Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information

by Jean-Louis Dessalles
(created 31 December 2008)
(updated August 2015)


Relevant situations are unexpected
Relevant features generate compression

Last Friday (3 June, 2015), I noticed that my neighbour (the house adjoining ours) owned an electric car. I couldn’t help but tell it to my family members. The news was regarded by them as definitely relevant. Why ?

According to an influential theory, an act of communication is relevant if the hearer can easily infer new knowledge from it. From the fact that my neighbour owns an electric car, I can easily conclude that he might be Green-friendly. What else? Not much. Maybe that there is a socket for electric cars at his workplace or that he has free parking in Paris. But I just figured this out now, not by the time I noticed the car nor when I told news.

Simplicity Theory offers another definition of Relevance. Contrary to definitions found in philosophy and in linguistics, ST’s definition is predictive (falsifiable) and quantitative. In a nutshell, relevant communication acts lead to complexity drop.

Relevant Situations

[ See also (Dessalles, 2013) for more details. ]

A situation or event is relevant if it is unexpected.
    This means that it is simpler to describe than to generate.    


A situation s is relevant iff    U(s) > 0

This definition captures all situations which are regarded as relevant. Conversely, it excludes all situations that would be regarded as irrelevant.

For instance, the fact that my neighbour owns an electric car is relevant because electric cars (in June 2015) are rare. The complexity of generating the event is large (see the Inverted Stamp example). On the other hand, the situation is simple to describe, as it involves my closest neighbour (see the Next door Effect). The event would have been less relevant if the car owner had been living two blocks away.

The influences of rarity and of distance are not predicted by philosophical definitions of relevance. On the other hand, I do not remember having inferred from the presence of the electric vehicle that my neighbour might be Green-friendly. Anyway, this inference is hardly contributing to relevance. 25% of inhabitants in my town are ready to vote for Green parties in local elections. It would at most contribute by two additional bits to relevance, not enough to make the event relevant by itself.

Relevance of features

Relevant aspects of events constitute the essential part of narratives. Consider a feature f that is present in situation s. Considering f as a logical predicate, this means that f(s) is regarded as true (see conceptual complexity).

Features are relevant with respect to a given situation if they contribute to unexpectedness.

f is relevant w.r.t. s if    U(f(s)) = Cw(f(s)) – C(f) > 0

Note that if f is the conjunction of several sub-properties, these sub-properties need not be relevant separately. The art of telling narratives is to assemble elements that, together, produce unexpectedness. A conjecture is that every descriptive element, in spontaneous narratives, is intended to make relevance maximal eventually.

The two preceding definitions control what is worth telling when reporting or signalling an event in conversation.

Second-order relevance

An admissible reaction to relevant topics consists in attempting to diminish their unexpectedness. The following definition concerns a piece of information t that may alter unexpectedness.

if U(s|t) < U(s), then t is 2-relevant w.r.t. s

In the example about the electric car, t may be the fact that the neighbour works in an electric car company. It would provide a causal reason that would diminish generation complexity Cw(s).
This definition covers not only the phenomenon of trivialization (Dessalles, 2008) ("The same happened to me..."), but also any attempt to diminish Cw(s) by simplifying the generation scenario (i.e. by providing an explanation).


Dessalles, J-L. (2008). La pertinence et ses origines cognitives - Nouvelles théories. Paris: Hermes-Science Publications.

Dessalles, J-L. (2013). Algorithmic simplicity and relevance. In D. L. Dowe (Ed.), Algorithmic probability and friends - LNAI 7070, 119-130. Berlin, D: Springer Verlag.

Back to the Simplicity Theory page.