The post of today is about an amazing book I'm currently reading called Complexity: A guided tour written by Melanie Mitchen, a professor on the Computer Science department of the Portland University. The book is absolutely well written and keeps you thrilled along every chapter. It starts, in chapter 1, by introducing the question of "What is Complexity" and by an informal approach to this topic. This first chapter is all about enumerating several examples of complex systems. Melanie give us the ant colonies, the brain, our immune system, the web, global economies to ilustrate the concept and use this same examples to synthesize several common properties of complex systems.
Those common properties are of qualitative nature and the chapter ends with the question of how is complexity measured, that introduces the need for a quantitative approach of concept of complexity.

Chapter two is an introduction of Dynamical Systems. It starts by giving us an historical overview of the path science need to travel to go from linear systems into non linear systems, the relationship between the deterministic world given by classic mechanics and the not so deterministic viewpoint given by contemporary quantum physics and use this different overviews to introduce the concept of problem of initial conditions she explores the concept of linear and non linear system and exemplifies the logistic map as a non linear system and shows some interesting properties that we get when several parameters are used in this mathematical construct which we call atractors.
By instantiating different parameters it is shown that attracts or problems sensitive to initial conditions are of essentially three types. Fixed point, periodic and chaotic (this last one also known as strange attractor). After build a taxonomy for dynamical systems are exploited and explained two general properties the The period-doubling route to chaos, and the Feigenbaum’s Constant and with this Melanie ends chapter 2.

Chapter 3 is all about information it starts with the obvious question of what is information and also take the opportunity to introduce the concept of computation. From here it follows the natural path of introducing the concept of entropy and by showing the relationship between energy, work, and the introduce the laws of thermodynamics. From here if follows the introduction of Maxwell Demon and the respective solution for the problem given by Leo Szilard on the paper On the decrease of entropy in a thermodynamic system by the intervention of inteligent beings that relates for the first time the concept of entropy and of information and how it give birth to the field of information theory and physics of information.

The book has twenty chapters and here I only give an overview of the first three to let you taste a little of what you can find. The rest of the book is a merge of this knowledge and a lot more, described in other chapters, to build a general and cross overview about the concept of complexity. I really recommend this book and acknowledge the great job done by Melanie on the subject. Hope you have fun as I have.

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