No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Magic, Bayes and wows: A Bayesian account of magic tricks
Abstract
Magic tricks have enjoyed an increasing interest by scientists. However, most research in magic focused on isolated aspects of it and a conceptual understanding of magic, encompassing its distinct components and varieties, is missing. Here, we present an account of magic within the theory of Bayesian predictive coding. We present the “wow” effect of magic as an increase in surprise evoked by the prediction error between expected and observed data. We take into account prior knowledge of the observer, attention, and (mis-)direction of perception and beliefs by the magician to bias the observer’s predictions and present a simple example for the modelling of the evoked surprise. The role of misdirection is described as everything that aims to maximize the surprise a trick evokes by the generation of novel beliefs, the exploitation of background knowledge and attentional control of the incoming information. Understanding magic within Bayesian predictive coding allows unifying all aspects of magic tricks within one framework, making it tractable, comparable and unifiable with other models in psychology and neuroscience.
... We find ourselves experiencing something that we know cannot happen and yet we see it happen in front of our eyes. There have been several theoretical frameworks that attempt to explain how or why we enjoy magic (Grassi & Bartels, 2021;Grassi et al., 2024;Kuhn, 2019;Lamont, 2017;Leddington, 2016Leddington, , 2017, but there is little empirical research on the topic. Medeiros et al. (2022) conducted a qualitative analysis examining what people enjoy about magic. ...
... Several theoretical accounts of magic predict that our experience of magic will be directly related to the extent to which the experience conflicts with what we believe to be possible (Grassi & Bartels, 2021;Kuhn, 2019). In support of this idea, Bagienski and Kuhn (2023) have shown that people's enjoyment of a magic trick was directly related to the extent to which they believed the event to be possible. ...
... However, it is much harder to isolate the psychological factors that constitute a strong trick or the emotions that such a trick will elicit. Magic can elicit a wide range of emotions -as we watch a magic trick, we experience an amazing event that we believe to be impossible (Bagienski & Kuhn, 2023;Lamont, 2017) which will elicit surprise (Grassi & Bartels, 2021;Grassi et al., 2024;Ozono et al., 2021) and wonder (Kuhn et al., 2008;Lamont, 2017). The trick may also elicit confusion (or bafflement) as we fail to resolve the mental conflict between the event that we have experienced and our beliefs about the world (Grassi et al., 2024). ...
Magic is a performance art that relies on tricking the spectator’s mind into experiencing things that seem impossible. Experience in performing these tricks in front of live audiences provides magicians valuable insights into how spectators experience such tricks. However, most of these assumptions have not been empirically tested. Three widely held assumptions were selected: active participation increases the sense of wonder that participants experience, naming a card feels freer to the participant than physically selecting a card from a deck, and a trick that happens in the spectator’s hand is more impressive than if it happens elsewhere. To validate those assumptions, we asked 201 magicians about their insights on performing magic. Data from our experimental studies did not support magicians’ assumptions about how magic is experienced. Magic that happened in the participant’s hand was not viewed as more impossible or engaging than when it happened elsewhere. Also, active participation did not increase enjoyment but increased confusion. Interestingly, contrary to magicians’ insights, we observed that participants felt that selecting a card was felt as being freer than naming a card. We discuss these findings in light of the sense of agency participants experienced over their own thoughts and behaviors. These findings provide interesting insight into how the art of magic is experienced and pave new avenues into the study of the sense of agency over one’s thoughts and behaviors.
... The experience of magic evoked by these events has a unique phenomenology. Recently, it has been proposed that this state should feature as a central element of a science of magic (Rensink and Kuhn 2015) and is an emerging topic of interest in psychology and cognitive science (Lamont 2017;Camí, Gomez-Marin and Martínez 2020;Grassi and Bartels 2021). Yet, it has been largely ignored by philosophers and art critics (with the exception of Leddington 2016). ...
... Hence, we can think of illusionists as sequentially presenting strong perceptual evidence using different methods of misdirection to create false beliefs about a situation that contradicts prior knowledge (e.g. giving false explanations, sleight of hand, etc.) (Kuhn et al., 2014;Camí, Gomez-Marin and Martínez 2020;Grassi and Bartels 2021). ...
... The experience of magic can then be thought of as an experience evoked by a profound mismatch between prior beliefs based on what we know and what we are currently witnessing (Fraps 2014;Grassi and Bartels 2021). The surprise induced by magic is special as it involves the apparent violation of deeply held beliefs about the general nature of the world by occurrences we directly perceive in the real world (e.g. ...
When engaging with magic, we are moved by seemingly impossible events that contradict what we believe to be possible in the real world. We are surprised, curious, and baffled when we cannot explain how the magic we are witnessing is possible. We generally understand the events to be illusions. But how is it possible to be moved by something we know to be unreal? This problem is related to the paradox of fiction in aesthetics. Here, we introduce the problem in the domain of theatrical magic, discuss possible solutions, and present a tentative account that allows us to accommodate inconsistent, seemingly incompatible beliefs at different representational levels in the viewers’ mind.
... Magicians exploit learned social cues, psychological behaviours, and optical illusions [4,5,6,7], alongside a conscious suspension of disbelief similar to that employed when watching films or reading books [8]. The effect emerges from a mismatch between predicted and observed events [9], much like the psychology of humour [10,11]. ...
... This is achieved using prior knowledge and real-world experiences which, in order for a robot to have equivalent knowledge, must be similarly experienced or explicitly programmed. Grassi and Bartels [9] consider predictive coding in the context of magic & magicians' techniques, in which magicians aim to maximise the prediction error between an anticipated prior and the observed sensory input, manipulating these inputs alongside the spectator's memory-based expectations. In this way, fooling can be explicitly quantified as the Shannon surprise between the predicted and observed distributions [31]. ...
... The final example of incomplete information which we consider is that of an incomplete or incorrect background knowledge. In the Bayesian framework, Grassi et al. [9] refer to 'deeply held hyperpriors' such as physical laws: we experience a high surprise if our sensor inputs suggest that these hyperpriors are violated. Robots do not necessarily need to follow the same hyperpriors as us, depending on their environmental niche [42]: an ice-hockey playing robot might experience high surprise if it encounters an object which does not glide smoothly along the floor, but its restriction to a 2D plane might mean that it requires no hyperpriors of gravitational laws, and experiences no impossibility when witnessing a levitation. ...
Based on real-world interactions in our lives and in the lives of our ancestors, humans have developed a multitude of psychological, social, and reflexive actions for efficient living. We consider the integration of similar behaviours into embodied robots through the design of their sensory systems, evaluating their impact through a novel lens: how magicians exploit these human behaviours in order to fool their spectators into experiencing impossible events. We explore the consequences of designing agents which can experience magic effects, and argue that such design facilities lifelike actions.
... However, combining the two methods made them virtually impenetrable. Grassi and Bartels (2021) have recently proposed a Bayesian approach to misdirection which uses a computational approach to explain how each of these different cognitive processes affect the way in which magicians can manipulate the observer's beliefs away from the real cause of the magic effect (i.e. the method) and accept the alternative beliefs about the effect (i.e. the magical effect). Bayesian predictive coding is a computational framework that is typiclally used to explain perception. ...
... This process of reducing prediction errors is seen as the basis of all human learning and this model has been applied to numerous cognitive processes. Grassi and Bartels (2021) have applied Bayesian predicative coding to explain misdirection, and this new model provides an effective way of explaining how misdirection principles interact with our current beliefs about the world. Grassi and Bartels (2021) argue that magic is best explained in terms of surprise, and an individual's level of surprise can be operationalized as the difference between our prior beliefs about the situation and the incoming sensory information -prediction error. ...
