In contemplating the profound messages delivered by prophets throughout history, such as the teachings of Prophet Muhammad, one cannot help but recognize their universal appeal and the inclusive language in which they were conveyed. These messengers of wisdom reached out to humanity at all levels, employing words that were not only comprehensible but also deeply inspiring. I often find myself looking at the world through the lens of physics due to my physics background, perceiving intricate connections and implications for our social existence. While my words are firmly grounded in the profound teachings of these revered figures, which I may never fully grasp with my limited expressions, my exploration invariably leads me to frequent references to the laws of physics. It is within this intriguing convergence of spiritual wisdom and scientific understanding that we embark on a journey to explore the concept of mirrors – not just as physical objects but as powerful metaphors that illuminate our path toward greater understanding, compassion, and enlightenment.

Let’s begin with one of these profound pearls of wisdom: “The believer is a mirror to his/her faithful fellow believer who protects them against loss and defends them behind their back.” The person who conveyed this saying, Abu Huraira, also shared his understanding in the presence of Prophet Muhammad (pbuh): “The believer is a mirror to his brother/sister. If he sees something wrong with them, he should correct it.” I believe that Abu Huraira’s interpretation of this hadith is direct and accurate. When we gaze into a mirror, we correct our appearance and enhance our presentation by viewing ourselves from an ‘outsider’ perspective while still remaining within ourselves. The image we observe in the mirror represents “us,” yet it is not us. We can analyze the image’s features, attributes, and relation to the object or person in front of the mirror. This image metaphor brings to mind the biblical passage, “God Created Humanity in His Image” (Genesis 1:26-31, Psalm 8:1-9, 1 Corinthians 15:47-49). Additionally, in paying tribute to Abu Huraira, who has inspired our discussion, we recall the words of Prophet Muhammad (pbuh): “Allah created Adam in His image” (Sahih al-Bukhari 6227).

Now, let’s direct our focus towards the fundamental laws of reflection, which are at the core of a mirror’s function. One of the three laws of reflection states that “the angle of incidence is equal to the angle of reflection when a beam of light strikes the reflecting surface. The reflected ray, incident ray, and normal lie on the same plane.” I understand that this sentence may appear quite complex, and filled with technical terminology. However, for reflection to take place effectively, everything must align harmoniously. This includes the incoming light, the mirror, and the reflected light. In a similar vein, a believer with sincere conviction, dedication, and faith finds themselves on a vast platform supported by the pillars of belief. Just as in the realm of optics where a mirror reflects light, in the realm of faith, every other believer can serve as a metaphorical mirror, revealing different aspects, dimensions, or angles of a fellow believer. This reflection is possible as long as they share the same plane of belief, understanding, mutual love, and cooperation.

Consider risky situations as analogous to mirrors placed on cars, roads, and sharp corners to prevent accidents. For instance, convex mirrors are particularly valuable in enhancing road safety because they aid in collision avoidance. These convex or domed mirrors provide a wide-angle view, enabling drivers to assess potentially hazardous intersections and see traffic around corners. Similarly, in our lives, we require individuals who serve as mirrors in various facets. Some reveal the risks of our life journeys, while others guide us in making decisions when we may not possess the full picture.

We are also familiar with face mirrors that magnify the objects they reflect, helping us discern details that might otherwise escape our notice. Are not some of the people in our lives akin to concave mirrors in this context? We might overlook or disregard seemingly insignificant details, yet they offer a broader perspective on these aspects, aiding us in making informed choices. Just as mirrors come in various sizes, shapes, and geometries, individuals in our lives exhibit diverse characteristics and qualities. Additionally, devices like kaleidoscopes, periscopes, and telescopes employ clever combinations or arrays of mirrors. The number, positioning, and alignment of these mirrors yield valuable outcomes and insights for us.

When we place two plane mirrors facing each other, between them, we see a corridor that extends to ‘infinity.’ Consider, for a moment, a close friend of yours with whom you share numerous common interests, understand each other deeply, and resonate harmoniously. In their presence, you never wish to part, cherishing endless conversations, because this person serves as a true mirror for you, with their heart perfectly aligned before you. In a sense, despite physical boundaries, you venture into the limitless corridors of companionship. As Bediuzzaman Said Nursi eloquently expresses regarding spouses: “Yes, the greatest fulfillment of a person’s needs is the presence of a heart corresponding to their own, so that both sides may exchange their love, passion, and enthusiasm, and share in pleasures together, and assist and support each other in times of sorrow and sadness.” This sentiment can be applied to spouses who are believers, serving as absolute perfect mirrors for each other.

We all know that, like everything in life, mirrors also require cleaning, care, and attention. They are fragile and delicate. They faithfully provide a complete reflection whenever you glance at them. Mirrors do not rely on batteries or electricity; they promptly and without delay respond with reflections. With consistent effort, positive investment, and proper care, you can combine multiple mirrors to gain deeper insights into the world or expand your horizons into heavenly realms. They compensate for your weaknesses, fill in your blind spots, and bring light from places where direct illumination is not possible. Indeed, every being in the universe serves as a mirror reflecting beauty, art, intelligence, compassion, and more.

Luminous entities spread, reflect, and exist in many places swiftly, while solid and concrete objects are confined to their immediate surroundings and require greater effort to transform and move. Just like a bubble contains the entire image of the Sun, qualities such as goodness, compassion, mercy, kindness, charity, smiles, care, and sincerity are light-like illuminating qualities that need mirrors to reflect them.

Connect with people, reflect the light you receive to others, be a mirror for others, and receive radiance at different wavelengths and frequencies. Amidst layers of darkness, let your gleam shine without concern for its apparent size. You will encounter mirrors in the darkness; as long as you reflect their faint glimmer, they will join you in challenging obscurities and darkness.

You lie not while joking or fighting, but when right
You didn’t do good for the temporary reward
You did not submit to false associations or pride
All you sought was the pleasure of your Lord

You were a slave by choice
To a master who deserved the best
Yet He demanded nothing but your heart,
Damaged but repaired with regrets

You didn’t sell your soul for a small price
You saved it until the market was high
And you sold it to the best buyer
Whose mercy welcomed you to Paradise

You were pleased with your Lord
And the faith He chose for you
You raced for His forgiveness
Sticking to hard work, submission, and what was true

You fulfilled your obligations, and were kind, too
You couldn’t give much but constantly gave your best
You were grateful to God no matter what
And you kept no grudges in your chest

You devoted your youth to the One
In solitude, you shed all your precious tears
You treated everyone with respect
And as a volunteer, looked after an orphan

You promoted good and forbade bad
Yet you never judged anyone
You followed a path in your quest for knowledge
But your parents, you never shunned

You restrained your gaze, even locked your tongue
You caged your thoughts and counted each breath fall
So now your soul is free in a body unbounded by death
As you never considered minor sins so small

So now you enter as a VIP, while everyone waits
You step in and already know your home
A private palace of jewels with no noise or rent
Purely customized to be your dome

You’re surprised how it’s exactly what you love
Intricacy in each, and everything so bold
Royally placed, silver doors and bricks of gold
Without the excessive heat or the bitter cold

You see golden butterflies fluttering around a tree outside
So you travel beneath the shade of its glory for 100 years
Colors your eyes have never seen
You start sweating musk at whatever that appears

Scenery being painted in front of you as you think
In lush green gardens, you ride your park
Suspended there thinking, Is this all mine?
Even when my report card had many red marks?

