Published date20 January 2005
Date20 January 2005
Explaining and hence understanding is one of the key characteristics of human
beings. Explaining is making logical, mathematical deductions based on a minimum
of unexplained properties, called axioms. Indeed, without axioms, one is not able to
make deductions. How these axioms are selected is the only non-explainable part of
the theory. In fact, different choices are possible leading to different, in themselves
consistent, theories which conflict when considered together. A typical example is
the construction of the different types of geometries, Euclidean and non-Euclidean
geometries which are in contradiction when considered together but which have their
own applications.
In this book the object of study is a two-dimensional information production process,
i.e. where one has sources (e.g. journals, authors, words, ...) which produce (or have)
items (e.g. respectively articles, publications, words occurring in texts, ...) and in
which one considers different functions describing quantitatively the production
quantities of the different sources. All functions can be reduced to one type of
function, namely the size-frequency function f: such a function gives, for every n = 1,
3, ..., the number f(n), being the number of sources with n items. This is the
framework of study and in this framework we want to explain as many regularities
that one encounters in the literature as possible, using the size-frequency function f.
As explained above, we need at least one axiom. The only axiom used in this book is
that the size-frequency function f is Lotkaian, i.e. a power function of the form
f(n)=C/na, where C> 0 and a3 0, hence also implying that the function f
decreases. The name comes from its introduction into the literature by Alfred Lotka in
see Lotka (1926). Based on this one assumption, one can be surprised about the
enormous amounts of regularities that can be explained. In all cases the parameter a
turns out to be crucial and is capable of, dependent on the different values that a can
explaining different shapes of one phenomenon.
In this book we encounter explanations in the following directions: other informetric
functions that are equivalent with Lotka's law (e.g. Zipf
law), concentration theory

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