Complexity/chaos stories: Butterflies, keystones and climbers

Don't read this post! Read the improved version, published as "Are We Ready for Complexity?" in the Journal on Policy and Complex Systems, Spring 2018 issue. Or read this PDF version.

If you want to read the original, unimproved version of the paper, you can go on and read the rest of this blog post.

Since I posted some thoughts about complexity a while back, I've been surprised both by the number of people who have been interested in what I said (and encouraged me to write more), and by the degree to which I find myself wanting to write more. I still have much to write about narrative, but I also seem to want to write more about complexity as it relates to sensemaking and decision support. Since this blog is supposed to be about narrative, I keep feeling a need to apologize whenever I write about complexity.

But really there is nothing to be sorry for. My work on the "listening side" of narrative centers on the place where stories and patterns come together. Narrative incorporates complexity because stories self-organize into emergent patterns, and complexity incorporates narrative because complex systems are historical systems. I remember when I first realized this, and what a rush it was to discover synergy between two fields I had come to love. Thus, dear reader, henceforth I resolve to stop apologizing for combining these topics!

So. After discovering both the encouragement and the motivation to write more about complexity, I began to think about what I would like to write. Immediately I thought of some curious things I've observed about the way people talk about complexity and chaos, mainly outside of science.

I first encountered these fields in graduate school studying ethology, and even participated in them a little (I presented a paper at the first Conference on Simulation of Adaptive Behavior in 1990). A decade later, I came round to complexity and chaos again through organizational narrative and sensemaking. I was amazed to discover that non-scientific exports from these fields had been transformed in ways that, to me, seemed to reduce their utility in practical application. I've always felt a need to point out these transformations and help people gain the benefits I think can be derived from moving past them, but I never got around to writing anything about it before. So I've made myself a list of ten such transformations and plan to go through them one at a time, not continuously but occasionally, hopefully giving people some food for thought along the way.

The butterfly and the underbutterfly

Butterflies

I begin with the butterfly effect. Many know the story of how meteorologist Edward Lorenz in 1961 reran his simple weather simulation, and for convenience copied the starting values of some variables from a previous printout. Because of rounding in the printout, he left the last few digits off one of the variables. Lorenz went to get a cup of coffee and returned to find the repeat simulation had generated a vastly different weather pattern. Those few digits altered the trajectory of the simulation dramatically. Lorenz called this phenomenon "sensitivity to initial conditions," meaning that small differences at the start of a process (one with a particular set of chaotic characteristics) could be amplified into large differences later on.

Lorenz was not the first to encounter this phenomenon. The point was over a century old when he made it. His statements are very similar to those made by mathematicians such as Maxwell, Poincaré, and Duhem in the latter part of the 19th century. W.S. Franklin wrote in 1889, in a review of a book by Duhem, that

Long range detailed weather prediction is therefore impossible, and the only detailed prediction which is possible is the inference of the ultimate trend and character of a storm from observations of its early stages; and the accuracy of this prediction is subject to the condition that the flight of a grasshopper in Montana may turn a storm aside from Philadelphia to New York!

But while Lorenz did not discover the possibility of this sensitivity, he was the first to create it in practice. Duhem would have been as surprised as Lorenz to find such unpredictable systemic behavior in a simple repetition of a handful of calculations.

Even though the story of the butterfly effect started a century before, a second parallel explanation of the results, a second story, began to form soon after Lorenz first spoke about the issue in public. It is this second story I want to draw your attention to.

Lorenz's first talk on the topic in 1972 was titled "Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" His answer was not "yes" but an emphatic "impossible to say." Here are some excerpts from his talk (it is in an appendix in his book The Essence of Chaos).

Lest I appear frivolous in even posing the title question, let alone suggesting that it might have an affirmative answer, let me try to place it in proper perspective by offering two propositions:

1. If a single flap of a butterfly's wings can be instrumental in generating a tornado, so also can all the previous and subsequent flaps of its wings, as can the flaps of the wings of millions of other butterflies, not to mention the activities of innumerable more powerful creatures, including our own species.