Now think of never having to feel hunger and stress
Never feeling intensity of pain inconceivable by the brain
All the truths unravel and it’s all clear at once:
No arguments to prove who’s sane or insane

No regrets, no waiting, no hatred or discrimination
No sorrow or fatigue; no wanting to catch a wink.
Boredom is a word you simply forget
Wishing that your eye would now never blink

What you seek is what you see and hear
Smelling the best and thinking the rest.
A world of perfection, with nothing to fear
It couldn’t get any better, yet you got the best

You squint at the special upper abodes
Far away from you, shining like bright stars
You keep thinking you couldn’t ever reach them
Until you get upgraded from where you are

Maybe you had daughters that you treated so well
Maybe your children died and your patience pulled you up
Maybe you died with them, never bidding peace farewell
Sticking to your testimony as the last words for a ticket above

The good character you taught your kids and their prayers
Added to your deeds, even after death
Maybe you never had kids, yet you collected
So much charity that you were out of breath

Maybe some among your pious mates are up there
They want you with them in the Garden
You couldn’t be happier for the blood you shared
Or maybe they were from the friends you chose

You go up there and are filled with awe
For you never imagined such beauty ever existed
Suddenly you see all the prophets gathered
Facing each other on raised thrones, coexisting

Surrounded by gold trees and soil more fragrant than musk
With pebbles underneath of ruby, pearl, and sapphire
Dressed in gold embroidered, fine green silk attire
Eating together: delicious food and fruits, melting in the mouth

Around them, servants revolve like scattered pearls
With never fading youth and cushions lined on stage
They have access to celebrities not surrounded by security
Adam, Moses, Jesus, and Muhammad; all the same age

You rush to them in excitement, and suddenly
Moses parts the sea with his staff
Your pace suddenly slows down, to absorb the grandeur;
You had to close your eyes to even imagine this

But now it’s a reality, your eyes wide open
Never did 4D have so many dimensions
Your overloaded senses make your heart burst
As your mind is stampeded with 1000 questions

The Seal of Messengers greet, taking your name
And you can’t decide whether to cry or faint with glee
So you just stand with them, shoulder to shoulder
And pray as he leads

The river of emotions flows through your veins
But a drenched soul can’t express your gratitude
The tides of rapture bring a hurricane inside you
The soul soars high, with your heartbeats engulfed

You ask for the staff from Moses
And rush to your mates to show off your delight
In your way you find Solomon
You ask for his winged horse and take it for a flight

You join the Angels and holy ones
Flying like green birds with freedom
You fill the cup at hand, with a delicious drink
Right from the flowing spring of Eden

You look down and see adorable babies around Abraham
Mountains humming along with the rhythm of David
You never heard a melody so beautiful
As more hypnotizing voices join in the mood

All your life you thought of meeting these ancestors in heaven
The ones who sacrificed their lives for your faith to be strong
Their efforts were what made it easy for you
You owed them a token of thanks all along

“Was it a woman with a smile?
When her hands and feet were pierced by nails?
Or was it a man, thrown into fire
When he didn’t put his faith on sale?”

The reward of those who suffered in the world
Made you yearn for your skin to be sliced
Now that they find delight in their past miseries
You hear their sad stories with a smile

Above all earthly cares they now soar
Beyond the hurts they patiently endured
You watch light flow from broken hearts
Maybe you’re one of them

Suddenly you’re interrupted by a magical voice
Which is even better than what you have heard before
The voice of your Creator addressing you
He’ll show Himself clear, like a full moon‘s wash

Goosebumps cover your skin in anticipation
And you hold your breath till you see His face
You feel like shouting at the top of your lungs
Glorified You are, when He uncovers His grace

And you whisper to yourself: “Praise be to the One,
My Master didn’t let me be influenced by them
Those who said there was no God, or heaven or hell;
If only they had a heart attached to a brain stem.

If only they could see what I’m seeing right now!
Their doubts wouldn’t have ever rid them of hope,
Hope of being able to see the invisible.
But womb to dust was their only known globe.”

You have every desire at your fingertips
Yet you want to do nothing but quietly stare
At One who’s guidance directed your soul
It’s like you’re new yet you, but enraptured

You don’t feel like going to the heavenly market anymore
For your beauty is enhanced with just a glance
Seeing Moses looking at His Lord without fainting
You just circulate in infinite loops of a euphoric trance

A single life seed you sowed and
Reaped into forever more
Each and every wish granted;
In fulfillment, you run out of more

Wanting this all will never end
So an end will be put to death forever
So much joy that you could just die,
But death has died forever

Never before were dreams so real
Never again can reality be more
Never before was ecstasy such
And never again can life be most

My imagination is made up of what I know
It doesn’t go beyond my thoughts
So I wait in serenity till that day comes
When reality will connect all the dots

The test is here and the results there
Do you just dream or do you strive?
For time is running out, and the price is high
A limited offer, but worth a life
Or more…

Note: The poem has been inspired by a beautiful Jannah poem by Ammar Alshukry.

The answer to all of these questions relies on understanding certain laws in the nature. Every existence, from stars to trees, and living to nonliving, is an example of the systems in the palace of our universe.

Closed systems never engage in any exchange of matter, energy, or information with their environments. There is not any closed system in the universe. For example, a “thermos” can be a partial example of a closed system, since the liquid contained inside it does not get cold or warm quickly.

Open systems take part in matter, energy, and information exchanges with their environments. Human bodies, plants, and animals are each open systems. For instance, chemical reactions take place under our skin: enzymes constantly move, and blood is continuously flowing; via sweating, body heat is maintained; we exhale and inhale. We feed ourselves with food and beverages for our energy needs. Unwanted materials are excreted from our body.

These are necessary exchanges, but there can be exchanges for intangible realities such as ideas and love.

As a guide for understanding systems and as an indicator of irregularities, entropy finds its true meaning in the second law of thermodynamics. The entropy of closed systems increases up to a certain value and remains constant. The higher the entropy, the higher the level of irregularity.

For example, we are born in an organized state; however, as life continues, it drives our entropy higher and we leave this world at the maximum level of entropy. In other words, we posses a lower entropy when we step into this world. We mature as our entropy gets higher and we migrate into the other world with the ticket of death at the maximum form of entropy.

When the events inside and outside ourselves are halted, death becomes inevitable. It is through the uptake of materials from the outside world (oxygen, water, food, etc) that entropy slows down, so that we can sustain an average lifespan. An open system allows us to survive.

If we close the borders and cut our relations with the outer world, open systems are observed to generate entropy quickly, causing an internal disruption that may lead to death. Hadrian’s Wall of England, the Great Wall of China, and the Berlin wall of Germany can be presented as examples of detrimental functions. Similarly, the former Soviet Union was a closed system, and the hardships it caused are further evidence that such systems are not natural when they violate the second law of thermodynamics and they are not sustainable.

It is possible to talk about the entropy of any organization by looking at the level of its irregularity. A loss of variations or tensions within an organization, or an increase in the number of units, may cause an elevation of entropy.

