Mathematical aesthetic principles/nonintegrable 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 system. 5. Nonlinear sine within sine system. 6. Nonlinear sine within sine behavior and the aesthetic fields program. 7. Wave packet solution. 8. A study of properties of the vacuum for the wave packet solution. 9. Assignment of origin point data. 10. A more viable wave packet solution. 11. Features of the more viable wave packet solution -- ch. 6. A study of some additional solutions to the gamma equations. 1. A lattice of closed string solitons. 2. Ladder symmetry. 3. Loop lattice with a doublet basis. 4. Concept of imperfect lattice. 5. "Chaotic" looking system. 6. Instanton solution. 7. A dynamical lattice. 8. Irregular oscillations along any path segment -- ch. 7. Mathematical aesthetics: additional topics. 1. Component to represent the particle system. 2. Lorentz invariance of the gamma equations. 3. Higher dimensions. 4. A brief summary. 5. Outstanding problems. 6. Mathematical aesthetics and epistemology

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