On René Thom, attractors, and metaphors

“If one doesn’t have a concept of an object, one can’t recognize it,” insisted mathematician René Thom in To Predict is not to Explain, a set of interviews published in 1991 in French and 2010 in English.

Thom is generally credited with the terms attractor and basin of attraction, concepts that are fundamental to chaos, complexity, and resilience theory, and as I noted last time, are now used to map galactic superclusters.

Although Thom is little discussed these days, he was once widely celebrated. He received the 1958 Fields Medal and inspired both a 1976 film by Jean-Luc Godard and 1983 paintings by Salvador Dali, who portrayed Thom’s ideas about discontinuity, often called catastrophe theory, in his final works.

What happened to Thom and catastrophe theory? I’ve collected a few notes.

“[C]atastrophe theory was propelled on a wave of hype and enthusiasm during the mid-1970s only to die out in bitter controversies by the end off the decade,” wrote David Aubin in a chapter on Thom in 2004’s Growing Explanations: Historical Perspectives on Recent Science.

“[C]atastrophe theory did not live up to its promise of useful predictions,” asserted George Johnson in Thom’s 2002 NYT obituary.

Against such charges, Thom’s response was succinctly captured in the title, To Predict is not to Explain. As quoted in Aubin: “The ultimate aim of science is not to amass undifferentiated empirical data but to organise this data in a more or less formalised structure, which subsumes and explains it.”

As for his legacy, Thom wryly observed (in Predict ≠ Explain): “As a sociological phenomenon, the theory has foundered. Yet it’s a rather subtle sort of shipwreck, because all of the ideas which I’ve introduced have been incorporated into the language of common scientific discourse.”

Discontinuity depicted: (left) redrawn from Marten Scheffer's Critical Transitions in Nature and Society; (right) Salvador Dali's 1983 The Swallow's Tail (image from Wikipedia, © Salvador Dalí, Fundació Gala-Salvador Dalí, Figueres).

The visual language of discontinuity is represented (1) on the left, in a figure I’ve redrawn from Marten Scheffer’s 2009 Critical Transitions in Nature and Society (p.267), describing “a disturbance pushing the system across the border of a basin of attraction,” and (2) on the right, in Dali’s The Swallow’s Tail, depicting what Thom called the swallowtail and cusp (low-resolution, fair-use image from Wikipedia, © Salvador Dalí, Fundació Gala-Salvador Dalí, Figueres).

Thom on metaphor (Predict ≠ Explain):

My critics said: ‘What you’re giving us is only a metaphor.’ How was I to interpret this, as a reproach or as a compliment? For my own part, I saw it as a compliment. To have created a metaphor in an area where previously there was nothing, that’s already progress! …

Analogies and metaphors, contrary to the popular opinion that considers them flexible or just approximations, impress me as exemplifying strict relations, ones which can, in many cases, be given exact mathematical expression.


To Predict is not to Explain, interviews by Emile Noël, translated by Roy Lisker, edited by S. Peter Tsatsanis, is currently available as a pdf at Roy Lisker’s website.

Regarding the origin of term attractor, Tsatsanis noted:

It is clear from his [Thom’s] 1990 unpublished article, ‘On attractors’, that the word ‘attractor’ was used by him in 1966. Thom says that Steven Smale [Stephen Smale] might have used it before then although Smale says it was Thom that coined the neologism ‘attractor’. The notion of a ‘strange attractor’ came later when chaotic systems were being studied.

For more on Dali’s The Swallow’s Tail, see the Gala–Salvador Dali Foundation, the Stockholm Resilience Centre, and an appreciation by Stephen Parker.

A remarkable pair of videos, posted a couple months ago, describe research by R. Brent Tully and colleagues to map out our region of the universe and its change over time.

“Now we know, on the edge of a supercluster called Laniakea, in a galaxy called the Milky Way, around a star we call the Sun, there is a small blue planet, our home.”

That’s from the voice-over to the more filmic of the video pair, which has garnered 2.5 million views to date. The second, more technical video is above, and the associated paper was published in Nature. Brad Plumer reported the story on Vox.

In addition to the cosmic scales and graphic simulations, one aspect of the research and videos that caught my attention was their use of concepts familiar from the modeling of complex systems: attractors and basins of attraction.

