PI, Darren Aronofsky, 1998

Epiphany or Apophenia?

Apophenia has been defined as the experience of seeing meaningful patterns or connections in random or meaningless data; that the patterns themselves do not really exist. It is often attributed to high levels of dopamine in the brain and in some cases is seen as symptoms of psychosis and schizophrenia. Yet pattern recognition is one, if not the, most critical of skills that a human possesses. As cognitive scientist Nick Chater states:

The cognitive system must cope with a world that is immensely complex but that is, nonetheless, highly patterned. The patterns are crucial. In a completely random world, prediction, explanation, and understanding would be impossible – there would be no patterns on which prediction could be based, to which explanations could refer, or the comprehension of which could amount to understanding. Even more fundamentally, without any patterns relating actions to consequences, there would be no basis to choose one action rather than another. The ability to find patterns in the world is therefore of central importance throughout cognition.[1]

So the idea that our minds subconsciously seek out patterns and connections is not contentious and neither is the idea that we all, to some degree, experience apophenia; we are all capable of making false connections. However, in the main, apophenia is attributed to people who have religious, paranormal and supernatural experiences. They believe in such things as God and UFOs, numerology, astrology, divination, and they see meaning in coincidences. But what makes certain experiences the areas of false connections and pattern recognition and others not? When does pattern recognition go from being a genuine understanding or insight into the nature of reality, to a delusion; from an epiphany to apophenia?

Max Cohen, the main protagonist in Darren Aronofsky’s directorial debut film  (Pi: Faith in Chaos), believes that the patterns that exist within nature can be represented by numbers and conversely, the numbers of the stock market represent a pattern; the film centres on Max’s quest to discover this pattern. He is depicted as a brilliant and gifted mathematician and number theorist. Sol, Max’s mentor, considers him to be his greatest pupil, published by 16 and achieving a PhD at 20. However, like John Nash in A Beautiful Mind, Max is also neurotic and paranoid. He displays phobic behaviour, shutting out most of the natural world – both physically and emotionally – and suffers crippling headaches, hallucinations and blackouts for which he heavily self medicates. Aronofsky adeptly sets up Max’s character so that Max can be seen as either a genius or as a psychotic. Clarification as to which he is, is never given and even at the end of the film, when Max perceives himself to be having an epiphany, it is very much left up to the audience to decide what it was that Max was actually experiencing and why. However, the decision is not an easy one to make. Max is a sought after expert in his field and if he says he has discovered the underlying order and structure of the universe then what grounds would we have in claiming that he is wrong?

Arguably one of the deciding factors on whether we perceive Max’s experience as an epiphany or apophenia is on how we view Max’s original assumptions and hypothesis. If we believe that Max’s position is a tenable one, that it is not only possible to discover a pattern in the stock market but that this pattern is also the underlying order and structure of reality, then his epiphany is entirely plausible. If we do not then the decision that he suffered a psychotic episode would become the most plausible. Yet if, as Chater states, pattern recognition is a universal behaviour then whose or which authority do we accept as a guide to help us make a decision? In other words which patterns offer insight on the nature of reality and which do not? It may be felt that only science and scientists have the authority and the wherewithal to offer us the best guidance, but it is not the case that science and scientists have a united voice on such issues. The prevalent scientific worldview is dominated by reductionism, viewing reality as particles in motion and considers that the deeper we go inside the atom the closer we will come to understanding the nature of reality. In part, it is the worldview of scientific materialism that has led to certain patterns that we discern within the world to be relegated to apophenia and under this worldview Max’s experience would be considered as such. As noted by Thomas Kuhn:

Normal science…whether historically or in the contemporary laboratory… seems an attempt to force nature into the preformed and relatively inflexible box that the paradigm supplies. No part of the aim of normal science is to call forth new sorts of phenomena; indeed those that do not fit the box are often not seen at all.[2]

Max’s assumptions and hypothesis cannot be accounted for within the reductive scientific paradigm and does not fit the remit of what constitutes ‘normal science’ and, therefore, would be dismissed as untenable.

However, with the advent of chaos theory the scientific climate is changing. Chaos theory, contrary to its name, is about orderliness within dynamical systems; systems that are capable of changing over time. Chaotic dynamical systems are non-linear which means that unlike linear systems where the output is proportional to the input, in non-linear systems the output is disproportional; it can either be more or less. This means that slight changes to the system – its initial conditions – can have dramatic effects to its overall progression. This sensitivity to initial conditions ensures that their futures are unpredictable. One of the features of chaotic systems is that they appear disorderly and random. Nevertheless, the overall behaviour of the systems or the patterning that they follow can be known and it is because of this that chaos theory is also known as deterministic chaos. Chaos theory, therefore, concerns itself with understanding the universal behaviour, patterning and hidden order of these systems and chaos theorists examine the data that has hitherto been considered random and meaningless.