... Grassi and Bartels (2021) have applied Bayesian predicative coding to explain misdirection, and this new model provides an effective way of explaining how misdirection principles interact with our current beliefs about the world. Grassi and Bartels (2021) argue that magic is best explained in terms of surprise, and an individual's level of surprise can be operationalized as the difference between our prior beliefs about the situation and the incoming sensory information -prediction error. For example, it is very unlikely that rabbits appear from nowhere, and thus our prior beliefs about this occurring are extremely low. ...
The art of magic relies on deception and illusions to create human experiences that appear impossible. Misdirection lies at the heart of this deceptive art, and yet there is little consensus as to what this concept aims to describe. The concept of misdirection is not limited to magic, and its principles are applied to wide aspects of our lives (e.g., politics, public health, marketing). In recent years, scientists have started to examine the psychological mechanisms that underpin misdirection and new theoretical frameworks have been developed to help understand the concept itself. This paper will provide two different perspectives on misdirection. In the first section we will discuss its use in magic and examine some of the key features involved in using misdirection to create magical illusions. This section will examine some common misconceptions of misdirection. The second section will provide a psychological perspective that discusses the key psychological mechanisms that are involved in misdirection (perception, memory, reasoning). This paper aims to provide a clearer understanding of how misdirection is used in magic which can serve as the basis for its use in other domains, such as public health.
... Similarly, the moment an audience generates any nonmagical explanation (however absurd) for what they're witnessing, the experience of magic is weakened (Leddington, 2020). Grassi and Bartels (2021) proposed a Bayesian model based on predictive coding to help explain our experience of magic. They described the magic experience as a prediction error that results from a mismatch between our beliefs about the world and the things we perceive. ...
Magic is ill-defined, and few published works in magic directly address magic’s underlying aesthetics or its theoretical basis. Instead, information is transmitted informally between magicians through lectures and personal conversations (see Rissanen et al., 2013). In order to capture some of this socially-disseminated information, we carried out a series of interviews with six acclaimed, expert magicians who think deeply about the techniques and meaning of their magic. We probed their personal definitions of magic, their beliefs about what constitutes “good” and “bad” magic, and their attitudes about the aesthetic boundaries of performance magic. We report the outcomes of a thematic analysis of these interviews. Participants highlighted many of the same fundamental features of good magic. However, they differentially weighted these features, perhaps explaining variability in their performing styles. These magicians felt that there may be no entirely adequate, singular definition of magic because magic is a non-linear system where small changes in the performer, audience, or environment feed forward in unpredictable ways to impact the experience of magic.
... To this aim, we created and validated videos for a naturalistic VOE paradigm 30 showing either dedicated magic tricks (to create the illusion of seemingly impossible 31 events to actually occur, cf. Grassi & Bartels, 2021) or matched control actions that 32 involved no violation of physical principles. The VOE videos were designed to evoke 33 surprise responses related to unexpected object appearance, disappearance of objects, 34 and feature change (color-changing objects). ...
Surprise responses signal both high-level cognitive alerts that information is missing, and increasingly specific back-propagating error signals that allow updates in processing nodes. Studying surprise is, hence, central for cognitive neuroscience to understand internal world representations and learning. Yet, only few prior studies used naturalistic stimuli targeting our high-level understanding of the world. Here, we use magic tricks in an fMRI experiment to investigate neural responses to violations of core assumptions held by humans about the world. We showed participants naturalistic videos of three types of magic tricks, involving objects appearing, changing color, or disappearing, along with control videos without any violation of expectation. Importantly, the same videos were presented with and without prior knowledge about the tricks’ explanation. Results revealed generic responses in frontal and parietal areas, together with responses specific to each of the three trick types in posterior sensory areas. A subset of these regions, the midline areas of the default mode network (DMN), showed surprise activity that depended on prior knowledge. Equally, sensory regions showed sensitivity to prior knowledge, reflected in differing decoding accuracies. These results suggest a hierarchy of surprise signals involving generic processing of violation of expectations in frontal and parietal areas with concurrent surprise signals in sensory regions that are specific to the processed features.
... According to Kuhn, the strength of an effect directly relates to the strength of the conflict. Grassi and Bartels (2021) recently developed a Bayesian account of magic, which explains the experience of magic within a Bayesian predictive coding theory. This computational theory operationalizes the "wow" effect that magic elicits as an increase in surprise evoked by the prediction error between the expected and observed data. ...
Magic is an art form that allows us to experience the impossible, but some magic tricks are more implausible than others. We present two experiments that examined whether the objective probability of a trick occurring by chance influences how people experience the trick. In Experiment 1, participants watched different versions of a magic trick in which we manipulated the statistical probability of the trick occurring by chance. We found that the objective probability had no significant impact on how much people enjoyed the trick or how impressed they were by it. Our participants enjoyed the trick equally when there was a 25% chance of it succeeding by chance as when it was virtually impossible. The same was true for how impressed they were by the performance. However, tricks that were less likely to succeed by chance were rated as more difficult and impossible. More implausible tricks resulted in more participant explanations stating they did not know how the trick was done, as well as explanations implying it was fake. In a follow-up experiment, participants were presented with vignettes describing the same trick, and they were asked to judge the magician’s chances of succeeding. The statistical probability of the trick occurring by chance did not affect these judgments adversely, but they did do so when the same feat was performed by a nonmagician.
... However, there is very little empirical work examining why people enjoy these impossible moments. In fact, despite the popular appeal of such magical illusions, there are only a handful of theoretical frameworks to explain why or how people enjoy magic (Leddington, 2016a(Leddington, , 2017Grassi & Bartels, 2021;Kuhn, 2019). Magic is unique in that it allows us to experience things that we believe to be impossible (Kuhn, 2019), and in this paper we examine the link between enjoyment and the perceived impossibility that such illusions elicit. ...
The performance art of magic allows us to experience the impossible, and this study used a balancing magic trick to investigate the relationship between participants’ enjoyment and perceived impossibility. Participants watched a live performance of a magic trick in which the magician balanced objects in progressively more impossible configurations. At seven different time points observers rated their enjoyment, and the extent to which they believed what they saw was impossible. Regression analysis revealed that participants’ enjoyment of the magical effect relates to their perceived impossibility of the magic trick, and this relationship was independent of how much they enjoyed magic in general. Moreover, a one-way within-subjects analysis of variance showed that participants enjoyed the performance More as the trick became more impossible. However, once the magical effect was anticipated, enjoyment began to plateau while perceived impossibility continued to increase. These results are discussed in the context of people's aesthetic appreciation of magic and current arts appreciation models.
... The distance measure is the Kullback-Liebler divergence measure. Several applications have recently used the Bayesian Surprise criteria to as part of a feedback criteria for improving the reliability of machine learning models such as neural networks and thematic maps [24,14,22]. ...
Background
In this work we employ Bayesian surprise to detect interesting/anomalous patterns from discrete sequence data.
Many domains consist of discrete sequential time-series such as DNA analysis, online transactions, web click-stream navigation, cyber-attacks, financial transactions and especially sociology life-course data. The difficulty is that each data set has its own unique characteristics and many anomalies defy categorization. Since anomalies are by nature infrequent and elusive, we often do not have enough data for a supervised approach. However, novelty and surprise play a fundamental role in human and animal behavior for survival, attention and adaptation.
Methods
We use three sequence datasets (Swiss Health, Sepsis, and BioFamilies) which are are composed of simpler motifs which are used to build Probabilistic Suffix Trees (PST) which can capture complex relationships based on motif location and frequency of occurrence. New data that deviates from established motifs either in location of appearance, frequency of appearance, or motif composition may represent recurring patterns that may be different in some way. Bayesian surprise is the result of mismatches between our expectations and actual results, hence the degree of surprise or anomalousness attached to a pattern will vary with respect to these differences.
