Archivos para la categoría: sistemas complejos

In a sense we approached the world in this book following the spirit of Christo and Jean-Claude. To look at the networks behind such complex systems as the cell or the society, we concealed all the details. By seeing nodes and links, we were privileged to observe the architecture of complexity. By distancing ourselves from the particulars, we glimpsed the universal organizing principles behind these complex systems. Concealment revealed the fundamental laws that govern the evolution of the weblike world around us and helped us understand how this tangled architecture affects everything from democracy to curing cancer.

Where do we go from here? The answer is simple. We must remove the wrapping. The goal before us is to understand complexity. To achieve that, we must move beyond structure and topology and start focusing on the dynamics that take place along the links. Networks are only the skeleton of complexity, the highways for the various processes that make our world hum. To describe society we must dress the links of the social network with actual dynamical interactions between people. To understand life we must start looking at the reaction dynamics along the links of the metabolic network. To undestand the Internet, we must add traffic to its entangled links. To understand the disappearance of some species in an ecosystem, we have to acknowledge that some prey are easier to catch than others.

In the twentieth century we went as far as we could to uncover and describe the components of complex systems. Our quest to understand nature has hit a glass ceiling because we do not yet know how to fit the pieces together. The complex issues with which we are faced, in fields from communication systems to cell biology, demand a brand new framework. Embarking on the journey ahead without a map would be hopeless. Fortunately the ongoing network revolution has already provided many of the key maps. Though there are still many “dragons” ahead, the shape of a new world has become discernible, continent by continent. Most important, we have learned the laws of web cartography, allowing us to draw new maps whenever we are faced with new systems. Now we must follow these maps to complete the journey, fitting the pieces to one another, node by node and link by link, and capturing their dynamic interplay. We have ninety-eight years to suceed at this, and make the twenty-first the century of complexity.



In my view complex systems science is branching off in two separate directions. Along one branch, ideas and tools from complexity research will be refined and applied in an increasingly wide variety of specific areas. In this book we’ve seen ways in which similar ideas and tools are being used in fields as disparate as physics, biology, epidemiology, sociology, political science, and computer science, among others. Some areas I didn’t cover in which these ideas are gaining increasing prominence include neuroscience, economics, ecology, climatology, and medicine—the seeds of complexity and interdisciplinary science are being widely sowed.

The second branch, more controversial, is to view all these fields from a higher level, so as to pursue explanatory and predictive mathematical theories that make commonalities among complex systems more rigorous, and that can describe and predict emergent phenomena.

At one complexity meeting I attended, a heated discussion took place about what direction the field should take. One of the participants, in a moment of frustration, said, “ ‘Complexity’ was once an exciting thing and is now a cliché. We should start over.”

What should we call it? It is probably clear by now that this is the crux of the problem—we don’t have the right vocabulary to precisely describe what we’re studying. We use words such as complexity, self-organization, and emergence to represent phenomena common to the systems in which we’re interested but we can’t yet characterize the commonalities in a more rigorous way. We need a new vocabulary that not only captures the conceptual building blocks of self-organization and emergence but that can also describe how these come to encompass what we call functionality, purpose, or meaning (cf. chapter 12). These ill-defined terms need to be replaced by new, better-defined terms that reflect increased understanding of the phenomena in question. As I have illustrated in this book, much work in complex systems involves the integration of concepts from dynamics, information, computation, and evolution. A new conceptual vocabulary and a new kind of mathematics will have to be forged from this integration. The mathematician Steven Strogatz puts it this way: “I think we may be missing the conceptual equivalent of calculus, a way of seeing the consequences of myriad interactions that define a complex system. It could be that this ultracalculus, if it were handed to us, would be forever beyond human comprehension. We just don’t know.”

Having the right conceptual vocabulary and the right mathematics is essential for being able to understand, predict, and in some cases, direct or control self-organizing systems with emergent properties. Developing such concepts and mathematical tools has been, and remains, the greatest challenge facing the sciences of complex systems.