Pi is a perfect example of Sagittarius on film. It explores the nature of reality and God through the language of mathematics and spirals. The story follows Max as he searches for patterns in the numbers underpinning reality and slowly losing his mind. It raises interesting questions about the dangers associated with the pursuit of truth and the line between genius and madness.
Pi was Darren Aronofsky’s debut and was shot in high contrast grainy black and white. This means there’s very little gradation between dark and light, giving it a unique look and feel. The excellent score by Clint Mansell reinforces the manic atmosphere and frenetic pacing which mirrors the protagonist’s state of mind. There’s also a fair bit of maths abuse going on, which may or may not be deliberate, depending on how you want to interpret the story.
Max Cohen is a genius mathematician obsessed with finding patterns in nature so he can understand reality and the mystery of existence. He lives in a cramped apartment with his self-built modular computer, called Euclid, that he uses to test his assumptions. He’s doing research into patterns within systems, like nature and the stock market.
Max is socially awkward and anxious and has multiple locks on his door. He avoids his neighbours and always makes sure there’s nobody about before he leaves the apartment. But a little girl called Jenna often manages to corner him so she can test his maths genius using her calculator. He never gets an answer wrong.
But Max also suffers from debilitating migraines and takes a lot of medication to keep his symptoms under control. It doesn’t work very well so he’s constantly passing out and getting nosebleeds.
All the headache sequences start with a thumb twitch, then escalate into screaming pain and hallucinations, and end with a white screen. But the hallucinations pop up in other places too, often on the subway. He spends a lot of time in the subterranean tunnels – his own personal underworld, like a labyrinth he can’t escape.
Max risks his sanity in pursuit of his obsession and constantly crosses the line between reality and imagination. He might be a genius or he might be crazy – or perhaps he’s both. Either way, it’s hard to tell what’s real and what isn’t, and the ambiguity is deliberate. There are several possible endings that relate to the various levels of reality going on in Max’s head.
In a voiceover, he tells us that the headaches started when he was six after he stared into the sun and damaged his eyes. His eyes recovered, but something inside him had changed. He’s driven to find answers, but it’s not clear what’s driving him.
In between bouts of research, Max visits his old maths tutor, Sol Robeson, who acts as a mentor figure. Sol gave up his research into pi after having a stroke, and now spends his days caring for his fish and playing Go with Max. He thinks Max is overdoing it and chasing something unattainable, like Icarus flying too high to the sun.
But Max’s paranoia gets worse when his work attracts the attention of two groups of people. Marcy Dawson, an agent for a Wall Street firm, wants his research so she can control the stock market. While Lenny Meyer, an Hasidic Jew, believes there’s a particular number that translates as the unspeakable name of God. That number is 216-digits long.
After running a test, Euclid crashes, but Max manages to print the result: a 216-digit number. He thinks it’s a bug, a mistake caused by human error, but then discovers it might be meaningful after all.
Before we get to the interesting stuff, let’s address the maths abuse. There are a lot of mistakes and the biggest howler presents the biggest problem: the 216-digit number, the result of Max’s research.
Towards the end of the film, Max is taken to meet the Hasidic sect who explain why they need the number. They want to usher in the Messianic age by pronouncing the true name of God, as represented by the number. Max tells the Rabbi:
“I’m sure you’ve written down every 216-digit number. You’ve translated all of them. You’ve intoned them all. Haven’t you?”
But that’s impossible. There are too many to count. In fact, there are 10216 216-digit numbers, which is an unimaginably large amount. In comparison, there are about 1023 stars in the universe, while the estimated number of atoms in the universe is only 1078! The Mind Blown blog explains:
“One billion computers, spitting out one number every second night and day since the dawn of human history, would not have generated every possible 216-digit number by now.”