Results
Each data set is assessed by Bayesian Surprise and several other criteria, providing indications of why certain patterns are interesting and why others are not.
Conclusions
Bayesian surprise can detect data with other properties that would be missed by information theoretic measures such as Shannon surprise and entropy for example.
... Specific connections to computer algorithms have been made, especially for teaching purposes (Curzon and McOwan, 2008). Most relevant, direct parallels have been drawn to AI with machines designing tricks (Williams and McOwan, 2016) and in the formalisation of surprise using Bayesian predictive coding (Grassi and Bartels, 2021). To our knowledge, however, we are the first to apply them in a principled way to the problem of goal recognition. ...
The “science of magic” has lately emerged as a new field of study, providing valuable insights into the nature of human perception and cognition. While most of us think of magic as being all about deception and perceptual “tricks”, the craft—as documented by psychologists and professional magicians—provides a rare practical demonstration and understanding of goal recognition. For the purposes of human-aware planning, goal recognition involves predicting what a human observer is most likely to understand from a sequence of actions. Magicians perform sequences of actions with keen awareness of what an audience will understand from them and—in order to subvert it—the ability to predict precisely what an observer’s expectation is most likely to be. Magicians can do this without needing to know any personal details about their audience and without making any significant modification to their routine from one performance to the next. That is, the actions they perform are reliably interpreted by any human observer in such a way that particular (albeit erroneous) goals are predicted every time. This is achievable because people’s perception, cognition and sense-making are predictably fallible. Moreover, in the context of magic, the principles underlying human fallibility are not only well-articulated but empirically proven. In recent work we demonstrated how aspects of human cognition could be incorporated into a standard model of goal recognition, showing that—even though phenomena may be “fully observable” in that nothing prevents them from being observed—not all are noticed, not all are encoded or remembered, and few are remembered indefinitely. In the current article, we revisit those findings from a different angle. We first explore established principles from the science of magic, then recontextualise and build on our model of extended goal recognition in the context of those principles. While our extensions relate primarily to observations, this work extends and explains the definitions, showing how incidental (and apparently incidental) behaviours may significantly influence human memory and belief. We conclude by discussing additional ways in which magic can inform models of goal recognition and the light that this sheds on the persistence of conspiracy theories in the face of compelling contradictory evidence.
This study assessed the preliminary results of an experimental protocol evaluating the impact of positive expectations on fingertip-to-floor distance during forward bending. Thirty-six participants were assigned to three groups, each receiving a sham physical manipulation in Immersive Virtual Reality (IVR). The first group received a neutral statement about the manipulation’s efficacy, while the second and third groups were told the manipulation would improve forward bending, emphasising its fictious positive effect to increase expectations for a beneficial motor improvement. Additionally, the third group also experienced a visual-haptic illusion, by lifting a tile in front of participants and raising the floor in the virtual scenario, creating the belief of reaching the floor thanks to the received manipulation. Fingertip-to-floor distance was measured at baseline, immediately after the manipulation (after-effect), and five minutes later (follow-up). Differences between baseline and after-effect/follow-up distances represented the gained distances. Only the third group, which experienced the combined effect of positive verbal statement reinforced by the visual-haptic illusion, showed a significant increase in gained distance during the after-effect and follow-up phases compared to the neutral statement group. These findings support the potential of this multifactorial intervention to promote motor improvement by enhancing positive expectations.
This chapter presents the notions connected to Shannon’s entropy and information, namely the joint, conditional, relative (Kullback–Leibler) entropies, and the mutual information, with their implementations in R. Applications to surprise quantification are shown, with their implementation in R. Examples show the use of the programs presented.
This chapter presents Monte-Carlo Markov Chain methods and connected topics, namely Importance Sampling, Metropolis-Hastings Algorithm, Kalman Filtering, Particle Filtering, and Bayesian Optimization. The use of UQ for the determination of the distribution of the noise is presented. Programs in R implement all the topics introduced, with examples of use.
This chapter presents the principle of maximum entropy, which furnishes a practical method for the generation of distributions. The representation of stochastic processes by Karhunen-Loève expansions is presented, including their combination with Hilbert’s approach of uncertainty quantification. Implementations in R are given, and their use is exemplified.
This chapter presents the Bayesian approach for practical tasks, such as estimation, hypothesis testing, model or variable selection, and regression. The choice of priors is analyzed, by using Jeffreys approach and uncertainty quantification techniques. The Expectation-Maximization Algorithm is presented in this chapter. Implementations in R are given for all the topics, with examples of use.
Cognitive scientists have paid very little attention to magic as a distinctly human activity capable of creating situations that are considered impossible because they violate expectations and conclude with the apparent transgression of well-established cognitive and natural laws. This illusory experience of the “impossible” entails a very particular cognitive dissonance that is followed by a subjective and complex “magical experience”. Here, from a perspective inspired by visual neuroscience and ecological cognition, we propose a set of seven fundamental cognitive phenomena (from attention and perception to memory and decision-making) plus a previous pre-sensory stage that magicians interfere with during the presentation of their effects. By doing so, and using as an example the deconstruction of a classic trick, we show how magic offers novel and powerful insights to study human cognition. Furthermore, live magic performances afford to do so in tasks that are more ecological and context-dependent than those usually exploited in artificial laboratory settings. We thus believe that some of the mysteries of how the brain works may be trapped in the split realities present in every magic effect.
We present two experiments investigating the effect of the perceived gender of a magician on the perception of the quality of magic tricks. In Experiment 1, tricks performed by an allegedly female magician were considered worse than those by an allegedly male magician. In Experiment 2, participants had to generate possible solutions to how the tricks were done. Under these conditions, male participants were better at explaining the tricks, but the gender effect found in Experiment 1 disappeared. We discuss the gender bias in Experiment 1 and the lack of bias in Experiment 2 in terms of specific social and cognitive mechanisms (e.g., cognitive dissonance).
In conditions of constant illumination, the eye pupil diameter indexes the modulation of arousal state and responds to a large breadth of cognitive processes, including mental effort, attention, surprise, decision processes, decision biases, value beliefs, uncertainty, volatility, exploitation/exploration trade-off, or learning rate. Here, I propose an information theoretic framework that has the potential to explain the ensemble of these findings as reflecting pupillary response to information processing. In short, updates of the brain's internal model, quantified formally as the Kullback-Leibler (KL) divergence between prior and posterior beliefs, would be the common denominator to all these instances of pupillary dilation to cognition. I show that stimulus presentation leads to pupillary response that is proportional to the amount of information the stimulus carries about itself and to the quantity of information it provides about other task variables. In the context of decision making, pupil dilation in relation to uncertainty is explained by the wandering of the evidence accumulation process, leading to large summed KL divergences. Finally, pupillary response to mental effort and variations in tonic pupil size are also formalized in terms of information theory. On the basis of this framework, I compare pupillary data from past studies to simple information-theoretic simulations of task designs and show good correspondance with data across studies. The present framework has the potential to unify the large set of results reported on pupillary dilation to cognition and to provide a theory to guide future research.
In their quest for creating magical experiences, magicians rely on a host of psychological factors. Here, we compare tricks based on attentional misdirection with tricks based on amodal completion. Based on the notion that amodal completion is a cognitively impenetrable perceptual phenomenon, we predicted that the tricks based on this perceptual effect should—to a much larger extent than tricks based on attentional misdirection—retain their deceptive power when the tricks are repeated. The results of an experiment with four magic tricks involving attentional misdirection and four magic tricks based on amodal completion lend strong support to this prediction. Asking subjects to try to figure out the secret behind these tricks after one, two, or three presentations of each trick, we found that the observed solution rates for tricks based on attentional misdirection increased much more with repeated viewing than those for tricks based on amodal completion, which remained very low throughout. Thus, the results lend further support to the idea that amodal completion is based on cognitively impenetrable perceptual mechanisms.