When a living or nonliving organization approaches the moment of death, or all units become independent or equilibrated, entropy reaches its maximum value and control starts to diminish.

Conversely, if all units have a perfect interaction with the administrator and each other, this time entropy trends towards the ideal value, which is minimal, and irregularity in the system decreases.

The flow-use of energy and information is critical in organized structures such as a factory, corporation, school, government, or living organism. Upon the degradation of this state, entropy increases and efficiency decreases. If in this system there is not a structure in which information is stored, and no effective flow of information and energy is present at all stages of the hierarchy, the information from the lowest layer cannot pass through many units on its way towards the administration, and the information/energy flow among units becomes unhealthy. Entropy inevitably increases in such a process. Therefore, to ensure the proper sustainability of all organized structures, the vertical (hierarchic) and horizontal information-energy flow channels must remain open.

If work-based conflicts are experienced in between certain units in an organization (for instance, the same task is being carried out by several units) or certain jobs are being neglected, this situation refers to a major irregularity in terms of information-energy flow.

If a great portion of the power remains at the head of the structure, it is easier to make decisions and organizational efficiency is higher. The intensity of power at the lower layers of the organization therefore reduces the effectiveness of the structure, leading to chaos and disruption in information transfers.

If all units in the organization have the same authority and are equal, they are independent for all matters, this case may be classified as maximum entropy, in other words, the end of the organization.

Entropy and infinity

To understand entropy, one must consider its relation to infinity. Infinity points to a place, a situation in which an infinite amount of information is present. We can think of a book as low-entropy, organized structure where letters of the alphabet make up the words by joining together under certain rules. These words form sentences, and sentences compose chapters. Now let’s imagine that we cut the pages with a pair of scissors, and then remove words by cutting them away one by one, finally separating the words into letters. Now we are only left with a pile of letters.

At this moment, let’s ask the following question by looking at the letters collected on the table: “What do I have now?” The first answer that comes to mind will be “a pile of very scrambled letters.” But in fact, you own more than a pile of scrambled letters, since a high level of entropy also means a large amount of information.

The collection of letters on the table possesses a very large potential of information. With these letters, not only can the original book be assembled, but many books by combining the letters into different forms; this is just like in the Book of the Universe.

When the body of each organism that experiences death decays and disintegrates under the soil, it is separated into its letters – in a physical sense. Thus, each organism is converted into a potential form of information with its death. Then each part (letter) is employed for various tasks. In other words, the remnants of deceased organisms are used for writing different words, sentences, and books in the universe. This cycle points to an infinite amount of information, and infinity.

Conversion from state to state

We are moving in a state of flow towards a maximum state of entropy, carried by the execution of natural laws. In this process, almost everything is transformed from one state into another. Instantaneous renewal and growth occurs. There are parameters that we can affect in addition to the ones we cannot. For instance, once cells reach a specific size, they divide into smaller units and growth starts again. Firms, stars, and living things are like that, too. These are systems that lose energy (dissipative systems).

These systems are constantly transformed into newer states and certain dynamically-stable statuses are built. Transformations occur by arriving at branching points and many alternative states may be possible at these divergence points. Some of these states may be beneficial for the system, and some are not. However we do know that maximum entropy and making selections, whether good or bad, at the divergence points is a result of the second law of thermodynamics. For this reason, efforts to remain constantly in the stable states, which we describe as “balanced,” will mean death in some way. Try not to change, if you like. Eventually, you will witness your break down and degradation. We now recognize that human society should act as an open system. To be able survive many years, both materially and spiritually, then the exchange of information and energy should take place in a natural fashion. The spiritual guidance of the masters of faith and thought in human history teach us to be in compliance with this nature.

Furthermore, all these incidents remind us each time that balance in its absolute meaning does not exist in this world, and that it will be established somewhere else.

Reference

• Hershey, Daniel. 2010. Entropy Theory of Aging Systems, Imperial College Press.

Fred (not his real name) is 21 years old, living in a university community. Last year, he did a project to “stretch into infinity”, i.e. he attempted suicide. Fortunately, his project failed. After his return to the normal life, he found an alternative way to infinity. I wanted to interview him as soon as I learned about his story, which he accepted.

“I am doing a double major in mathematics and biology. Unlike the regular biology students who are educated to think traditionally and memorize constantly, my way of thinking is rather mathematical and rational.”

I wanted to punch a hole in this super confident young boy’s claims about himself. “So, you never fell in love, but instead, rationally proved some girl to be the one meant for you?”

He chuckled. “I guess, I did fall in love, but suppressed my feelings since they were irrational.”

“Then you must have a strong will. How do you rationally explain the human will? I mean, we are talking about a young man whose hormones are keeping him at the verge of love. And how do you think your will fights against these molecules that pervade your body?”

“My thoughts on this are different now, but at the time, I was trying to express everything in terms of testable, concrete concepts. There is so much research on the effects of genes and the environmental conditions on human behavior. So, my will had to be some proteins synthesized from my DNA.”

“So do you think, or did you think that one day people could use love pills for keeping up their love for their partners, and to have compassion for their children?”

“Why not? Actually, it is not just that. I had many thoughts that engulfed my mind and motivated my actions, including my attempt to suicide. I couldn’t receive rationally satisfactory alternatives to my conclusions.”

Then Fred took me on a tour d’horizon of his view of life and people. There were many elements in his views that you could hear from other people, but this one was unique and noteworthy:

“This is a bit irrelevant, but I can tell you a funny one too. If the speeding tickets are issued not due to an actual harm but due to the increased risk of harm, then people who drink more than a minimal amount should be given drinking tickets. Statistically speaking, the number of crimes linked to speeding is nowhere close to the number of crimes linked to drinking. So, if I am getting a ticket for speeding, although I haven’t harmed anyone, then why isn’t my friend for whom I am the designated driver, getting a ticket for his increased potential to harm someone?”

Speechless, I tried to steer him back to his conclusions that led him to what he did.

“You know, I was never hospitalized for depression. Nobody thought that I was in deep trouble, including me. I was considered to be an intellectual, an extraordinary friend. I don’t know how it goes with other people, but when the idea came, it wasn’t like a freaky idea to entertain myself for a minute. It came as an irrefutable theory. It only made sense. Really.”

The idea of suicide making sense? That didn’t make sense to me! Seeing my blurred gaze at him, he picked up again.

“If motivation is essential to accomplish your ideals, how come things that bring motivation are considered harmful?”

He was talking about drugs.

“If success is all about hard work, then why is it forbidden to pave your way to success rather than leave it to luck?”

That is fortifying hard work through taking drugs.

“If my mental activity is nothing but complex dynamics of molecules in my brain, then shouldn’t I take drugs that are the embodiment of rejuvenating and exhilarating inspirations leading to innovations?”

After a second of pause, he concluded:

“If happiness is all about certain molecules in my body, then what is wrong about getting it directly rather than mining it through the thorny relationships with people?”

How would you answer these questions, knowing that they are asked by an individual in the making who is trying to make sense of life but who is bewildered by the discrepancies of the mature people?

“My line of thought and other people’s line of thought in this matter are similar to the graph of 1/x. We are both aiming for the same point, i.e. zero. But our distinct approaches take us to opposite directions. The two couldn’t be more divergent than this.”

