Volume II: The Simplicity of Complexity

Abstract

Whereas most of the cosmos is comprised of rather simple large-scale structures, on Earth, we find breathtaking complexity, down to microscopic scales. Indeed, it appears as though the universe is driven by a propensity to assemble ever more complex structures around us, guided by self-organized and emergent behavior. Naively one would expect complexity to be complicated to comprehend. Luckily, in the universe we inhabit, complex systems are encoded by simple rules of interaction. Like Volume I of the Book of Nature being written in the language of mathematics, Volume II, addressing complexity, is composed of simple algorithms decoding reality. Complex systems theory has a long history and raises philosophical questions. One of its most successful formal tools are networks. In fact, complex networks are ubiquitous in the domains of living and non-living complexity. One particular organizational property in complex systems is akin to a “law of nature,” giving rise to universal behavior. These patterns, known as scaling laws, are to be found everywhere. Level of mathematical formality: medium to low.