We are going to model first a kind of conversation which occurs very frequently: conversations that start with the mention of some unusual event. This includes current facts (we feel compelled to draw attention on the fact that a tortoise is walking through the garden), or past "incredible" stories. All these facts share the property of being a priori improbable, and this is precisely what we should expect if we look at conversations using the Shannon paradigm. [ex_antenna, p.9] was a typical example of this : at that time, parabolic antennas were pretty seldom on private houses, and seeing one in the neighborhood is worth a conversation.
How can we link this to the Shannon model ? Spontaneous conversations are often presented as an information exchange. But what exactly is information ? We wish to use this term here in its narrow meaning as it was established by Claude Elwood Shannon [Shannon 1948]. The amount of information brought by a symbol coming from the message source is measured by log(1/p). In this formula p stands for the symbol a priori probability. Thus a very improbable event (reception of a rare symbol) produces much information when it occurs. This was actually the case for " there is a parabolic antenna nearby ". This requires that the mentioned event is recognized by the receptor (here the addressee). It means that the addressee has be able to assign an a priori probability of each event that may be mentioned ! We hold now a first condition for a topic to be relevant :
It would be interesting to study how such probabilities are assessed (see [Dessalles 1993]). We may just suggest here that they involve an egocentric point of view (thus the importance, in the example, of the antenna being located in the neighborhood). The transposition of the Shannon model is particularly suggestive and fits very well with our data. More precisely, it allows to express constraints on what can be replied after an introduction in the improbable mode, as we will see. Let us turn to another criterion for relevance.