In mathematical elegance, Fred was describing the state that nurtured his suicidal thoughts. He could not establish ties with the rest of us. With an intention to never come back, Fred used drugs to become a zero in our world, and to stretch into unknown infinity. Did he succeed?

“But you know, like a sad love story, 1/x never converges to zero. I failed, too, in that sense. The way I conceived it, death was going to be a culmination of motivation, success, and happiness. I aimed for it head on. According to my conviction, I was supposed to have achieved all of those. When I opened my eyes in the hospital, I realized that I had neither success nor happiness.”

You don’t have to be a sage in order to understand that suicide is not a key to success or happiness. But a brief journey to death made Fred a sage.

“It is possible in this life that one receives death while perfectly healthy. It is also possible that one can survive despite a miserable health. In other words, just like being healthy doesn’t necessarily mean you can’t die, there isn’t a mechanic relationship between being unhealthy and arriving at death. My own failure to die despite what happened to me is a living proof of this.”

I noted in my mind that this was a good example of learning from your failures.

“The moment I realized that death is given, just like life is, my suicide attempt transformed from being a story of failure to a story of success, because that’s when I started believing in the unseen.”

Believing in the unseen was a quality that Fred did not have before, but why and how had it been the elixir that changed his failure into success?

“It is so ironic and controversial. In the beginning, what I was missing was my acceptance of self-deficiency in grasping the existence. In the end, by admitting to be incomplete, I was becoming complete; being completed by God.”

Suicide is one of the most severe sins one can commit according to the monotheistic religions. Yet, this young man found God in the very sin that could throw him light years away from God.

“I don’t define myself anymore as an outstanding, perfect intellectual as my friends used to call me. Instead, I am a story in progress. No matter how severe the calamities or how satisfying the joys are, I don’t come to an end unless my author ends the story.”

Zeno of Elea was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. He argued that an object in motion can never pass from one position to another, because between the two there is always an “infinity” of other positions, however close, that must be successively traversed in the course of the motion, and this “infinity” can never be exhausted. David Hilbert is a German mathematician who postulated a hypothetical hotel with “countably infinitely” many rooms, all of which are occupied. Since the hotel has “infinitely” many rooms, we can move the guest occupying room 1 to room 2, the guest occupying room 2 to room 3, and so on, and fit a newcomer into room 1. By repeating this procedure, it may be argued that it is possible to make room for any finite number of new guests, although every room of this hotel initially contains a guest.

The following two quotations from two contemporary authors may provide more substance about the nature of the problem:

On the other hand, involvement with the infinite brings with it a huge range of difficulties. In particular, there are the many puzzles and paradoxes that have been outlined in the pages of this book. Moreover, there are the many quite fundamental problems that arise for such apparently simple notions as counting, adding, maximizing, and so forth. Because we are so firmly wedded to limit notions-“best,” “first,” “greatest,” “maximum,” and so forth-that do not sit easily with the infinite, it is very hard to see how we can make our peace with the infinite.

The infinite has always been a slippery concept. Even the commonly accepted mathematical view, developed by Georg Cantor, may not have truly placed infinity on a rigorous foundation.

In the present article, we attempt to summarize Rene Guenon’s (1886-1951) alternative way of thinking on the idea of infinite from the perspective of the traditional metaphysical science. Much more detailed presentation of his perspective can be found in his (1886-1951) valuable study The Metaphysical Principles of the Infinitesimal Calculus from which we will extensively quote here.

Guenon considered mathematics as providing a particularly proper symbolism for the expression of metaphysical truths to the extent that they are expressible. However, he states that “in order for this to be so it is above all necessary that these sciences be rid of the various errors and confusions that have been introduced by the false views of the moderns.” To follow Guenon’s paradigm it is necessary to start with the metaphysical notion of the universal-All which comprehends all possibilities, the non-manifested as well as the manifested Universe, that is, the cosmos. The universal All leaves outside itself only the impossible that is a pure nothing. A determination is to define a certain domain of possibilities in relation to all the rest which is expressed by Spinoza (1632-1677) as omnis determinatio negatio est (all determination is a negation). The first of all determinations is Being itself. “Number is only a mode of quantity, and quantity itself only a category or special mode of being, not coextensive with it, or more precisely still, quantity is only a condition proper to one certain state of existence in the totality of universal existence.” Number, space, and time are all determined conditions.

The Infinite, understood in its true, metaphysical sense, has no limits since its opposite, finite is synonymous with limited. Therefore, according to Guenon,

… one cannot correctly apply this term to anything other than that which has absolutely no limits, that is to say the universal All. Furthermore, there can obviously be only one Infinite, for two supposedly distinct infinities would limit and therefore inevitably exclude one another.

He further states, “The Infinite, in its true sense, can have neither opposite nor complementarity.” The scholastic distinction between “the infinite in a certain respect” and “the absolute infinite” cannot be accepted. If a thing is not limited in a certain sense or in a certain respect than one can legitimately conclude that it is limited in no way at all, and since a determined thing does not include every possibility, as such it can only be finite.

Given any number, one can form the next by adding a unit gives the sequence of numbers to us. Therefore, we cannot actually reach its limits. However, the impossibility of reaching the limits of certain things in the manifested Universe should not cause the illusion that these determined things have no limits at all. In order to replace the false notion of “determined infinite,” Guenon introduces, the idea of the indefinite, which is precisely the idea of a development of possibilities the limits of which we cannot actually reach; and this is why we (Guenon) regard this distinction between the Infinite and the indefinite as fundamental to all questions in which the so-called mathematical infinite appears.

According to Descartes (1596-1650), the indefinite is that of which we do not perceive the limits, and which in reality could be infinite. On the contrary, Guenon affirms that

(T)he indefinite cannot be infinite because it always implies a certain determination, whether it is a question of extension, duration, divisibility, or some other possibility; in a word, whatever the indefinite may be, and according to whatever aspect it is considered, it is still of the finite and can only be of the finite.

The idea of an “infinite number” understood as “the greatest of all numbers,” or “the number of all numbers” is contradictory. The impossibility of an “infinite number” can be established by various arguments:

(T)o every whole number (integer) there corresponds another number equal to its double, such that one can make the two sequences correspond term by term, with the result that the number of terms must be the same in both; but there are obviously twice as many whole numbers as there are even, since even numbers alternate by twos in the sequence of whole numbers; one thus ends up with a manifested contradiction.

Guenon insists that number, despite its indefinitude, is by no means applicable to all that exists and the multitude of all numbers cannot constitute a number, which, moreover, is finally only an application of the incontestable truth that what limits a certain order of possibilities must necessarily be beyond and outside that which it limits.

On the other hand, the idea of multitude, contrary to that of number, is applicable to all that exists which allows one to speak of the multitude of divine attributes for example, or again of the multitude of angels, that is, of beings belonging to states that are not subject to quantity, where, consequently, there can be no question of number.

Number itself can also be regarded as a species of multitude, but on the added condition that it be a “multitude measured by the unit” according to the expression of Saint Thomas Aquinas (1225-1274).

The term “indefinite” consists of something unfinished. The “non-measured” is that which has not yet been defined, which is only incompletely realized within manifestation. The multitude of all numbers is “innumerable” or “non-measured,” which is not to say they are infinite, but merely that they are indefinite.

