Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information
by Jean-Louis Dessalles
(created 31 December 2008)
(updated August 2015)
Relevant situations are unexpected
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.
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.
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
The two preceding definitions control what is worth telling when reporting or signalling an event in conversation.
if U(s|t) < U(s), then t is 2-relevant w.r.t. s
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.
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