautiful poem, whereas it will leave others cold.

Likewise, the famous mysterious symbols of mathematics, e, i, , are nothing more than some alphabetical signs for most of us, nevertheless they must have meant a lot to the famous physicist, Richard Feyman, since he wrote the following equation in his diary, noting that he admired it: ei+1=0

If we write f (z) = Z2 + c;, this will not be a meaningful sentence for most people. But that will not change the fact that it is an incredibly simple expression of biological and physical reality in an expression which concerns our lives (as in fractal logic). And the picture you see here (Figure 1) is nothing but the analytical projection of this equation on a computer screen.

The spiral form (Figure 2) which can be seen in various things from cone shells to nebulas, has a very simple formula, r2=a2/A which is fascinating for those who spend some time to think about it. All these examples have a point in common. These numbers, which are abstract concepts, are as real as the concrete objects of the physical world. While other sciences make sense, more or less, for a layperson, mathematics can only be appreciated by people who know it well.

The mythological Princess Dido of Phoen-icia fled from the city where her husband (the King;s brother) had been slain by the King. She wanted to settle in Carthage, in North Africa. There the King only allowed her to buy as much land as could be covered by the skin of a cow. Dido decided to interpret the word ;cover; in a wider sense. She had her servants cut the skin in thin strips, connecting them to each other. In the end, she obtained a long cord, estimated to be somewhere from between 1,000 to 2,000 m. long. When it came to placing it on the ground, Dido wanted to find the shape that would cover the largest area. She found the right shape. She made a circle on the ground and she was able to encompass quite a large area of land. As a matter of fact, looking at some ancient castles, we can understand that they were built in this way in order to create the largest structure over the smallest possible area. This explains why the cross-section of a vessel tissue is circular, because it occupies minimal space in the body (Figure 9).

Did you know that mathematical reality applies in our body and in the universe? This fact was realized when scientists developed fractal geometry. The fractal structure we see in the roots and leaves of plants and in the human respiratory and vascular systems are very good examples of this fact. Such excellence indicates the All-Knowing Omnipotent One Who is behind these geometrical designs (Figures 4, 5, 6).

What is the invisible secret of this visible structure? Dido had to enclose the maximum area by using limited material, which she accomplished. Such optimization also exists in the human body and in other living things. The biological systems we have mentioned above have vessel systems designed as fractal networks, delivering the necessary substances to cells. Essentially, these systems are designed in such a way that the vessels occupy minimal space while serving all the cells within the system; this can only be realized through such a fractal structure.

The most striking proof supporting this idea is that if the human veins, which do not take up a great deal of space in the body, were all added together, they would reach a length that is three times the circumference of the world.

How can this be possible? This can be explained quite simply: find an equilateral triangle and carry out the following instructions. First, divide each side of the triangle into three equal sections and place another (smaller) equilateral triangle on the middle section of each side you have divided, facing outwards. If you repeat the same thing for each of these small triangles, you will create the pattern below (Figure 8).

In a fractal structure, as the number of branches near infinity, the shape of the structure resembles a circle more and more. The new area we will find cannot be bigger than the area of the circle, and the points of contact with the circle will approach the maximum value (Figure 9).

We can also explain this fact in the following way: take a circle with a radius of 3 cm. This will serve as the cross-section of a cylindrical object. Then draw seven smaller identical circles inside the first circle. You will see that the proportion between the sum of circumferences and the sum of areas is 5/7. Those who are interested in mathematics will see that as the value of the r (radius) decreases, the difference increases. This clearly indicates that fractal structures are always advantageous. So, what about organs like the brain or the lungs? They do not have a completely fractal structure, yet they really need to have a larger surface area than other objects of equal size. These organs have been enabled to have the largest possible surface area by being convoluted. Otherwise, man would be a strange creature, burdened with a huge mass on his back. Similarly, when we look at a map that shows the coastlines, we see that a coastline that has many capes and bays has a longer coast line than its counterparts, which run straight along the land. All these living things or organs (man, trees, brain etc) have such structures from the very moment they are created. This system or project (Figure 10) cannot have developed on its own, by chance, without there having been a Creator.

Sir James Jean says, ;The Creator must be a perfect Mathematician; in his book The Mysterious Universe. In so saying, he draws attention to mathematics, the mysterious pattern in the universe, and points to the Artist behind the ornamented beauty seen in Creation. The magical science of mathematics whispers its secrets to those who try to perceive it through the eyes of wisdom.