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This chapter introduces the theme of the book (i.e., the challenge of chance) and includes brief surveys of the individual chapters.

In everyday language, the use of such words as “chance,” “coincidence,” “luck,” “fortune” or “randomness” strongly overlap. In fact, in some languages, such as German, they coincide in one word (). In others, there is a clear separation between chance events with positive connotations (e.g., “luck,” “fortune”) and those with bad ones (e.g., “accident,” “hazard”). In this essay, we try to sketch the main lines of development of several of these concepts from the ancient Greeks up to modern times, or more precisely, from Democritus and Aristotle up to the world of quantum mechanics. Three elements emerge with particular force. First, “chance,” “fortune,” “randomness,” etc. are in some instances invoked as explanations of events, but in others designate events that occur without an explanations. Second, the meaning of these terms only becomes clear when one understands which alternatives they exclude. Finally, it is conspicuous to see how, after a rigid exclusion of “chance” or “randomness” from the domain of scientific explanation in the early modern period, they were restored to full glory in nineteenth- and twentieth-century biology and physics.

We give a nontechnical account of the mathematical theory of randomness. The theory of randomness is founded on computability theory, and it is nowadays often referred to as algorithmic randomness. It comes in two varieties: A theory of finite objects, that emerged in the 1960s through the work of Solomonoff, Kolmogorov, Chaitin and others, and a theory of infinite objects (starting with von Mises in the early 20th century, culminating in the notions introduced by Martin-Löf and Schnorr in the 1960s and 1970s) and there are many deep and beautiful connections between the two. Research in algorithmic randomness connects computability and complexity theory with mathematical logic, proof theory, probability and measure theory, analysis, computer science, and philosophy. It also has surprising applications in a variety of fields, including biology, physics, and linguistics. Founded on the theory of computation, the study of randomness has itself profoundly influenced computability theory in recent years.

Human interaction often appears to be random and at times even chaotic. We use game theory, the mathematical study of interactive decision making, to explain the role of rationality and randomness in strategic behavior. In many of these situations, humans deliberately create randomness as a best response and equilibrium strategy. Moreover, once out of equilibrium, individual beliefs about the real intentions of others introduce significant randomness into otherwise quite simple and deterministic situations of interaction. In a second step we discuss the role of randomness on financial markets, which are prototypical institutions for the aggregation of individual behavior. As in certain simple games, financial markets can produce outcomes that are close to perfect randomness. In fact, random walks in financial returns are considered by most scholars to be efficient and desirable. Finally, we apply game theoretical insights to behavior on financial markets and show how strategic speculation on ‘greater fools’ can create a ‘madness of crowds’ that often ends in chaotic swings, bubbles and crashes.

Recently it has become clear that too many findings reported in the scientific literature are irreproducible. We study the causes of this phenomenon from a statistical perspective. Although a certain amount of irreproducible research is unavoidable due to the randomness inherent to scientific observation, two related phenomena conspire to increase the proportion of such findings: publication bias, i.e. the custom that negative findings are usually not published, and confirmation bias, i.e. the human inclination to interpret observations in a way that confirms prior beliefs. Both biases are poorly held in check in the current scientific publication model in which there is no explicit role for the views of a critic, i.e. a scientist with opposing theoretical views. We argue that if researchers are able to play the critic’s role imaginatively, they will publish science of higher methodological quality that is not only more reproducible, but also more relevant for theory. To allow for this, we must promote a different view on statistical methodology, seeing statistics not as the gatekeeper of scientific evidence, but as a language scientists may use to discuss uncertainty when they talk about the implications of observations for theory.

