This talk will explore some essential dimensions of complex systems research: the hard limits on what is achievable (laws), the organizing principles that succeed or fail in achieving them (architectures and protocols), the resulting behavior observed in real systems (behavior, data), and the processes by which systems evolve (variation, selection, design). Hard limits on measurement, prediction, communication, computation, decision, and control, as well as the underlying physical energy and material conversion mechanism necessary to implement these abstract process are at the heart of modern mathematical theories of systems in engineering and science (often associated with names such as Shannon, Poincare, Turing, Gödel, Bode, Wiener, Heisenberg, Carnot,…). They form the foundation for rich and deep subjects that are nevertheless now introduced at the undergraduate level. Unfortunately, these subjects remain largely fragmented and incompatible, even as the tradeoffs between these limits are of growing importance in building integrated and sustainable systems.
Insights into the universal laws, architecture, and organizational principles of such integrated systems can be drawn from three converging research themes. First, detailed description of components and a growing attention to systems biology and neuroscience, the organizational principles of organisms and evolution are becoming increasingly apparent. Biologists are articulating richly detailed explanations of biological complexity, robustness, and evolvability that point to universal principles and architectures. We will aim connect these insights with the role of layering, protocols, and feedback control in structuring complex multiscale modularity. While the components differ and the system processes are far less integrated, advanced technology’s complexity is now approaching biology’s and there are striking convergences at the level of organization and architecture. Determining what is essential about this convergence and what is merely historical accident requires a deeper understanding of architecture — the most universal, high-level, persistent elements of organization — and protocols. Protocols define how diverse modules interact, and architecture defines how sets of protocols are organized.
Finally, new mathematical frameworks for the study of complex networks suggests that this apparent network-level evolutionary convergence within/between biology/technology is not accidental, but follows necessarily from their universal system requirements to be fast, efficient, adaptive, evolvable, and robust to perturbations in their environment and component parts. The universal hard limits on systems and their components have until recently been studied separately in fragmented domains of physics, chemistry, biology, communications, computation, and control, but a unified theory is needed and appears feasible. We will sketch the underlying mathematical ideas and illustrate the key results with case studies from statistical mechanics, turbulence, cell biology, human physiology and medicine, wildfire ecology, earthquakes, the Internet, market volatility, toys, and fashion.
If there is time we will also review (i.e. poke fun at) a remarkably popular and persistent source of error and confusion, namely the many past and ongoing attempts to find “new sciences” of complex systems and networks. This highlights another apparent tradeoff we must overcome in complex systems, between the popularity of ideas versus both their mathematical rigor and practical relevance.
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