Chaos theory, the anguish of freedom, and the banality of evil
Unpredictability as a connecting point between science, existentialism, and political philosophy
An extended version is available at philpapers.org.
I n the 1960s, Edward Lorenz (1917–2008), a meteorologist and mathematician at MIT, set out to understand the climate. Using an LGP-30 computer from Royal McBee, which weighed approximately 360 kg, he simulated a simplified climate model that greatly simplified atmospheric convection processes. One day, while repeating a simulation, he entered values rounded to three decimal places (instead of six) as the initial conditions. After some time, the simulation produced a radically different result to the previous one, which had used six-digit numbers. Initially, he believed that the difference was due to an error in the simulation. Perhaps there were flaws in the magnetic drum or some error in the implemented algorithm. At that time, computers were still new and unreliable. However, upon investigating more carefully, Lorenz realised that the reason was the rounding of the initial conditions. The computer stored numbers with six decimal places, but only printed three. When he entered the rounded values (e.g. 0.506 instead of 0.506127), the difference appeared minimal, yet it grew exponentially over time. Then, he realised that the divergence was not a computer error, but rather a characteristic of the dynamic system itself. This led him to formulate the idea of sensitivity to initial conditions, a concept that would later become known as the ‘butterfly effect’. In other words, small changes to the initial conditions of complex systems, such as the climate, can have unpredictable consequences.
“Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” — Edward Lorenz.
In 1963, Lorenz published the article ‘Deterministic Nonperiodic Flow,’ in which he presented the famous Lorenz attractor, which generates a fractal geometric structure in phase space (the ‘strange attractor,’ see below). His discovery demonstrated that even perfectly deterministic systems — governed by exact mathematical laws — are capable of exhibiting unpredictable behaviour in the long term due to their extreme sensitivity to initial conditions.
A deterministic system is one in which it is possible to predict the future state of a system, such as the position of a particle or the voltage in an electrical circuit, with complete accuracy, given the initial conditions and the forces acting on it. For example, if we know the speed, acceleration and position of a car on a road, we can calculate its future position exactly. The same reasoning applies to the past: simply work backwards through the equations of motion to determine where the car was an hour earlier. In other words, the past and future of a deterministic system are entirely predictable.
However, in a random system, it is impossible to predict the exact outcome of an experiment; only the probabilities of each possible outcome can be calculated. When tossing a coin, for example, the outcome of ‘heads’ or ‘tails’ is unknown, but the probability of each outcome can be calculated. By repeating the experiment a large number of times, we can demonstrate using the law of large numbers that the frequency of ‘heads’ approaches the actual probability. In other words, although the results of random experiments are unpredictable, probability patterns emerge. Below, we present the results of a computer simulation of a fair coin toss.
In this way, Lorenz discovered that a deterministic system could be unpredictable in the future. He identified a characteristic of random systems in a deterministic system. It was something unexpected. Since the 19th century, Laplace had defended the idea that knowing all the initial conditions and the laws of nature would make it possible to predict the past and the future with absolute precision — the famous concept of “Laplace’s demon”. However, Henri Poincaré (1854–1912) demonstrated through his studies of the three-body problem that, even in deterministic systems, small variations in the initial conditions could quickly amplify to the point where practical prediction becomes impossible. Thus, Lorenz’s discovery confirmed an intuition already present in Poincaré through numerical simulations. This discovery confirmed that uncertainty prevails in nature.
“We can consider the current state of the universe as the effect of its past and the cause of its future. An intellect that, at a given moment, knew all the forces that set nature in motion and all the positions of all the elements that compose it, if that intellect were also vast enough to submit this data to analysis, would encompass in a single formula the movements of the largest bodies in the universe and those of the smallest atom; for such an intellect, nothing would be uncertain, and the future, like the past, would be present before its eyes.” — Pierre Simon, Marquis de Laplace, in “A Philosophical Essay on Probabilities”.
Lorenz’s discovery has had a profound impact on science and philosophy, transforming our understanding of the predictability of natural systems. Although we can measure the state of the atmosphere with great precision, it is impossible to predict the weather accurately beyond a few days. This is because small differences in initial conditions can quickly lead to large variations, making the future unpredictable. This phenomenon shows that systems such as the climate, ecosystems and ocean currents, which are deterministic, can exhibit chaotic behaviour and become unpredictable in the long term.
In philosophical terms, everyday decisions can be interpreted in light of the butterfly effect theory, which states that seemingly small actions can trigger vast and unpredictable consequences. A notable example is Charles Darwin’s decision to participate in the HMS Beagle expedition (1831–1836), which ultimately led to the publication of On the Origin of Species (1859). Captain Robert FitzRoy wanted an educated companion with scientific knowledge for the voyage, someone with whom he could discuss science and philosophy, as he feared feeling lonely at sea. Darwin accepted the invitation in 1831, aged 22, unaware of the impact the voyage would have on his life and on science.