Fueled by developments in computational neuroscience, there has been increasing interest in the underlying neurocomputational mechanisms of psychosis. One successful approach involves predictive coding and Bayesian inference. Here, inferences regarding the current state of the world are made by combining prior beliefs with incoming sensory signals. Mismatches between prior beliefs and incoming signals constitute prediction errors that drive new learning. Psychosis has been suggested to result from a decreased precision in the encoding of prior beliefs relative to the sensory data, thereby garnering maladaptive inferences. Here, we review the current evidence for aberrant predictive coding and discuss challenges for this canonical predictive coding account of psychosis. For example, hallucinations and delusions may relate to distinct alterations in predictive coding, despite their common co-occurrence. More broadly, some studies implicate weakened prior beliefs in psychosis, and others find stronger priors. These challenges might be answered with a more nuanced view of predictive coding. Different priors may be specified for different sensory modalities and their integration, and deficits in each modality need not be uniform. Furthermore, hierarchical organization may be critical. Altered processes at lower levels of a hierarchy need not be linearly related to processes at higher levels (and vice versa). Finally, canonical theories do not highlight active inference—the process through which the effects of our actions on our sensations are anticipated and minimized. It is possible that conflicting findings might be reconciled by considering these complexities, portending a framework for psychosis more equipped to deal with its many manifestations.
When confronted with an insight problem, some factors limit our capacity to discover the optimal solution. Previous research on problem solving has shown that the first idea that comes to participants’ minds can inhibit them from finding better alternative solutions. We used a magic trick to demonstrate that this mind fixing effect is more general than previously thought: a solution that participants knew to be incorrect and impossible inhibited the discovery of an easy alternative. We show that a simple exposure to an obvious false solution (e.g., the magician hides the card in the palm of his hand to secretly transfer it to his back pocket) can inhibit participants from finding the real secret of the trick (e.g., he used a duplicate card), even if the magician proves that this false solution is impossible (e.g., he shows his hand is empty). We discuss the psychological processes underlying this robust fixing effect.
Recent work in cognitive and computational neuroscience depicts human brains as devices that minimize prediction error signals: signals that encode the difference between actual and expected sensory stimulations. This raises a series of puzzles whose common theme concerns a potential misfit between this bedrock informationtheoretic vision and familiar facts about the attractions of the unexpected. We humans often seem to actively seek out surprising events, deliberately harvesting novel and exciting streams of sensory stimulation. Conversely, we often experience some wellexpected sensations as unpleasant and to-be-avoided. In this paper, I explore several core and variant forms of this puzzle, using them to display multiple interacting elements that together deliver a satisfying solution. That solution requires us to go beyond the discussion of simple information-theoretic imperatives (such as 'minimize long-term prediction error') and to recognize the essential role of species-specific prestructuring, epistemic foraging, and cultural practices in shaping the restless, curious, novelty-seeking human mind.
Repeated exposure to the same stimulus results in an attenuated brain response in cortical regions that are activated during the processing of that stimulus. This phenomenon, called repetition suppression (RS), has been shown to be modulated by expectation. Typically, this is achieved by varying the probability of stimulus repetitions (Prep) between blocks of an experiment, generating an abstract expectation that ‘things will repeat’. Here, we examined whether stimulus-specific expectations also modulate RS. We designed a task where expectation and repetition are manipulated independently, using stimulus-specific expectations. We investigated to which extent such stimulus-specific expectations modulated the visual evoked response to objects in lateral occipital cortex (LOC) and primary visual cortex (V1), using functional magnetic resonance imaging (fMRI). In LOC, we found that RS interacted with expectation, such that repetition suppression was more pronounced for unexpected relative to expected stimuli. Additionally, we found that the response of stimulus-preferring voxels in V1 was generally decreased when stimuli were expected. These results suggest that stimulus-specific expectations about objects modulate LOC and propagate back to the earliest cortical station processing visual input.
When magicians perform spectacles that seem to defy the laws of nature, they do so by manipulating psychological reality. Hence, the principles underlying the art of conjuring are potentially of interest to psychological science. Here, we argue that perceptual and cognitive principles governing how humans experience hidden things and reason about them play a central role in many magic tricks. Different from tricks based on many other forms of misdirection, which require considerable skill on the part of the magician, many elements of these tricks are essentially self-working because they rely on automatic perceptual and cognitive processes. Since these processes are not directly observable, even experienced magicians may be oblivious to their central role in creating strong magical experiences and tricks that are almost impossible to debunk, even after repeated presentations. We delineate how insights from perceptual psychology provide a framework for understanding why these tricks work so well. Conversely, we argue that studying magic tricks that work much better than one intuitively would believe provides a promising heuristic for charting unexplored aspects of perception and cognition.
Intentional deception, as is common in the performance of magic tricks, can provide valuable insight into the mechanisms of perception and action. Much of the recent investigations into this form of deception revolve around the attention of the observer. Here, we present experiments designed to investigate the contributions of the performer to the act of deception. An experienced magician and a naïve novice performed a classic sleight known as the French Drop. Video recordings of the performance were used to measure the quality of the deception—e.g., if a non-magician observer could discriminate instances where the sleight was performed (a deceptive performance) from those where it was not (a veridical performace). During the performance we recorded the trajectory of the hands and measured muscle activity via EMG to help understand the biomechanical mechanisms of this deception. We show that expertise plays a major role in the quality of the deception and that there are significant variations in the motion and muscular behaviors between successful and unsuccessful performances. Smooth, minimal movements with an exaggerated faux-transfer of muscular tension were characteristic of better deception. This finding is consistent with anecdotal reports and the magic performance literature.
Psychologists and cognitive scientists have long drawn insights and evidence from stage magic about human perceptual and attentional errors. We present a complementary analysis of conjuring tricks that seeks to understand the experience of impossibility that they produce. Our account is first motivated by insights about the constructional aspects of conjuring drawn from magicians' instructional texts. A view is then presented of the logical nature of impossibility as an unresolvable contradiction between a perception-supported belief about a situation and a memory-supported expectation. We argue that this condition of impossibility is constructed not simply through misperceptions and misattentions, but rather it is an outcome of a trick's whole structure of events. This structure is conceptualized as two parallel event sequences: an effect sequence that the spectator is intended to believe; and a method sequence that the magician understands as happening. We illustrate the value of this approach through an analysis of a simple close-up trick, Martin Gardner's Turnabout. A formalism called propositional dynamic logic is used to describe some of its logical aspects. This elucidates the nature and importance of the relationship between a trick's effect sequence and its method sequence, characterized by the careful arrangement of four evidence relationships: similarity, perceptual equivalence, structural equivalence, and congruence. The analysis further identifies two characteristics of magical apparatus that enable the construction of apparent impossibility: substitutable elements and stable occlusion.
In everyday life, several factors limit the human capacity to think differently. The present study shows that implanting an unlikely and unfamiliar idea in the mind can prevent participants from finding a more obvious one. To demonstrate this, we used a technique often adopted by magicians to misrepresent the method of a trick: the false solution. Our results reveal that a single exposure to an unlikely false solution (the magician can influence the spectator’s choice with his gesture) before the presentation of a card trick can prevent participants from finding the real (more obvious) secret of a trick, even if they are invited to search for an alternative solution.
In 2007, we proposed an explanation of delusion formation as aberrant prediction error-driven associative learning. Further, we argued that the NMDA receptor antagonist ketamine provided a good model for this process. Subsequently, we validated the model in patients with psychosis, relating aberrant prediction error signals to delusion severity. During the ensuing period, we have developed these ideas, drawing on the simple principle that brains build a model of the world and refine it by minimizing prediction errors as well as using it to guide perceptual inferences.
