The Beautiful & the Interesting in Complexity Science
A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute.
When the Scholastic cosmologists evaluated the Copernican contender against the Ptolemaic incumbent, it was not only the beauty of the simplicity of Copernicus’ contribution to calculating celestial tables that recommended his thesis, but the interesting possibility that the “wandering stars,” or what we now call the planets, were like our own Earth and teeming with the industry of contingent life — a plurality of worlds.
My colleague and collaborator Anthony Eagan recently published his new book, Kierkegaard’s Concept of the Interesting. Some philosophical background will be helpful in understanding the development of Eagan’s argument. The German idealists make a distinction between the outer and the inner. Immanuel Kant describes these as the sensible and the super-sensible, where the first describes the beauty of the mechanisms of physical law, and the second interesting features of the freedom of thought. The Romantic philosopher Friedrich Schlegel described Greek poetry in terms of “beauty” (closer to universal forms) and modern poetry as merely “interesting,” and confounded by the subjective details of human action and its fascination with content. Whereas Homer’s Hector enshrines the essential symmetries of beauty, Shakespeare’s Hamlet is full of the broken symmetries of the interesting; and hence to Schlegel, is the lesser creation.
As Eagan demonstrates in his book, Kierkegaard significantly enriches this debate by making the interesting relational — one might say that the interesting is a mapping or morphism from the latent or hidden laws of nature onto lived reality. The interesting is not merely the incompressible property of any work or idea but the noisy image encoded in a finite being of a pre-image mapped from a purely mechanical process, or in the religious context, from ultimate reality. And Kierkegaard describes the inverse mapping as the aesthetic impulse — the doomed attempt to construct the logic or function of the original (the natural world) from the degenerated counterpart (the cognitive world). In his Critique of Judgement, Immanuel Kant describes this sensation as trying to discern rather hopelessly in some physical object “formal purposiveness by the feeling of pleasure or displeasure.” This all reminds me of something the painter Robert Rauschenberg wrote in his journals: “Painting relates to both art and life. Neither can be made. I try to act in that gap between the two.” Rauschenberg carefully avoids concluding which of these two is interesting or beautiful.
Complexity science as articulated across the twentieth century has exactly this bijective character. When Warren Weaver described complexity as “organized complexity” as opposed to simplicity, he was describing the evolved world of the interesting emergent historically from a universe of the beautiful. The same point was made by Philip Anderson in his paper “More is Different,” where he writes, “Thus, with increasing complication at each stage, we go on up the hierarchy of the sciences. We expect to encounter fascinating and, I believe, very fundamental questions at each stage in fitting together less complicated pieces into the more complicated system.” Finding some principled measure of this more complicated system drove the mathematicians Andrey Kolmogorov, Gregory Chaitin, Charles Bennett, and Ray Solomonoff into the domain of Turing machines, those evolved mechanisms that lie at the heart of the modern relational account of complexity: mappings from physical micro-configurations into coarse-grained logical categories.
In his 1843 Either/Or, Kierkegaard presents several pseudonymous authors, foremost among them the Aesthete, “A.” “A” writes on music and on Mozart’s Don Giovanni, more specifically. Kierkegaard makes the point that “the medium through which an idea becomes visible could be made the object of consideration,” and that the medium of music is the most abstract and hence best suited to describe or encode the symmetries of ultimate reality. In this connection he foreshadows the debate on the power of mathematics to encode universal regularities. As the mathematician Morris Kline wrote in Mathematics and the Physical World (1959), “Insofar as it is a study of space and quantity, mathematics directly supplies information about these aspects of the physical world.” But insofar as we are studying a specific space and quantity, and complications at different stages, then we need another aesthetic, and a rather different kind of “A,” who focuses less on the simply beautiful and more on the complexly interesting.
— David Krakauer
President, Santa Fe Institute
From the Winter 2024 edition of the SFI Parallax newsletter. Subscribe here for the monthly email version, or email “news at santafe.edu” to request quarterly home delivery in print.