“We call the watershed feeding our basin of attraction the Laniakea Supercluster.” In other words, within the basin of attraction that is used to describe Laniakea, galaxies flow toward a “Great Attractor” at its dense center, while in the neighboring supercluster of Perseus-Pisces, galaxies flow toward its attractor.

The use of attractor concepts in describing superclusters is another example of the trend toward systemicity across numerous fields of contemporary science.

Indeed, per a 2013 article on complex systems in The Encyclopedia of Earth: “As Science has begun to ask where the enduring features of nature come from and how they work, the answer seems to be ‘complex systems’. Every kind of thing and event seems to require them.”

A conversation on “clearing”

Portland-based artist Dana Lynn Louis has a wonderfully immersive show called “clearing” at the Lewis & Clark Hoffman Gallery, on exhibit until December 14.

On the afternoon of November 16, there will be an immersive conversation as well.

Please join us for a facilitated dialogue on “clearing,” the subject of the 2014 Hoffman Gallery show by Dana Lynn Louis. This afternoon of conversation will feature a panel discussion with Ms. Louis, followed by small-group discussions in which you are invited to participate. Together, we will explore the varied meanings of clearing – as understood through our professional practices, through our personal experiences, and through our impressions of the artwork on exhibition.

In particular, we hope to trace links between art, social justice, and the natural environment.

Panelists include: Kathleen Maloney (legal consultant, American Society for the Positive Care of Children; professor in international criminal law, Lewis & Clark), Ethan Seltzer (professor in the School of Urban Studies and Planning, and interim director for the School of Art+Design, Portland State University), Howard Silverman (instructor in systems thinking, Pacific Northwest College of Art). The afternoon’s facilitator will be Tod Sloan (professor of counseling psychology, Lewis & Clark).

More info.

Discussing change at NYU

This weekend I’ll be teaching at NYU’s Interactive Telecommunications Program (ITP). Here’s the syllabus (pdf) for the workshop, Getting Good at Change: Systemic Thinking and Practice.

Gregory Bateson, designer (slides)

I’ve been writing about design for a chapter in the SAGE Handbook of Action Research (3rd Edition, to be released next year). Design, that is, in the broad sense. Design as “plan[ning] for something new to happen,” per Nigel Cross’s 2011 book, or as “creat[ing] possibilities,” per Klaus Krippendorff’s 2007 paper.

So when I recently re-watched An Ecology of Mind, Nora Bateson’s documentary film about her father, I couldn’t help but think about Gregory Bateson as a design extraordinaire.

These are my slides for a talk with Jeff Bloom’s class on An Ecology of Mind, in the College of Education at Northern Arizona University.

Margaret Mead’s evolutionary clusters today

Dave Witzel's photo of Mead t-shirtIn my experience, the famous Margaret Mead quote elicits widely divergent reactions.

Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has.

Some find it inspiring, but I’m pretty skeptical. So I was delighted to see the photo at top, in which the quote is hilariously dissected on a t-shirt. (From a tweet by Dave Witzel, reprinted with permission.)

At the same time, the claim by the t-shirt’s creator that Mead’s “writings contain nothing similar” caught my attention. To be sure, the attribution is disputed. Still, Mead did write about these topics. How similar is similar? You be the judge.

Glancing through Mead’s 1964 Continuities in Cultural Evolution, the primary theme is indeed the significance of the “small group” in the processes of cultural change. To get a sense of what the book is about, I’ll suggest a comparison. Think of it as a 60s version of Steven Johnson’s Where Good Ideas Come From.

Like Johnson, Mead’s sensibility is evolutionary. She’s writing about how cultures evolve, not about how activists might intervene to “change the world.” In a word — today’s omnipresent buzzword — both Mead and Johnson are in search of innovation. They wonder and examine what types of cultural contexts afford the rapid emergence of social innovations.


If we are indeed to participate in evolution not merely by creating new technology, new medical techniques, new kinds of foods, and new forms of communication, but more specifically by participating in the very process of cultural creation, what hope does our accumulated experience of the last thirty years give us?

Today, our experiences have accumulated further. Johnson can draw from post-Mead research on complexity theory (e.g., the adjacent possible) and network theory (e.g., strong and weak ties).

