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. We inhabit a very particular place in the universe. The planet we find ourselves residing on is unlike any other patch of cosmic space containing matter. Every day we witness the interaction of a myriad of structures creating a vast richness of intricate behavior. We are surrounded by, and embedded in, a microcosm seething with complexity. Specifically, we are exposed to chemical, biological, and, foremost, technological and socio-economical complexity. Until very recently in the history of human thought, the adjective "complex" was thought to be synonymous with "complicated"-in other words, intractable. While the universe unveiled its fundamental mysteries through the Book of Nature-the age-old metaphor for the circumstance that the regularities in the physical world are explained mathematically by the human mind-the complexity surrounding us seemed incomprehensible. However, one specific cosmic coincidence allowed the human mind to also tackle and decode the behavior of complex systems. Before disentangling complexity itself, the next section will briefly review the notions introduced throughout the narrative of Part I: the two volumes of the Book of Nature.