“Blessed is the nation that doesn’t need heroes" Goethe.
“Hero-worship is strongest where there is least regard for human freedom.” Herbert Spencer.
"My 80% friend isn't my 20% enemy" Ronald Reagan.
Explain the assumption of a rational actor. Do consumers or firms live up to this assumption?
The assumption of a rational actor, also known as the rationality assumption, is a foundational principle in economics. It posits that individuals, consumers, or firms make decisions based on rational behavior to maximize their self-interest and achieve their objectives.
According to the rational actor assumption:
Consistent Preferences: Rational actors have well-defined and consistent preferences. They have a clear understanding of their needs and desires and can rank different options or outcomes based on their preferences.
Cost-Benefit Analysis: Rational actors engage in cost-benefit analysis when making decisions. They assess the costs and benefits associated with various choices and select the option that maximizes their overall satisfaction or utility.
Optimization: Rational actors strive to optimize their decision-making. They make choices that provide the highest possible benefit or utility given their available resources and constraints.
While the assumption of a rational actor provides a useful framework for economic analysis, it is important to recognize that in real-world situations, individuals and firms may not always perfectly adhere to the assumptions of rationality.
In the case of consumers, there are several factors that can influence their decision-making and deviate from perfect rationality:
Limited Information: Consumers may have limited information or imperfect knowledge about products, prices, or market conditions, leading to decisions that are not fully rational or optimized.
Behavioral Biases: Consumers can be influenced by behavioral biases, such as heuristics, social norms, emotions, or cognitive biases, which may lead to decisions that deviate from strict rationality.
Time Constraints: Consumers may face time constraints or cognitive limitations, making it difficult to thoroughly analyze all available options and make fully rational choices.
Regarding firms, while they are often assumed to be profit-maximizing rational actors, their decision-making can also deviate from perfect rationality due to various factors:
Managerial Discretion: Firms may be influenced by managerial discretion, where managers' personal goals, biases, or organizational constraints can affect decision-making, potentially deviating from strict profit maximization.
Incomplete Information: Firms may have incomplete information about market conditions, competitor behavior, or future uncertainties, leading to decisions that are based on imperfect knowledge rather than perfect rationality.
Organizational Considerations: Firms may also consider factors beyond profit maximization, such as corporate social responsibility, ethical considerations, or long-term sustainability, which may influence decision-making and deviate from strict rationality.
In summary, while the assumption of a rational actor provides a useful framework for economic analysis, individuals, consumers, and firms may not always fully live up to the assumption of perfect rationality. Factors such as limited information, behavioral biases, time constraints, managerial discretion, and organizational considerations can influence decision-making and lead to deviations from strict rationality in real-world economic behavior.
An assumption, in the context of economic models, refers to a simplifying belief or proposition about the behaviour of individuals, firms, or the overall economic system. These assumptions are necessary because economic models attempt to capture the complexity of real-world phenomena and make them more understandable and analysable.
Assumptions serve as building blocks for economic models, providing a foundation upon which the analysis can be conducted. They help economists create a framework that abstracts away unnecessary details and focuses on key variables and relationships of interest. By making assumptions, economists can isolate specific factors and explore their impact on economic outcomes.
For example, when constructing a model to analyse consumer behaviour, economists may assume that individuals are rational decision-makers who seek to maximise their personal satisfaction or utility. While this assumption may not accurately capture every aspect of real-world consumer behaviour, it simplifies the decision-making process and allows economists to predict how individuals might respond to changes in prices, incomes, or other factors.
Similarly, in the study of market dynamics, economists often assume perfect competition, which assumes a large number of buyers and sellers, identical products, and perfect information. Although perfect competition is rarely found in reality, this assumption enables economists to study market equilibrium, price determination, and the effects of various policy interventions in a more manageable way.
Assumptions in economic models also often employ the ceteris paribus principle, which means "all else equal." This principle assumes that while analysing the relationship between two variables, all other factors remain constant. This allows economists to focus on the specific relationship of interest without getting entangled in the complexities of simultaneous changes in multiple factors.
It is important to note that assumptions are simplifications and abstractions, and they may not always perfectly reflect reality. However, they serve a crucial role in economic modelling by making the analysis feasible, highlighting key relationships, and providing initial insights into economic behaviour and outcomes. While assumptions are necessary, it is also important for economists to continuously test and refine them based on empirical evidence to improve the accuracy and reliability of economic models.
Assumptions and simplifications in mathematical economic models can introduce potential biases and limitations in several ways:
Inaccurate representation of reality: Economic models are abstractions that aim to simplify the complex real world. However, by making assumptions and simplifications, models may fail to capture the full complexity and nuances of economic phenomena. These simplifications can lead to a mismatch between the model's assumptions and the actual behaviour of individuals, firms, or markets, potentially introducing biases in the model's predictions.
Omission of relevant variables: Economic models often involve simplifications that exclude certain variables or factors that may be important in real-world situations. This exclusion can limit the model's ability to provide a comprehensive understanding of the economic system under study. The omission of relevant variables can result in biased or incomplete analysis, as important drivers of economic behaviour or outcomes may be neglected.