While previously we focused on the prediction error signal per se, an updated view takes into account its precision as well as the precision of prior expectations. With this expanded perspective, we see several possible routes to psychotic symptoms – which may explain the heterogeneity of psychotic illness as well as the fact that other drugs, with different pharmacological actions, can produce psychotomimetic effects.
In this paper, we review the basic principles of this model and highlight specific ways in which prediction errors can be perturbed, in particular considering the reliability and uncertainty of predictions. The expanded model explains hallucinations as perturbations of the uncertainty mediated balance between expectation and prediction error. Here, expectations dominate and create perceptions by suppressing or ignoring actual inputs. Negative symptoms may arise due to poor reliability of predictions in service of action. By mapping from biology to belief and perception, the account proffers new explanations of psychosis. However challenges remain. We attempt to address some of these concerns and suggest future directions, incorporating other symptoms into the model, building towards better understanding of psychosis.
Our perceptual experience is largely based on prediction, and as such can be influenced by knowledge of forthcoming events. This susceptibility is commonly exploited by magicians. In the Vanishing Ball Illusion, for example, a magician tosses a ball in the air a few times and then pretends to throw the ball again, whilst secretly concealing it in his hand. Most people claim to see the ball moving upwards and then vanishing, even though it did not leave the magician’s hand (Kuhn & Land, 2006; Triplett, 1900). But what exactly can such illusions tell us? We investigated here whether seeing a real action before the pretend one was necessary for the Vanishing Ball Illusion. Participants either saw a real action immediately before the fake one, or only a fake action. Nearly one third of participants experienced the illusion with the fake action alone, while seeing the real action beforehand enhanced this effect even further. Our results therefore suggest that perceptual experience relies both on long-term knowledge of what an action should look like, as well as exemplars from the immediate past. In addition, whilst there was a forward displacement of perceived location in perceptual experience, this was not found for oculomotor responses, consistent with the proposal that two separate systems are involved in visual perception.
Dopamine is implicated in a diverse range of cognitive functions including cognitive flexibility, task switching, signalling novel or unexpected stimuli as well as advance information. There is also longstanding line of thought that links dopamine with belief formation and, crucially, aberrant belief formation in psychosis. Integrating these strands of evidence would suggest that dopamine plays a central role in belief updating and more specifically in encoding of meaningful information content in observations. The precise nature of this relationship has remained unclear. To directly address this question we developed a paradigm that allowed us to decompose two distinct types of information content, information-theoretic surprise that reflects the unexpectedness of an observation, and epistemic value that induces shifts in beliefs or, more formally, Bayesian surprise. Using functional magnetic-resonance imaging in humans we show that dopamine-rich midbrain regions encode shifts in beliefs whereas surprise is encoded in prefrontal regions, including the pre-supplementary motor area and dorsal cingulate cortex. By linking putative dopaminergic activity to belief updating these data provide a link to false belief formation that characterises hyperdopaminergic states associated with idiopathic and drug induced psychosis.
The past few years have seen a resurgence of interest in the scientific study of magic. Despite being only a few years old, this "new wave" has already resulted in a host of interesting studies, often using methods that are both powerful and original. These developments have largely borne out our earlier hopes (Kuhn, Amlani, & Rensink, 2008) that new opportunities were available for scientific studies based on the use of magic. And it would seem that much more can still be done along these lines.
But in addition to this, we also suggested that it might be time to consider developing an outright science of magic—a distinct area of study concerned with the experience of wonder that results from encountering an apparently impossible event . To this end, we proposed a framework as to how this might be achieved (Rensink & Kuhn, 2015). A science can be viewed as a systematic method of investigation involving three sets of issues: (i) the entities considered relevant, (ii) the kinds of questions that can be asked about them, and (iii) the kinds of answers that are legitimate (T Kuhn, 1970). In the case of magic, we suggested that this could be done at three different levels, each focusing on a distinct set of issues concerned with the nature of magic itself: (i) the nature of magical experience, (ii) how individual magic tricks create this experience, and (iii) organizing knowledge of the set of known tricks in a more comprehensive way (Rensink & Kuhn, 2015). Our framework also included a base level focused on how the methods of magic could be used as tools to investigate issues in existing fields of study.
Lamont & colleagues (Lamont, 2010; Lamont, Henderson, & Smith, 2010) raised a number of concerns about the possibility of such a science, which we then addressed (Rensink & Kuhn, 2015). More recently, Lamont (2015) raised a new objection, arguing that although base-level work (i.e., applications of magic methods) might be useful, there is too little structure in magic tricks for them to be studied in a systematic way at the other levels, ruling out a science of magic. However, we argue here that although this concern raises some interesting challenges for this science, it does not negate the possibility that it could exist, and could contribute to the study of the mind.
In many magic tricks, magicians fool their audience by performing a mock action (a socalled "ruse"), which merely serves the purpose of providing a seemingly natural explanation for visible movements that are actually part of the secret move they want to hide from the audience. Here, we discuss a special magic ruse in which the action of secretly putting something somewhere is "explained away" by the mock action of fetching something from the same place, or vice versa. Interestingly, the psychological principles underlying the amazing potency and robustness of this technique seem to be very similar to the general perceptual principles underlying figure-ground perception and the assignment of border ownership. This analogy may be useful for exploring the possibility that this and similar magical effects involve immediate "unconscious inferences" about intentions more akin to perceptual processing than to explicit deliberations based on a reflective "theory" of mind.
The problem is not simply that the list would be interminable. The problem is more fundamental: since any effect can be performed in many ways, at what point does it become a different effect? Since there are no clear boundaries, we need to make a host of decisions about how to construct any list of magic effects. We cannot possibly list every variation, so we need to decide which differences matter, and which do not. Is “card to lemon” not essentially the same effect as “card to orange”? But is it essentially the same as “bill to lemon,” in which a bill (banknote) disappears and reappears inside a lemon? Bills also reappear inside oranges and envelopes because, in magic, they often serve much the same function as a playing card. They also reappear inside bananas. However, at what point on the slippery slope from “card to lemon” to “bill to banana” do we draw a line? And, just as importantly, where do we draw the line: between cards and bills, or between lemons and bananas? In other words, do we categorize on the basis of object (cards, bills, etc.) or location (lemons, bananas, etc.)? As it happens, many “cups and balls” routines also end with the production of fruit: lemons, oranges, sometimes a melon, and I have seen the occasional tomato (which is also a fruit, scientifically speaking, based on a natural set of criteria).
Magicians often trick spectators' senses by relying on cognitive limitations. To do so, they use intuitive but age-old knowledge of human cognition. Research into the relationship between magic and psychology has been growing for a number of years now. This work offers an original ground for studying cognitive processes, while also providing the opportunity to discover processes that are still poorly understood. In this respect, the study of magic in psychology resembles the domain of "cryptozoology," the name given to the search, real or humoristic, for unknown species. This article begins by briefly presenting some of the major research conducted over the past 10 years in the psychology of magic. We argue that, unfortunately, so far, no unknown cognitive species have been added to the "hunting bag" of these studies; in the second part of the article, we discuss the wide range of psychological facets of magic that are still to be explored.
Magic tricks violate the expected causal relationships that form an implicit belief system about what is possible in the world around us. Observing a magic effect seemingly invalidates our implicit assumptions about what action causes which outcome. We aimed at identifying the neural correlates of such expectation violations by contrasting 24 video clips of magic tricks with 24 control clips in which the expected action-outcome relationship is upheld. Using fMRI, we measured the brain activity of 25 normal volunteers while they watched the clips in the scanner. Additionally, we measured the professional magician who had performed the magic tricks under the assumption that, in contrast to naïve observers, the magician himself would not perceive his own magic tricks as an expectation violation. As the main effect of magic – control clips in the normal sample, we found higher activity for magic in the head of the caudate nucleus (CN) bilaterally, the left inferior frontal gyrus and the left anterior insula. As expected, the magician’s brain activity substantially differed from these results, with mainly parietal areas (supramarginal gyrus bilaterally) activated, supporting our hypothesis that he did not experience any expectation violation. These findings are in accordance with previous research that has implicated the head of the CN in processing changes in the contingency between action and outcome, even in the absence of reward or feedback.