2. If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.

... The question which really interests us is whether ... two particular weather situations differing by as little as the immediate influence of a single butterfly will generally after sufficient time evolve into two situations differing by as much as the presence of a tornado. In more technical language, is the behavior of the atmosphere stable with respect to perturbations of small amplitude?

The paradigm-shaking element of these statements is that it had always been supposed that if a person could know everything there is to know about everything, that person could predict the future with perfect accuracy. This supposition had been questioned by Duhem and others, but only in a fanciful way, as though there might be small exceptions to the general rule that omniscience guarantees prediction. Lorenz's feat (or luck) was to demonstrate that omniscience does not guarantee prediction even in a small, simple simulation.

In Chaos, James Gleick describes the butterfly effect perfectly:

[S]uppose the earth could be covered with sensors spaced one foot apart, rising at one-foot intervals all the way to the top of the atmosphere. Suppose every sensor gives perfectly accurate readings of temperature, pressure, humidity, and any other quantity a meteorologist could want.... The computer will still be unable to predict whether Princeton, New Jersey, will have sun or rain on a day one month away. At noon the spaces between the sensors will hide fluctuations that the computer will not know about, tiny deviations from the average. By 12:01, those fluctuations will already have created small errors one foot away. Soon the errors will have multiplied to the ten-foot scale, and so on up to the size of the globe.

Now let me quote a few lines from a few business books on complexity. This is from Uri Merry's Coping With Uncertainty:

The inescapable conclusion is reached that man is living in a world in which under certain conditions, tiny causes can have enormous effects. This is called the butterfly effect.... The flapping of the wings of a butterfly in Hong Kong can affect the course of a tornado in Texas.

From Jeffrey Goldstein's The Unshackled Organization:

With all of these nonlinear interactions, it is no wonder that the weather is said to include the extremely nonlinear "butterfly effect" made famous by chaos theory. The butterfly effect refers to how air currents from a butterfly flapping its wings in Asia are amplified to influence the weather in North America!

From Margaret Wheatley's Leadership and the New Science:

Edward Lorenz, a meteorologist, first drew public attention to this with his now famous "butterfly effect." Does the flap of a butterfly wing in Tokyo, Lorenz queried, affect a tornado in Texas (or a thunderstorm in New York)? Though unfortunate for the future of accurate weather prediction, his answer was "yes."

From T. Irene Sanders' Strategic Thinking and the New Science:

The Butterfly Effect describes the image of a butterfly flapping its wings in Asia and causing a hurricane in the Atlantic, which is a metaphor for how small changes or events create complex results.... A small change in the initial conditions of one system multiply upward, expanding into larger and larger systems, changing conditions all along the way, eventually causing unexpected consequences at a broader level sometime in the future.

These excerpts, and almost all popular and business interpretations of the butterly effect, transform a statement about uncertainty to one about certainty. The second story changes the butterfly effect from tiny actions piling up in unpredictable ways to tiny actions having predictable and controllable impacts. I have taken to calling this second story the "underbutterfly effect," because the butterfly in these versions is a powerful underdog who changes the world, not one of millions of other butterflies (not to mention innumerable more powerful creatures) whose feeble flaps are lost in the sea of uncertainty in which we live.

Finding the exact place where the underbutterfly first flapped its wings would take more time than I have to spend on this, but my suspicion is that it arose almost immediately. In Chaos, Gleick describes an incident where Lorenz explains the butterfly effect to his colleague Robert White.

"Prediction, nothing," he said. "This is weather control." His thought was that small modifications, well within human capacity, could cause desired large-scale changes.

Lorenz saw it differently. Yes, you could change the weather. You could make it do something different from what it would otherwise have done. But if you did, then you would never know what it would otherwise have done. It would be like giving an extra shuffle to an already well-shuffled pack of cards. You know it will change your luck, but you don’t know whether for better or worse.

Another curiousity is that even though Gleick gives a wonderfully useful description of the butterfly effect in his metaphor of sensors covering the earth, he also tells the underbutterfly story, perhaps without noticing it. He says:

[S]ensitive dependence on initial conditions was not an altogether new notion. It had a place in folklore:

"For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost!"

