Complexity & Universality

Santa Fe Institute
3 min readFeb 21, 2019

A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute

“As we peel the skins of the onion…Sometimes even the old mathematics is sufficient.” Photo: K8 on Unsplash.

Science strives to explain the world through elegant and judicious exposition. And the hallmarks of good science have always consisted in some combination of coverage (the breadth of phenomena encompassed), minimalism (the efficient encoding of observation), naturalness (appealing to the mind and connecting to existing ideas), and predictive power.

The domain of complexity science might seem on the surface to be one that controverts these characteristics: system-dependent, maximal, unnatural, and contingent. And over the years I have certainly met many who derive a mild pleasure, let’s call it an epistemological schadenfreude, from all of those failed efforts to apply to complexity the wrecking ball of physical theory with all of its symmetries, equalities, laws, and “back of the envelope” hubris.

And while it certainly could be true that the human imagination has more than met its match in complexity, such that for certain phenomena it is appropriate to forgo understanding in favor of over-sized models and simulations in order to better predict (as we routinely do with weather forecasting), I do not believe that it is time to throw in the towel.

In his wonderful essay, “Nature conformable to herself,” Murray Gell-Mann builds on Isaac Newton’s insight into the “consonance” or “conformability” of nature, whereby the same laws apply at many different scales.

Murray writes, “As we peel the skins of the onion, penetrating to deeper and deeper levels of the structure of the elementary particle system, mathematics with which we become familiar because of its utility at one level suggests new mathematics, some of which may be applicable at the next level down — or to another phenomenon at the same level. Sometimes even the old mathematics is sufficient.”

Murray points out that conformability is in large measure the key to the utility of parsimony. This is because the frugality of nature permits a prudence of mind. And over the last few decades multi-scale general patterns have been observed across a large swathe of complex systems, from the networks governing metabolism up through ecologies and cities — all promoting advances in theory development.

After thirty years pursuing areas in which complexity might be approached through the lens of simplicity, the Santa Fe Institute is teaming up with the National Science Foundation to explore via a meeting on “Convergent Paths towards Universality in Complex Systems” in early December in Washington D.C.

This is a very exciting meeting as it represents a summa and a summary of SFI and affiliated research work across a range of areas including Information Processing Systems; Adaptive Dynamics; Regularities in Ecology; and Scaling in Biological and Urban Systems. In each of these areas we shall be exploring how far the community has progressed towards universality — principles that transcend mechanism, scale and history — and discussing the long-term prospects for intervention and thoughtful management of complex systems. This event is also timely as it brings SFI to Washington at a moment when rational discourse and collaboration are more important than ever.



Santa Fe Institute

The Santa Fe Institute is an independent research center exploring the frontiers of complex systems science.