It’s astonishing to me how closely complexity science is related to Hermann Hesse‘s Glass Bead Game.
Adam Elkus recently pointed those who follow him to Cosma Rohilla Shalizi, Methods and Techniques of Complex Systems Science: an Overview, and just a quick dip there gave me the graphic I’ve put at the head of this post, together with this quote about “patterns” as Shalizi understands that term:
I mean more or less what people in software engineering do: a pattern is a recurring theme in the analysis of many different systems, a cross-systemic regularity. For instance: bacterial chemotaxis can be thought of as a way of resolving the tension between the exploitation of known resources, and costly exploration for new, potentially more valuable, resources (Figure 1.2). This same tension is present in a vast range of adaptive systems. Whether the exploration-exploitation trade-off arises among artifcial agents, human decision-makers or colonial organisms, many of the issues are the same as in chemotaxis, and solutions and methods of investigation that apply in one case can profitably be tried in another. The pattern “trade-off between exploitation and exploration” thus serves to orient us to broad features of novel situations. There are many other such patterns in complex systems science: “stability through hierarchically structured interactions”, “positive feedback leading to highly skewed outcomes”, “local inhibition and long-rate activation create spatial patterns”, and so forth.
Let’s start with patterns. The “people in software engineering” Shalizi mentions gleaned their use of the term “pattern” from the architect Christopher Alexander, author of the extraordinary, seminal book A Pattern Language, which in turn has hugely influenced computer science. Alexander distilled the essence of his thinking in his “Bead Game Conjecture”:
That it is possible to invent a unifying concept of structure within which all the various concepts of structure now current in different fields of art and science, can be seen from a single point of view. This conjecture is not new. In one form or another people have been wondering about it, as long as they have been wondering about structure itself; but in our world, confused and fragmented by specialisation, the conjecture takes on special significance. If our grasp of the world is to remain coherent, we need a bead game; and it is therefore vital for us to ask ourselves whether or not a bead game can be invented.
Manfred Eigen, Nobel laureate in Chemistry, called his book with Ruth Winkler-Oswatitsch Laws of the Game — and it deals with molecular biology, cellular automata, game theory, and games. But not just that — it is specifically written with Hesse’s concept in mind:
We hope to translate Hermann Hesse’s symbol of the glass bead game back into reality.
While we’re on about cellular automata, what about Stephen Wolfram? I don’t know that he talks about the Glass Bead Game himself, but at least three people talk about Wolfram’s book, A New Kind of Science, and/or his search engine, Wolfram Alpha as being strongly analogous to Hesse’s game — Jason Dyer, Graeme Philipson, and most recently, Mohammed AlQuraishi. Here’s a key para from Quraishi’s piece:
I think the Game is an intriguing concept, and I think it may one day be realized. In fact I think we are already on our way toward realizing it. In the simplest and most general sense, mathematics and programming languages allow us to formalize all knowledge. Contenders for the language of the Game already exist, at least in principle. But we are further along than that. Search engines like Wolfram Alpha have already begun the process of formalizing diverse pieces of knowledge, unifying them in a single medium, and providing the means to connect and reason about them. A repeated example in the book, the mapping of musical compositions to mathematical formulas or even historical events, is eminently doable within Wolfram Alpha. Much remains to be done of course, and there is no “game” yet that can be played across the vast sea of all human knowledge, but some enterprising individuals have already gotten started on creating it.
And then there’s John Holland, the “father of genetic algorithms”. Holland told an interviewer:
I’ve been working toward it all my life, this Das Glasperlenspiel. It was a very scholarly game, starting with an abacus, where people set up musical themes, then do variations on it, like a fugue. Then they’d expand it to where it could include other artistic forms, and eventually cultural symbols. It became a very sophisticated game for setting up themes, almost as a poet would, and building variations as a composer. It was a way of symbolizing music and of building broad insights into the world.
If I could get at all close to producing something like the glass bead game I can’t think of anything that would delight me more.
I’ve been working on a playable variant on the Glass Bead Game too, for twenty years quite consciously, and more if you count subterranean stirrings. And I don’t think glass beads, or stones, or chess or go pieces, or beads on an abacus, or strings of ones and zeros, or cells in an agent-based model for that matter, are the way to go. Which is not to say those approaches shouldn’t be tried, or don’t have remarkable things to teach us. I just don’t believe they give us quite what Hesse envisioned:
a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.
I think what’s important in Hesse’s game is that concepts that humans can grasp should reveal their stunning interrelations to heart and mind. And for that reason, the “moves” in my games [Hipbone, and more recently Sembl] consist of concepts — musical, verbal, visual, mathematical — and the links, the analogies, the “semblances” between them.
And thus the game is a search for analogies.
The human mind must inevitably perform what Shalizi calls the “trade-off between exploitation and exploration”. Some thoughts are proximate to others, they can be developed without any special insight by regular “linear” thinking. We do this every day, every minute — but it is not particularly revelatory. It doesn’t solve thorny problems, much less create beauty. There is another mode of thinking, however, that leaps between thoughts that are not so “close” but are nevertheless deeply related. To leap the apparent distance between such deeply related thoughts, we deploy analogy and creative thinking, and that is where the aha! of revelation occurs.
So I would suggest there is a close analogy here with the point Shalizi is making with the diagram atop this post. The human mind, to slightly paraphrase Shalizi’s caption, will “exploit the currently-available patch of food” for thought by linear, inside-the-patch thinking, but at full stretch it will also “explore, in hopes of ?nding richer patches elsewhere” — the “elsewhere” being attained precisely by “creative leaps” — by seeing semblances, patterns, analogies.
And to return to my earlier post, Thinking outside the cocoon, of which this post is a continuation, and perhaps the completion….
Shalizi’s “random walk” is thus also the archangel’s “zig-zag wantonness” in that great poem, Tom O’Roughley — when William Butler Yeats asks, “how but in zig-zag wantonness / could trumpeter Michael be so brave?” and writes, “wisdom is a butterfly / and not a gloomy bird of prey”…