From mere coincidences to meaningful discoveries

People's reactions to coincidences are often cited as an illustration of the irrationality of human reasoning about chance. We argue that coincidences may be better understood in terms of rational statistical inference, based on their functional role in processes of causal discovery and theory revision. We present a formal definition of coincidences in the context of a Bayesian framework for causal induction: a coincidence is an event that provides support for an alternative to a currently favored causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability. We test the qualitative and quantitative predictions of this account through a series of experiments that examine the transition from coincidence to evidence, the correspondence between the strength of coincidences and the statistical support for causal structure, and the relationship between causes and coincidences. Our results indicate that people can accurately assess the strength of coincidences, suggesting that irrational conclusions drawn from coincidences are the consequence of overestimation of the plausibility of novel causal forces. We discuss the implications of our account for understanding the role of coincidences in theory change.     

The connection between random sequences,everyday coincidences,and belief in the paranormal

This paper argues against the theory that people interpret unusual coincidences as paranormal because they misunderstand the probability of their occurring by chance. In the two studies reported here, 214 subjects were given a questionnaire on the frequency of coincidences in their lives, a series of probabilistic problems, and a scale assessing their belief in the paranormal. Believers reported more coincidences than disbelievers. Believers made more errors than disbelievers in tasks reflecting sensitivity to the relationship between expected distribution of chance events and total number of occurrences; and avoided repetitions of identical alternatives in a random sequence to a greater extent. However, the last two effects completely disappeared in a subsample of university students. It is proposed that a more frequent experience of coincidences, on the one hand, and a more biased representation of randomness, on the other, are independent consequences of a stronger propensity of believers in the paranormal to connect separate events. Copyright © 2002 John Wiley & Sons, Ltd.     

Allusive thinking (cognitive looseness) and the propensity to perceive “meaningful” coincidences

This study aimed at evaluating relations between the disposition to make “meaningful” associations between random events and potentially predisposing factors related to a more “loose” cognitive control, that is, loose associative processing (allusive thinking) and poorer inhibition of irrelevant memory content. As the findings of this study suggest, individuals with a higher disposition to perceive coincidences produced a higher rate of unusual associations in the Bridge-the-Associative-Gap test than low scorers, and showed poorer inhibition of no longer relevant memory content in the Recent Probes Task. These relationships were independent from individual differences in paranormal belief. Performance in a random generation task (Mittenecker Pointing Test) yielded no support for an important role of a biased concept of randomness in the perception of coincidences. The findings suggest that common mechanisms may underlie the propensity to perceive meaningful coincidences, cognitive looseness, and positive schizotypy.     

Sensitivity to coincidences and paranormal belief

Often it is difficult to find a natural explanation as to why a surprising coincidence occurs. In attempting to find one, people may be inclined to accept paranormal explanations. The objective of this study was to investigate whether people with a lower threshold for being surprised by coincidences have a greater propensity to become believers compared to those with a higher threshold. Participants were exposed to artificial coincidences, which were formally defined as less or more probable, and were asked to provide remarkability ratings. Paranormal belief was measured by the Australian Sheep-Goat Scale. An analysis of the remarkability ratings revealed a significant interaction effect between Sheep-Goat score and type of coincidence, suggesting that people with lower thresholds of surprise, when experiencing coincidences, harbor higher paranormal belief than those with a higher threshold. The theoretical aspects of these findings were discussed.     

Allusive thinking (cognitive looseness) and the propensity to perceive “meaningful” coincidences

This study aimed at evaluating relations between the disposition to make “meaningful” associations between random events and potentially predisposing factors related to a more “loose” cognitive control, that is, loose associative processing (allusive thinking) and poorer inhibition of irrelevant memory content. As the findings of this study suggest, individuals with a higher disposition to perceive coincidences produced a higher rate of unusual associations in the Bridge-the-Associative-Gap test than low scorers, and showed poorer inhibition of no longer relevant memory content in the Recent Probes Task. These relationships were independent from individual differences in paranormal belief. Performance in a random generation task (Mittenecker Pointing Test) yielded no support for an important role of a biased concept of randomness in the perception of coincidences. The findings suggest that common mechanisms may underlie the propensity to perceive meaningful coincidences, cognitive looseness, and positive schizotypy.     

The propensity to perceive meaningful coincidences is associated with increased posterior alpha power during retention of information in a modified Sternberg paradigm

There are ample inter-individual differences in the frequency with which people perceive meaningful coincidences. Previous research has identified increased proactive interference, that is a reduced working memory capacity, as one possible mechanism associated with this phenomenon. The present study aimed at extending this finding into the domain of neuroscience, (1) by assessing EEG alpha oscillations during the retention of information, (2) by replicating the behavioral link between meaningful coincidences and proactive interference. In a sample of 52 participants, the behavioral replication was successful. Furthermore, participants who perceived more meaningful coincidences showed higher alpha power increases at parietal-occipital sites, and at the same time, displayed lower alpha power increases at frontal areas, during retention of information. This neurophysiological activation pattern further underlines the assumption that participants who perceive more meaningful coincidences show lower working memory capacities, since increased alpha power at parietal areas reflects a higher load on working memory demands.     