During the voyage, Darwin collected thousands of plant, animal and fossil specimens, and kept detailed journals. Upon his return to England in 1836, his notes and collections were studied intensely and served as the basis for the theory of evolution by natural selection, which he presented in his book. Although Alfred Russel Wallace (1823–1913) arrived at similar conclusions independently, he did not have the same volume of evidence, which would likely have delayed the acceptance of his ideas. Therefore, Darwin’s decision to embark on the expedition ultimately led to the development of one of the most influential theories in the history of science.
This butterfly effect can also be observed throughout history, such as in the assassination of Archduke Franz Ferdinand in Sarajevo. This relatively minor event triggered a complex sequence of political alliances, military mobilisations, and diplomatic decisions that culminated in the First World War (1914–1918). In other words, just as chaotic systems are full of unpredictability, so too are our lives and world history.
Chaos theory is also present in everyday life. Societies, economies, social networks, ecosystems and even individual lives comprise numerous interacting variables that produce unpredictability about the future. One consequence of this is anguish of freedom, which was addressed by Jean-Paul Sartre (1905–1980) in his 1943 work Being and Nothingness. Anguish arises when individuals realise that they are radically free and therefore responsible for their choices and their consequences. In other words, our future depends on decisions that only we can make. These decisions influence not only our own future, but also the futures of others. Each decision leads to a series of events whose outcome is unpredictable. The butterfly effect can be seen as a metaphor for existential responsibility: our small actions or choices can have enormous and unexpected future consequences.
“For lack of a nail, the shoe was lost. For lack of the shoe, the horse was lost. For lack of the horse, the message was lost. For lack of the message, the war was lost.” — Chinese proverb.
Decisions such as changing jobs, moving to another city or beginning a relationship can be distressing because they confront us with the radical responsibility of our own lives and the fact that we cannot fully predict the consequences of our actions. Similarly, we feel distressed when our decisions affect other people, such as family members or friends. For example, refusing a management position may result in someone else being appointed who may dismiss colleagues. Likewise, failing to participate in community decisions, such as voting, could lead to corrupt candidates being elected. All our actions lead to unpredictable long-term results, and this is a source of anxiety.
“Man is condemned to be free.” — Jean-Paul Sartre.
Michael Faraday (1791–1867), for example, was a young man with little education. He began his career as an apprentice bookbinder in a printing shop, but his curiosity and studious nature led him to greater things. In 1812, he attended a series of lectures by the renowned scientist Humphry Davy in London, sending him detailed notes which demonstrated his keen interest and considerable ability. Impressed by his dedication and talent, Davy hired Faraday as a laboratory assistant in 1813, launching his scientific career. This would lead him to make fundamental discoveries in electricity and magnetism. Without Davy’s support, Faraday might never have made the discoveries that revolutionised electricity and magnetism, paving the way for modern motors and electricity generation. In other words, we might still be years behind current advances, and you would not be reading this text on a computer. Davy’s decision to hire Faraday triggered a series of events that would revolutionise physics and engineering.
As we are constantly faced with decisions throughout our lives, the anguish that Sartre describes seems inevitable. But is it possible to avoid it? There is a seemingly simple solution: not to care about our choices, ignoring the consequences of our actions. In other words, if our decisions have negative consequences, we simply would not worry about them. However, this attitude would have even more serious implications. Let us consider an example.
During the Second World War (1939–1945), Adolf Eichmann was a high-ranking Nazi officer and a key figure in organising the Holocaust. Working at the Central Office for Jewish Emigration and the RSHA (Reich Main Security Office), he coordinated the deportation of millions of Jews to concentration and extermination camps. Following the war, Eichmann fled to Argentina, but was captured by Israeli agents in 1960 and brought to trial in Jerusalem the following year.
In 1963, the German-born Jewish philosopher, political theorist and writer Hannah Arendt (1906–1975) followed the trial of Adolf Eichmann, expecting to find a sadistic monster or psychopath in the dock — some villain like those we see in Hollywood films, such as Darth Vader or Thanos. However, she noticed that he seemed completely ordinary: a typical bureaucrat who followed orders without reflecting on the gravity of his actions. He simply did what he was told and claimed to be acting within the law, without considering the consequences. He even claimed to adhere to Kantian ethics — an ethics based on duty rather than the consequences of actions. Imagine, for example, that a murderer comes to your door and asks you where their intended victim is. Would it be morally correct to lie in order to save the victim’s life? According to Kant’s categorical imperative, lying is always wrong. Therefore, we should tell the truth without worrying about the consequences. This was the attitude Eichmann adopted.
