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The next logical question concerns how we explain the nearly universal acceptance
of the normal distribution by the scientific community. Answering this question consti-
tutes the second step of our journey and, like the first, requires some historical review.
We need to understand how scientists first began to learn about the sources of com-
plexity that the fluctuations in measurements often manifest. The arguments of the last
section explained the formal properties of the experimental results but not the reasons
for those properties. Without the reasons we have a mathematical model, but with the
reasons the mathematical model can become a scientific theory. In the area of mathe-
matics these concerns spawned the disciplines of statistics and probability theory; the
difference between the two will be taken up in due course. In the physical sciences
these concerns led to investigations of the influence of the microscopic world on the
macroscopic world and to the laws of thermodynamics.
Historically thermodynamics was the first quantitative discipline to systematically
investigate the order and randomness of complex webs, since it was here that the natural
tendency of phenomena to become disordered was first articulated. As remarked by
Schrödinger in his ground-breaking work What Is Life ?[ 28 ]:
The non-physicist finds it hard to believe that really the ordinary laws of physics, which he regards
as prototypes of inviolable precision, should be based on the statistical tendency of matter to go
over into disorder.
In the context of physical networks the quantitative measure of disorder, which has
proven its value, is entropy and the idea of thermodynamic equilibrium is the state of
maximum entropy. Of course, since entropy has been used as a measure of disorder,
it can also be used as a measure of complexity. If living matter is considered to be
among the most complex of webs then it is useful to understand how the enigmatic state
of being alive is related to entropy. Schrödinger maintained that a living organism can
hold off the state of maximum entropy, namely death, only by giving up entropy or by
absorbing negative entropy, or negentropy, from the environment. He pointed out that
the essential thing in metabolism is that the organism succeeds in freeing itself from all
the entropy it cannot help producing by being alive and sheds it into the environment.
Here it is probably reasonable to point out that we have entered a conceptual thicket
associated with the concepts of knowability, disorder, complexity and entropy, as well
as other related notions. Various mathematical theories have developed over the years to
illuminate these difficult concepts, including generalized systems analysis, cybernetics,
complexity science, information theory, graph theory and many more. Each theory has
its advocates and detractors, each has its own domain of application, and each has its
non-overlapping sets of limitations. We have elected to present from this plethora of
intellectual activity only those concepts that contribute to our vision of what constitutes
a simple or a complex web. Consequently, we are not always overly precise in our
definitions, intending to be inclusive rather than exclusive, hoping that the reader will
not be too harsh in having to wait while the big picture is being laid out. Key among the
choices made is probably the decision to use the term web rather than network or system
in order to be selective regarding the properties we choose to associate with a web, some
of which overlap with what other investigators would call a network or system. We do
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