Coincidence and Common Cause

According to the traditional view of the causal structure of a coincidence, the several parts of a coincidence are produced by independent causes. I argue that the traditional view is mistaken; even the several parts of a coincidence may have a common cause. This has important implications for how we think about the relationship between causation and causal explanation—and in particular, for why coincidences cannot be explained.     

Localized measures for nonstationary time-series of physiological data

We will discuss localized measures related to the concepts of dimension, Lyapunove exponents (entropy), and recurrence diagrams. We stress the relevance of localized events and coincidences in physiological time series that often are lost when statistical averaging methods are applied. We suggest event-based statistics as an alternative to spectral or averaged-based statistics. The use of wavelets bases for characterizing localized structures is discussed as a potential alternative to Fourier-based analysis. Finally we mention how local domains in state space could be applied as triggers for external stimuli and thereby improve the statistics of ERP recordings.     

Roles of causation and meaning for interpreting correlations

The essays by Tougas and Willeford address, among other things, a number of ways to understand causation, which play crucial roles in the framework of thinking proposed by Pauli and Jung. The intention of my following reply is to say a few words about how these options are related to one another within our reconstruction of the Pauli‐Jung conjecture. In the tradition of the sciences, looking for causation has become a virtually innate reflex to interpret empirically observed correlations. The concept of synchronicity suggests looking for meaningful coincidences as an alternative, complementary interpretation, particularly appropriate for psychophysical correlations.     

Astrophysical Fine Tuning,Naturalism, and the Contemporary Design Argument

Evidence for instances of astrophysical ‘fine tuning’ (or ‘coincidences’) is thought by some to lend support to the design argument (i.e. the argument that our universe has been designed by some deity). We assess some of the relevant empirical and conceptual issues. We argue that astrophysical fine tuning calls for some explanation, but this explanation need not appeal to the design argument. A clear and strict separation of the issue of anthropic fine tuning on one hand and any form of Eddingtonian numerology and teleology on the other, may help clarify arguably the most significant issue in the philosophy of cosmology.     

Process theory as a framework for comprehensive psychodynamic formulations.

In this article, we have proposed a method for developing integrative psychiatric formulations based on process theory, as contrasted to eclectic attempts to combine separate, often disparate, theories. Congruent with chaos theory and "far from equilibrium" thermodynamics, process theory proposes that normal development and psychopathology are creative processes open to chance, choice, and meaningful coincidences and governed by harmonious and conflictual interactions between opposites. We have illustrated our method by discussing a case, previously described by Perry, Cooper, and Michels (1987) from three psychoanalytic perspectives. We interpret this case to result from a possible neuroamine depletion, poor family life, social defects, and habitual conflictual/depressive patterns of interaction.     

Local Anaesthesia, The Increase of the Evil Through Emotional Impoverishment

Evil should be characterised as a specific constellation, which results from destructive connections between individual activities and systemic influences. The article shows some important aspects of the structure of evil and prefers the terms of wickedness and obscene coincidences to describe its own character. Therefore, also the division between rationality and affectivity appears as inadequate, because evil has on the one side an intrinsic attractiveness for individuals and is on the other side in modern societies more and more a product of a rationality, which is free from passion. Especially the emotional impoverishment is responsible for the increase of evil, which is demonstrated by two examples. Based on Paul Ricoeur, the evolution of malum can be developed by a short analyse of the relationship between Ethics and Emotions.     

Comment on 'the case of Melanie' by Joseph Cambray

The discussion comments firstly on the role of synchronicity which seems so natural and significant for Jungians but which Freudians would think no more than interesting coincidences. This gives an idea of how different the two schools' approach to the psyche can be. Some theoretical elaboration is made regarding archetypes and primal phantasies: primal phantasies are much related to sexuality, but sexuality understood as intimately linked to the great mysteries of life. The discussion of the clinical work shows more similarities than differences. This suggests that for both perspectives the clinical is sovereign. As we know, respect and care for the patient's evolution, true concern for the patient and skilful use of technique remain the most important indicators of successful therapeutic work in the different psychotherapeutic approaches.     

Unsupervised Statistical Learning of Higher-Order Spatial Structures From Visual Scenes

Three experiments investigated the ability of human observers to extract the joint and conditional probabilities of shape co-occurrences during passive viewing of complex visual scenes. Results indicated that statistical learning of shape conjunctions was both rapid and automatic, as subjects were not instructed to attend to any particular features of the displays. Moreover, in addition to single-shape frequency, subjects acquired in parallel several different higher-order aspects of the statistical structure of the displays, including absolute shape-position relations in an array, shape-pair arrangements independent of position, and conditional probabilities of shape co-occurrences. Unsupervised learning of these higher-order statistics provides support for Barlow's theory of visual recognition, which posits that detecting "suspicious coincidences" of elements during recognition is a necessary prerequisite for efficient learning of new visual features.     