Assumptions about individual behaviour: Many economic models rely on assumptions about the behaviour of individuals, such as the assumption of rationality or self-interest. However, these assumptions may not always hold true in reality. Individuals may exhibit bounded rationality, have imperfect information, or behave altruistically, which can deviate from the assumptions made in economic models. Such deviations can lead to biased predictions or inaccurate representations of real-world phenomena.
Simplified market structures: Economic models often assume simplified market structures, such as perfect competition, monopoly, or oligopoly. While these assumptions provide a useful framework for analysis, they may not reflect the complexities of actual markets. Real-world markets can exhibit various degrees of competition, market power, and imperfect information, which can introduce biases when using simplified market structures in economic models.
Linear relationships: Many economic models assume linear relationships between variables for simplicity and tractability. However, in reality, relationships between variables may be nonlinear or exhibit diminishing returns. Assuming linearity can introduce biases in predictions or policy recommendations, as it may not accurately capture the actual dynamics and interactions among variables.
Limited scope of analysis: Economic models often focus on specific aspects or sectors of the economy, neglecting interdependencies and feedback effects. This limited scope can introduce biases by overlooking broader systemic effects or failing to capture the full consequences of policy interventions. It is important to recognise that economic systems are complex and interconnected, and simplifications in models can restrict the understanding of these interconnections.
To mitigate these limitations and biases, economists employ various techniques, such as sensitivity analysis, robustness checks, and empirical validation, to test the assumptions and evaluate the robustness of model predictions. Additionally, economists strive to develop more realistic and nuanced models by incorporating more accurate assumptions, relaxing unrealistic assumptions, or adopting alternative modelling approaches to address the limitations and biases introduced by simplifications.
Principles of Economics Translated by Yoram Bauman
“It is difficult to get a man to understand something, when his salary depends on his not understanding it.” Explain with examples this quote.
The quote mentioned is attributed to Upton Sinclair, an American writer and social reformer. It highlights the idea that people may be resistant to accepting certain truths or realities when it conflicts with their personal interests, particularly when it comes to their financial well-being.
Here are a few examples to help illustrate this concept:
Climate Change and Fossil Fuel Industry: The fossil fuel industry has a significant influence on the global economy, employing millions of people and generating substantial profits. However, the burning of fossil fuels is a major contributor to climate change. Despite overwhelming scientific evidence linking human activities to climate change, some individuals within the industry may deny or downplay the issue. Their salary and livelihood depend on the continued production and consumption of fossil fuels, so acknowledging the environmental consequences could jeopardize their financial interests.
Tobacco Industry and Health Risks: For decades, the tobacco industry engaged in efforts to downplay the health risks associated with smoking. Studies have consistently shown that smoking causes severe health problems, including cancer, heart disease, and respiratory issues. However, the tobacco industry funded research and disseminated misinformation to create doubt and prevent public awareness. Executives within the industry, whose salaries were tied to tobacco sales, had a vested interest in maintaining the status quo despite the harmful effects on public health.
Corporate Lobbying and Regulation: Various industries engage in lobbying activities to influence government policies and regulations that could impact their business operations. In some cases, this lobbying can lead to the blocking or dilution of regulations that would protect public health, safety, or the environment. Those employed by these industries often participate in lobbying efforts to protect their company's profits and job security, even if it means disregarding the potential negative consequences for society at large.
Conflict of Interest in Research: Researchers who receive funding from certain industries or organisations may face conflicts of interest that can bias their findings or interpretations. Pharmaceutical companies, for instance, may financially support clinical trials for their own drugs. In such cases, there is a risk that researchers may have a bias toward positive outcomes or downplay any adverse effects, as their salary or future research funding could be tied to the success of those drugs.
These examples demonstrate how financial incentives can create a cognitive bias that hinders individuals from fully understanding or accepting certain realities. When people's salaries or economic interests are directly linked to a particular outcome, they may be inclined to ignore or dismiss information that challenges their existing beliefs or threatens their financial stability.
---
In the context of the quote, "not understanding" does not imply a lack of intelligence or education. Rather, it refers to the act of consciously or subconsciously refusing to accept or acknowledge certain truths or realities due to personal interests or biases.
While individuals who fall into this category may indeed be highly educated and rational, their understanding may be clouded or biased by their financial dependence on a particular outcome. The quote suggests that people may be resistant to accepting information or evidence that contradicts their existing beliefs or challenges their financial interests, even if they possess the intellectual capacity to comprehend it.
In many cases, these individuals may be aware of the information or facts being presented to them, but their motivations or incentives prevent them from fully embracing or acknowledging the implications of that information. This can manifest as denial, scepticism, or selective interpretation of evidence to protect their financial interests or maintain the status quo.
It is important to note that the quote does not imply that every person in such a situation will exhibit this behaviour, nor does it suggest that all individuals with financial interests are incapable of understanding or accepting opposing viewpoints. Rather, it highlights a common tendency for some individuals to resist or downplay information that may threaten their financial well-being, regardless of their level of education or rationality.
