“9.13. Personal note:
When I was a little kid, my mother told me not to stare into the sun. So once when I was six I did.”
-Max Cohen in the film Pi
Darren Aronofsky’s award-winning directorial debut Pi, is a science-fiction thriller about the haunting journey into the genius mind of a renegade visionary Maxamillion Cohen (Sean Gullette).
I was first introduced to Aronofsky's work when a friend lent me Requiem for a Dream (2001). Based on the novel by Hubert Selby Jr, the film sacrifices dialogue in favour of beautiful and harrowing visual imagery. The unique style of cinematography captured my imagination and I began looking for other examples of Aronofsky's work.
Watching Pi for the first time was an arduous yet ultimately rewarding experience. Shot in black and white, the monochrome images are grainy and underexposed. The script is dense with mathematical dialogue that is cipher like in its complexity and the underlying themes are nothing less than biblical. Not to mention the sequences in which Max's 'headaches' are shown in increasingly graphic detail to the point of self mutilation.
I have no intention of reviewing Pi for the purposes of this critical diary report. I invite open minded individuals to watch the film to inform their own opinions and I would warn mainstream cinema goers to proceed with caution. That being said I would like to explore in more detail some of the fascinating tributaries allured to in the film.
After watching Pi, for days I found myself contemplating the nature and possible implications of the following ideas. It’s just possible that they have altered my perception of the world we live in forever.
“12.45. Restate my assumptions.
1: Mathematics is the language of nature.
2: Everything around us can be represented and understood through numbers.
3: If you graph the numbers of any system, patterns emerge. Therefore, there are patterns everywhere in nature.”
- Max Cohen
The Fibonacci sequence
Max tells us that Fibonacci (or Leonardo of Pisa) was an Italian mathematician in the 13th century. In fact Fibonacci has been called the greatest European mathematician of the Middle Ages because he made a discovery which has excited natural biologists and mathematicians for hundreds of years.
In mathematics the sequence in which each number is the sum of the two preceding numbers is widely known as the Fibonacci series:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, ...
Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.
Fibonacci number patterns occur so frequently in nature (flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal "laws of nature".
In fact the Fibonacci sequence appears everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.
Spirals and the Golden Section
"My new Hypothesis: If we're built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?"
- Max Cohen
If you draw two small squares together, then draw another square using the combined lengths of the two squares as one side and carry on repeating this process you create a set of Fibonacci rectangles. This is a set of rectangles whose sides are two successive Fibonacci numbers in length, composed of squares with sides that are Fibonacci numbers, or in other words, the ratio of the sides of these rectangles equals that of the golden section.
The Golden Spiral is a mystical shape that is an absolute in both abstract mathematics and chaotic nature. It was first discovered by Pythagoras, a failed Greek messiah and mathematical cult leader in the 5th century B.C.The Pythagoreans loved the golden spiral shape for they found it everywhere in nature: the Nautilus Shell, Ram's horns, milk in coffee, the face of a Sunflower, our fingerprints, our DNA, and the shape of the Milky Way.
Dr. Stephen Marquardt, a former plastic surgeon, has used the golden section to make a mask that he claims is the most beautiful shape a human face can have.
The Mask of a perfect human face
Chaos Theory
" That is the truth of our world, Max. It can't be easily summed up with math..."
- Sol in Pi
Max is looking for a way to understand our world. He applies the principles of Chaos Theory to the Stock Market (a non-linear, dynamic, chaotic system) in order to determine the pattern behind apparent random nature of market prices.Chaos Theory can be generally defined as the study of forever-changing complex systems. Discovered by a meteorologist in 1960, chaos theory contends that complex and unpredictable results will occur in systems that are sensitive to small changes in their initial conditions. The most common example of this, known as the "Butterfly Effect," states that the flapping of a butterfly's wings in China could cause tiny atmospheric changes which over a period of time could effect weather patterns in New York.Although chaotic systems appear to be random, they are not. Beneath the random behaviour patterns emerge, suggesting, if not always revealing, order.
Plato's Cave
Plato (427–c.347 BC) likens people untutored in the Theory of Forms to prisoners chained in a cave, unable to turn their heads. All they can see is the wall of the cave. Behind them burns a fire. Between the fire and the prisoners there is a parapet, along which puppeteers can walk. The puppeteers, who are behind the prisoners, hold up puppets that cast shadows on the wall of the cave. The prisoners are unable to see these puppets, the real objects that pass behind them. What the prisoners see and hear are shadows and echoes cast by objects that they do not see.
From this we can infer that human beings are incapable of comprehending absolute truth. Our own preconceptions and the limited capacity of our own cognitive powers and senses distort meaning in everything; all that is left is conjecture and partial truth.
Were the prisoner's in Plato's cave able to turn and see the truth behind them they would know God, as God is infallible and absolute.Max's own search to find meaning in the universe can therefore be read as an attempt to find God. Max's severe headaches could therefore be attributated to his attempts to atain God like knowledge. His mentor and friend Sol warns him of the dangers of reaching for these heights by recounting the greek myth of Ikarus to his former student.
Kabala
Kabala is an ancient aspect of Jewish mysticism dating back to the time of Moses. Consisting largely of speculations on the nature of divinity, creation and the soul, Kabala is said to have originated from the oral law which Moses received from God. The principle root of Kabalistic tradition is a belief in the divinity of the Torah (the first five books of the bible), and that by studying it one can unlock the secrets of creation.
"The Torah is just a long string of numbers. Some say that it's a code sent to us from God."
- Lenny Meyer, in Pi
During the course of the film Max is approached by Lenny Meyer a Hasidic scholar and evangelist who educates Max about the practices of Gammantria; the use of mathematics to unlock the secrets of the Torah.
Ancient Hebrews used the alphabet as their numerical as well as there lettering system, therefore, each letter was assigned a numerical value. For example the Hebrew "A," aleph, is equal to one, while "B," bet, is equal to two and so on. Taking this into consideration, we can then convert the entire Torah into a large string of numbers. When these numbers are analysed, patterns emerge, not unlike the patterns revealed in the hotly contested and now widely discredited book, The Bible Code By Michael Drosnin.