Magic tricks usually remain a mystery to the observer. For the sake of science, we offered participants the opportunity to discover the magician's secret method by repeatedly presenting the same trick and asking them to find out how the trick worked. In the context of insightful problem solving, the present work investigated the emotions that participants experience upon solving a magic trick. We assumed that these emotions form the typical “Aha! experience” that accompanies insightful solutions to difficult problems. We aimed to show that Aha! experiences can be triggered by magic tricks and to systematically explore the phenomenology of the Aha! experience by breaking it down into five previously postulated dimensions. 34 video clips of different magic tricks were presented up to three times to 50 participants who had to find out how the trick was accomplished, and to indicate whether they had experienced an Aha! during the solving process. Participants then performed a comprehensive quantitative and qualitative assessment of their Aha! experiences which was repeated after 14 days to control for its reliability. 41% of all suggested solutions were accompanied by an Aha! experience. The quantitative assessment remained stable across time in all five dimensions. Happiness was rated as the most important dimension. This primacy of positive emotions was also reflected in participants' qualitative self-reports which contained more emotional than cognitive aspects. Implementing magic tricks as problem solving task, we could show that strong Aha! experiences can be triggered if a trick is solved. We could at least partially capture the phenomenology of Aha! by identifying one prevailing aspect (positive emotions), a new aspect (release of tension upon gaining insight into a magic trick) and one less important aspect (impasse).
Recent studies (e.g., Kuhn and Tatler, 2005) have suggested that magic tricks can provide a powerful and compelling domain for the study of attention and perception. In particular, many stage illusions involve attentional misdirection, guiding the observer's gaze to a salient object or event, while another critical action, such as sleight of hand, is taking place. Even if the critical action takes place in full view, people typically fail to see it due to inattentional blindness (IB). In an eye-tracking experiment, participants watched videos of a new magic trick, wherein a coin placed beneath a napkin disappears, reappearing under a different napkin. Appropriately deployed attention would allow participants to detect the “secret” event that underlies the illusion (a moving coin), as it happens in full view and is visible for approximately 550 ms. Nevertheless, we observed high rates of IB. Unlike prior research, eye-movements during the critical event showed different patterns for participants, depending upon whether they saw the moving coin. The results also showed that when participants watched several “practice” videos without any moving coin, they became far more likely to detect the coin in the critical trial. Taken together, the findings are consistent with perceptual load theory (Lavie and Tsal, 1994).
Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals’ explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants’ explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people’s interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events.
Over the centuries, magicians have developed extensive knowledge about the manipulation of the human mind—knowledge that has been largely ignored by psychology. It has recently been argued that this knowledge could help improve our understanding of human cognition and consciousness. But how might this be done? And how much could it ultimately contribute to the exploration of the human mind? We propose here a framework outlining how knowledge about magic can be used to help us understand the human mind. Various approaches—both old and new—are surveyed, in terms of four different levels. The first focuses on the methods in magic, using these to suggest new approaches to existing issues in psychology. The second focuses on the effects that magic can produce, such as the sense of wonder induced by seeing an apparently impossible event. Third is the consideration of magic tricks—methods and effects together—as phenomena of scientific interest in their own right. Finally, there is the organization of knowledge about magic into an informative whole, including the possibility of a science centered around the experience of wonder.
Magicians use misdirection to prevent you from realizing the methods used to create a magical effect, thereby allowing you to experience an apparently impossible event. Magicians have acquired much knowledge about misdirection, and have suggested several taxonomies of misdirection. These describe many of the fundamental principles in misdirection, focusing on how misdirection is achieved by magicians. In this article we review the strengths and weaknesses of past taxonomies, and argue that a more natural way of making sense of misdirection is to focus on the perceptual and cognitive mechanisms involved. Our psychologically-based taxonomy has three basic categories, corresponding to the types of psychological mechanisms affected: perception, memory, and reasoning. Each of these categories is then divided into subcategories based on the mechanisms that control these effects. This new taxonomy can help organize magicians' knowledge of misdirection in a meaningful way, and facilitate the dialog between magicians and scientists.
In a popular magic routine known as "multiplying billiard balls", magicians fool their audience by using an empty shell that the audience believes to be a complete ball. Here, we present some observations suggesting that the spectators do not merely entertain the intellectual belief that the balls are all solid, but rather automatically and immediately perceive them as such. Our observations demonstrate the surprising potency and genuinely perceptual origin of amodal volume completion.
It is an established finding that neuronal activity is decreased for repeated stimuli. Recent studies revealed that repetition suppression (RS) effects are altered by manipulating the probability with which stimuli are repeated. RS for faces is more pronounced when the probability of repetition is high than when it is low. This response pattern is interpreted with reference to the predictive coding (PC) account, which assumes that RS is influenced by top-down expectations. Recent findings challenge the generality of PC accounts of RS by showing repetition probability does not modulate RS for other visual stimuli than faces. However, a number of findings on visual processing are in line with PC. Thus, the influence of repetition probability on RS effects during object processing requires careful reinvestigations. In the present fMRI study, object pictures were presented in a high (75%) or low (25%) repetition probability context. We found increased RS in the high-probability context compared to the low-probability context in the left lateral occipital complex (LOC). The dorsal-caudal and the ventral-anterior subdivisions of the LOC revealed similar neuronal responses. These results indicate that repetition probability effects can be found for other visual objects than faces and provide evidence in favor of the PC account.
Novelty and surprise play significant roles in animal behavior and in attempts to understand the neural mechanisms underlying it. They also play important roles in technology, where detecting observations that are novel or surprising is central to many applications, such as medical diagnosis, text processing, surveillance, and security. Theories of motivation, particularly of intrinsic motivation, place novelty and surprise among the primary factors that arouse interest, motivate exploratory or avoidance behavior, and drive learning. In many of these studies, novelty and surprise are not distinguished from one another: the words are used more-or-less interchangeably. However, while undeniably closely related, novelty and surprise are very different. The purpose of this article is first to highlight the differences between novelty and surprise and to discuss how they are related by presenting an extensive review of mathematical and computational proposals related to them, and then to explore the implications of this for understanding behavioral and neuroscience data. We argue that opportunities for improved understanding of behavior and its neural basis are likely being missed by failing to distinguish between novelty and surprise.
This paper reviews recent developments under the free energy principle that introduce a normative perspective on classical economic (utilitarian) decision-making based on (active) Bayesian inference. It has been suggested that the free energy principle precludes novelty and complexity, because it assumes that biological systems-like ourselves-try to minimize the long-term average of surprise to maintain their homeostasis. However, recent formulations show that minimizing surprise leads naturally to concepts such as exploration and novelty bonuses. In this approach, agents infer a policy that minimizes surprise by minimizing the difference (or relative entropy) between likely and desired outcomes, which involves both pursuing the goal-state that has the highest expected utility (often termed "exploitation") and visiting a number of different goal-states ("exploration"). Crucially, the opportunity to visit new states increases the value of the current state. Casting decision-making problems within a variational framework, therefore, predicts that our behavior is governed by both the entropy and expected utility of future states. This dissolves any dialectic between minimizing surprise and exploration or novelty seeking.
