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[ by Charles Cameron — achieving something like closure on a post I started for Adam Elkus here, with a side dish along the way here ]
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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.

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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.

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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.

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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”…

[ by Charles Cameron — here’s today’s windfall apple from the tree of creative delight ]
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On March 31st, 2012 (or very likely the evening of the day before, because the clock this blog runs on is always way ahead of me) I posted a graphic here:

The upper image illustrates Theodore von Kármán‘s mathematics of turbulent flow, the lower image Vincent van Gogh‘s view of the night sky, and I juxtaposed them using my “DoubleQuotes” format to illustrate the underlying unity of the arts and sciences, and the breathtaking beauty and insight we can derive when we recognize a “semblance” — a rich commonality that transcends our usual division of concepts into separate and un-mutually-communicative “disciplines” and “silos”.

Apparently, this kind of cognition — the basis of every DoubleQuote, and of every move in one of the Hipbone / Sembl games — has now been termed “pattern thinking”.

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According to Amazon, Temple Grandin and Richard Panek‘s book The Autistic Brain: Thinking Across the Spectrum was released April 30, 2013 although books are often available a couple of weeks ahead of release date, and galleys and proofs earlier still).

I read about it for the first time today, in Grandin & Panek’s piece, How an Entirely New, Autistic Way of Thinking Powers Silicon Valley in Wired. That article begins with a pull-quote from Grandin’s book:

I’ve given a great deal of thought to the topic of different ways of thinking. In fact, my pursuit of this topic has led me to propose a new category of thinker in addition to the traditional visual and verbal: pattern thinkers.

Obviously, that’s something i’d want to find out more about, so I read on into the article, expecting good things. Imagine my surprise when I read this paragraph, though:

Vincent van Gogh’s later paintings had all sorts of swirling, churning patterns in the sky — clouds and stars that he painted as if they were whirlpools of air and light. And, it turns out, that’s what they were! In 2006, physicists compared van Gogh’s patterns of turbulence with the mathematical formula for turbulence in liquids. The paintings date to the 1880s. The mathematical formula dates to the 1930s. Yet van Gogh’s turbulence in the sky provided an almost identical match for turbulence in liquid.

Boom!

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Okay, I just received my review copy of Hofstadter and Sander, Surfaces and Essences: Analogy as the Fuel and Fire of Thinking — I guess I’ll have to review Grandin and Panke here, too.

[ by Charles Cameron — mission statement? perhaps not — but definitely mission critical ]
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In five words:

Know your enemy: that’s intelligence.

Weiner may not have the whole picture, but he sure puts an interesting spin on things.

[ by Charles Cameron — on caterpillars, butterflies, psyche and the alephs of Georg Cantor, with a glance at the vertiginous idea it might be “boxes all the way up and down”… ]
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Let’s get the science — which is quite fascinating — taken care of first. Here’s our best current visualization of how a caterpillar, after crafting its cocoon, prepares to become a butterfly:

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Words can sometimes tell us some things that images can’t — or explain things to parts of us that simply cannot comprehend them visually — so here for parallel processing is an account of part of the same business from Scientific American:

How does a caterpillar rearrange itself into a butterfly? What happens inside a chrysalis or cocoon?

First, the caterpillar digests itself, releasing enzymes to dissolve all of its tissues. If you were to cut open a cocoon or chrysalis at just the right time, caterpillar soup would ooze out. But the contents of the pupa are not entirely an amorphous mess. Certain highly organized groups of cells known as imaginal discs survive the digestive process. Before hatching, when a caterpillar is still developing inside its egg, it grows an imaginal disc for each of the adult body parts it will need as a mature butterfly or moth—discs for its eyes, for its wings, its legs and so on. In some species, these imaginal discs remain dormant throughout the caterpillar’s life; in other species, the discs begin to take the shape of adult body parts even before the caterpillar forms a chrysalis or cocoon. Some caterpillars walk around with tiny rudimentary wings tucked inside their bodies, though you would never know it by looking at them.

Once a caterpillar has disintegrated all of its tissues except for the imaginal discs, those discs use the protein-rich soup all around them to fuel the rapid cell division required to form the wings, antennae, legs, eyes, genitals and all the other features of an adult butterfly or moth.

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It’s just possible that the bear’s ability to “die” in the winter and “be reborn” in spring gave use the original cirumpolar bear cult — and more generally, a propensity to believe that resurrection from the dead might be a physical, existential human possibility.

Humans watch animals pretty diligently — my old friend and mentor Wallace Black Elk once told me:

We watch the deer, and when they’re sick they know which plant is their aspirin: they eat that green medicine, and drink water. So we have deer medicine. We don’t need the mass-produced kind.

I don’t have the exact quote, but he also observed somewhat wryly that scouts from pharmaceutical companies used to watch him and see what medicines he used, in much the same way…

And if there’s any natural process that humans have watched with equivalent metaphysical interest to that which they may have shown in observing the bear’s pattern of hibernation and return, it would have been the process of metamorphosis in butterflies — whose name in Greek, psyche, is also the word for soul.

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WB Yeats had a sense of the butterfly transcending both day-to-day human logic and death itself, when he wrote in his poem Tom O’Roughley:

‘Though logic choppers rule the town,
And every man and maid and boy
Has marked a distant object down,
An aimless joy is a pure joy,’
Or so did Tom O’Roughley say
That saw the surges running by,
‘And wisdom is a butterfly
And not a gloomy bird of prey.

adding just a few lines later:

What’s dying but a second wind?

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What I’d like to do here is to take us from the plodding science of linear thought to which Yeats was (among other forms of linearity) objecting, towards the science — and poetry — of complexity, of nuance.

And I’d like to do it by skipping a couple of thoughts like a stone across water, inviting you to watch the ripples…

These are the leaps that connect the dots.. the creative leaps. And some leaps, it seems to me, are bigger and more demanding than others.

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Is the leap from cocoon to butterfly in Hutching‘s quote really quite a huge leap? It certainly keeps some of our best scientists busy uncovering its hidden secrets. And the leap from butterfly to tornado, that Lorenz made? That would appear to me to be a larger leap, requiring a different mode of perception. And skipping from Hutchings to Lorenz, can we skim our stone of thought even further?

Putting two and two together is one thing: imagining “aleph null” for the first time, as Cantor did, that would be something else altogether. From two to four, I’m tempted to say, is a quantitative leap, while the imaginative leap from four, ten, or ten thousand to the alephs is qualitative.

How should we recognize and connect widely separated — yet deeply entangled — dots? What would prove to be the richest and most profound of creative leaps? Is there a move that will take us not just out of this box into the box it came in — but out of a whole matrioshka nest of boxes?

Those are the questions in my sandbox about now.

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When we next meet, I’ll try to tie them in with this diagram that Adam Elkus recently pointed us to —

and with Hermann Hesse‘s Glass Bead Game for good measure.