The Nonlinear World: Conceptual Analysis and Phenomenology

Abstract

This book explains a certain way of appreciating “the world filled with non- linearity.” Its core is conceptual analysis and phenomenology, which is backed up by renormalization philosophy. The main target of the book is young peo- ple who have just started to appreciate the world seriously. The author wishes the book to be helpful also for those who have been observing the world, but who wish to appreciate it afresh from a different angle. The most important feature of the nonlinear world is that disparate space– time scales (e.g., macroscopic and microscopic scales) can interfere with each other. Consequently, events of the world directly observable on our own space–time scale are, generally speaking, not closed within themselves. That is, to understand a phenomenon occurring within our human space–time scale, we must often take into account the things happening at space–time scales disparate from ours. It is usually the case, however, that we cannot know what is actually going on at scales far from the ones we can directly observe. The so-called chaos clearly exhibits consequences of this intrusion of the unknowable (at small scales) into the world we experience directly. These intrusions of the unobservable into our directly observable world make the world we wish to comprehend not self-contained. Thus, nonlinearity gener- ates various phenomena that are difficult for us to comprehend. We cannot know everything we need to in order to understand the world in terms of its fundamental laws (even if they exist).