Guenon calls whole number as true number or pure number. He accepts that the numbers other than whole numbers can be considered as the extensions or generalizations of the idea of number. However, he adds that these extensions are also distortions. According to Guenon, numerical quantity has a discontinuous character, whereas spatial or temporal magnitudes, for example, are continuous quantities. “Between these two modes of quantity is a difference of nature such that a correspondence between the two cannot be perfectly established.” He distinguishes the arithmetical unit from the “units of measurement,” which are magnitudes of another sort than number, notably geometric magnitudes. He defines a continuous quantity as an extension-however small it might be that will always remain indefinitely divisible.

Guenon is against atomism, which necessarily implies the discontinuity of all things. He argues extension cannot be composed of indivisible elements, for these elements would have to be extensionless to be truly indivisible, and a sum of elements with no extension can no more constitute an extension than a sum of zeros can constitute a number, that is why points are not the elements or parts of a line; the true linear elements are always distances between points, which latter are only their extremities. Points multiplied by any quantity at all can never produce length, since, rigorously speaking, they are null with respect to length; the true elements of a magnitude must always be of the same nature as the magnitude, although incomparably less: this leaves no room for indivisibles.

Further,

The point, which, being indivisible, is by that very fact without extension, that is, spatially null, but which, as we (Guenon) have explained elsewhere, is nonetheless the very principle of all extension.

For Guenon, Zeno of Elea’s arguments are against atomism and indeed, they prove that without continuity there would be no possible motion.

It is this very conception of motion that is in error, for it amounts in short to regarding the continuous as if it were composed of points, or of final, indivisible elements, like the notion according to which bodies are composed of atoms; and this would amount to saying that in reality there is no continuity, for whether it is a question of points or atoms, these final elements can only be discontinuous.

And, “The possibility of motion presupposes the union, or rather the combination, of both temporal and spatial continuity.”

We consider Guenon as an important and prominent example of thinkers who tried to remind people of the traditional metaphysical ideas. This metaphysical perspective does not share the modern tendency to attribute more importance to the practical applications of science than to science itself. This perspective attempts to link science back to principles of a higher order so that a particular science can be used as a support for elevating oneself to a higher knowledge.

With fire in their hearts and a blissful composure

They take everywhere armfuls of peace

Inside their eyes dews of infinity appear

The luminous riders, divine light on their faces

Like censers giving off fragrance all around

Leaving wisps behind, everywhere they pass

Offering the secrets of eternity to the world

Never-fading values in their thoughts

Like censers, giving off fragrance all around

In their gardens, like a legendary land

Springs of Paradise pour from crystal fountains

In their evergreen realm where no fall is seen

Everyday a new spring, everyday new blooms

In their gardens, like a legendary land

Angels hover in their horizons at each moment

They breathe the same air as heavenly spirits

Skies open their arms, constellations stand in salute

With their inner worlds like bays of Paradise

Angels hover in their horizons at each moment.

To some it brings bliss, to others perdition

Suddenly shows up at an unexpected location

Beyond which is Paradise or the pit…

The spirit is anxious to flee this world,

Breaths dying down in gasps

Everyone broods by the cold corpse;

The steps of the Angel of Death echo all around

Lonely lives reach death alone

Falling, standing and crawling in this abyss

Horizons stalked by nameless fears

In the end, buried in the void within

For the believer, calls are heard from the beyond,

They may fall, but like a drop, they still reach the sea,

Transcending the limits, extending to infinity

Free from the narrow confines of the mortal abode.

They step into the garden of spirits,

Walking under arches like rainbow,

Showers of joy, springs of bliss overflow,

A life-long journey unfolds its mystery.

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. David Hilbert

The concept of infinity has always fascinated humankind. The excitement and awe that are affiliated with the very idea of this concept inspire us. Poets, philosophers, artists, astronomers, mathematicians and ordinary people have pondered the questions related to infinity over the centuries. Is the universe finite or infinite? Is matter or space infinitely divisible? Is there eternal life? Where does a finite being get the idea of infinity from?

In this article, we first consider the concept of infinity from a mathematical point of view and then try to explain how that is connected to Divinity and the Attributes of God. An incorrect understanding of infinity in mathematics leads to seemingly irresolvable paradoxes; likewise, an incorrect understanding of the Attributes of God leads to an incomplete or incorrect understanding of creation.

Mathematical infinity

Any serious consideration of infinity inevitably leads to mathematics, where the concept has its deepest roots. Mathematicians use the symbol ∞ to denote infinity. To many people infinity is a sort of number that is larger than all other numbers. However, that is not an adequate description of infinity. Strange things can happen in the realm of infinity. Many intuitive ideas fail when infinity enters into the picture. This leads to apparent paradoxes. Here is one example that is attributed to David Hilbert (1862–1943), the famous mathematician whose quotation appears above.¹ Consider a hypothetical hotel with infinitely many rooms. On a stormy night all the rooms of the hotel are occupied, and a wet and miserable couple shows up asking for a room. The concierge comes up with this clever idea to make room for these people. He says, “The hotel is full but here is what I can do for you. I can move the guests from room 1 into room 2, the guests from room 2 into room 3, and so on. The guests in room n will move into the room n+1, for each n = 1, 2, 3, …”.

So, if we can have a hotel with infinitely many rooms it is possible to accommodate an incoming guest even if the hotel is totally full. But then we see that by a similar reasoning we can accommodate any number of guests, and in fact infinitely many more guests! Clearly, this is not possible in ordinary hotels with finitely many rooms that we are familiar with.

To get more sense of what might happen in the realm of infinity let us consider a couple of other examples. You would have no trouble accepting that two sets have the same number of elements if there is a one-to-one correspondence between them. For example, the set {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} has seven elements because it is in a one-to-one correspondence with the set {1, 2, 3, 4, 5, 6, 7} given by Monday1, Tuesday2,Wednesday3, Thursday4, Friday5, Saturday6, Sunday7. Note that there are other possible ways of setting up a one-to-one correspondence between these two sets but what matters is the existence of one such correspondence.

There is absolutely nothing surprising about this example. We all know that there are seven days in a week. However, if the concept of infinity pops up in a similar situation, counterintuitive conclusions are obtained. You may be surprised to find out that the set of all positive integers {1, 2, 3, 4, 5, 6,…} is in a one-to-one correspondence with the set of even positive integers {2, 4, 6,…}. One way of setting such a correspondence is

1 2 3 4 5

← ← ← ← ←

2 4 6 8 10 …

Therefore, there are as many even (positive) integers as there are of all (positive) integers (this is a mathematically correct statement), even though the set of even integers is a strictly smaller subset of all integers. Such a situation is not possible with finite sets.

There are other well-known examples of “paradoxes” involving infinity such as Zeno’s paradox, and Gabriel’s horn.²

Treating infinity as if it is like other numbers, even with the assumption that it is greater than all other numbers, is a major reason for these “paradoxes.” Their resolutions are obtained with a proper understanding of the nature of infinity and the concept of limit. For example, adding or subtracting one element, or any finite number of elements, from an infinite set does not change its size. In some cases adding or subtracting infinitely many elements from an infinite set does not change its size either!

