Games of Truth
A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute.
In his Ethics, published in 1677, philosopher Benedictus de Spinoza introduces a distinction between Knowledge of the First Kind (KFK), consisting largely of fragments of direct experience presented to the senses, and Knowledge of the Second Kind (KSK), or reason associated with the application of rules widely shared by everyone. The ability to distinguish the true from the false requires KSK. Spinoza uses the example of a geometric series to illustrate his point: the choice of starting numbers, let’s say (0, 1), lies firmly within KFK, whereas the derivation of a series or sequence of numbers — for example, the Fibonacci sequence (0,1,1,2,3,5, etc.) — lies within KSK. We might say that KFK is an input and KSK a function or a rule.
Between 1930 and 1933, Ludwig Wittgenstein gave a series of lectures at Cambridge University audited by the philosopher G.E. Moore, who kept very literal transcripts of Wittgenstein’s remarks. The lectures are filled with an abiding fascination with games. There is a point late in the course where Wittgenstein describes a very clear example of a rule of a game as writing down the development of the irrational number pi. This is what Spinoza had described through the idea of KSK. Wittgenstein also states that “discovering a game is quite different from discovering a fact” and facts are Spinoza’s KFK. For Wittgenstein, “Calculus is a game.” Indeed, every reason is only a reason within a game.
Midway through the Second World War in 1943, Hermann Hesse completed his novel The Glass Bead Game. The novel describes a community of scholars all hard at work on a game developed in the mid-21st century and built on mnemonics and melodics. In the game, dueling composers challenge each other to complete musical themes according to the strict application of formal rules. In its developed form several centuries later, the game involves advanced systems of deduction able to relate musical themes to mathematical propositions and Laplacian configurations of the physical world. Hesse sought to develop the kind of person who “would at any time be able to exchange his discipline or art for any other.” Assuming, of course, that all phenomena participate in the same game as described by Spinoza’s KSK.
When Richard Feynman published his Lectures on Physics in 1963, he presented physical theory as the effort to understand physical reality. Feynman writes, “What do we mean by ‘understanding’ something? We can imagine that this complicated array of moving things which constitutes ‘the world’ is something like a great chess game being played by the gods, and we are observers of the game. We do not know what the rules of the game are; all we are allowed to do is to watch the playing. . . The rules of the game are what we mean by fundamental physics.”
In an effort to provide an intuition for how evolved structure funnels chance into adaptive work, Manfred Eigen and Ruthild Winkler wrote their book The Laws of the Game (1981). The book contains a number of grid-based games, rather like Go. Many are inspired by the universalist goals of Hesse, which they describe in terms of “The dice and the rules of the game — these are our symbols for chance and natural law.” Reviewing the book in the London Review of Books, the evolutionary game theorist John Maynard Smith describes The Laws of the Game as an effort to show how understanding comes down to intuition for how “systems with different structures and relationships are likely to behave.”
The historian of religion James P. Carse, Spinoza-inspired to his core, wrote Finite and Infinite Games in 1986. In many ways, Carse extends Hesse’s premise by tempering it with Wittgenstein’s rule systems to achieve the open-ended possibilities for physical reality intimated by Feynman — and thereby promoting the kind of understanding sought by Eigen and Winkler. Carse writes, “There are at least two kinds of games. One could be called finite; the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.”
I like to think of complexity science as the natural continuation of these wide-ranging inquiries into the rules of the infinite game of reality. We might think of this science as the pursuit of Knowledge of the Second Kind conditioned on the happenstance of history and the debilitating finitude of our imagination.
— David Krakauer
President, Santa Fe Institute
From the Winter 2024–2025 edition of the SFI Parallax newsletter. Subscribe for our monthly e-Parallax, or email “news at santafe.edu” to request quarterly home delivery in print.