Significance
This study investigates the brain mechanisms by which people disregard their previous beliefs about their environment and start forming new beliefs. Surprising events are often a signal that one’s previous beliefs are no longer valid. Using brain imaging, we identified separate brain systems involved in dealing with the immediate consequences of surprise (i.e., reprogramming actions) and in updating one’s beliefs about the environment to predict future events accurately. We present a mathematical and neuroanatomical model of how brains adjust to change in their environment that may inform our understanding of neurological disorders in which this adjustment process fails.
The eye movements of expert players trying to solve a chess problem show that the first idea that comes to mind directs attention toward sources of information consistent with it and away from inconsistent information. This bias continues unconsciously even when players believe they are looking for alternatives. The result is that alternatives to the first idea are ignored. This mechanism for biasing attention ensures a speedy response in familiar situations, but it can lead to errors when the first thought that comes to mind is not appropriate. We propose that this mechanism is the source of many cognitive biases, from phenomena in problem solving and reasoning to perceptual errors and failures in memory.
Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to adaptive success. This target article critically examines this "hierarchical prediction machine" approach, concluding that it offers the best clue yet to the shape of a unified science of mind and action. Sections 1 and 2 lay out the key elements and implications of the approach. Section 3 explores a variety of pitfalls and challenges, spanning the evidential, the methodological, and the more properly conceptual. The paper ends (sections 4 and 5) by asking how such approaches might impact our more general vision of mind, experience, and agency.
It has long been recognized that the amplitude of the P300 component of event-related brain potentials is sensitive to the degree to which eliciting stimuli are surprising to the observers (Donchin, 1981). While Squires et al. (1976) showed and modeled dependencies of P300 amplitudes from observed stimuli on various time scales, Mars et al. (2008) proposed a computational model keeping track of stimulus probabilities on a long-term time scale. We suggest here a computational model which integrates prior information with short-term, long-term, and alternation-based experiential influences on P300 amplitude fluctuations. To evaluate the new model, we measured trial-by-trial P300 amplitude fluctuations in a simple two-choice response time task, and tested the computational models of trial-by-trial P300 amplitudes using Bayesian model evaluation. The results reveal that the new digital filtering (DIF) model provides a superior account of the trial-by-trial P300 amplitudes when compared to both Squires et al.’s (1976) model, and Mars et al.’s (2008) model. We show that the P300-generating system can be described as two parallel first-order infinite impulse response (IIR) low-pass filters and an additional fourth-order finite impulse response (FIR) high-pass filter. Implications of the acquired data are discussed with regard to the neurobiological distinction between short-term, long-term, and working memory as well as from the point of view of predictive coding models and Bayesian learning theories of cortical function.
The dorsal anterior cingulate cortex (dACC) has been implicated in a variety of cognitive control functions, among them the monitoring of conflict, error, and volatility, error anticipation, reward learning, and reward prediction errors. In this work, we used a Bayesian ideal observer model, which predicts trial-by-trial probabilistic expectation of stop trials and response errors in the stop-signal task, to differentiate these proposed functions quantitatively. We found that dACC hemodynamic response, as measured by functional magnetic resonance imaging, encodes both the absolute prediction error between stimulus expectation and outcome, and the signed prediction error related to response outcome. After accounting for these factors, dACC has no residual correlation with conflict or error likelihood in the stop-signal task. Consistent with recent monkey neural recording studies, and in contrast with other neuroimaging studies, our work demonstrates that dACC reports at least two different types of prediction errors, and beyond contexts that are limited to reward processing.
Recent articles calling for a scientific study of magic have been the subject of widespread interest. This article considers the topic from a broader perspective and argues that to engage in a science of magic, in any meaningful sense, is misguided. It argues that those who have called for a scientific theory of magic have failed to explain either how or why such a theory might be constructed, that a shift of focus to a neuroscience of magic is simply unwarranted, and that a science of magic is itself an inherently unsound idea. It seeks to provide a more informed view of the relationship between science and magic and suggests a more appropriate way forward for scientists.
How the scientific study of magic reveals intriguing—and often unsettling—insights into the mysteries of the human mind.
What do we see when we watch a magician pull a rabbit out of a hat or read a person's mind? We are captivated by an illusion; we applaud the fact that we have been fooled. Why do we enjoy experiencing what seems clearly impossible, or at least beyond our powers of explanation? In Experiencing the Impossible, Gustav Kuhn examines the psychological processes that underpin our experience of magic. Kuhn, a psychologist and a magician, reveals the intriguing—and often unsettling—insights into the human mind that the scientific study of magic provides.
Magic, Kuhn explains, creates a cognitive conflict between what we believe to be true (for example, a rabbit could not be in that hat) and what we experience (a rabbit has just come out of that hat!). Drawing on the latest psychological, neurological, and philosophical research, he suggests that misdirection is at the heart of all magic tricks, and he offers a scientific theory of misdirection. He explores, among other topics, our propensity for magical thinking, the malleability of our perceptual experiences, forgetting and misremembering, free will and mind control, and how magic is applied outside entertaiment—the use of illusion in human-computer interaction, politics, warfare, and elsewhere.
We may be surprised to learn how little of the world we actually perceive, how little we can trust what we see and remember, and how little we are in charge of our thoughts and actions. Exploring magic, Kuhn illuminates the complex—and almost magical—mechanisms underlying our daily activities.
In the past two decades, reinforcement learning (RL) has become a popular framework for understanding brain function. A key component of RL models, prediction error, has been associated with neural signals throughout the brain, including subcortical nuclei, primary sensory cortices, and prefrontal cortex. Depending on the location in which activity is observed, the functional interpretation of prediction error may change: Prediction errors may reflect a discrepancy in the anticipated and actual value of reward, a signal indicating the salience or novelty of a stimulus, and many other interpretations. Anterior cingulate cortex (ACC) has long been recognized as a region involved in processing behavioral error, and recent computational models of the region have expanded this interpretation to include a more general role for the region in predicting likely events, broadly construed, and signaling deviations between expected and observed events. Ongoing modeling work investigating the interaction between ACC and additional regions involved in cognitive control suggests an even broader role for cingulate in computing a hierarchically structured surprise signal critical for learning models of the environment. The result is a predictive coding model of the frontal lobes, suggesting that predictive coding may be a unifying computational principle across the neocortex.
Wonder may be an important emotion, but the term wonder is remarkably ambiguous. For centuries, in psychological discourse, it has been defined as a variety of things. In an attempt to be more focused, and given the growing scientific interest in magic, this article describes a particular kind of wonder: the response to a magic trick. It first provides a historical perspective by considering continuity and change over time in this experience, and argues that, in certain respects, this particular kind of wonder has changed. It then describes in detail the experience of magic, considers the extent to which it might be considered acquired rather than innate, and how it relates to other emotions, such as surprise. In the process, it discusses the role of belief and offers some suggestions for future research. It concludes by noting the importance of context and meaning in shaping the nature of the experience, and argues for the value of both experimental and historical research in the attempt to understand such experiences.
Despite its enduring popularity, theatrical magic remains all but ignored by art critics, art historians, and philosophers. This is unfortunate, since magic offers a unique and distinctively intellectual aesthetic experience and raises a host of interesting philosophical questions. Thus, this article initiates a philosophical investigation of the experience of magic. Section I dispels two widespread misconceptions about the nature of magic and discusses the sort of depiction it requires. Section II asks, “What cognitive attitude is involved in the experience of magic?” and criticizes three candidate replies; Section III then argues that Tamar Szabó Gendler's notion of “belief-discordant alief” holds the key to a correct answer. Finally, Section IV develops an account of the experience of magic and explores some of its consequences. The result is a philosophically rich view of the experience of magic that opens new avenues for inquiry and is relevant to core issues in contemporary aesthetics.
