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High technology industries are in desperate need for adequate tools
to assess the validity of simulations produced by ever faster
computers for perennial unstable problems. In order to meet these
industrial expectations, applied mathematicians are facing a
formidable challenge summarized by these words - nonlinearity and
coupling. This book is unique as it proposes truly original
solutions: (1) Using hypercomputation in quadratic algebras, as
opposed to the traditional use of linear vector spaces in the 20th
century; (2) complementing the classical linear logic by the
complex logic which expresses the creative potential of the complex
plane.The book illustrates how qualitative computing has been the
driving force behind the evolution of mathematics since Pythagoras
presented the first incompleteness result about the irrationality
of 2. The celebrated results of Goedel and Turing are but modern
versions of the same idea: the classical logic of Aristotle is too
limited to capture the dynamics of nonlinear computation.
Mathematics provides us with the missing tool, the organic logic,
which is aptly tailored to model the dynamics of nonlinearity. This
logic will be the core of the "Mathematics for Life" to be
developed during this century.
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