Imagine, for a moment, a rectangular canvas that is painted blue… OK, you’re done. That’s all you had to imagine. Yes, that’s the whole painting. No other shapes, no other colors, no subject. Is this Art?

In 2006, this painting was on display at MoMA, the Museum of Modern Art in NYC. It was painted in 1961 by Yves Klein. Klein, like many other painters who have also used monochrome abstraction as a technique, wished to challenge and expand peoples’ conception of art. Another artist who defied a classic definition of art was John Cage. John Cage (1912-1992) was most notably an American composer who wrote the famous piece for piano 4’33. This piece consists of a pianist approaching a piano and sitting there for 4 minutes and 33 seconds. A stopwatch is used to time the piece. The pianist never plays a single note. Is a silent piece of music, music?

Art is the expression of ideas or emotions. Under that definition, both the blue canvas and 4’33 are works of art. Artists created both with very clear ideas in mind.

But, surely neither the blue canvas nor 4’33 can compare to work by Leonardo Da Vinci or Mozart. Neither requires much skill, if they require skill at all. And both could definitely fall under the category of “my 5-year-old could do that.” Yet I am still going to argue that they are indeed works of art. Art doesn’t require skill. It is the expression of a thought or feeling through a medium.

However, I am not thick. I’m not going to say that one can compare 4’33 to the New World Symphony. The two pieces are by no means in the same class of music. The New World Symphony is an extremely intense and powerful piece that also includes gorgeous melodies and phrases. No one can say that about 4’33. The New World Symphony is clearly more interesting to listen to and as such, is a far better piece of music. But 4’33 cannot be discredited due to its lack of musicality. One could easily claim that Cage’s piece is more interesting conceptually.

So what about the power in art? If both the New World Symphony and 4’33 are meant to convey ideas and emotions, does one do a better job than the other? It seems that the New World Symphony has the leg up. This is because it uses music’s power to transform the audience emotionally in addition to conceptually. It uses beautiful phrasing and dynamics to provoke its audience emotionally. 4’33, on the other hand, cannot transform one emotionally in the same way because it never actually makes use of the medium: music. 4’33 can only make one think and question. And when you boil it down, what causes people to deeply react and take action? What leads people to do things — emotions or thoughts?

The question “What is art” will continue to plague people for years to come, as it is yet another unanswerable problem. But, art must include more than just work that requires enormous skill and aesthetic beauty. The umbrella of “Art” should cover pieces that hope to spark people’s minds and get them thinking. The Mona Lisa and the blue canvas can never be compared. Nevertheless, both can be included in the definition of art.

Catherine Hochman

The artist at work

I walked down the street, Paris coughing its winds into my pale skin. My eyelashes were soon clumped with the snowfall sweeping across the pin-top skyscrapers of the city. Suitcases and coats passed by down the snow covered street.

“What are we eating”, I asked as an overwhelming intoxication of hunger swept over me, the café’s smells being a large contributing factor.

“Would you like crepes?” my mother asked.

I responded with an enthusiastic yes and soon found myself in refuge of the cold by the warmth of a jelly filled crepe. Just like being in refuge from my past.

With a smile on her face she whispered in my ear, “Do you like it?” My eyes lit up giving her an answer to suffice.

A titan of architecture now but once a feat of engineering, the Eiffel Tower stood, a symbol of the ever changing French nation. Its large brown skeleton snoozed beneath its blanket of snow. Its limbs crisscrossing with its series of nails and bolts. A wow escaped my mouth as I looked up.

“Could I please see the camera?” I asked my father.

He reached inside his jacket and pulled it out. I quickly began taking pictures of the Eiffel Tower like a child with its toys; the legs, the different floors, and even a flash into the inside of the clausal structure. Five flashes flared from the camera’s pupil until I finally noticed a change in sound. The music was a whisper in my ear at first but as I walked closer, the lyrics began to form. And as I took another step I began to see a faint outline of where it was coming from. My parents wondering where I was going soon followed. The source of the song was a street performer. He held in his hands a guitar and in his throat a song. On him was a patched up jacket, beaten to a brown tinge from dirt and grime. His jeans were torn exposing his knees to the raw elements. I asked my mother, somewhat fluent in Canadian-French, what he was singing.

“I don’t know,” she responded inquisitively.

People passed by him, his hazel eyes darting back and forth searching for a potential customer; in front of him was a styrofoam cup, a rock in it to keep it from blowing in the wind, he was on qui vive.

I could feel the passion blowing through the monotone hues of winter, a new beat to an ever-changing world, the chords warming me. Helping me forget why we came here, my mother’s cancer the cloud that had been overwhelming us.