We present results from two experiments, in which subjects watched continuous videos of a professional magician repeatedly performing a maneuver in which a ball could "magically" appear under a cup. In all cases, subjects were asked to predict whether the ball would appear under the cup or not, while scalp EEG recordings were performed. Both experiments elicited strong and consistent behavioral and neural responses. In the first experiment, we used two blocks of videos with different probabilities of the ball appearing in the cup and found that, first, based on the behavioral responses, the subjects could track this probability change; and second, the different probabilities modulated the neural responses. In the second experiment, we introduced a control condition in which the magician performed the maneuver under the table, out of subjects' view. Comparing the two conditions (i.e., performing the maneuver within or out of the subjects' view), we found that, first, the magic trick dramatically biased the subjects' behavioral responses; and second, the two conditions led to differential neural responses, in spite of the fact that the stimulus triggering the evoked responses (seeing the ball in the cup) was exactly the same. Altogether, our results show how new insights into sensory and cognitive processing can be obtained using adapted magic tricks. Moreover, the approach of analyzing responses to continuous video presentations offers a more ecological setting compared to classic evoked potential paradigms, which are typically based on presenting static images flashed at the center of the screen.
The capability of the human brain for Bayesian inference was assessed by manipulating probabilistic contingencies in an urn-ball task. Event-related potentials (ERPs) were recorded in response to stimuli that differed in frequency of occurrence (.18 to .82). Single-averaged ERPs with sufficient signal-to-noise ratio (relative frequency of occurrence > .5) were utilized for further analysis. Research hypotheses about relationships between probabilistic contingencies and ERP amplitude variations were formalized as (in-)equality constrained hypotheses. Conducting Bayesian model comparisons, we found that manipulations of prior probabilities and likelihoods were associated with separately modifiable and distinct ERP responses. P3a amplitudes were sensitive to the degree of prior certainty such that higher prior probabilities were related to larger frontally distributed P3a waves. P3b amplitudes were sensitive to the degree of likelihood certainty such that lower likelihoods were associated with larger parietally distributed P3b waves. These ERP data suggest that these antecedents of Bayesian inference (prior probabilities and likelihoods) are coded by the human brain.
In recent years, neuroscientists have shown an increasing interest in magic. One reason for this is the parallels that can be drawn between concepts that have long been discussed in magic theory, particularly misdirection, and those that are routinely studied in cognitive neuroscience, such as attention and, as argued in this essay, different forms of memory. A second and perhaps more attractive justification for this growing interest is that magic tricks offer novel experimental approaches to cognitive neuroscience. In fact, magicians continuously demonstrate in very engaging ways one of the most basic principles of brain function — how the brain constructs a subjective reality using assumptions based on relatively little and ambiguous information.
In a well-known magic trick known as multiplying balls, conjurers fool their audience with the use of a semi-spherical shell, which the audience perceives as a complete ball [1
• Ekroll V.
• Sayim B.
• Wagemans J.
Against better knowledge: the magical force of amodal volume completion.Iperception. 2013; 4: 511-515
• PubMed
• Google Scholar
]. Here, we report that this illusion persists even when observers touch the inside of the shell with their own finger. Even more intriguingly, this also produces an illusion of bodily self-awareness in which the finger feels shorter, as if to make space for the purely illusory volume of the visually completed ball. This observation provides strong evidence for the controversial and counterintuitive idea that our experience of the hidden backsides of objects is shaped by genuine perceptual representations rather than mere cognitive guesswork or imagery [2
• Michotte A.
• Thinès G.
• Crabbé G.
Les Compléments Amodaux des Structures Perceptives. Studia Psychologica, 1967
• Google Scholar
].
In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a computerized database for storing and representing large amounts of information on connectivity patterns, and (3) the application of these data to the analysis of hierarchical organization of the cerebral cortex. Our analysis concentrates on the visual system, which includes 25 neocortical areas that are predominantly or exclusively visual in function, plus an additional 7 areas that we regard as visual-association areas on the basis of their extensive visual inputs. A total of 305 connections among these 32 visual and visual-association areas have been reported. This represents 31% of the possible number of pathways it each area were connected with all others. The actual degree of connectivity is likely to be closer to 40%. The great majority of pathways involve reciprocal connections between areas. There are also extensive connections with cortical areas outside the visual system proper, including the somatosensory cortex, as well as neocortical, transitional, and archicortical regions in the temporal and frontal lobes. In the somatosensory/motor system, there are 62 identified pathways linking 13 cortical areas, suggesting an overall connectivity of about 40%. Based on the laminar patterns of connections between areas, we propose a hierarchy of visual areas and of somato sensory/motor areas that is more comprehensive than those suggested in other recent studies. The current version of the visual hierarchy includes 10 levels of cortical processing. Altogether, it contains 14 levels if one includes the retina and lateral geniculate nucleus at the bottom as well as the entorhinal cortex and hippocampus at the top. Within this hierarchy, there are multiple, intertwined processing streams, which, at a low level, are related to the compartmental organization of areas V1 and V2 and, at a high level, are related to the distinction between processing centers in the temporal and parietal lobes. However, there are some pathways and relationships (about 10% of the total) whose descriptions do not fit cleanly into this hierarchical scheme for one reason or another. In most instances, though, it is unclear whether these represent genuine exceptions to a strict hierarchy rather than inaccuracies or uncertainties in the reported assignment.
Associative learning theory assumes that prediction error is a driving force in learning. A competing view, probabilistic contrast (PC) theory, is that learning and prediction error are unrelated. We tested a learning phenomenon that has proved troublesome for associative theory - retrospective revaluation - to evaluate these two models. We previously showed that activation in right lateral prefrontal cortex (PFC) provides a reliable signature for the presence of prediction error. Thus, if the associative view is correct, retrospective revaluation should be accompanied by right lateral PFC activation. PC theory would be supported by the absence of this activation. Right PFC and ventral striatal activation occurred during retrospective revaluation, supporting the associative account. Activations appeared to reflect the degree of revaluation, predicting later brain responses to revalued cues. Our results support a modified associative account of retrospective revaluation and demonstrate the potential of functional neuroimaging as a tool for evaluating competing learning models.
We propose a new approach to differentiate between insight and noninsight problem solving, by introducing magic tricks as problem solving domain. We argue that magic tricks are ideally suited to investigate representational change, the key mechanism that yields sudden insight into the solution of a problem, because in order to gain insight into the magicians' secret method, observers must overcome implicit constraints and thus change their problem representation. In Experiment 1, 50 participants were exposed to 34 different magic tricks, asking them to find out how the trick was accomplished. Upon solving a trick, participants indicated if they had reached the solution either with or without insight. Insight was reported in 41.1% of solutions. The new task domain revealed differences in solution accuracy, time course and solution confidence with insight solutions being more likely to be true, reached earlier, and obtaining higher confidence ratings. In Experiment 2, we explored which role self-imposed constraints actually play in magic tricks. 62 participants were presented with 12 magic tricks. One group received verbal cues, providing solution relevant information without giving the solution away. The control group received no informative cue. Experiment 2 showed that participants' constraints were suggestible to verbal cues, resulting in higher solution rates. Thus, magic tricks provide more detailed information about the differences between insightful and noninsightful problem solving, and the underlying mechanisms that are necessary to have an insight.
Bell System Technical Journal, also pp. 623-656 (October)
The capacity to predict future events permits a creature to detect, model, and manipulate the causal structure of its interactions
with its environment. Behavioral experiments suggest that learning is driven by changes in the expectations about future salient
events such as rewards and punishments. Physiological work has recently complemented these studies by identifying dopaminergic
neurons in the primate whose fluctuating output apparently signals changes or errors in the predictions of future salient
and rewarding events. Taken together, these findings can be understood through quantitative theories of adaptive optimizing
control.