Under this scientific worldview Max’s hypothesis is a cogent one. Chaos theorists have already established that trends in the stock markets can be assessed so that the patterning, or overall behaviour of the stock market, is taken into account when attempting to predict fluctuations. The world is seemingly filled with chaotic dynamical systems, systems that follow patterns, and chaos theory has already established itself in disciplines such as biology, geology, economics, psychology, population dynamics, robotics, meteorology,  and politics, to name but a few. As more disciplines become aware of the validity of chaos theory the more widespread its use is becoming.

The patterns that chaotic dynamical systems form or make – by following strange attractors – are called fractals. Fractals are phenomena which are self similar. Their basic structure is formulated by a self repeating pattern which increases exponentially, dominated by a power law and displaying symmetry across scale. Whether you zoom in or out on a particular fractal the patterning is consistent. For example, if you zoomed in on a branch of a tree, you would not be able to distinguish if it was a branch, a tree or a twig. Only by including background information are you able to differentiate. In the same way, you can only appreciate that you are examining an atom and not a galaxy by taking into consideration the context of your investigatory process.

Just what pattern recognitions this new science validates remains to be seen and undoubtedly not all that is considered as being apophenia now will become justified. However, it is interesting to note that if an atom and a galaxy follow a similar pattern then how far-fetched is the notion that astrological charts can depict the pattern of an individual’s life? If the axiom held by many ancient traditions “as above so below” is shown to be a truism, as fractals would seem to suggest, then how many of our sacrosanct scientific and philosophical premises would need to be revised? How many theories, such as those of Heraclitus and Leibniz, will need to be taken back down off the shelves, brushed off and looked at again in a new light? We’ll see.

Maria Taylor


[1] Nick Chater, ‘The Search for Simplicity: A Fundamental Cognitive Principle?’ The Quarterly Journal of Experimental Psychology, 52 (A), (1999) pp. 273-302 (p.273)

[2] Kuhn, structure of scientific revolution p.24


Chater, N., ‘The Search for Simplicity: A Fundamental Cognitive Principle?’ The Quarterly Journal of Experimental Psychology, 52 (A), (1999) 273-302

Kuhn, Thomas, The Structure of Scientific Revolutions, 3rd edn.,(Chicago: University of Chicago Press, 1996)

BLACK SWAN, Darren Aronofsky, 2010

Dionysus’s dance with Apollo.

“One must have chaos in oneself in order to give birth to a dancing star.” Friedrich Nietzsche, Thus Spoke Zarathustra, I, v.

Upon seeing Darren Aronofsky’s Black Swan and having particularly enjoyed the Nietzschean interpretations of There Will be Blood (Issue 74) and The Departed (Issue 65) in Philosophy Now film columns, I felt compelled to produce a Nietzsche-inspired piece myself.

Aronofsky’s haunting creation captivated me not only because of its spectacle as an aesthetically-powerful movie, but also for the resonance that it had with my own area of study – Nietzsche’s belief that language fails to render the cosmic symbolism of music. That said, I’m not so much interested here in Tchaikovsky’s powerful composition for the ballet Swan Lake (around which the story of Black Swan revolves), as in what I consider to be the clashing of two world-views. These are what Nietzsche coined the Dionysian and the Apollonian. ‘Dionysian’ is from Dionysus, the Ancient Greek god representative of intoxication and frenzy (known as ‘Bacchus’ to the Romans), while ‘Apollonian’ is from Apollo, the Greek god of a variety of things, including light, the sun, and medicine; but for the purpose of Nietzsche’s argument, he is mainly representative of reason. To Nietzsche, these two divine aspects form the distinct sides of artistic expression: the ‘Dionysian’ being the passionate, emotional element, and the ‘Apollonian’ being the visionary, intellectual element (see for example, his The Birth of Tragedy, 1872).

Nina: The Consummate ‘Apollonian’

Black Swan depicts the protagonist, Nina – played by Natalie Portman – on a frenzied journey in pursuit of the perfect performance in the lead double role in the ballet Swan Lake as both Odette, the White Swan, and Odile, the Black Swan. Overseen by her neurotic mother, Nina has become the consummate performer, and as the hottest prospect in her ballet company, is awarded the mantle of the lead role for the coming season’s shows. Through fastidious practice, complimented with intense discipline, she embodies the precise nature of the Apollonian White Swan. However, in the eyes of her domineering director Thomas – played by the excellent Vincent Cassel – she fails to capture the primordial essence of the Dionysian Black Swan for which he yearns. The visceral portrayal of Nina’s tumultuous journey in pursuit of embodying the Black Swan in order to deliver the perfect performance is provided not through a particularly complex script or dialogue, but predominantly through Aronofsky’s uniquely dark direction, which in turn is wonderfully accompanied by the cinematography of Matthew Libatique and the enthralling score by Clint Mansell (inspired in no small part of course by the work of Tchaikovsky). Through its highly stylised approach, the film builds relentlessly to an overture of epic proportions in its rendering of what embodying the Dionysian spirit of art entails.

