Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information
Extremes are unexpected because they are simple in their class.
Extreme situations or objects are unexpected. Why and how much?
Cw(b|r) = log2 Nwhere N is the number of elements in class r. This is because the "world-machine" needs log2 N bits to discriminate among all elements in r which one it will present to you (for details, see the Inverted Stamp example).
C(b|r) = C(f) + C(b|r&f)If b is thought to be unique in its kind, then C(b|r&f) = 0. We get:
U(b|r) = log2 N – C(f)Finally, if r is not itself unexpected (i.e. Cw(r) = C(r)):
U(b) = log2 N – C(f) – C(r)The corrective term C(f) accounts for the fact that records must be kept as simple as possible for unexpectedness to remain meaningful. Some recorded achievements are borderline in this respect: "Fastest speed while swapping places on a motorcycle", recorded on the 2003 edition of the British edition of the Guinness book, requires a more complex description than "Fastest motorcycle speed" or "Earliest bicycle", listed on the same page.
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Dessalles, J-L. (2008). La pertinence et ses origines cognitives - Nouvelles théories. Paris: Hermes-Science Publications.
Dimulescu, A. & Dessalles, J-L. (2009). Understanding narrative interest: Some evidence on the role of unexpectedness. In N. A. Taatgen & H. van Rijn (Eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society, 1734-1739. Amsterdam, NL: Cognitive Science Society.