Qualitative computing: a computational journey into nonlinearity

High technology industries are in desperate need for adequate tools to assessthe 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 Gödel 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 organiclogic, 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 thiscentury. INDICE: Introduction to Qualitative Computing; Hypercomputation in DicksonAlgebras; Variable Complexity within Noncommutative Dickson Algebras; Singular Values for the Multiplication Maps; Computation Beyond Classical Logic; Complexification of the Arithmetic; Homotopic Deviation in Linear Algebra; The Discrete and the Continuous; Arithmetic in the Four Dickson Division Algebras; The Real and the Complex; The Organic Logic of Hypercomputation; The Organic Intelligence in Numbers.

• ISBN: 978-981-4322-92-8
• Editorial: World Scientific
• Encuadernacion: Cartoné
• Páginas: 600
• Fecha Publicación: 15/08/2012
• Nº Volúmenes: 1
• Idioma: Inglés