Even mathematicians struggled with the idea of infinity a great deal before rigorously formulating the concept and the rules about it. The fundamental notion of modern calculus is limit, which is intimately connected to infinity, in terms of either infinitely small quantities referred to as “infinitesimal” or infinitely large quantities. It took mathematicians a long time to formulate the modern rigorous definition of limit, the rules involving infinity and infinite quantities, and sets of infinite size.

Infinity and understanding the Attributes of God

While the concept of infinity is essential in mathematics, it is not the only field where it is so important. Another field in which the concept is very important is theology. The concept of infinity is intimately connected to the concept of Divinity. In mathematics, compared to infinity all numbers are equal, and equally small. This fact is mathematically expressed as a/∞ for any number a, whether it is 7 or 17 million. This is parallel to the theological fact that compared to God we, and the rest of the creation, are infinitely small. Nobody can claim to be greater than any other human being or any other being in the universe, no matter how powerful or wealthy he or she might be. Therefore, we cannot attribute to anybody greatness to the degree of regarding him or her as divine. Nursi expresses this view in the following words:

“O human! It is a Qur’anic principle that you must not consider anything other than God Almighty as greater than you to the degree that you worship it. Nor must you consider yourself greater than anything and thus claim greatness before and dominion over it. For, just as all creatures are equally far from being the Object of Worship, they are also equal in being creatures.”³

We have seen that treating infinity like other numbers (even with the understanding that it is greater than all other numbers) leads to seemingly irresolvable paradoxes. Similarly, treating God like humans leads to an incomplete and incorrect understanding of God and the creation. God is not only greater than all that is created, He is also not bound by the kinds of restrictions that created beings are subject to. With His infinite power, creating one flower is as easy for Him as creating all the creatures on earth every spring. Creating all the trees in the world is no more difficult for God than creating one piece of apple. He can create countless things at the same moment. Creating a trillion things is no more difficult for Him than creating one thing.

Unfortunately, it is all too common to see the evidence of attributing incorrect characteristics and restrictions to the Almighty. For example, some “try to free God from the burden of special acts of creation”4 by attributing the development of species to evolution, natural selection, and random phenomena. They do not seem to understand that it is no “burden” for God to create anything, whether it be a tiny individual or billions of species. He can create a great number of things at once. He is not forgetful or incompetent. Nothing He does interferes with another one of His actions. He continues to create every moment everywhere in the universe and He has power to do so. He is closer to every one of us every moment than we are to ourselves: Assuredly, it is We Who have created human and We know what suggestions his soul makes to him, and We are nearer to him than his jugular vein (Qaf 50:16). Therefore, there is no burden for God in dealing with special acts of creation.

Since we are subject to many restrictions as humans, we may fall into the error of attributing similar restrictions to God. So, we need to be more careful when we consider the Attributes of God. One of the restrictions by which we are bound is time. Unlike us, God is above and beyond time. Many people have difficulty comprehending the idea of destiny (or qadar, or divine decree in Islamic literature). If we understand that God is not restricted by time, it becomes much easier to understand this concept. Since He is beyond time, He does not need to “wait” to see the consequences of events in the universe. While it is not our purpose to have a full discussion of this important article of faith here, we want to point out one of its connections with the topic. A detailed explanation of divine decree can be found in Said Nursi’s Twenty-sixth Word.5 Those who do not understand that God is not restricted by time ask questions like, “What was God doing before creating the universe?” This question is meaningless with a proper understanding of the Attributes of God.

Attributing to God deficiencies by which we are constrained, such as forgetfulness, tiredness, and incompetence, is a great mistake, one similar to treating ordinary numbers like infinity. It leads to paradoxes that we cannot resolve. It prevents us from having a proper understanding of God and the creation. We can only understand the mystery of the creation by a proper understanding of its Creator, and we need to be very careful when talking about the Attributes of this Creator.

Nuh Aydin is an associate professor of Mathematics at Kenyon College, in Ohio, USA.

Notes

1. Maor, E. To Infinity and Beyond: A Cultural History of Infinity, Birkhauser, 1987. See also http://www.brainyquote.com/quotes/quotes/d/davidhilbe181572.html; http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Hilbert.html; http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
2. Ibid.
3. Nursi, Bediüzzaman Said, The Gleams, Seventeenth Gleam, NJ: Tughra Books, p. 160.
4. Collins, F. S. Language of God, Free Press, 2006, p. 140.
5. Nursi, The Words, Twenty Sixth Word, NJ: Tughra Books, pp. 479–494.

Intention and sincerity

Excluding childhood and the time spent in sleep, an average person has about thirty years in total for everything else during his or her lifetime. Out of these thirty years, we spend most of our time on eating, school, work, family commitments, and other essential, but non-religious activities. As a matter of fact, in today’s world where everybody is busy, even a person who deems himself or herself “religious” might be considered lucky if he or she can spend an hour a day on traditional religious activities such as reading religious books, praying, and so on. Assuming an hour a day for thirty years, we would spend about fifteen months in total on traditional religious activities, and this is perhaps the upper limit for most people. So, the finite-to-infinite dilemma becomes even more interesting: keeping in mind that even one trillion years is nothing compared to eternity, how can one earn eternal paradise in all its beauty that is far beyond human imagination by spending not more than fifteen months to earn it? The answer is what Bediüzzaman Said Nursi describes as one of the four culminations of his life: intention.

The intention of an action can simply be defined as the true motive behind that action. A “sincere and pure” intention, in a religious context, can perhaps be defined as the true motive of drawing closer to God, and drawing closer to God only. Nursi states that “Intention changes ordinary acts and customs into acts of worship. It is a penetrating and pervading spirit through which inanimate states and deeds acquire life and become ‘living’ acts of worship. It is also through a special quality of intention that evil changes into virtue or good deeds. Intention is a ‘spirit’ that causes ordinary deeds and customs to become ‘living’ acts of worship.” Our intentions are indeed the soul of our actions and, provided that we believe in God, what makes our actions worthy of earning eternal paradise solely lies in the sincerity of our intentions. In a sense, our actions are a sequence of zeros and a sincere intention is a positive 1 in front of those zeros, whereas an insincere intention is a negative 1. That being said, we must pay particular attention not to act against well-established principles of the religion and claim that our actions still carry a good intention. For instance, under no circumstances is one allowed to harm an innocent civilian, even during war, and therefore there can be no good intention behind this crime.

By striving to achieve purity and sincerity in our intentions (known as ikhlas), we can expect the Most Compassionate and Most Merciful God to treat our activities as if we spend our entire life worshipping Him while still leading a regular, balanced life-provided that we respect the basic principles of the religion and avoid committing major sins. Throughout the Risale-i Nur collection, Nursi places tremendous emphasis on sincerity of intention. Nursi describes the fundamental characteristics of ikhlas in the Twenty-first Gleam: “[I]n this world, and particularly in the services done for the afterlife, a most important foundation, and a greatest power, and a most acceptable intercessor, and a firmest point of reliance, and a shortest way to the truth, and a most answerable prayer, and a most blessed and marvelous means of achieving one’s goal, and a most sublime virtue, and a purest form of worship is sincerity, or doing something good or any religious deed purely for God’s sake.” Nursi points out the relationship between actions, intentions, sincerity, and salvation as follows: “[Intention’s] ‘soul’ is sincerity or acting solely for God’s sake. Salvation is found only in sincere actions done in His way. Sincerity multiplies an action’s worth, and through it one can reach Paradise with a little action and in a short life.” Obviously, we can do only a finite number of good deeds during a finite lifetime. Thus, at least from a technical point of view, we cannot earn eternal paradise unless infinite reward is given to our finite actions. God is so merciful that He promises Heaven to believers with the good deeds of a short lifetime, and in order for this to happen, He demands purity and sincerity in the intentions of those good deeds. In other words, the secret component in this finite to infinite transformation is nothing but sincerity of intention.

