dences are all the more surprising as they reveal the possibility of an alternative hidden causal structure that is itself highly unlikely. If the less unlikely causal explanation for the double suicide is that the two women influenced each other through telepathy, the feeling of coincidence remains high. If, however, one can believe that they met and decided to commit suicide simultaneously, the coincidence fades away. Our model accounts for the phenomenon, without relying on the notion of probability. Suppose that some causal explanation H accounts for both e1 and e2. This means that Cw(e1|H) and Cw(e2|H) are negligible. If e1 and e2 are explained by H, then:

## Cw(E1*E2) < Cw(H*E1*E2)  Cw(H) (8)

The W-complexity Cw(H) of a causal explanation H is the amount of information required for the "world" W to generate H. It measures the credibility of the theory (Chaitin, 2004). If H is easy to believe, U(e1*e2) does not take significant values and there is no reason to be surprised. Conversely, if H is hard to accept, as for the telepathy hypothesis,2then Cw(H) takes high, prohibitive, values. The sequence H*e1*e2 no longer provides the lowest value for Cw(e1*e2) and the hypothesis should be rejected.

## Discussion: What The Model Predicts

The perception of coincidences is a definite ability, like the ability to decide whether a sentence in one"s mother language is grammatical or not. Individuals *know* when a state of affairs makes a good coincidence, and they know if some variation of a given parameter makes a difference. This cognitive ability has to be accounted for, and this is what is attempted here.

The model proposed in this paper meets all the specifications concerning the perception of coincidences that have been listed above, by explaining the systematic role of analogy, of association, of prominence, of round numbers, of closeness, of remoteness, of egocentricity and of causality. Probabilistic models at best predict certain of these features, while the others remain mysterious. The model derived from formula (1) succeeds in predicting them all. Moreover, it does it in a quantitative way. For instance, the effect of spatial closeness is expected to obey a logarithmic law 2log2 d, and time will affect coincidence logarithmically as well. In the case of fortuitous encounters, the complexity (= shortest description) of the place is predicted to be the determining factor, not distance. These various dependencies are all testable and thus make the model falsifiable.

A classical critique addressed to complexity-based approaches is that Kolmogorov complexity is proven to be uncomputable (Li & Vitányi, 1993). Models based on Kolmogorov complexity are thus sometimes believed to lack any real predictive power. This led authors (Simon, 1972; Feldman, 2004) to consider alternative measures of complexity, such as Boolean complexity or algebraic complexity, that are computable. Indubitably, human minds are not ideal computing device that would be free to run any kind of program. Minds are bound to process signals and representations in certain particular ways. However, they are sensitive to the complexity of their own processes, as shown for instance by the existence of strong perceptive biases toward simplicity (Chater, 1999; Chater & Vitányi, 2003). The law encapsulated in formula (1) suggests that this preference for simplicity operates at higher levels of abstraction as well, and across various modalities.

Unexpectedness conflates all available sources of complexity (perceptual, structural, spatio-temporal, conceptual) into one single measure that constitutes the judgment of coincidence. This is why the analogy with Kolmogorov complexity is justified, as the only absolute criterion is the size of the shortest *available* description.

One can legitimately worry about the existence of two types of models that address the issue of coincidence perception. If the complexity-based model proposed here is correct, why would probabilistic or Bayesian accounts have partial predictive power? And why are coincidences systematically accompanied by a subjective feeling of low probability (Griffiths & Tenenbaum, 2007)? The relation between descriptive complexity and probability has always been noticed (Solomonoff, 1997), but its usual formulation as p = 2
–C(D)is unsatisfactory for our purpose. It would mean that the probability of structures is a decreasing function of their complexity, but coincidences are often striking just because they are simple. To account for the subjective perception of probability in case of lottery results, we introduced an alternative way of deriving probability from complexity (Dessalles, 2006), by defining *cognitive* probability as:
p = 2–U(9)
Cognitive probability is defined only for unexpected situations, which means that U > 0. This definition reverses Shannon"s definition, where unexpectedness plays the role of information. It suggests that unexpectedness, as defined by (1), is a more fundamental cognitive notion from which cognitive probability is derived. Formula (9) offers a nonextensional definition of cognitive probability.3It explains why individuals do not find that all actual states of the world have zero probability, despite the fact that each is unique. It also explains why certain features are regarded as relevant while others (like the horizontal orientation of dice) 
are spontaneously discarded. In the case of coincidences, the sensation of low probability appears to result, not from the evaluation of a set of alternatives, but from the perception of 
 
3 Checking whether the probabilities of all elementary alternatives sum to 1 would be quite artificial in most cases, as situations are rarely perceived as exclusive. 66666 km or 67426 km on the clock are respectively read as "one repeated digit" and "any amount" and are assigned probability 10–4and 1.