Thus, Arendt observed that ‘evil’ does not stem from explicit intentions to destroy or hatred, but from a lack of critical thinking and blind obedience to rules. In order to commit an evil act, one need only fail to do good. In other words, evil arises when we fail to consider the consequences of our actions. Therefore, although not considering the effect of our actions may free us from anguish, it can lead to disastrous consequences. Based on these observations, Arendt formulated the concept of the ‘banality of evil’.
“The most shocking thing about Eichmann’s trial was not the monstrosity of his actions, but his mediocrity and apparent inability to think about what he was doing.” — Hannah Arendt.
The banality of evil can manifest itself in various everyday contexts. For instance, a teacher might set tests without considering whether students are actually learning, treating education as mere bureaucracy and perpetuating inequalities by failing to prepare them adequately for life in society. Similarly, a judge may apply the law strictly and mechanically, even when this results in injustice. They may, for instance, severely punish someone who commits a crime to feed themselves, ignoring their social vulnerability. Likewise, a lawyer may defend clients or companies that cause harm, such as pollution or worker exploitation, justifying their actions as fulfilment of their professional duty. Likewise, a chemist may develop foods full of additives or sugar, which are harmful to health, on the grounds that they reduce costs. A journalist may publish false or biased information to please their media outlet or sponsors, disregarding the social impact of their actions. While these are not crimes or intentional acts of cruelty, these practices contribute to the production and perpetuation of evil due to a lack of ethical reflection.
Therefore, based on what we have discussed so far, it seems that we have no choice: we either experience anguish with every decision we make, or we live without reflection, running the risk of becoming complacent and committing evil acts. Is there another alternative? Actually, yes. We can turn to Greco-Roman philosophy for this.
Around 300 BC, Zeno of Citium (c. 334–262 BC), a Phoenician merchant, settled in Athens following a shipwreck. There, he began studying philosophy. Coming into contact with Cynics, Megarians and Academics, he developed his own school from this mixture. He taught at the Stoa Poikile (“Painted Portico”), which gave rise to the name “Stoics”. Zeno laid the foundations of classical Stoicism, which were further developed by Chrysippus, Seneca, Epictetus and Marcus Aurelius. Each of these philosophers adapted the doctrine to their own time. Stoicism essentially seeks to understand the world and offer tools for living well with wisdom and virtue, regardless of external circumstances.
“What we do now echoes for eternity.” — Marcus Aurelius.
Stoics argue that we cannot control the course of the world; only our actions and attitudes towards it are within our control. The key is to focus on the things that depend on us, such as virtue, conscious choices and moral rectitude, and to calmly accept the things that do not. This approach reduces anxiety because we are not trying to control the uncontrollable, yet we are also not becoming indifferent. We have an obligation to act virtuously whenever we can. In other words, as the Stoics would say, we cannot control the ultimate consequences of our actions, but we have a duty to act fairly and correctly in every decision we make.
Therefore, we should not be held responsible for actions whose consequences are completely unpredictable. For instance, the evaluators at the Academy of Fine Arts Vienna cannot be blamed for rejecting the works of a young Austrian painter in 1907 and 1908, deeming his depictions of human figures inadequate, despite recognising merit in his landscapes. This rejection led the painter to abandon art and pursue a career in politics. He later became the leader of the Nazi Party and was responsible for some of the greatest tragedies of the 20th century, resulting in the deaths of millions of people.
Conversely, there are decisions whose consequences are more predictable and for which we are accountable. For example, maintaining a healthy diet tends to reduce the risk of disease, just as offering support to someone with depression can aid their recovery. Similarly, teachers who dedicate themselves to teaching and motivating their students tend to produce more skilled professionals and contribute to societal development. This was the case with Michael Maestlin (1550–1631), who ended up decisively influencing his student, Johannes Kepler (1571–1630), by teaching the Copernican model at the University of Tübingen — a risky move at the time. Kepler, in turn, formulated the laws of planetary motion and drove the scientific revolution in the early modern age. Therefore, it is essential to reflect on our actions and seek those that generate positive outcomes, even if we cannot predict all of their long-term consequences. As John Stuart Mill (1806–1873) wrote in his book On Liberty (1859), ‘Every individual should be free to act as he wishes, provided he does not harm others.’
“Every individual should be free to act as he wishes, provided he does not harm others.” — John Stuart Mill (1806–1873), in his book On Liberty (1859).
Therefore, we must address the anxieties revealed by the unpredictability of the world, as suggested by chaos theory. However, we must avoid falling into a state of indifference that trivialises evil. We must take responsibility for making conscious, ethical and well-considered decisions, critically evaluating the consequences of our actions.
Further reading
- Chaos: Making a New Science, James Gleick.
- Being and Nothingness: An Essay in Phenomenological Ontology, Jean-Paul Sartre.
- Eichmann in Jerusalem: A Report on the Banality of Evil, Hannah Arendt.
