The goal of this
project was to assess the statistical properties of human
traffic on length scales of a few to a few thousand
kilometers. A very simple question that initially motivated
this was “What is the probability of a human being
travelling a certain distance in a short period of time?”
taking into account all possible means of transportation.
Simple as it is, this question is difficult to answer
because in order to do so one would have to collect and
compile date for various involved human traffic networks:
air transportation, highway traffic as well as railroad
Movie 1: The scaling laws
of human travel: Television Feature on DW-TV. (Click on
image to watch.)
In this project we approached the problem from an unusual
angle. Instead measuring the geographical movement of
individuals, we evaluated data collected at the online bill
tracking system www.wheresgeorge.com in order to assess the
statistical properties of the geographic circulation of
money instead. The idea behind this project was to use the
dispersal of money as a proxy for human travel as bank
notes are primarily transported from one place to another
by traveling humans.
Wheresgeorge.com, which was invented by Hank Eskin in 1998,
is a popular US internet game in which participants can
register individual dollar bills for fun and monitor their
geographic circulation. Since its beginning a vast amount
of data has been collected at the website, over 100
millions of dollar bills have been registered by over 3
million registered users and over 10 million bills have had
"hits", that means they resurfaced somewhere else.
Our initial study was based on a dataset of roughly a
million individual displacements. We found that the
dispersal of dollar bills can be described by a set of
simple mathematical laws. First, the probability of
traveling a distance in a short period of time days decays
as a power law, i.e.
This observation lead us to conjecture that the
trajectories of dollar bills are reminiscent of Lévy
flights, superdiffusive random walks characterized by a
power law in the single step distribution.
The situation turned out to be more complex, as also
broadly distributed waiting time distributions play a role
which leads to a subdiffusive component of money dispersal
and a competition of long jumps and long waiting times.
Effectively money dispersal can be described with a
bi-fractional diffusion equation.