Mathematical aesthetic principles/nonintegrable systems

Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as "aesthetic" and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems

Ch. 1. Mathematical aesthetics. 1. Why mathematical aesthetics. 2. All things are numbers. 3. Flat space versus curved space. 4. Some nonlinear equations. 5. Mathematical aesthetic principles. 6. The aesthetic field equations (gamma equations). 7. Other relations obtained from the basic principles. 8. The integrability equations. 9. Computer project. 10. Sinusoidal wave solutions to the gamma equations. 11. Multiparticle solutions -- ch. 2. Nonintegrable systems. 1. The ABJL equations. 2. A formulation of no integrability theory. 3. Generalized derivatives. 4. Summation over path method. 5. Second approach to nonintegrable systems. 6. Computer results for a soliton lattice system -- ch. 3. Commutator method. 1. The commutator method and the ABJL equations. 2. Commutator method for a three component lattice. 3. The product method. 4. Random path approximation -- ch. 4. Nonintegrability and the arrow of time. 1. The arrow of time -- ch. 5. The gamma equations as a source of fundamental building blocks. 1. Introduction. 2. Sinusoidal behavior along any path segment arising from mathematical aesthetics program. 3. Linear sine within sine system. 4. Another linear sine within sine syst…