So it turns out that ikhlas, that is, sincerity of intention, is not optional: it is mandatory, and it is of the utmost importance. So, how do we achieve ikhlas? Nursi defines the first rule for gaining and preserving ikhlas as follows: “You should pursue God’s good pleasure in your actions. If He is pleased with you, even if the whole world is displeased, it is of no consequence. If He approves, it has no effect even if all others reject your ideas and actions. When He is pleased and approves, even if you do not seek the approval of others, should He will it to be so and His Wisdom requires it, He will make others accept it and be pleased with you.” In our daily lives, we might be performing daily prayers, reading religious books, and performing other traditional worship activities. During these activities, it is critical that we make sure that our intention is to draw closer to God and nothing else. A prayer performed to make others think one is pious, a fast observed for health benefits, a Pilgrimage made to enjoy the journey, or wealth distributed to obtain good reputation will not only dishonor the owner of these deeds in the hereafter, but also be rejected as the intentions behind these actions are impure, insincere, and have no ikhlas in them.

There are numerous other activities in our daily lives that are essential to our well-being and social lives, but nonreligious in nature. We go to school or work every day, we eat, we sleep, we love our parents, spouses, and children, we spend time with our families and friends, we brush our teeth, and so forth. God the Most Merciful tells us that he will treat these activities as worship, but only if they are done with good, sincere intention (again, conditioned upon respecting the basic principles of the religion and avoiding major sins).

The key to being rewarded for simple, regular activities such as those above and achieving ikhlas in our daily lives is to ensure that our sole intention in every one of our activities is to draw closer to God and to draw closer to God only. Every individual can achieve ikhlas in different ways in different situations, but the ultimate goal is always the same: to have good intention and be sincere about it. For example, a man might work late every day so that he earns halal money to provide for his family and still has enough money to make donations for just causes. Another person might go to school to study, thus recognizing the names of God, the All-Knower and All-Wise. One might eat in order to be grateful for the food and be healthy enough to perform the daily prayers. Another person might sleep to rest and be more productive at work so as to really earn his or her wages honestly. A person might brush his or her teeth because he or she knows the body is a gift from God and he or she is responsible for taking good care of it. Another way to achieve ikhlas in our lives, as Nursi suggests, is to make sure that love for worldly things, such as delicious foods and fruits, parents, spouses, children, and friends, is for the sake of God and that all this love is given to God Almighty’s essence, attributes and names. Again, from an ikhlas perspective, perhaps we should reconsider plans to buy a huge flat-screen TV, or a luxury SUV, or a house by the lake with ten bedrooms and start asking ourselves how things such as these that we intend to do in the future will help us draw closer to God, if they ever will.

As argued above, good intention is able to convert daily activities into worship through sincerity and therefore earn its owner eternal paradise by the mercy of God. A second critical dimension of sincerity in intention is its continuity. That is to say, if a sincere believer lived not sixty or seventy years, but a thousand years, he or she would still be doing what he or she was doing all along: trying to respect the basic principles of the religion, avoid major sins, and do as many good deeds as possible with pure and sincere intention. This would not change if he or she lived five thousand years, or even fifty thousand years, and thus, he or she would still be seeking ways to draw closer to God even he or she did live in this world forever. This is why it makes sense that eternal paradise can be earned within a short lifetime.

If God is pleased with our intentions in our activities and if He wishes to do so, He might bestow upon us worldly rewards as well, such as success in career, health, or blessed offspring. A potential pitfall here is that the person might start expecting these rewards to continue and see his or her actions as a prerequisite for them, losing the purity in his or her intention as well as those worldly rewards. Prophet Muhammad, peace be upon him, said, “If anyone’s intention is to seek the hereafter, God will place his sufficiency in his heart and order his affairs, and the world will come to him submissively; but if anyone’s intention is to seek worldly good, God will place poverty before him and disorder his affairs, and only so much of it as has been ordained for him will come to him.”

Nursi warns that believers should avoid things which would harm sincerity the same as they would avoid snakes and scorpions. One should, however, keep in mind that achieving sincerity in each and every one of our actions is a process and might not happen right away. Yet we also should keep in mind that nothing done for His sake shall go unrewarded.

Denying or recognizing Infinite Attributes of God

All the attributes of Almighty God are infinite, although what we see in this world is a finite projection of those infinite attributes, as the world itself is a finite domain in all respects. For example, God is the All-Knower, but what we know about God’s knowledge is very limited. God is the All-Wise, but we do not know the reason behind many things. God is the Absolute Ruler, but the universe that God rules is finite. God is the All-Powerful Creator, but there are only a finite number of creatures in this world. All these examples illustrate that what we experience in this three-dimensional world is a vague shadow of God’s true attributes.

A nonbeliever who claims that there is no Creator and that things just happen by themselves therefore ignores God’s attribute of being the All-Powerful Creator. Someone who claims that there is no God and that there is nobody who rules this universe thus ignores the Absolute Ruler attribute of God, and so on. Denying God’s existence and ignoring God’s infinite attributes is the biggest sin that can ever be committed and it deserves infinite punishment-the fact that this sin is committed in only a short lifetime is irrelevant. (This is the case in worldly affairs too: punishment is determined according to the nature of the crime, not on how long it takes to commit the crime. For instance, a person can commit a murder in one minute, but the murderer may spend the rest of his or her life in prison.) Similarly, consider someone who believes in God, recognizes His infinite attributes, and tries to do good deeds with pure and sincere intention. It makes sense for this person to be rewarded with eternal paradise. From a similar point of view, it can be argued that even one hour of adult life spent with the firm belief in God and in His attributes is sufficient for paradise, and even one hour spent denying God’s existence and his infinite attributes suffices for eternal hellfire.

The intentions argument can also be used to explain how a nonbeliever deserves eternal punishment. As in the case with a sincere believer, a nonbeliever has the intention to continue to commit the sin he or she has been committing: if a nonbeliever lived not sixty or seventy years, but a thousand or five thousand years, or even infinitely many years, he or she would still be doing what he or she was doing all along: denying God’s existence and ignoring God’s infinite attributes, and this is why it makes sense for a nonbeliever to deserve eternal punishment.

