Simplicity Theory

Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information

 

by Jean-Louis Dessalles
(created 2008.12.31)

(updated 2010.02.18)

Example: The "Robert Wadlow" effect  (record)

 

Records are unexpected because they are simple in their class

 


(from flickr.com)

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.

 

By definition, unexpectedness is the difference between generation complexity and description complexity: Cw – C. Let’s compute both terms.

Generation complexity Cw

Suppose you consider the extreme person, object or situation b as member of a reference class r. In R. Wadlow’s example, r may be the class of human beings, the class of men, the class of tall men, the set of all men you ever encountered, etc. If b is considered as randomly drawn from r (i.e. feature f (here the extreme size) has no causal effect on b being chosen), then:

Cw(b|r) = log2 N

where 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).

Description complexity C

The feature f may be used as the best way to discriminate b in class r. Therefore:

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.

Bibliography

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

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

Dessalles, J-L. (2008). La pertinence et ses origines cognitives - Nouvelles théories. Paris: Hermes-Science Publications (in Press).

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