Information Technology Reference
In-Depth Information
Consequently, the functional form of the distribution is the same at every scale in
k
and there is no single scale with which to characterize the web. We emphasize that
this definition is a mathematical idealization and may require modification when deal-
ing with empirical data, such as time series of finite length and with finite resolution.
Subsequent investigations have focused on defining parameters with which to charac-
terize scale-free webs, such as the clustering coefficient, the betweenness coefficient,
the average size of the web and other such properties. Moreover, assumptions regard-
ing how new links are formed that were intended to modify and replace preferential
attachment have been made. But, before we introduce more formalisms, let us examine
a concrete example of these ideas in the realm of communications.
The way people treat one another has always been a great mystery and understanding
that mystery is the basis of great literature, art, drama and psychology. Consequently,
when someone with the pedigree of a scientist, for example, Sigmund Freud, comes
along, with his insight into the psyche and his gift for writing, society listens. How-
ever, given that psychoanalysis is a science, it can be tested, and in that regard many of
Freud's ideas about the human psyche have not withstood the test of time. On the other
hand, another area of psychology stemming at least in part from nineteenth-century
psychophysics, although somewhat less glamorous than psychoanalysis, has been mak-
ing steady progress. At about the same time as psychophysics was being introduced
by Fechner [
16
], sociophysics appeared as well. These two disciplines, as their names
imply, were attempts to apply the quantitative methods of the physical sciences to the
human domain. One aspect of this interaction between people is communication and
one question concerning communication is whether the dynamical element of humans
has changed as society has changed.
The nineteenth century saw the transformation of society from the rural to the urban.
In this period most private communication was done by letter writing, with items of cor-
respondence sometimes taking months to reach their destination. In this slower-paced
time there were many inconveniences in correspondence; one needed pen, paper, ink,
sealing wax, literacy (in itself rare) in both oneself and the recipient of the letter, as
well as access to a mail carrier. Consequently, it is interesting to consider whether peo-
ple of that age are any different in any fundamental way from people of today who
send and receive dozens of emails every day. This question was addressed by Oliveira
and Barabási [
27
] using the lifelong correspondence of two scientists, Albert Einstein
(1879-1955) and Charles Darwin (1809-1882). Both these men of science were pro-
lific letter writers with an average number of letters sent approaching one for each day
of life.
Oliveira and Barabási determined that the patterns of Einstein's and Darwin's letter
writing follow the same scaling laws as the electronic transmission of today, namely
an inverse power-law. On the other hand, given the difference in time scales between
letter writing and emails the power-law indices of the two methods of communication
are found to be distinctly different. They interpreted this consistency in the existence
of an inverse power-law distribution for the two methods of communication as evi-
dence for a new class of phenomenon in human dynamics even though the indices are
different.
