We review our research on a system of equations not satisfying integrability. We show how to formulate the no integrability theory within the "aesthetic" field framework. Although we emphasize this aesthetic field framework, many of our remarks concerning no integrability are not dependent on the aesthetic field concept. We show how to handle the no integrability theory by two different methods. We discuss some numerical work made on the no integrability system and show that the results lead to planar maxima and minima and are thereby suggestive of multiparticles. Although symmetry of mixed derivatives has been taken to be the norm in contemporary physics, it is not a compelling hypothesis, and we suggest such a restriction unduly limits our scope. In addition, the absence of symmetry for mixed derivatives may have considerable implications for physics. The way we introduce derivatives is consistent with the no integrability field equations and is the same as conventional derivatives when the integrability equations are satisfied. © 1988.
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