Mirrors of the World
A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute.
Arthur I. Miller subtitled his parallel biography of Einstein and Picasso Space, Time, and the Beauty that Causes Havoc. The upheaval to which Miller alludes is nothing less than the assault on our intuitive beliefs about space (cubism) and time (relativity). Put differently, familiar representations used to encode regular patterns in the world are, in fact, conventions. At a certain point these are deemed insufficient, or rather boring, and replaced. It is like the experience of touring through the Metropolitan Museum in New York City by starting in Greece with a Balsamarium decorated in lion skin, ambling through the Pacific past an Asmat ancestor, hastening through the Middle Ages fleeing from its terrifying two-handed swords, and coming to a stop at the inevitable lion in a Rousseau painting. They are different means of seeing not progressively but of encountering alternative depictions of reality.
The overall effect is to wonder at the multiplicity of descriptions of very similar objects and events. In 1781 Immanuel Kant made the question of “representation” the foundation-stone of a theory of knowledge. Kant kicks us off with his section on “Metaphysical Exposition of this Conception” in the Critique of Pure Reason:
“What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind . . .”
When are we entitled to call a representation objective (O) and when subjective (S)? There is a reasonable, operational form of naive realism that makes S mind and O sensation. Start with S1,O1: Ptolemaic astronomy (S1) viewed through the naked eye (O1) and replace it with S2,O2: Newtonian mechanics (S2) constructed from telescopic observations (O2). In this way, the accumulation of exact knowledge is the sequence Si,Oi → Si+1,Oi+1. And there is of course an evolutionary counterpart to epistemology — the sequence of adaptive steps mapping successive traits onto environmental factors described through a lineage.
Let’s just say that reality lies somewhere between the relatively simple history of science and life and a complex day trip to the Metropolitan Museum. What is striking is that in both cases — Miller’s central point in his biography — is that we must think of life and cognition as systems of reflection. This fact is what establishes, or delimits, what we call complex reality. Physics and chemistry have no need of S,O pairs, but we cannot begin to talk about biology, culture, or technology without some version of this duality.
John Holland and Murray Gell-Mann made the S,O pair the centerpiece of their definitions of complex systems, both describing the mirroring mechanism in the S as a schema of the O. For Holland a schema is a binary string whose fixed elements (as opposed to wild cards) define an equivalence class of coordinates encoding optimal solutions in adaptive landscapes. Complex systems are, for Holland, agents in possession of map-like schemata. For Gell-Mann, schemata, which he also called the IGUS (Information Gathering Utilizing System), are compressed rule systems capable of receiving inputs from history and environment in order to predict and act on states of the world. These span genomes, nervous systems, and even material culture.
Returning to Miller’s interest in the revolutionary transformation in the representation of time and space, we find the late James Hartle formalizing the IGUS in order to explore the origin of what he described as the emergent concepts: present, past, and future. These are not, contrary to received opinion, physical properties but representational concepts. By placing an IGUS in Minkowski space, Hartle traced what he called their “subjective” world lines. And in this way connected complexity (life) to simplicity (physics). What Hartle, re-representing Gell-Mann, re-representing Kant, initiated is a new science that might make aesthetics a fundamental principle of complexity — a rigorous connection between life, mind, and matter.
— David Krakauer
President, Santa Fe Institute
From the Autumn 2023 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.
