Chaos theory finding new applications in the life sciences

Supported in the Newtonian laws of Physics described by differential equations, scientists have long believed that nature was determinist knowing that on that basis, it was possible to predict all phenomena. Around the turn of the nineteenth to the twentieth century, advances in the natural sciences and mathematics put serious doubts on the validity of Newtonian mechanistic view. Quantum Mechanics has questioned the determinist worldview introducing the uncertainty principle. In the traditional deterministic approach, the uncertainty was seen as a result of ignorance of the different causes involved in holding an event, and the complexity of it. Chaos Theory or the new Science of Complexity suggests that the world should not strictly follow the deterministic Newtonian model, predictable and certain, because it has chaotic aspects. The observer is not who creates instability or unpredictability due to their ignorance because these phenomena exist in nature. A typical example is the weather. The processes of reality depend on a huge set of uncertain circumstances that determine, for example, that any small change in one part of the planet, there will be in the coming days or weeks a considerable effect on the other side of the Earth. Chaos Theory or Science of Complexity represented one of the great advances in scientific research of the twentieth century ending with the dichotomy that existed in the traditional deterministic approach between determinism and randomness.

This book describes the birth of the new theory of Chaos. This is a difficult new concept that is still evolving but it popularized the term: Butterfly Effect and introduced new concepts to a popular audience, such as fractals and introduced pioneering thinkers, such as Feigenbaum and Mandelbrot; it inspired the novel and movie Jurassic Park. This concept opens up a new view of nature: where previously randomness had to be forced in to explain the unpredictable variations, now chaos is seen as spanning both order (patterns) and disorder. Now, this phenomenon helps explain the shape of clouds, smoke, water eddies, mountain ranges and coastlines. Implicitly, it shows how Newtonian mathematics has constrained physics (and science in general) to make simplifying assumptions that enable the calculus to become the universal tool-set of the scientific viewpoint. The book describes how this tough problem was cracked by five theoreticians described herein with a novelist's eye. Key to the solution was the early use of computers to repeat simple calculations, very many times. The viewpoint changed from static 'state' to dynamic process: becoming rather than being. Chaos is everywhere, it is switching the simple mathematical models of classical physics. It is the science of the global nature of systems. I show here (but not in the book or Wiki) that this is the start of the Death of Newtonian Physics and the Calculus: a TRUE REVOLUTION.

2001

Explaining Chaos is an informative, original and enjoyable introduction to chaos theory and its associated philosophical problems. The book does not presuppose any previous background in chaos theory. Nevertheless, the discussion may be as interesting to experienced readers as it is to novices. In particular, several mathematical interludes deepen the discussion of technical issues and provide numerous interesting insights that could further enlighten readers already familiar with the central ideas. The reader will ®nd an accessible discussion striking a good balance between scienti®c and philosophical topics. Unfortunately, the physical and the philosophical parts are uneven in quality. While the treatment of the scienti®c issues is thorough and skilful, the philosophical discussions have signi®cant lacunas. Nevertheless, Smith's enthusiasm for exploring these issues is contagious and the book is a valuable contribution to a ®eld that has, despite its importance, received little attention from philosophers so far. Explaining Chaos consists of ten chapters that could be divided into two main categories: the mathematics and physics of chaos, and the implications of chaos for scienti®c practice and methodology. In Chapters 1 (dynamical systems), 2 (fractals), 6 (universality), 8 (experimental evidence for chaos), and 9 (randomness), Smith introduces the central topics of chaos theory and discusses important results. In Chapter 10, he addresses the question of how chaos could adequately be de®ned. On the whole, these chapters provide a very knowledgeable and skilful presentation of the basics of chaos theory. In Chapters 3 (models and simplicity), 4 (prediction), 5 (approximate truth), and 7 (explanation), Smith considers the methodological implications of chaos theory. Here, he aims at showing that chaos, though an interesting and exciting ®eld of investigation, by no means requires a revision of the basic traits of scienti®c methodology. Smith successfully resists the temptation to be carried away by fancy bold claims and, on the contrary, argues that chaos theory may be considered a respectable tool for decent scienti®c research.

Quality & Quantity, 1994

This article investigates the relevance of chaos theory for social science. The application of chaos models in the analysis of social phenomena is accompanied by some important scientific problems. First, whether observations of social phenomena are generated by nonlinear dynamics cannot be ascertained beyond considerable doubt, especially when these observations contain measurement errors; i.e., there is a problem of external validity. Secondly, and more important, as a theory of irregular cyclical social behaviour is lacking, inductivestatistical theory-formation about such behaviour, which is based on fitting a mathematical model of chaos to observations of social phenomena, is impossible unless additional information is used concerning the context and circumstances wherein the social phenomena occur; i.e., the internal validity of any theoretical explanation that is derived from only a fitted mathematical model (of chaos) cannot be assessed. So, research into the suggestion derived from mathematical chaos theory that irregular cycles may be present in the development of social phenomena over time requires theory-formation about irregular cyclical social behaviour on the basis of established theoretical insights and empirical evidence instead of fitting sophisticated mathematical models of chaos to observations of social phenomena.