Simplicity Theory
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Simplicity, Complexity, Unexpectedness, Cognition,
Probability, Information
by Jean-Louis Dessalles
(created
2008.12.31)
(updated 2010.02.11)
Example: The "Rabid
Bat" effect
The causal complexity of an event adds to its unexpectedness
The following comic scene (original
in French; see also video)
illustrates how events that require a complex
story for the "world-machine" to make
them happen are considered unlikely.
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"There is one in ten million chance of
getting bitten by a rabid bat. So, I’m not curious, but I would really like to
know how the guy managed to estimate that we have ALL – on average – one
chance in ten million of getting bitten. Yes, because well… Myself, I’m living in the
10th district [of What’s more, I’m living five floors up
without a lift, I’ll tell you, there is a digital
lock at the entrance door and an entry phone. Ha, ha ! So, I’ll tell you, the bat can always turn
up, you see ! So, but ok, suppose it does. A bat arrives. A
rabid one. (…) So... Hop ! It starts tinkering with my code. It’s there,
tinkering. It tries, it tries. (…) Pan ! It hits on the right code ! It still needs to imitate the voice of a guy
I know !!! Otherwise, I won’t open
! (…) Well ! It reaches my floor ... What proves that it will knock at MY door?
There’re four apartments on the floor..." (c) JEAN-MARIE BIGARD / |
By definition, unexpectedness is the difference
between generation complexity and description complexity: Cw – C. An event that is complex
to generate (large Cw) will appear more
unexpected. It will therefore appear more improbable, thanks to the formula p=2–U.
You may appreciate the
accumulation of details aiming at increasing generation
complexity Cw. The
target situation (Bigard getting bitten by a rabid
bat) is difficult to generate in the known world, since:
- there are few bats in the 10th
district of Paris
Bringing
one rabid bat by chance to Bigard’s building is
difficult. Various computations of Cw are possible (bat-centred or
building-centred). They all end up with: Cw = log2 B1 – log2 B2 + constant, where B1
and B2 represent the
number of buildings and the number of bats in the 10th district.
Note that the ‘constant’ includes the logarithm of the proportion of rabid bats
in the bat population. Note also that the mention of the 10th
district (a homogeneous, densely populated district) aims at increasing the
difference log2 B1 – log2 B2 (but it is “paid” on the
complexity side, C; therefore, the
authors do not mention “I am living in the south-west part of the 10th
district”).
- there are many combinations for the digital lock
Finding one
of them by chance amounts to log2 C1 + constant,
where C1 is the number of
combinations.
- it is difficult for a bat to imitate the voice
of one of Bigard’s friends
Here, there
are two sources of high generation complexity: the rabid bad is
not supposed to know Bigard’s friends (hence a term
in log2 V1
where V1 is the total
number of recognizable voices); and even in the alternative reality that is
already installed, bats are not supposed to be very good at imitating human
voices.
- there are four apartments on the floor
This adds
two bits to Cw.
We could push the analysis
even further (why the 10th district and not the 1st one?; why mentioning the absence of lift...). The point is that
in the absence of a model of how the world works (e.g. that climbing stairs is tiring,
therefore higher motivation is required to get higher...),
there is no chance to understand the funny aspects of the story. Conversely,
any proper assessment of Cw
is sufficient here to understand why the event (Bigard
getting bitten by a rabid bat) is highly improbable. Moreover, the difference Cw – C provides a strict
relevance criterion for the story. For instance, Bigard
does not mention that the entrance door is blue, as it would have no bearing on
Cw
and would unnecessarily increase C.
Bibliography
Dessalles, J-L. (2007). Spontaneous
assessment of complexity in the selection of events. Technical Report ParisTech-ENST
2007D011.
Dessalles, J-L. (2008). La pertinence et ses origines cognitives - Nouvelles théories. Paris: Hermes-Science Publications (in Press).
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