---
Brand loyalty and religious beliefs can also fall into the category described in the quote. While they may not be directly tied to salaries, they can still involve deeply ingrained personal interests and biases that affect one's ability to understand or accept certain information.
Brand Loyalty: Brand loyalty refers to the tendency of consumers to consistently choose and support a particular brand over others. When individuals develop strong brand loyalty, they may become resistant to accepting or considering information that challenges their perception of the brand's superiority. This loyalty can be driven by emotional connections, personal experiences, or even social identity. Even when presented with evidence or information about better alternatives, individuals may continue to support their preferred brand due to the sense of identity, familiarity, or other psychological factors associated with it.
Religious Beliefs: Religious beliefs often form a significant part of a person's identity and worldview. People's religious beliefs can provide them with a sense of purpose, meaning, and moral framework. When faced with information or evidence that contradicts their religious beliefs, individuals may experience cognitive dissonance or resistance to accepting alternative perspectives. This can be particularly true when the information challenges core tenets or fundamental beliefs that are integral to their religious identity. As a result, individuals may be inclined to dismiss or rationalize conflicting information in order to maintain the coherence of their religious worldview.
In both cases, brand loyalty and religious beliefs can create cognitive biases that hinder individuals from fully understanding or accepting alternative viewpoints. The emotional, psychological, and social dimensions associated with these beliefs can strongly influence how individuals process and interpret information, leading to a resistance to accepting conflicting evidence or perspectives.
It is important to note that not all brand loyalists or religious individuals exhibit this behavior, and there are individuals who are open-minded and receptive to alternative viewpoints. However, for some individuals, brand loyalty and religious beliefs can become factors that influence their ability to objectively assess information or consider perspectives that contradict their established loyalties or deeply held beliefs.
Explain how rules of thumb and irrationality can affect consumers’ demand for goods and
services.
Rules of thumb and irrationality can have a significant impact on consumers' demand for goods and services. Here are some examples:
Anchoring Bias: Consumers often rely on initial pieces of information as reference points when making decisions. For example, a consumer may see a product with a higher original price marked down to a lower sale price. The consumer's perception of value may be influenced by the initial higher price, leading them to believe they are getting a better deal than they actually are. This can affect their demand for the product.
Loss Aversion: Consumers tend to experience the pain of losses more intensely than the pleasure of gains. For instance, a consumer may be reluctant to purchase a product even at a discounted price if they feel it would entail a loss of money or regret in the future. This bias can impact their demand for goods and services, as they may avoid certain purchases due to a fear of potential losses.
Availability Heuristic: Consumers often rely on immediate examples or information that is readily available to make judgments or decisions. For instance, a consumer may base their perception of the quality of a product on the ease with which they can recall positive reviews or personal experiences with similar products. This heuristic can influence their demand for goods and services, as they may prefer products with readily available positive associations.
Social Proof: Consumers are often influenced by the actions and behaviors of others. For example, if a product or service is highly popular or endorsed by influential individuals, consumers may be more inclined to demand it based on the perception that it is desirable or of higher quality. This can create demand trends and drive consumer behavior even if the actual value of the product may not justify the demand.
Status and Conspicuous Consumption: Consumers may make purchasing decisions based on the desire to display social status or to signal their wealth and success. For example, consumers may choose luxury brands or high-end goods to project a certain image or to align with societal norms. This can affect their demand for specific products and services that are associated with prestige or exclusivity.
These examples illustrate how rules of thumb and irrationality can influence consumers' demand for goods and services. Consumers' decision-making processes are not always rational or based solely on objective evaluations of value. Instead, psychological biases and heuristics play a role in shaping their preferences and behaviors, leading to deviations from traditional economic models of rational decision-making.
Discuss the view that individual economic agents will always act as rational decision
makers so as to maximise their utility.
To properly discuss the view that individual economic agents will always act as rational decision-makers to maximize their utility, it's important to define and explain the key terms involved.
Rational Decision-Making: Rational decision-making refers to the process of making choices that are consistent with one's preferences and objectives, based on a careful evaluation of available information and the expected outcomes of different options. Rational decision-makers aim to optimize their choices to maximize their expected utility.
Utility: In economics, utility represents the satisfaction or value that individuals derive from consuming goods or services. It is a subjective measure of individual preferences and can vary from person to person. Utility can be expressed in different ways, such as happiness, well-being, or satisfaction.
Now, let's discuss the view that individual economic agents will always act as rational decision-makers to maximize their utility.
Supporters of this view argue that individuals possess rationality and have a clear understanding of their own preferences. They believe that individuals carefully assess the available choices, evaluate the costs and benefits associated with each option, and select the one that maximizes their utility. The rational decision-making model assumes that individuals have perfect information, are able to process information accurately, and act in their self-interest.