Physicalism, Teleology and the Miraculous Coincidence Problem

I focus on Fodor's model of the relationship between special sciences and basic physics, and on a criticism of this model, that it implies that the causal stability of, e.g., the mental in its production of behaviour is nothing short of a miraculous coincidence. David Papineau and Graham Macdonaldendorse this criticism. But it is far less clear than they assume that Fodor's picture indeed involves coincidences, which in any case their injection of a teleological supplement cannot explain. Papineau's and Macdonald's problem is subtly different from a similar one presented by Adrian Cussins. This is no more effective against Fodor's picture, but the kind of account of the relation between the physical and the psychological which could constitute a solution to Cussins' problem is one which, for independent reasons, a physicalist of Fodor's stripe ought to provide.     

Can Planck's constant be measured with classical mechanics?

An interesting case of the complex interaction between theory and experiment can be found in many experiments in quantum physics employing classical reasoning. It is expected that this practice would lead to quantitative inaccuracy, unless the measurements’ results were averaged. Whether or not this inaccuracy is significant depends critically on the details of the particular experimental situation. The example of Millikan's photoelectric experiment, in which he obtained a precise value of Planck's constant, provides a good case for illustrating the process of estimating the inaccuracy resulting from the classical‐quantum discrepancy. In the case of Millikan's experiment, it seems that a significant inaccuracy was avoided because of fortunate coincidences. In general, in the absence of a careful analysis, it is impossible to say whether the use of classical reasoning interferes with the accuracy of a quantum‐physical experiment.     

Visual causal impressions in the perception of several moving objects

Several kinds of visual causal impressions occur when people observe stimuli involving objects in motion. It is hypothesized that these impressions occur when the visual system avoids coincidences by matching the observable kinematic features of the stimulus to a template of a physical mechanism. This was tested by constructing a stimulus in which several spatially separated objects move in a coordinated manner. Variations on this stimulus were constructed such that some were inconsistent with a possible physical mechanism that could explain the motions of the objects and others were consistent with it. Mechanism‐inconsistent variations yielded significantly lower ratings of the causal impression and mechanism‐consistent variations did not, supporting the hypothesis. Misperceptions of features of the stimulus were also reported by a majority of participants, and the nature of these misperceptions is also consistent with the hypothesis that the stimulus is interpreted as a representation of a kind of physical mechanism.     

The relationship between anomalistic belief,misperception of chance and the base rate fallacy

Abstract

A poor understanding of probability may lead people to misinterpret every day coincidences and form anomalistic (e.g., paranormal) beliefs. We investigated the relationship between anomalistic belief (including type of belief) and misperception of chance and the base rate fallacy across both anomalistic and control (i.e., neutral) contexts. Greater anomalistic belief was associated with poorer performance for both types of items; however there were no significant interactions between belief and context. For misperception of chance items, only experiential (vs. theoretical) anomalistic beliefs predicted more errors. In contrast, overall anomalistic belief was positively related to the base rate fallacy but no specific subtype of anomalistic belief was a significant predictor. The results indicate misperception of chance may lead people to interpret coincidental events as having an anomalistic cause, and a poor understanding of base rates may make people more prone to forming anomalistic beliefs.     

Cognitive-experiential self-theory and subjective probability: further evidence for two conceptual systems.

Three experiments (N = 1,331) demonstrated that research findings on suspiciousness about coincidences (Miller, Turnbull, & McFarland, 1989) can be accounted for in terms of subjective probability, as predicted by cognitive-experiential self-theory (CEST) but in contrast with the norm theory (NT) account offered by Miller et al. (1989). Ss participated in a hypothetical (Experiments 1 and 2) or real (Experiment 3) lottery game in which they chose between 2 bowls offering equivalent probabilities of winning or losing but differing with respect to absolute numbers (e.g., 1 in 10 vs. 10 in 100). Responses across 4 conditions (2 probability levels x 2 outcome types) and across the 3 experiments supported predictions derived from CEST but not those derived from NT. Results are discussed in terms of 2 conceptual systems, rational and experiential, that operate by different rules of inference.     

COSMIC PURPOSE AND THE CONTINGENCY OF HUMAN EVOLUTION

Some understand the evolutionary process as more or less predictable; others stress its contingency. I argue that both Christian evolutionists who have assumed that the purposes of the Creator can be realized only through more or less predictable processes as well as those who infer from the contingency of the evolutionary process to the lack of purpose in the universe generally, are mistaken if the Creator escapes from the limits imposed on the creature by temporality, as the traditional Augustinian account supposes. The notion of “purpose” must itself be reinterpreted in such a case. It makes no difference whether the appearance of Homo sapiens is the inevitable result of a steady process of complexification stretching over billions of years, or whether it comes about through a series of coincidences that would have made it entirely unpredictable from the (causal) human standpoint. Either way, the outcome is of God's making, and from the biblical standpoint may appear as part of God's plan.