The interpretation of physical, chemical and biological
phenomena as linear relationships between variables, or as simple
functions of the variables, has been a significant scientific and
mathematical strategy to their elucidation for centuries. It is
often the case that the nature of linearity is to follow
mathematical functions, e.g. power, exponential or logarithmic
functions, nevertheless the desire to fit data to simple
predictable expressions is imbued in every scientist and engineer.
From a philosophical standpoint there is no reason to criticize
this approach as it allows us to interpret the natural world and
has a lofty heritage going back to the classical world.
However, non-linear phenomena have been identified in many
fields and interpreted as periodic, catastrophic, chaotic or
complex involving a variety of mathematical tools for analysis.
Benoit Mandelbrot s now classic book on the fractal geometry of
nature and the many subsequent texts, most recently Wolfram s
magnum opus "A New Kind of Science" have raised questions about the
nature of reality and the interpretation of observed phenomena. It
seems clear that the complexity of dynamic events (on any scale)
can rarely be explained by linear interpretations. The rare
exceptions are likely to represent a convergence of multiple
phenomena giving the appearance of a linear relationship between
variables.
In fields related to pharmaceutical sciences some texts have
been written by pioneers such as Brian Kaye. His eminently readable
"A random walk through fractal dimensions" and "Chaos and
complexity" were seminal volumes for the editors. Tracing the
mathematics of complexity back to the nineteenth century and beyond
gives a validity to the search for more accurate interpretations of
experimental observations that should impact on the pharmaceutical
sciences as significantly as other fields of endeavor.
The chemistry and physics literature is replete with papers on
complexity from such notables as Ilya Prigogine and Murray
Gell-Mann. A broad range of biological phenomena, the most complex
imaginable from molecular biology to ecology, are now the subject
of complexity analysis. Pharmaceutical sciences encompass the
biology, chemistry, physics and mathematics associated with drug
discovery, delivery, disposition and action. This text describes a
range of topics of importance in the pharmaceutical sciences that
indicate a need for a non-linear interpretation if they are to be
characterized accurately, understood fully and potentially
controlled or modulated in the service of improved therapeutic
strategies.
It is likely that the future will involve increasingly complex
interpretations of data related to drug design and delivery,
particularly as our knowledge of the human genome leads inexorably
to the potential for individualized therapy. We hope that this text
will promote discussion of the varied phenomena leading to
pharmacological effect and the complex interactions ultimately
resulting in improved disease control and health maintenance."
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