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This book brings together the personal accounts and reflections of
nineteen mathematical model-builders, whose specialty is
probabilistic modelling. The reader may well wonder why, apart from
personal interest, one should commission and edit such a collection
of articles. There are, of course, many reasons, but perhaps the
three most relevant are: (i) a philosophicaJ interest in conceptual
models; this is an interest shared by everyone who has ever puzzled
over the relationship between thought and reality; (ii) a
conviction, not unsupported by empirical evidence, that
probabilistic modelling has an important contribution to make to
scientific research; and finally (iii) a curiosity, historical in
its nature, about the complex interplay between personal events and
the development of a field of mathematical research, namely applied
probability. Let me discuss each of these in turn. Philosophical
Abstraction, the formation of concepts, and the construction of
conceptual models present us with complex philosophical problems
which date back to Democritus, Plato and Aristotle. We have all, at
one time or another, wondered just how we think; are our thoughts,
concepts and models of reality approxim&tions to the truth, or
are they simply functional constructs helping us to master our
environment? Nowhere are these problems more apparent than in
mathematical model ling, where idealized concepts and constructions
replace the imperfect realities for which they stand."
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