“Do you suppose he’s going to be okay? I sympathetically pondered. Though impossible for my mother to answer she gave a comforting yes, as I hugged close to her black corduroy jacket, guilt yanking at my heart strings. We smiled, sugar-coating what we both knew. I wasn’t asking about the man. We went up the elevator holding tight to the time we had left.

Philip Chowdry

Above the sky

Few people have been

But most people wonder

They look up each day and think

What goes on above the sky

Above the sky is where infinity lies

Infinity goes on way past the sky

Perhaps there is more than infinity

But how will we find out

What hides above the sky

Brandon Reiter

Random House Webster’s (4th ed) defines art as “1. the production, expression, or realm of what is beautiful.” Traditionally, art is used to refer to paintings, sculptures, or other masterpieces of the visual arts. Art can also include performing arts, such as music and theatre.

Yet it has also been used in reference to many other disciplines. For example, Sun Tzu’s famous manual The Art of War is a treatise on complex military stratagems, ideas as intricate and finely crafted as any sculpture. Its visual beauty is surely lacking, but Sun Tzu’s vision is for a military campaign as masterful as any canvas. Indeed, this campaign is set to paint a picture: with tactics and small-unit actions as the individual brushstrokes, but a grand vision as wide and broad of that of any “traditional” artist. Another example is Vladimir Vukovic’s classic Art of Attack in Chess. A chess attack can be as subtle and multifaceted as any great work of art, and even the smallest misstep can turn a clear win into a dead loss. Vukovic teaches the reader how to creatively work the pieces in a delicate tango, in a fine balance, to ensure ultimate victory. Yet, just as much as any of these things, mathematics is the production of the beautiful, and thus is an art.

How is math an art? In most high school classes, math is anything but an art, most often focused primarily on dull computations and repetitive operations. Yet unlike this “plug-and-chug” style of math that usually involves simply plugging numbers into formulae, real math has strategy as complex as anything in Sun Tzu’s book. And like the choreographed ensemble of pieces working in harmony found in Vukovic’s book, high-level math has a profound beauty all to its own. Real math is not computation, but proof.

A mathematical formula or idea means nothing until proven. Generally, a mathematician has an idea for what he or she wants to achieve, and must conjure the end formula. Just as an artist must transform a canvas into his beautiful vision, a mathematician must turn the familiar properties of the tangible world, the real numbers, into a formula that seems as if it was from another world. These proofs require immense creativity. Although there are general principles just as in painting or in the chess attack – for example, proof by contradiction or mathematical induction – no two proofs are the same.

Math is entirely based on a set of axioms, which are things that we assume about our world.  From these basic axioms, ideas as simple as 1 + 0 = 1, all of math can be constructed. Of course, the math that appears in our everyday lives, addition and multiplication and so on, follow from this. But that’s not all. There is so much more math that results – even the limitations of what can be discovered are unknown.

There is a group of seven famous conjectures (results that are suspected but not proven) many of which are very old, each of which has a million-dollar prize attached to its resolution. These are known as the Clay Millennium Problems. They have resisted attack by the best mathematicians in the world for hundreds of years and despite the sweat and tears of the greatest mathematical minds ever to roam the earth, they remain unresolved.

Some conjectures of this difficulty are relatively simple to explain. The famous Goldbach Conjecture states that every even number greater than two can be written as the sum of two prime numbers (a prime number is a number that cannot be expressed as the product of two other numbers). Although it is true for all numbers less than a billion, efforts to prove it for all numbers have stymied the world’s best mathematicians for over 250 years.

Another easily explainable mathematical result was stated by Pierre de Fermat in 1637. He claimed that the equation xⁿ + yⁿ = zⁿ has no positive integer solutions for n ≥ 3. For over 350 years, this had the status of a conjecture, as the world’s best mathematical minds ran into a brick wall. However, within the last 20 years, it has advanced to theorem status. One Andrew Wiles had dreamt of proving this incredible result from an early age. Eventually, the work of Ken Ribet made a major step towards proving Fermat’s Last Theorem, linking it to another conjecture. Wiles realized that the opportunity for a final proof was at hand, and devoted years to finding it. Eventually he was successful, and detailed his proof in a paper over 100 pages long. This paper is as masterful as any of the works of Michelangelo or Raphael. Of course, it is in a different form; instead of a large canvas, the proof is a smaller and thicker pamphlet. Instead of brushstrokes of color, Wiles used mathematical symbols: in this case, operations from what is known as Galois Theory. To the lay observer, these may seem arcane and incomprehensible, but to the mathematician they are no less beautiful than brushstrokes, masterfully combined and commingled to produce a finished work.

Instead of the painting masters, such as da Vinci and Monet, or chess masters, such as Tal and Shirov, math has its own personalities: notably, Carl Friedrich Gauss and Leonhard Euler. Their names and artistic results litter the pages of mathematics textbooks in many fields, where it is impossible not to encounter a beautiful proof by one of these two.