The film culminates with Nina delivering a mesmerizing performance as the Black Swan. In the preceding hour and a half, viewers have witnessed her practice indefatigably in pursuit of perfection. However, we have also seen her go down a path of self-destruction due to her obsession: she has habitually scratched herself feverishly, to the point of bleeding; suffered torrid hallucinations; and, as a bulimic, also frequently induced herself to vomit. A final hallucination depicts her stabbing and killing a fellow dancer whom she perceives as a competitive threat. What is revealed, after she has delivered the performance of her life as the Black Swan, is that in the course of this hallucination she has actually stabbed herself. As the film nears its end, we see Nina bleeding, in all probability, to her death. Lying with tears in her eyes and an ever-so-slight smile, she appears a shattered figure, but at the same time enormously satisfied. She proceeds to utter a bittersweet reflection on all that she has suffered: “I felt it. Perfect. It was perfect.” The film then fades to white as the roar of the crowd chanting her name echoes on.

The fellow dancer whom she perceives as a threat is her hedonistic, sensual understudy Lily, played by the aptly cast Mila Kunis. On the face of it, Lily is the Black Swan incarnate. She even has a large tattoo of the wings of a black swan adorning her back – alluring, but also menacing. However, while Lily can deliver a more than capable performance as the Black Swan, Nina is an outstanding White Swan, and would attain perfection if only she could display an unbridled frenzy and passion in the role of the Black Swan to the same degree that her steely dedication masters her portrayal of the White. This perfection is something Lily cannot attain, for she is not as exceptional as the Black as Nina is as the White. As we’ll see, for Nietzsche, it would not be possible for anybody to excel as the Black Swan without crushing the White Swan part of themselves.

Welcome to The Well of Dionysus

For Nietzsche, the Dionysian spirit is more than just a way of thinking. Rather, it is a state of ecstasy and a ‘frenzy of becoming’, through which the Apollonian ‘veil of reason’ is torn asunder. In Daybreak (1881), Nietzsche exclaims that “what are wanted are blindness and intoxication, and an eternal song over the waves in which reason has drowned.” This dramatic proclamation summarises the purpose of his life’s work – and in particular, his endeavour to propagate the Dionysian way of thinking over that of the Apollonian. The outcome of this Dionysian outlook is displayed in all its intensity in Black Swan – that is to say, in the primal transformation of Nina into the Black Swan as she reaches her breaking point, having just, to her mind, stabbed and killed her understudy. She then enters the stage for the viewer to see her literally sprouting magnificent black wings, as we see her give herself over to the Dionysian frenzy which results in the primal, perfect performance of a lifetime: she has embodied Nietzsche’s cry for Dionysian passion.

The perfection for which Nina strives is analogous to what Nietzsche ascertains to be the supreme goal of art. This for Nietzsche can only be reached through immersing oneself in the unadulterated primordial passion of Dionysus. Accordingly, this passion is then able to unshackle one from the confines of the Apollonian realm of reason. But this paradigmatic shift in being, much like its messenger Nietzsche, is not for everyone. Nietzsche believes that the Dionysian is only for those strong enough, who have reached the limits of reason enmeshed in the Apollonian spirit. Hence, the Dionysian is only accessible by way of the Apollonian – the two are inextricably linked. Nina’s journey of suffering, and the manner in which she pushes Apollonian art to its limits, is a necessary pre-requisite for her to be able to enter Dionysus’s awe-inspiring well of the primordial. Furthermore, the Dionysian mentality is not something superficial, or something which can be dipped into on a whim. Rather, it requires unmediated passion – something of which Nina is actually capable, but Lily is not.

Not unlike the notion of Plato’s ‘Allegory of The Cave’, in which (crudely put) one falsely believes a shadow of an object to be the actual thing itself, Nietzsche argues that those who believe that the Apollonian is the truth of human perfection invariably perpetuate the relegation of the truly liberating Dionysian spirit, exclusively favouring works of reason as the ultimate expression of artistic freedom. As a result, unlike many reviewers, I do not consider Nina’s suffering in the film to be about mental illness per se, nor about the supernatural. Rather, I read Nina’s experience as the pain associated with transcending the confines of Apollonian reason, i.e., the pain of reaching for the Dionysian light outside the Apollonian cave.

Perfection Beyond Reason

Black Swan vividly depicts the struggle to transcend the limits that one has established and reach perfection. This is a painful process, and it may crush one to death. But as the pioneering martial artist Bruce Lee once said: “There are no limits. There are plateaux; but you must not stay there, you must go beyond them. If it kills you, it kills you.” Aronofsky increases the intensity continuously from the very first scene. This enables the viewers to immerse themselves in Nina’s surging to overcome her limits, and to feel the process of her embodiment of Dionysian frenzy. In a similar vein, Nietzsche’s provocative discourse in his books is emblematic of his Dionysian artistic purpose as a gadfly to provoke what he saw as a stagnated fin-de-siècle European society into striving onwards and upwards to greatness.

Nina’s striving towards, and ultimate attainment of, a form of perfection, illustrates the terrifying power of the Dionysian spirit in liberating its practitioners from the constraints of Apollonian ‘reasonableness’. In Black Swan, Aronofsky remarkably captures the clashing of two Nietzschean worldviews, and what results is an intense, dark and memorable audio-visual experience.

Dharmender Dhillon