However, critics of this view highlight several limitations and challenges to the assumption of universal rationality:
Bounded Rationality: Human beings have cognitive limitations, and their ability to process information and make decisions is bounded. Limited time, cognitive biases, and imperfect information can lead to decision-making that deviates from the rational model.
Emotion and Psychology: Emotional factors and psychological biases can influence decision-making. People may make choices based on non-economic factors, social norms, or irrational beliefs, even if they are not in their best economic interest.
External Influences: The decisions of individuals are influenced by external factors such as social pressure, cultural norms, and advertising. These influences may divert individuals from making strictly rational choices.
Risk and Uncertainty: Rational decision-making assumes that individuals can accurately assess the risks and uncertainties associated with different options. However, people often face situations of uncertainty where the outcomes and probabilities are unknown, leading to decision-making based on imperfect information.
In reality, individuals exhibit a combination of rational and non-rational behavior, and their decision-making is influenced by a range of factors. While economic theory often assumes rationality, behavioral economics has highlighted the importance of understanding human behavior in a more realistic and nuanced way.
In conclusion, while the view that individuals always act as rational decision-makers to maximize their utility provides a useful framework for analyzing economic behavior, it is important to recognize the limitations and deviations from rationality that exist in real-world decision-making. Understanding the complexities of human behavior can provide valuable insights into economic outcomes and policy interventions.
How does the "rational economic actor" fallacy overlook the role of cognitive biases, imperfect information, and bounded rationality in decision-making within a capitalist system?
The "rational economic actor" fallacy assumes that individuals in a capitalist system always make decisions in a perfectly rational and self-interested manner. However, this belief overlooks the influence of cognitive biases, imperfect information, and bounded rationality, which can lead to suboptimal decision-making. Let's understand this concept with simple examples:
Cognitive biases: Humans are prone to cognitive biases, which are systematic errors in thinking that affect decision-making. For example, the availability bias occurs when people rely on easily accessible information rather than considering a broader range of data. In a capitalist system, this bias can lead individuals to make decisions based on recent news or vivid examples rather than carefully analyzing all relevant information. This can result in suboptimal choices, such as investing in trendy but risky assets without considering their long-term potential.
Imperfect information: In many economic transactions, individuals do not have access to complete and accurate information. For instance, when buying a used car, the seller may withhold information about the vehicle's hidden problems. This information asymmetry can lead to suboptimal decisions. Buyers, lacking complete knowledge, may overpay for a faulty car. In a capitalist system, imperfect information can distort market outcomes and hinder individuals from making fully rational choices.
Bounded rationality: Bounded rationality recognizes that individuals have limited cognitive abilities to process information and make complex decisions. People often rely on simplifying heuristics and rules of thumb instead of undertaking thorough analysis. For example, when choosing a product, individuals may rely on brand reputation rather than researching all available options. In a capitalist system, bounded rationality can lead individuals to make decisions based on incomplete information or superficial analysis, resulting in suboptimal outcomes.
Emotional influences: Human decision-making is also influenced by emotions, which can deviate from strict rationality. For example, investors may be driven by fear or greed during market fluctuations, leading to irrational investment decisions. In a capitalist system, emotional biases can contribute to market volatility and inefficient allocation of resources.
Social influences: People's decisions are often influenced by social factors, such as peer pressure or social norms, which may override individual rationality. For instance, individuals may conform to popular trends or engage in conspicuous consumption to fit into a particular social group. In a capitalist system, social influences can drive individuals to make choices that prioritize social acceptance over their own best interests.
In summary, the "rational economic actor" fallacy overlooks the role of cognitive biases, imperfect information, bounded rationality, emotional influences, and social factors in decision-making within a capitalist system. Recognizing these limitations is crucial for understanding that individuals do not always act in perfectly rational and self-interested ways. Policymakers and market participants should consider these factors to design regulations, incentives, and interventions that account for the complexity of human decision-making and promote better outcomes in the capitalist system.
The rationalist in me knows that coincidences are inevitable, mundane, meaningless. But I can’t deny there is something strange and magical in them, too wonders Paul Broks in The Guardian
In the summer of 2021, I experienced a cluster of coincidences, some of which had a distinctly supernatural feel. Here’s how it started. I keep a journal, and record dreams if they are especially vivid or strange. It doesn’t happen often, but I logged one in which my mother’s oldest friend, a woman called Rose, made an appearance to tell me that she (Rose) had just died. She had had another stroke, she said, and that was it. Come the morning, it occurred to me that I didn’t know whether Rose was still alive. I guessed not. She’d had a major stroke about 10 years ago and had gone on to suffer a series of minor strokes, descending into a sorry state of physical incapacity and dementia.
I mentioned the dream to my partner over breakfast, but she wasn’t much interested. We were staying in the Midlands at the time, in the house where I’d spent my later childhood years. The place had been unoccupied for months. My father, Mal, was long gone, and my mother, Doreen, was in a care home, drifting inexorably through the advanced stages of Alzheimer’s. We’d just sold the property we’d been living in, and there would be a few weeks’ delay in getting access to our future home, so the old house was a convenient place to stay in the meantime.