Our laws of nature and our cosmos appear to be delicately fine-tuned for life to emerge, in a way that seems hard to attribute to chance. In view of this, some have taken the opportunity to revive the scholastic Argument from Design, whereas others have felt the need to explain this apparent fine-tuning of the clockwork of the Universe by proposing the existence of a ‘Multiverse’. We analyze this issue from a sober perspective. Having reviewed the literature and having added several observations of our own, we conclude that cosmic fine-tuning supports neither Design nor a Multiverse, since both of these fail at an explanatory level as well as in the more quantitative context of Bayesian confirmation theory (although there might be other reasons to believe in these ideas, to be found in religion and in inflation and/or string theory, respectively). In fact, fine-tuning and Design even seem to be at odds with each other, whereas the inference from fine-tuning to a Multiverse only works if the latter is underwritten by an additional metaphysical hypothesis we consider unwarranted. Instead, we suggest that fine-tuning requires no special explanation at all, since it is not the Universe that is fine-tuned for life, but life that has been fine-tuned to the Universe.

There are a variety of views on ‘chance’ to be found in the Hebrew Bible, or Old Testament. In this chapter we will discuss the Book of Job and the opening chapter in the Book of Genesis, i.e. Genesis 1, both as narratives and as poetic texts and explore the philosophical and theological consequences for a better understanding of the concept of chance. In the prologue of the Book of Job, chance is referred to as the result of a wager between God and the satan, who is described as one of the sons of God. In the dialogue between Job and his friends, bad luck is viewed as a consequence of bad behaviour while good luck is the result of good behaviour. In this sense, chance clearly functions within a moral framework of retribution. At the end of the Book of Job, in God’s speech out of the whirlwind, chance is linked to a multifocal view of the universe and understood in terms of position, perspective, and scale. Also the opening chapter of the Book of Genesis offers a non-deterministic view on chance. Chance is not the exception in a causal or necessary chain of events, but it stands out in a framework of non-linear thinking in which totality and instantaneity alternate. With regard to both biblical texts, God’s speech in the Book of Job and Genesis 1, chance can be conceived as a disqualifier of this chain of events, and even as an ultimate denial of the existence of necessity.

Since the beginning of Western philosophy, thinkers have discussed how one might lead a good, i.e. a happy, life and what role luck plays in flourishing. According to one dominant Ancient Greek tradition, life’s circumstances are not relevant for our happiness, and, moreover, they fall outside of our control. What is up to us is how we respond to life’s circumstances and adversities. Christianity, however, rejected ancient tradition and moved happiness to a new home: heaven. Because Adam and Eve were disobedient in Paradise, God punished the human species with a ‘genetic’ defect which made life miserable for each and every individual. Chance or (bad) luck is an inevitable ingredient of human suffering. Buddhism also perceives chance or luck as intrinsic to life, but locates it into the sphere of human control. It is not the gods, but we, who, through our own actions, are responsible for what happens to us. This is called the law of : we reap what we have sown. There are striking parallels between the Greek methods to train our mental responses to (bad) luck and the Buddhist analysis of unwholesome actions and corresponding advice to improve our karma. Both traditions are still helpful today in our attempts to secure happiness in the face of chance adversity.

In this chapter, we focus on psychological and brain perspectives on the experience of coincidence. We first introduce the topic of the experience of coincidence in general. In the second section, we outline several psychological mechanisms that underlie the experience of coincidence in humans, such as cognitive biases, the role of context and the role of individual differences. In the third and final section we formulate the phenomenon of coincidence in the light of the unifying brain account of predictive coding, while arguing that the notion of coincidence provides a wonderful example of a construct that connects the Bayesian brain to folk psychology and philosophy.

Faithful and stable inheritance of DNA is coupled with occasional random errors of replication that lead to a change in the DNA code known as mutation. Mutations can be considered as “good” because they are the fuel that drives evolution of species. On the level of the individual they are mostly harmful. In fact, the majority of severe intellectual disabilities derives from such random mutational events. In my experience, the tendency to ascribe all events to definite causes is still highly prevalent. Against this background of presumed guilt, parents who are confronted with the birth of a severely handicapped child tend to take solace form the knowledge that the condition was not their “fault”. Our recent understanding that severe handicaps may strike anyone, may well lead to the acceptance of a more universal offer of prenatal diagnosis than previous strategies which were based on the identification of high risk groups.