Still, Mead and Johnson come to strikingly similar conclusions. Examples of good environments for incubating good ideas, according to Johnson: the lab meetings where researchers exchange information (e.g., in Kevin Dunbar’s research), Freud’s salons, Paris cafés.

Mead’s version:

I find myself returning to the model of the city or the great university and to the model of the meeting place to which certain people go often enough so they may hope to meet one another but not so often that the element of surprise and excitement is lacking. In the modern American setting, seminars and small shared projects (provided these do not become a new set of confining walls within which development is subordinated to the timely completion of the project) replace the cafés and coffee houses that we have never been able to reproduce.

Fifty years later, the city is widely celebrated, America finally has coffee houses, and designing for creative interactions has become an industry in itself. I wonder what she’d think.

Here’s the key quote from Mead, the one about the small groups that she called “evolutionary clusters,” the one that’s probably closest to the bumper-sticker quote:

The unit of cultural micro-evolution is a cluster of interacting individuals who within the special conditions provided by period and culture make choices which set a direction — a channel — in which events tend to flow until other points of divergence are reached.

Similar? I love the t-shirt regardless of the similarities I see.

Does the concept of clusters place greater emphasis on strong ties than Johnson did? Seems that way to me. Certainly, network theory highlights “the strength of weak ties.”

As for Mead’s personal clusters, two are about to gather again. Today begins the 58th meeting of the International Society for System Sciences, next week is the 50th anniversary of the American Society for Cybernetics. Not changing the world, that’s for sure. “Making choices [that] set a direction” is ambitious enough for any group of thoughtful, committed citizens.

There’s more about the quote at the website of the defunct Institute for Intercultural Studies, which Mead founded, and more about evolutionary clusters in Steve Joshua Heims’s The Cybernetics Group, which tells a story of the Macy Conferences, where Mead was a key participant.

spectroscope, The British Library

I’ve posted an article on Medium:

Jill Lepore’s popular essay in The New Yorker, “The Disruption Machine: What the Gospel of Innovation Gets Wrong,” requires some annotation.

More >>

Image: spectroscope, The British Library, on flickr

A simple model of knowledge production

Peter Chekcland: Knowledge production

The flux of everyday life — both physical and mental — surrounds and subsumes us. Amidst this flux we find ourselves immersed in life’s situations.

Some situations are satisfying, others less so. These less-satisfying situations are perceived as areas of concern or opportunity.

Perceiving an area of concern or opportunity, and developing a theory for learning about or effecting change in this focus area is the beginning of the process of knowledge production.

This process might be take the form of research, inquiry, and/or engagement; and this process — based on theories, embodied in practices, and applied to an area of concern or opportunity — yields learning about all three: the theories, practices, and focus area.

That’s my basic re-telling of Peter Checkland’s “learning for action” narrative.

The simple model above is adapted from Checkland’s 1985 paper, “From Optimizing to Learning: A Development of Systems Thinking for the 1990s.” It’s also given prominence at the beginning of Michael Jackson’s 2000 book, Systems Approaches to Management — and used to good effect, for it communicates much in its simplicity.

Whereas Checkland used the model to describe a shift in practice or methods, from hard to soft, from “optimizing to learning,” Jackson took a broader view. He used it to describe shifts in the the nature of science itself: from knowledge production in-service-to-theory to knowledge production in-service-to-action.

These days, such approaches are often called transdisciplinarity or action research.

From the introduction to 2008′s The SAGE Handbook of Action Research: Participative Inquiry and Practice:

[T]he primary purpose of action research is not to produce academic theories based on action; nor is it to produce theories about action; nor is it to produce theoretical or empirical knowledge that can be applied in action; it is to liberate the human body, mind and spirit in the search for a better, freer world.

>> See more models in the gallery.

Grappling with climate emotions

In recent media about climate change, a couple of voices and emotions linger with me.

Here’s one, from a commenter on the June 3rd Diane Rehm show about new US policies on carbon dioxide emissions: “It’s frustrating that there is no answer on how much CO2 reduction is needed to halt global warming.”

We don’t hear the actual voice, because Diane reads out the commenter’s written words. Still, the raw sentiment comes through loud and clear.

How would you respond to this person?