I gave no further thought to my strange dream until, a fortnight later, we returned from the supermarket to find that a note had been pushed through the letterbox. It was addressed to my mother, and was from Rose’s daughter, Maggie. Her mother, she wrote, had died “two weeks ago”. The funeral would be the following week. I handed the note to my partner and reminded her of my dream. “Weird,” she said, and carried on unloading the groceries. Yes, weird. I can’t recall the last time Rose had entered my thoughts, and there she was, turning up in a dream with news of her own death.
So, what am I to make of this? Here’s one interpretation: Rose died, and her disembodied spirit felt the need to tell me and found its way into my dream. Perhaps she had first tried to contact Doreen, but for one reason or another – the impenetrable wreckage of a damaged brain? – couldn’t get through. Here’s another interpretation: the whole chain of events occurred by sheer coincidence, a chance concatenation of happenings with no deeper significance. There’s nothing at all supernatural about it.
If you ask me which of those two interpretations I prefer, it would, unequivocally, be the second. But here’s the thing. There is a part of me that, despite myself, wants to entertain the possibility that the world really does have supernatural dimensions. It’s the same part of me that gets spooked by ghost stories, and that would feel uneasy about spending a night alone in a morgue. I don’t believe the universe contains supernatural forces, but I feel it might. This is because the human mind has fundamentally irrational elements. I’d go so far as to say that magical thinking forms the basis of selfhood. Our experience of ourselves and other people is essentially an act of imagination that can’t be sustained through wholly rational modes of thought. We see the light of consciousness in another’s eyes and, irresistibly, imagine some ethereal self behind those eyes, humming with feelings and thoughts, when in fact there’s nothing but the dark and silent substance of the brain. We imagine something similar behind our own eyes. It’s a necessary illusion, rooted deep in our evolutionary history. Coincidence, or rather the experience of coincidence, triggers magical thoughts that are equally deep-rooted.
The term “coincidence” covers a wide range of phenomena, from the cosmic (in a total solar eclipse, the disc of the moon and the disc of the sun, by sheer chance, appear to have precisely the same diameter) to the personal and parochial (my granddaughter has the same birthday as my late wife). On the human, experiential, scale, a broad distinction can be drawn between serendipity – timely, but unplanned, discoveries or development of events – and what the 20th-century Lamarckian biologist and coincidence collector Paul Kammerer called seriality, which he defined as “a lawful recurrence of the same or similar things or events … in time and space”.
The biography of the actor Anthony Hopkins contains a striking example of a serendipitous coincidence. When he first heard he’d been cast to play a part in the film The Girl from Petrovka (1974), Hopkins went in search of a copy of the book on which it was based, a novel by George Feifer. He combed the bookshops of London in vain and, somewhat dejected, gave up and headed home. Then, to his amazement, he spotted a copy of The Girl from Petrovka lying on a bench at Leicester Square station. He recounted the story to Feifer when they met on location, and it transpired that the book Hopkins had stumbled upon was the very one that the author had mislaid in another part of London – an advance copy full of red-ink amendments and marginal notes he’d made in preparation for a US edition.
The vision thing … a solar eclipse. Photograph: Chiwi Giambirtone/Reuters
Hollywood provides another choice example of seriality. L Frank Baum was a prolific children’s author, best-known for The Wonderful Wizard of Oz (1900). He didn’t live to see his novel turned into the iconic musical fantasy film, yet he reputedly had a remarkable coincidental connection with the movie. The actor Frank Morgan played five roles in The Wizard of Oz (1939), including the eponymous Wizard. He makes his first appearance in the sepia-toned opening sequences as Professor Marvel, a travelling fortune-teller. Movie lore says that, when it came to screen testing, the coat he was wearing was considered too pristine for an itinerant magician. So the wardrobe department was sent on a thrift-shop mission to find something more suitable, and returned with a whole closetful of possibilities. The one they settled on, a Prince Albert frock coat with a worn velvet collar, was a perfect fit for the actor. Only later was it apparently discovered that, sewn into the jacket was a label bearing the inscription: “Made by Hermann Bros, expressly for L Frank Baum”. Baum had died 20 years before the film was released, but the coat’s provenance was allegedly authenticated by his widow, Maud, who accepted it as a gift when the film was completed.
Some coincidences seem to contain an element of humour, as if engineered by a capricious spirit purely for its own amusement. Not long after first moving to Bath in 2016, I made a dash across the busy London Road, misjudged the height of the kerb on the other side, tripped, fell awkwardly and fractured my right arm. Over the next five years, I lived variously in Bath, rural Worcestershire and London. Soon after moving back to Bath on a more permanent basis, I noticed a stylish mahogany chair in the window of a charity shop on London Road, went straight in and bought it. I thought I’d have no trouble lugging the chair back to my flat half a mile away, but it turned out to be heavier than I expected and awkward to carry. As I was crossing the road where I’d had my fall, the chair slipped, crashed to the ground and splintered its right arm. Hear the chuckles of the coincidence imp.
