Simplicity Theory

Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information

by Jean-Louis Dessalles
(created 2008.12.31)

(updated 2010.02.18)

Example: The running nuns (departure from norm)

Situations that depart from norm are unexpected

(Original at BBC)

In May 2004, while I was jogging, I met two nuns who were running on the jogging trail, not far from the convent. I couldn’t help telling the event when back home.

How much is such a situation unexpected? By definition, unexpectedness is the difference between generation complexity and description complexity: C_w – C. Let’s compute both terms.

Generation complexity C_w

Situations that depart from norm shouldn’t have happened. But nothing is impossible to the "world-machine". One only needs a causal story (for instance the two nuns got suddenly mad; or they are obeying some order given to them by some saint; …) The generation complexity C_w of a situation s amounts to the complexity of the simple causal story H that explains how s could happen.

C_w(s) = C_w(H)

Description complexity C

The qualitative feature f (here the fact that the nuns are running) may be used as the best way to discriminate s in its class r (here, r may be the class of nuns). Therefore:

C(s) = C(r) + C(f) + C(s|r&f)

(in most cases, C(f|r) = C(f)). If s can be considered unique in its class, then C(s|r&f) = 0.

Finally:

U(s) = C_w(H) – C(f) – C(r)

The corrective terms C(f) and C(r) account for the fact that some departures from norm concern only specialists for whom these two complexities are small.

Bibliography

Dessalles, J-L. (2007). Complexité cognitive appliquée à la modélisation de l'intérêt narratif. Intellectica, 45 (1), 145-165.

Dessalles, J-L. (2007). Spontaneous assessment of complexity in the selection of events. Technical Report ParisTech-ENST 2007D011.

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.

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