One might focus on “how much.” Tell the story of 350 (parts per million of CO2 in the atmosphere) and that current levels are already at 401.28 (June 8th Scripps reading from Mauna Loa).

Or one might focus on the word “halt” — a problematic word for describing a process that will continue for millennia.

My sense, though, is that the word to start with is “frustration.” This emotion needs to be acknowledged and engaged.

Easy to say from the sidelines or in hindsight perhaps. Diane’s guest, Frances Beinecke of the Natural Resources Defense Council, responded (~36:20), “I don’t think the number is as important as the trend.”

In one sense, this is a strong response. Talking about trends puts the emphasis on action. And in fact the trend has already turned for US energy-related CO2 emissions.

Still, while talk of numbers, processes, and trends might work for some people, we’ve got to learn to better speak to people’s emotions as well.

Which brings me to the other lingering voice I mentioned, the voice of atmospheric scientist Katharine Hayhoe, dealing with her own emotions on the TV series Years of Living Dangerously: “I naively thought I would study climate science until we fixed the problem, and then I’d go back to astrophysics. That was a long time ago.”

Resilience 2014 master class

If you’d like to check out the recent Resilience 2014 conference, this video embedded above offers an inside look at the interdisciplinary conversations.

Social anthropologist Melissa Leach, economist Luca Alinovi, and ecologist Brian Walker each begin by describing the influence of resilience thinking on their work. Leach focuses on the relationship between resilience and the STEPS Centre pathways approach. Alinovi relates his efforts at bringing a resilience perspective into the Food and Agriculture Organization. Brian Walker thinks back forty years to recall his reaction to Buzz Holling’s landmark 1973 paper.

These introductions begin at 16:00 of this 1:45:00-long video and are followed by questions from the PhD students gathered for the evening’s “master class.”

Here are a couple of segments that caught my attention.

Brian Walker, responding to the question: How do you understand and elicit the mental models of participants about the ecosystems they are involved with? (~50:00)

In the studies that we are doing with groups, where we try to elicit from them what their mental model is of the system they are working in, we begin by asking: What is it that you value in the system? What does it produce? Or what does it have that you particularly value?

Then we use, deliberately, the word identity. What gives that system its identity and makes it somewhat different to some other system? And that combination of trying to figure out a limited set of values — because you can’t have a long one — and what is the identity of that system, that is a first way in.

And another way that we then go beyond that — I don’t know if you’ve come across the notion of state-and-transition modeling. You ask: What is the current state of the system now? Tell us what it is now, in terms of those values you really value. And then: What other states could it be in? Could it be in a better state? Could it be in worse states? And then you start asking: What would cause it to go from one state to another?

Out of that, you start to get the dynamics, the mental model that people have. [For example] you would need to have a long drought before it could go from this state to that. Or if you had a big fire, you could get it from there to there. So you ask them what is it that would move it from this state to this other state you said it could be in.

You’ve got to elicit from them the dynamics and the processes that are involved. And gradually what comes out of this is an iterative process of developing a mental model of the system.

Melissa Leach, responding to the question: What if good policy design fails to result in good policy implementation? (1:09:20)

The way that I think about policy … has not been to make a big distinction between design and implementation. That’s the standard way that policy processes are thought about: there’s design, and implementation, and then evaluation, and then sometimes you get a feedback.

Whereas I think if we look at the way policy happens in the real world, it’s a much more iterative process, where feedbacks between what’s happening on the ground and what’s happening in design are much more constant, much more interactive. And often policy is de facto made, not by people sitting in offices, writing policy documents, but by what’s happening on the ground.

I find the literature on street-level bureaucrats and field-level bureaucrats very interesting, because this actually shows the agency of agricultural extension workers or urban sustainability planners, or front-line medical workers in actually de facto making policy, in a way that is sometimes much more responsive to local realities — and can sometimes feed back up into higher level decisions.

So I think one of the things one needs to do to make things implementable is to start with implementation, start with the practices. And then ask how good practices, which are sometimes a bit deviant from the norm, can be made more normal, can be institutionalized. And how you can get those channels of knowledge and practice working up from the grassroots, from the day-to-day practice, which is very engaged with local knowledge and realities on the ground — how those areas of wisdom and discretion can feed back up into shaping implementable, designable policies.

That would be one response.