While some coincidences seem playful, others feel inherently macabre. In 2007, the Guardian journalist John Harris set out on “an intermittent rock-grave odyssey”, visiting the last resting places of revered UK rock musicians. About halfway through, he went to the tiny village of Rushock in Worcestershire to gather thoughts at the headstone of the Led Zeppelin drummer John Bonham, who died at the age of 32 on 25 September 1980, after consuming a prodigious quantity of alcohol. A Guardian photographer had visited the grave a few days earlier to get a picture to accompany the piece. It was, writes Harris, “an icy morning that gave the churchyard the look of a scene from The Omen”, and, fitting with one of the key motifs of that film, the photographer was “spooked by the appearance of an unaccompanied black dog, which urinates on the gravestone and then disappears”. Black Dog (1971) happens to be the title of one of the most iconic songs in the Led Zeppelin catalogue.
If we picture a continuum of coincidences from the trivial to the extraordinary, both the Hopkins and the Baum examples would surely be located towards the strange and unusual end. My “broken arms” coincidence tends towards the trivial. Other still more mundane examples are commonplace. You get chatting to a stranger on a train and discover you have an acquaintance in common. You’re thinking of someone and, in the next breath they call you. You read an unusual word in a magazine and, simultaneously, someone on the radio utters the same word. Such occurrences might elicit a wry smile, but the weirder ones can induce a strong sense of the uncanny. The world momentarily seems full of strange forces.
It’s a state of mind resembling apophenia – a tendency to perceive meaningful, and usually sinister, links between unrelated events – which is a common prelude to the emergence of psychotic delusions. Individual differences may play a part in the experience of such coincidences. Schizotypy is a dimension of personality characterised by experiences that in some ways echo, in muted form, the symptoms of psychosis, including magical ideation and paranormal belief. There is evidence to suggest that people who score high on measures of schizotypy may also be more prone to experiencing meaningful coincidences and magical thinking. Perhaps schizotypal individuals are also more powerfully affected by coincidence. Someone scoring high on measures of schizotypy would perhaps be more spooked by a death dream than I (a low scorer) was.
Ihave set naturalism and the supernatural in binary opposition, but perhaps there is a third way. Let’s call it the supranatural stance. This was the position adopted, in different ways, by Kammerer, and by the Swiss psychologist Carl Jung. Arthur Koestler’s The Roots of Coincidence (1972) introduced Kammerer’s work to the English-speaking world and was influential in reviving interest in Jung’s ideas. Kammerer began recording coincidences in 1900, most of them mind-numbingly trivial. For example, he notes that, on 4 November 1910, his brother-in-law attended a concert, and number 9 was both his seat number and the number of his cloakroom ticket. The following day he went to another concert, and his seat and cloakroom ticket numbers were both 21.
Kammerer’s book Das Gesetz der Serie (1919), or The Law of Seriality, contains 100 samples of coincidences that he classifies in terms of typology, morphology, power and so on, with, as Koestler puts it, “the meticulousness of a zoologist devoted to taxonomy”. Kammerer’s big idea is that, alongside causality, there is an acausal principle at work in the universe, which, as Koestler puts it, “acts selectively to bring similar configurations together in space and time”. Kammerer sums things up as follows: “We thus arrive at the image of a world-mosaic or cosmic kaleidoscope, which, in spite of constant shufflings and rearrangements, also takes care of bringing like and like together.” Albert Einstein, for one, took Kammerer seriously, describing his book as “original and by no means absurd”.
The theory of synchronicity, or meaningful coincidence, proposed by Jung, follows a similar line. It took shape over several decades through a confluence of ideas streaming in from philosophy, physics, the occult and, not least, from the wellsprings of magical thinking that bubbled in the depths of Jung’s own prodigiously creative and, at times, near-psychotic mind. Certain coincidences, he suggests, are not merely a random coming-together of unrelated events. They are connected acausally by virtue of their meaning. Synchronicity was the “acausal connecting principle”.
The theory of synchronicity. Photograph: cyano66/Getty Images/iStockphoto
According to the physicist and historian of science Arthur I Miller’s book Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung (2009), Jung considered this to be one of the best ideas he ever had, and cites Einstein as an influence. In the early years of the 20th century, Einstein was on several occasions a dinner guest at the Jung family home in Zurich, making a strong impression. Jung traces a direct link between those dinners with Einstein and his dialogue, 30 years later, with the Nobel prize-winning physicist Wolfgang Pauli, a dialogue that brought the concept of synchronicity to fruition.
Jung’s collaboration with Pauli was an unlikely coalition: Jung, the quasi-mystic psychologist, a psychonaut whose deep excursions into his own unconscious mind he deemed the most significant experiences of his life; and Pauli, the hardcore theoretical physicist who was influential in reshaping our understanding of the physical world at its subatomic foundations. Following his mother’s suicide and a brief, unhappy marriage, Pauli suffered a psychological crisis. Even as he was producing his most important work in physics, he was succumbing to bouts of heavy drinking and getting into fights.
