Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information
by Jean-Louis Dessalles
(created 31 December 2008)
(updated July 2015)
Extremes are unexpected because they are simple in their class.
Robert Pershing Wadlow is thought to be the tallest man in human history.
His size (2,72m) made him well-known in the USA and around the world.
Extreme situations or objects are unexpected. Why and how much?
By definition, unexpectedness U is the difference between generation complexity and description complexity: Cw – C.
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.
Dessalles, J-L. (2008). Coincidences and the encounter problem: A formal account. In B. C. Love, K. McRae & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society, 2134-2139. Austin, TX: Cognitive Science Society.
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.
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