A word of caution

It should be noted that this article does not claim to provide a complete logical explanation of why there is an afterlife, why the afterlife is eternal, or why some people will go to Heaven and some people will not. This article simply attempts to illustrate that all these concepts are reasonable and they make sense. Lastly, these are issues of faith and the author believes that matters related to faith and religion cannot be confined within the boundaries of logical, physical, or mathematical principles. After all, it was God who created the universe and everything in it, including the rules of logic, physics, and mathematics. Matters of faith are just that, and it is by our free will that we choose what to believe in. That being the case, one should still keep in mind that if there is indeed eternal life after death, paradise, and hellfire (which we believe there is), disbelief in them will not make them just disappear (just like closing our eyes will not make the sun disappear).

Vedat Akyuz has a PhD in applied mathematics and statistics.

Notes

1. Nursi, Bediüzzaman Said. Al-Mathnawi Al-Nuri, NJ: Tughra Books, 2007, p. 113.
2. Ibid.
3. Nursi. The Gleams, NJ: Tughra Books, 2008, p. 225.
4. Nursi, 2007, p. 113.
5. Nursi, 2008, p. 226.
6. Nursi. The Words, NJ: Tughra Books, 2005, pp. 649–650.
7. Tirmidhi 5320.
8. Holy Qur’an, Al-Zalzalah 99:7.

For the care of baby Zero, the numbers decided to take turns. Each number would hold the baby beside it. As the days passed, the numbers realized a puzzling fact. Those numbers who gave care in the right manner saw a never-seen abundance at home; everything would increase tenfold. The numbers who passed their turns superficially did not see any difference in their living. Was it a sign from God that the numbers could not grasp?

Days passed, and the numbers were expecting to see some developments in the newborn. It was supposed to make facial expressions, start uttering some meaningful sounds, make purposeful movements with its arms, and so on. But zero did not exhibit any of the expected qualities. The numbers thought, “Maybe it’s a late-developer.” But soon they understood that this number was disabled in many respects. It would not give any known response to any of the stimuli. It would not make a difference when used in summation or subtraction games. In the multiplication game, it would give a deep silence as the result, no matter how big a number it played with. And in the division game, no matter what number divided Zero, the result would be a hopeless reluctance to change. The numbers could not reconcile in their minds the miraculous abundance upon the proper care for Zero with its extraordinary disability. What was the deal with this baby?

Years flew by like a stream, and Zero entered adolescence. Now its body was not only growing very fast but was also assuming a more rounded shape, leaving its primitive seed-like dot form. With the rebellious instincts of adolescence, Zero discovered its ability to roll, instead of the step-by-step walk of the others. And soon it discovered that it was able to move much faster than the others by rolling. This unexpected burst of motor skills from Zero made the numbers very happy. They did not have to put burden themselves anymore to move Zero. Once a totally disabled baby, Zero was now the new roller in the numbers kingdom that even the wealthiest numbers could not catch up with.

The downside of this was that Zero was not able to stop. It had to hit another number for that, just like in the multiplication game. Maybe part of the wisdom of the apparent disability of Zero at the beginning of its life was that it needed to gain wisdom to control its super ability to move. However, especially within the first months of the discovery of its new skill, Zero just rolled, rolled and rolled. Even some accidents did not scare Zero from its attempts to roll farther and faster. After all, it had a proper justification for it, considering its long years of immobility.

As Zero grew even more, and as the numbers watched it closely, they realized it had another interesting feature. It possessed an enthralling beauty due to its perfect symmetry. How was it possible that such unparalleled elegance emerged in a number that was initially thought to be disabled? The numbers decided to consult the Savant One. One was the oldest among the numbers, was held noble among all others, and knew history very well. As knowledgeable and noble as it was, One was humble as well, as it would bend its torso to talk with children, instead of distinguishing itself among everybody by raising its head straight up.

Savant One said, “I have been looking at the ancient books about the signs of this number. As told, it was born disabled, and it was raised by its relatives; it then surpassed everyone else by its speed of motion and its perfect rotational symmetry. More than that, as Zero grows, it is assuming the shape that we observe in all heavenly objects. This young member of our community has more to teach us. We need to wait and see.”

After the numbers had left the house of One, Prime Minister Two could not hold back its words and raised its voice: “Could it be that the old guy is mixing things up due to its age? I mean, how do we know that the things written in those books are authentic? Zero is not totally different from us; it is just another number, anyway. Why are we bothering ourselves with something that no one has seen before? Are we going to leave the greatest numbers for the sake of this fledgling egg?” And then, Two burst into laughter. Some of the numbers joined it in laughing, and some others said, “We’ll see!”

As the years passed, Zero started questioning its existence, and contemplating its character as a number. It had heard the words of both the Savant One and the Prime Minister Two, but it could not come to an exact conclusion about itself. Maybe Two was right. Even if the ancient books did actually talk about someone, who said that it was Zero that was expected, anyway? So, with this mindset, Zero preferred a midway between that of Savant One and that of Prime Minister Two.

As Zero was leaving adolescence, something started bothering Zero from inside again. It was as if somebody were periodically disturbing its comfortable life by triggering emotions that were not satisfied with the daily stuff that Zero did. So, Zero started reflecting again. This time, it considered the things it had experienced so far in its unusual life story: its initial disability in life and the consequent burst of motor skill, its initial negligible size and the unparalleled beauty it exhibited as it grew, the words of the Savant One and those of Prime Minister Two, and so on.

It was one of those times that Zero felt a sudden shiver with the coolness of an inspiration that penetrated its whole body. Zero felt that its life was full of opposites, so that, by pondering over the respective non-existence and existence of its qualities, it might understand infinity. These thoughts motivated Zero to investigate infinity by talking to other numbers.

The answer that best resonated with what Zero felt was from Savant One: “I have not seen infinity, but I do know that I was the first one to exist among numbers. I feel that I could not have come to be out of nothing. And seeing all these numbers that came after me, I better understand that what made me is infinity. And, oh my little one, if you ask what one step before me was, the ancient books say that it is you who is going to reveal that.” And the answer that Zero did not like much was from the Prime Minister Two: “There is no such thing as infinity. No matter how great a number you imagine, by adding one, you can always obtain a greater number.

And, this is all there is about it; there is no one who has actually seen infinity, anyway; it is no more than a figment of our imagination.”

When alone, Zero thought, “I can understand Two because when it came to the world, it saw One already there; so, Two cannot comprehend coming to existence without an ancestor. But what I feel inside is more like what One tells me. One can realize the existence of something that triggered its existence because when it came to the world, there was none other than One.” After a silence, Zero mumbled, “If I exist, then you exist. But where are you? If only I could see you…”

Life had been very turbulent for Zero. First, disabilities that burdened it, then a sudden explosion of skills and emotions, then the painful questioning it went through without satisfactory answers, and finally a conclusion that brought peace along with a wish for homecoming. Soon after, not being able to stand the harshness of such turbulence, Zero fell sick. It started losing weight to the point that it almost returned to its initial state at birth. With this final sickness at such a young age, Zero had had enough of it here. Although everybody was sad about what was going on, at the same time they thought that the best thing for this unique number was to die.

And Zero died. They buried it under the quotient line. Roses grew on its grave, as beautiful as Zero, as noble as One. Thus commemorated was the phrase “one over zero,” in order to refer to this beauty. It was then that the numbers understood what Zero felt inside. And the numbers visited Zero from time to time, whenever they needed a glimpse of beauty stretching from infinity. As powerless as it was, Zero helped others understand infinity not by its existence among them, but by lying below them.