The other mistakes relate to the Golden Ratio, which Max writes down incorrectly as: “A : B :: A : A + B” which means A / B = A / A + B. It should be: “A / B = A + B / A.” He also says the golden mean is represented by the Greek letter theta (θ), but it’s actually represented by phi (φ). He says theta but then writes it correctly and draws a spiral out from the symbol:
The maths errors might be down to bad research on the part of the filmmakers (although Aronofsky acknowledges the golden ratio mistake in his commentary). Or it might be a deeper clue to what’s going on. It’s possible to interpret the mistakes as evidence that Max isn’t a genius mathematician. Perhaps he really is crazy and hallucinating the whole thing. His symptoms could be the result of temporal lobe epilepsy or some other problem.
This makes sense of the movie, but I think it’s a less interesting interpretation. It’s too safe – explaining away what happens as: it’s all in his head and he’s nuts. Considering Aronofsky’s other films and his obvious interest in Kabbalah and mysticism, it’s more likely that the maths is just wrong. Most people wouldn’t recognise the mistakes – I certainly didn’t (cos I’m thick!).
The filmmakers didn’t bother making the maths accurate because for the majority of the audience it wouldn’t be an issue. They could have used the fact of there being too many 216-digit numbers to count, but that would have raised its own questions, like: why would everybody assume this was the correct number? To be honest, that question comes up anyway…
Whatever. Limiting the possibilities enabled them to streamline the storytelling and keep it simple, even if it is factually incorrect. The film is ambiguous enough as it is, and you can easily interpret the maths mistakes as evidence of Max’s breakdown. Perhaps he really is a genius – or was – but the migraines have tipped him over the edge.
Max isn’t the only one stepping over the edge. Lenny Meyer is doing his own mathematical research using gematria. (See the “Amazing!” clip here.) Gematria is a type of numerology developed by Kabbalah scholars where each Hebrew letter is assigned a number. Once you know the numbers you can calculate the numerical value of any word from the sum of its letters.
Lenny and his group believe the Torah contains a code, hidden by God, and they’re looking for the specific code for God’s name. Max recognises the Fibonacci sequence in some of the numbers and realises that spirals may hold the key to the answer he’s seeking.
“If we’re built from spirals, while living in a giant spiral, then everything we put our hands to is infused with the spiral.”
He may be right, but it’s not that simple. Max is pursuing the unknowable. He’s trying to understand pi, an infinite number, so it’s an impossible quest. Lenny and his Rabbi want to pronounce the name of God and bring themselves closer to the Garden of Eden – a return to innocence and simplicity. Another impossible quest.
The Rabbi explains that only the pure can speak the name of God, and that Max isn’t worthy. He’s just a messenger. But Max has now developed a full-blown Messianic complex and believes he’s the chosen one. The Rabbi says the number isn’t meant for him because he isn’t pure:
“It’s killing you! Because you are not ready to receive it.”
Every time Max has a headache, it ends with light bursting in and obliterating everything else – as if he’s seeing God. In a final attempt to gain understanding, he throws away his medication and allows the light to overwhelm him. He disappears into a white void and slowly recites the number under his breath. According to the director’s commentary, this is meant to represent an encounter with God and the sound of ‘Om’ is mixed into the soundtrack.
But when Max comes back to reality, he’s alone in his wrecked apartment. Nothing has changed. He saw the light, but did he understand it?
Sol knows his quest is impossible and warns Max to slow down and take a break. Max is over-thinking everything, not just in their game of Go, but in his research. In an echo of Bruce Lee in Enter the Dragon or Obi Wan in Star Wars, Sol tells him:
“Stop thinking, Max. Just feel. Use your intuition.”
But Max is in the grip of an obsession and can’t stop. He thinks Sol has given up on life and stopped believing in patterns. But Sol knows where this obsession is leading. Over a game of Go, he tries to get through to his ex-protégé and explains the dangers of confirmation bias:
There are worse things than ending up a numerologist (!) but Max doesn’t listen and plunges headlong into disaster. Of course, it turns out that Sol knew the number all along and finding it caused his stroke. He gave up his research because he realised the number was dangerous.
When Max returns from his encounter with the light, he comes to the same conclusion. The stock market crashed because the Wall Street agents used part of the number and it caused a meltdown – just as Euclid crashed before spitting out the number. In a similar way, it caused Sol’s brain to crash in a stroke. Max realises that nobody should possess this knowledge so he burns the paper containing the number. Unfortunately, it’s still in his head.