Pauli turned for help to Jung, who happened to live nearby. His therapy involved the recording of dreams, a task at which Pauli proved remarkably adept, being able to remember complex dreams in exquisite detail. Jung also saw an opportunity: Pauli was a willing guide to the arcane realm of subatomic physics; and furthermore, Pauli saw Jung’s theory of synchronicity as a way of approaching some fundamental questions in quantum mechanics – not least the mystery of quantum entanglement, by which subatomic particles may correlate instantaneously, and acausally, at any distance. From their discussions emerged the Pauli-Jung conjecture, a form of double-aspect theory of mind and matter, which viewed the mental and the physical as different aspects of a deeper underlying reality.
Jung was the first to bring coincidences into the frame of psychological inquiry, and made use of them in his analytic practice. He offers an anecdote about a golden beetle as an illustration of synchronicity at work in the clinic. A young woman is recounting a dream in which she was given a golden scarab, when Jung hears a gentle tapping at the window behind him and turns to see a flying insect knocking against the windowpane. He opens the window and catches the creature as it flies into the room. It turns out to be a rose chafer beetle, “the nearest analogy to a golden scarab that one finds in our latitudes”. The incident proved to be a transformative moment in the woman’s therapy. She had, says Jung, been “an extraordinarily difficult case” on account of her hyper-rationality and, evidently, “something quite irrational was needed” to break her defences. The coincidence of the dream and the insect’s intrusion was the key to therapeutic progress. Jung adds that the scarab is “a classic example of a rebirth symbol” with roots in Egyptian mythology.
Whereas Kammerer hypothesised impersonal, acausal factors intersecting with the causal nexus of the universe, Jung’s acausal connecting principle was enmeshed with the psyche, specifically with the archetypes of the collective unconscious. Jung’s archetypes are primordial structures of the mind common to all human beings. Resurrecting an ancient term, he envisioned an unus mundus, a unitary or one world, in which the mental and physical are integrated, and where the archetypes are instrumental in shaping both mind and matter. It’s a bold vision, but where, we are bound to ask, is the evidence for any of this? There is more than a grain of plausibility in the suggestion that archetypal structures have an influence in shaping thought and behaviour. But the entire universe? Pauli aside, the idea of synchronicity received little support from the wider scientific community.
Contemporary cognitive science offers a more secure, if less colourful, conceptual framework for making sense of the experience of coincidence. We are predisposed to encounter coincidences because their detection, it might be said, reflects the basic modus operandi of our cognitive and perceptual systems. The brain seeks patterns in the flow of sensory data it receives from the world. It infuses the patterns it detects with meaning and sometimes agency (often misplaced) and, as a part of this process, it forms beliefs and expectations that serve to shape future perceptions and behaviour. Coincidence, in the simple sense of co-occurrence, informs pattern-detection, especially in terms of identifying causal relationships, and so enhances predictability. The “world” does not simply present itself through the windowpanes of the eyes and channels of the other senses. The brain’s perceptual systems are proactive. They construct a model of the world by continually attempting to match incoming, “bottom-up” sensory data with “top-down” anticipations and predictions. Raw sensory data serve to refine the brain’s best guesses as to what’s happening, rather than building the world afresh with each passing moment. The brain, simply put, is constantly on the lookout for coincidence.
The black dog at John Bonham's grave. Photograph: David Sillitoe/The Guardian
From a wide-ranging survey of psychological and neurocognitive research, Michiel van Elk, Karl Friston and Harold Bekkering conclude that the overgeneralisation of such predictive models plays a crucial part in the experience of coincidence. Primed by deeply ingrained cognitive biases, and ill-equipped to make accurate estimates of chance and probability, we are innately inclined to see (and feel) patterns and connections where they simply don’t exist. “Innately inclined” because, in evolutionary terms, the tendency to over-detect coincidences is adaptive. Failure to detect contingencies between related events – for example, rustling in the undergrowth/proximity of a predator – is generally more costly than an erroneous inference of a relationship between unrelated events. Another driver of coincidence is what the linguist Arnold Zwicky calls the “frequency illusion”, a term that originated in a blogpost but has since found its way into the Oxford English Dictionary:
frequency illusion n. a quirk of perception whereby a phenomenon to which one is newly alert suddenly seems ubiquitous.
Van Elk and his colleagues were not the first to signal the unreliability of intuitive judgments of probability as a factor in the perception of coincidence. Various authors before them – such as Stuart Sutherland in his book Irrationality (1992) – have suggested that paranormal beliefs, including the belief that some coincidences are supernatural, arise because of failures of intuitive probability. The so-called birthday problem, a staple of introductory classes in probability theory, reliably exposes the flaws of our intuitions. It asks what is the likelihood that two people will share a birthday in randomly selected groups. Most people are surprised to learn that a gathering of only 23 people is required for the chances of two of them sharing a birthday to exceed 50%. I’d been meaning for some time to try a simple empirical exercise involving “deathdays” to mirror the birthday problem. When I found myself again staying briefly at my parents’ old house, a short drive from Rushock, I decided I would use Bonham’s grave as the starting point for my research, for no reason other than the vague pull of that black dog story.