For those interested in math, there are several websites and books that I highly recommend. The Art of Problem Solving company has a series of very interesting books that do an excellent job of livening up the high school curriculum. They also have a forum whose participants include some of the best mathematical minds in the world. There are also math competitions for high school students that I have found to be extremely enriching and fun. One of the primary sequences is the American Mathematics Competition (AMC) that culminates in the selection of the American Team for the International Mathematics Olympiad.

Yet in high school mathematics we rarely are aware of the art of math. High school results do not descend deep enough to see this: they barely skim the surface. Sadly, most high school interpretations of math are purely formulaic. Thus, mathematics is thought of as a boring subject. Something is fundamentally wrong with this approach to teaching math. Even at my high school, Stuyvesant, one of the foremost mathematical schools in the country, math is treated by many teachers and students alike as dull. This truly reveals the extent to which our math education system is broken.

But regardless of the boring way it is taught in high school, mathematics at a certain level indeed can be beautiful. Once one reaches the point of proving instead of plugging, math is, I feel, the most interesting subject there is. To me, mathematics is most definitely an art.

Acknowledgements: I’d like to acknowledge Joseph Stern (now at Columbia) and Jim Cocoros, both my teachers and mentors at Stuyvesant, for inspiring me to see the light of math.

Zachary Young

Come back on October 11th to read Eric Greitens article on how his involvement in humanitarian work around the world led to Strength and Compassion, his book of photographs and essays.

A smile yearning for happiness, although she always gratefully accepted what she was given. Liesel’s soul was spotless, white, and beautiful. Perhaps that’s exactly why Death seemed to be so attracted to the young German child. Very soon, however, her sheltered home erupted into something much more dark, cascading into a greater world. An evil world. A Nazi world.

The Book Thief, by Markus Zusak, is an astonishing story that seems to contain every genre possible. From romance, to tragedy, to humor, to historical fiction, The Book Thief encompasses it all.

Once I was introduced to Liesel, I could feel my hands clasp tighter to the book’s binding. The very moment Liesel Meminger arrives on Himmel Street, Germany, her dead brother’s eyes continue to haunt her. After her mother intends to transport Liesel, as well as her brother, to a foster family, tragedy strikes, and alters her life forever. Even with the enormous dilemma of her brother’s death, Liesel is forced to overlook her sorrow, and is compelled to continue onward to her new home, her new parents, her new world. Yet there is one thing that binds the strong young girl together: a mere book. Ironically, Liesel is illiterate, yet her absolute adoration of literature is touching. She soon arrives in the secluded town, and is welcomed by her new family: Hans and Rosa Hubermann. While Hans, a gentle accordionist, soothes her cold nightmares, Liesel’s foster mother is far more brutal. As Hans begins his late night reading lessons with Liesel, the German family’s sequestered town is gradually utterly engulfed by the enormous plague sweeping the world: Hitler’s words and the actions that come of them. Liesel’s surreal perspective on both life and death soon alters. Liesel’s giddy outlook on life, her pleasant home and family, soon morph into something entirely different: the will to survive.

All the while, Liesel is having a minor love affair, yet with an unexpected item: books. Once her current book becomes tattered and worn, it comes time to steal yet another story. However, she only steals when needed, and this is exactly what I admired most about the young book thief, her perspective on the process of give and take. She took so little, yet returned great love and passion to the world. Liesel knew precisely what she required for herself, yet also knew what to reward those surrounding her. I began the story utterly furious with Liesel and her will to only take so much, when she deserved so much more.

Yet in the end, I came to a cold, stone truth: I was envious of the poor, nearly starving child. Unlike Liesel, I seem to devour everything that would give me any form of benefit, and when it comes time to give something back, I do it merely because I feel I am so very generous, and should be praised. Yet Liesel is a unique young lady. She gives back to the world not because it makes her feel generous, or she feels she deserves to be commended, but because it is merely the right thing for her to do. If there is a God, perhaps there shouldn’t be religion simply because we should all feel compelled to live under Liesel’s code: when she does right, it feels like, and is, the right thing. When she does wrong, it feels, and is wrong.

Liesel and her foster family soon find themselves within the tricky predicament of hiding a Jew named Max. Liesel unveils more and more of herself to her new, dangerous Jewish friend, and also discovers what might happen to those who try to help him. The Book Thief not only revealed to me what was being described, but also let me touch it, emotionally. My favorite attribute of the book, was its writing ability that twisted and turned its reader.

This story gave me a challenge. A great challenge. Markus Zusak creates an evocative and wry portrayal of death, and a sense of what evil, and what beauty really is. The Book Thief unlocked sections of myself I truthfully didn’t know existed. It’s ironic. You can find yourself through losing yourself within The Book Thief.