Using a phrenology map, he finds the part of his brain that deals with numbers and maths. There’s a scar on his scalp at that spot that looks like a Hebrew letter. It resembles Tsade in its final form, used at the end of a sentence. Tsade is related to the word Tzaddik, which means a just and righteous person who is humble in the face of God. The tzaddikim are also said to be God’s messengers, which is what the Rabbi calls Max.
In Kabbalah it’s believed that God created the world by withdrawing in an act of tzimtzum, or contraction. Because the word for this act begins with the letter Tsade, it’s seen as God humbling Himself to make room for the life He was creating. If God didn’t withdraw, the creation would be overwhelmed by His light and nothing could exist except that light. This is why God is ultimately unknowable. From New Kabbalah:
“Creation does not involve a limitation in the divine being, which remains completely intact, but rather a limitation in knowledge of the Divine: an estrangement of certain points within the ‘world’ from the knowledge that all is One. God does not change in His being, it is rather that His presence is obscured.”
Now Max understands that some things should remain unknown and mysterious, and in an infamous scene, does a spot of self-trepanning with a power drill. (I’m not posting that cos it’s pretty grim but you can see it here – if you dare!)
Max no longer wants the knowledge he’s been chasing all this time and is humbled in the face of the truth. The answer he found wasn’t what he expected and had consequences he didn’t foresee. The wise know that not knowing is true wisdom.
These ideas are also found in the philosophy that underpins Go. The game was adopted by Buddhists as part of their practice because it helps in overcoming attachment. It also embodies the four Buddhist principles of emptiness, interconnectedness, impermanence, and selflessness.
The number of possible games is astronomical so game play is open-ended, like reality, and the stones only have significance in relation to other stones. The point of the game isn’t necessarily to win but to explore the possibilities within the game. You become a master, not by winning but by creating interesting games.
There’s no point in being attached to winning because trying to win actually undermines the nature of the game itself, and you learn more from losing than winning. If you want to play more interesting games and become a more skilful player, then losing isn’t a bad thing. You have better games when you don’t try to control the outcome.
In the final scene, Max sits on a bench and watches the leaves dance in the breeze while little Jenna fires maths questions at him. But he doesn’t know the answers – and for the first time in the film, he smiles.
Before we end, I can’t write about a fictional genius finding patterns in pi without mentioning the real life version. Martin Armstrong has found cycles in human behaviour that conform to pi, but it’s a lot more complicated than in Pi. His Economic Confidence Model follows the rules of non-linear fractal geometry and is created from cycles of various lengths that interconnect to form longer cycles of time. It’s fiendishly complex and yet underpinned by some simple ideas.
All of reality is formed from cycles, right down to the molecular level and can be understood using Wave Theory and what Armstrong calls the Geometry of Time:
“The entire universe is constructed upon the model of self-referral that replicates perpetually into the future. This is a delicate complex pattern of interaction combining to create space, time, matter, motion, and energy. It is the interaction between these elements that create the beat or pulse of the universe that flows in waves of energy in a cyclical motion.”
One of the cycles he identified is 8.6 years long and contains 3,141 days. This is pi x 1000. There’s also a 224 year cycle made up of 26 of these shorter cycles. In his article, It’s Just Time, Armstrong notes the interesting coincidence that the number 26 is the number of the Hebrew name of God: Yahweh. It also relates to the length of the Precession of the Equinoxes that creates the Great Year in astrology, and it shows up in the Mayan calendar too.
We can’t control these cycles, we can only ride them like a wave. We’re like ants, running on hidden patterns we don’t understand.
Whether you’re a genius or crazy – or both – the truth is the same either way. That truth is the wisdom of not trying to control life and recognising that you can’t know everything with your puny human mind.
- Read Martin Armstrong’s article It’s Just Time here (pdf)
- More on the Economic Confidence Model here
- Read more on the Game of Go and philosophy here