His headstone is easy to locate, festooned as it is with drumsticks and cymbals left as offerings by the many pilgrims who make their way to the shrine from around the world. The grave lies in the shade of a spreading, blue-needled conifer and, to the right, there’s a row of three other graves – so just four graves in total (there is also a small, sandcastle-like monument at the base of the tree trunk, which I discounted for lack of name and dates). The plan was to conduct a self-terminating search. Starting with Bonham’s headstone, and with my notebook in hand, I would inspect the other graves in the row and then the rows behind and in front, working my way methodically around the graveyard, until I found any two matching dates of death, but my mission ended almost as soon as it had begun. I needed to go no further than the four graves (with five occupants) in Bonham’s row. The occupants of the two on the right shared 29 September as their date of death (21 years apart). I wish I could report that the mysterious black dog made an appearance, but it didn’t.
Turning to the probability of dream coincidences, suppose for the sake of argument that the probability of a dream coincidentally matching real-world events is 1 in 10,000, and that only one dream per night is remembered. The probability of a “matching” dream on any given night is 0.0001 (ie, 1 in 10,000), meaning that the probability of a “non-matching” dream is 0.9999. The probability of two consecutive nights with non-matching dreams is 0.9999 x 0.9999. The probability of having non-matching dreams every night for a whole year is 0.9999 multiplied by itself 365 times, which is 0.9642. Rounding up, this means that there is a 3.6% chance of any given person having a dream that matches or “predicts” real-world events over the course of a year. Over a period of 20 years, the odds of having a matching/precognitive dream would be greater than even.
A golden scarab beetle (Plusiotis resplendens). Photograph: Minden Pictures/Alamy
Rose, the woman in the death dream I experienced, was 90 years old, and the chances of a 90-year-old woman in the UK dying before her 91st birthday are around one in six, which is to say, not unlikely. Given her medical history, the likelihood that Rose would die before her 91st birthday was probably much greater than that. But why should I dream about her in the first place? It’s true, I hadn’t been consciously thinking about Rose, but, staying in my childhood home, there would have been many implicit reminders. She used to live close by, and came to our house often. Also, visiting my ailing mother more often than usual at her care home would have me thinking about death at both conscious and unconscious levels, and perhaps (unconsciously) about her friendship with Rose.
Attempts at understanding coincidence thus range from extravagant conjectures conceiving of acausal forces influencing the fundamental workings of the universe, to sober cognitive studies deconstructing the basic mechanisms of the mind. But there is something else to consider. Remarkable coincidences happen because, well, they happen, and they happen without inherent meaning and independently of the workings of the pattern-hungry brain. As the statistician David Hand puts it, “extremely improbable events are commonplace”. He refers to this as the improbability principle, one with different statistical strands, including the law of truly large numbers, which states that: “With a large enough number of opportunities, any outrageous thing is likely to happen.” Every week, there are many lottery jackpot winners around the globe, each with odds of winning at many millions to one against. And, in defiance of truly phenomenal odds, several people have won national and state lottery jackpots on more than one occasion.
I am a naturalist, but coincidences give me a glimpse of what the supernaturalist sees, and my worldview is briefly challenged. Soon, though, for good or ill, I am back on my usual track. One final coincidence story: it was a warm afternoon in mid-June, and I was feeling sorry for myself. My partner had walked out on me just the week before, and I thought a good way to deal with self-pity would be to launch into a new project. I would do some research into the psychology of coincidence. I settled in an armchair surrounded by books and articles on the subject, including Koestler’s The Roots of Coincidence. Among other things, I’d been reading his account of Jung’s golden scarab story.
In need of coffee, I set Koestler aside and went to the kitchen, returning to find, set squat on the back of my armchair, a golden beetle, a rose chafer like the one that had made its way through the window of Jung’s consulting room. It must have flown in through the wide-open balcony door. I quickly took a picture in case the insect took flight again, and then nudged it on to my palm to return it to the wild, but it simply rolled on to its back and lay motionless. Dead.
I sent the picture to my ex, and asked how she was doing. She didn’t reply, but later that evening called with unsettling news. Zoe, an acquaintance of ours, had that afternoon killed herself. My brain by now was in magical thinking mode, and I said I couldn’t help but link Zoe’s death to the appearance, and death, of the golden beetle. I didn’t believe there was a link, of course, but I felt there might be. There was something else at the back of my mind. In Greek mythology, all that king Midas touched turned to gold. His daughter’s name was Zoe, and she too was turned to gold.
Ah, but rose chafers are quite common in the south of England; they are active in warm weather; the balcony opens out on a water meadow (a typical rose chafer habitat); et cetera. And it has since been suggested to me that the beetle was quite likely “playing dead” rather than truly dead. Perhaps, after I’d thrown it back out on to the meadow, there was a “rebirth” of the kind these creatures are said to symbolise.
