March 25, 2007

Complexity and Life

The Kolmogorov
complexity
of a string x is the length of the
description
of the minimal computer program that outputs x,
relative to a given model of computation. Hence, complexity
describes the amount of redundant information, or structure,
in the string: as the string’s complexity approaches its
length, the string becomes increasingly random. (A string’s
complexity can be no greater than an additive constant of
its length, since we can always emit the string by embedding
it in a Turing machine that just prints out the string).

I’d like to write more about Kolmogorov complexity later,
but for now I’ll just point to an interesting application
of this idea to studying biological life. Zhanna Reznikova has
applied information theory to studying the communication
between animals, in particular ants. This paper
describes an interesting result: an experiment was setup in
which a “scout” ant communicates the location of some food
to another group of “forager” ants. The path from the ants
to the food is a binary maze, so the path can be represented
as a series of left or right turns (e.g. “RRR”, “RLR”,
etc.). Reznikova measured the time it took for the scout to
transmit the location of the food to the other ants, and
then varied the path, to see how the time of transmission
varied with the complexity of the route. As it turns out (p.
9, table 2), the ants were able to more
efficiently communicate paths that could be encoded as
strings with low complexity. For example, the path “RRRRRR”
required a mean duration of 88 seconds to transmit, whereas
“RLRLRL” took 135 seconds.

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