Simplicity, Complexity, Unexpectedness, Cognition, Probability, Information

by Jean-Louis Dessalles     (created 31 December 2008, updated March 2020)

# The "Robert Wadlow" effect (record)

 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.

#### Generation complexity Cw

Suppose you consider the extreme object, situation or person 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

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. (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.