Ali Merrill

What would happen if she touched it? With no one in sight, Katherine extends her arm just inches too far. This is a tragic mistake. Rachel, her sister, screams for help. Their father, however, is convinced that she pushed her baby sister into the fire. She is accused of pushing the person she loves so greatly into the pit. She’s accused by her own father. Did Katherine really just reach out too far? Or is her only sister responsible for the scars that will stay with her forever?

“The petrol burnt fiercely. Acid flames covered Katherine’s brown hair and her head, burning her hair, her face, her body. Acid flames covered her arms and her little body’s chubby folds and soft baby skin.”

The agony that Katherine experiences throughout her lifetime is carefully depicted throughout these pages. Set in Australia, you do feel as if you are there. From the wildlife to the slightly different vocabulary, we know we aren’t in the United States.  The main character is a swimmer, a big sport in Australia. She is a swimmer whose own coach wants her off the team because she’s so different looking. While Katherine is always outside and in nature, I’m not sure why the author picked the title “Butterflies.” Maybe it’s because of the symbolic aspect of butterflies. They are transformed so dramatically. Whether it is the painful fire that practically consumes Katherine or the rough behavior from upperclassmen in her school that make her feel even more self-conscious, either way, Katherine comes across as an everyday girl. Yet, she has elements of heroism in her blood, and one truly loyal friend who helps her cope. It is fascinating to find regular teen problems combined with a terrible disaster. The problems Katherine faces create an amazing page turner.

This book is a phenomenal work of art. It portrays the most subtle, yet deep emotions that make you crave more. The main character is continually trying to figure out how she really feels. Her life is out of balance, and she’s always trying to get some equilibrium. Will the bully stop taunting her? Will the others stop laughing at her?

Susanne Gervay uses unusual techniques to tell this story. The author introduces her main character in the present moment, during an awkward incident at school. But then, there are flashbacks. Through these flashbacks, you come to understand Katherine. The author introduces her main character’s unimaginable horrific scarring, but at the same time, successfully makes you feel as if you were the one living with burns. Wishing you were someone different. Gervay also effectively portrays Katherine’s relationships with her sister, mother, friends and most noticeably, her father.

Aside from the conflict of her being ‘different’ from everyone, a large part of the plot focuses on the main character being curious about her father. She doesn’t really know him. He left her mother because raising the children was too difficult. Not only has he become an alcoholic, but it is never clear if one of his daughters injured the other on purpose. Did he just imagine it while he was drinking? Katherine’s father cannot deal with this uncertainty at all. It is heartbreaking to experience Katherine’s intensifying anger towards him, as he comes to visit at random times. Many years without him makes it hard to tell if she will let him back into her life, or forget him forever.

Katherine just wants to lead a normal life, one with a father and with the skin everybody else has. She is tired of the endless skin grafts and how differently people treat her. Will Katherine’s wishes be fulfilled? Will she learn to live with her looks, with who she is? Or will she get the scars removed, the way one doctor suggests. If her scars are no longer evident, will she change entirely? Is it more important to fit in, or to be yourself?

I would rate this book a solid 4 out of 5. Susanne Gervay does a great job of creating a believable character with unique needs, and a dream that might come true. Read it and find out if it does!

Katie Champlin

One step at a time

I noticed how the sun shines through the trees shedding canopies

I gaze at the light dancing onto forest floor,

I stare at leaves descending down

the scent of cedar fills the moist air.

All the sound around me slowly dimmed

like the last slow song at a hushed dance

but in this case, the last course.

My feet are firmly on the wobbling wire

hands resting beside me, holding the harness

my gloves warm and damp, with my hands locked on the harness.

I take a quick glance at my feet and the ground some thirty feet below,

my ankles shaking and weak.

I can feel the breeze swaying the wire.

The faint sound of children laughing and playing below

one step at a time.

I feel soft footsteps on the wire

the wobbly wire creates a rhythm

I turn around to catch a glimpse of a familiar face

she’s walking ever so slowly.

With one slip that familiar face is hanging suspended in the air

I watch as she strains her body to reach the rope feet above her head

I monitor her as she pulls her arms up in agony

and she regains her balance.

I still walk I step on the wooden platform

into safety.

I unhook my clips and re-hook them on the zip line

they click together like a million pins hitting the floor

without a thought I swiftly soar through the air

fear is absent in my mind

I accelerate hands free dangling in the open air.

Sometimes I wish everything was that easy

and when I look up into the cloudless blue sky

I wish I could be able to just let go and fly

instead of going to a soccer practice for two hours,

and doing homework for a few more.

But I still wish I could just be able to just let go and fly.

Kaeleigh Morton