This particular bit of folklore does not in fact communicate the impossibility of prediction. It exhorts people to action with the explanation that small actions can have large effects. Nowhere can I find this proverb used to convey the impossibility of knowing which of the millions of horseshoe nails (not to mention innumerable more powerful objects) might have been involved in the loss of the kingdom. A web site on "nursery rhymes, lyrics and origins" says the proverb is "often used to gently chastise a child whilst explaining the possible events that may follow a thoughtless act." The proverb is not used to gently explain to a child that predicting complex patterns in the long term is impossible.

Here is another curious pattern. Did you notice in those quotes from business books that the underbutterfly lives in Asia? Don't you think it's strange that four completely unrelated (but all US) authors have told the underbutterfly story as Asia impacting North America? Lorenz's original talk had it going from Brazil to Texas -- but Lorenz himself didn't write that title. The editor who did name the talk said later that he chose those names primarily for their alliterative value (butterfly-Brazil, tornado-Texas). Lorenz had it as a seagull before that talk, and didn't mention any locations. And the 1889 book review I cited above had the grasshopper effect going from Philadelphia to New York. Why the move to Asia?

Curious about this, I searched Google for the phrase "a butterfly flapping its wings in" and looked at the first 100 links given. Here is what I found.

As you can see, most of the butterflies flap their wings in South America or Asia, and most of the tornadoes spin in North America. I wrote, and then deleted, some rampant speculation on this pattern, having to do mostly with the US-centric internet and the location of mystery in foreign lands ... but you can draw your own conclusions, and this is not my central point anyway. My point is that people have taken a statement about uncertainty and transformed it into one about certainty.

The keystone and the topstone

Keystone

In 1969 Robert T. Paine introduced the idea of a keystone species to ecology. Paine discovered this phenomenon in an experiment during which he removed a single species of sea star from a small area of shoreline and found that it had far-reaching effects on species diversity. Most importantly, the effect produced by its removal was out of proportion to its relative abundance in the community. This is a central element of Paine's keystone species concept. Other species which have high abundance and large impacts were termed "key" or "dominant" to distinguish them from the smaller keystone species.

Keystone species are also by definition difficult to discover without observing what happens when they are removed. As Paine said in his original 1969 paper on the phenomenon:

Within both these fairly or very complex systems the species composition and physical appearance were greatly modified by the activities of a single native species high in the food web. These individual populations are the keystones of the community's strucutre, and the integrity of the community and its unaltered persistence through time, that is, stability, are determined by their activities and abundance. They may be unimportant as energy transformers. The two keystone species discussed above have little in common. Pisaster is abundant and is somewhat of a trophic generalist; Charonia is rare and a food specialist.... Both are starfish feeding on a variety of prey .... The significance of these carnivores could not have been guessed beforehand, since other carnivores coexist with them.

As with the butterfly effect, this story is about a system in which complex relationships among small influences produce large difficulties in a priori prediction. As with the butterfly effect, a second story about keystone species arose, and again it favors certainty over uncertainty. Essentially, what I've come to call the "topstone" story discards the more unpleasant parts of the keystone concept having to do with minor players whose influences only become apparent in retrospect. What I'm calling a "topstone" species is one people call a keystone species but which is actually dominant. It is unfortunate that Paine chose the keystone analogy, because a keystone is usually smaller than the other stones in an arch, which fits the first story, but it is also above other stones in the arch, which fits the topstone story.

As with the underbutterfly story, the topstone story began to surface soon after Paine started publishing papers about his concept. What seems to have happened is that people involved in wildlife conservation started trying to identify keystone species in order to wisely use limited conservation budgets. Political, cultural and special-interest complexities joined the mix, and the keystone species concept widened and weakened as a result. For environmental study, retrospective discovery might suffice, but for environmental action, people wanted certainty.

Consider this definition of the concept in a 1993 paper:

[T]here are two hallmarks of keystone species. First, their presence is crucial in maintaining the organization and diversity of their ecological communities. Second, it is implicit that these species are exceptional, relative to the rest of the community, in their importance.

This definition discards the element of disproportional effect. In the mid-90s a group of scientists self-dubbed the "Keystone Cops" were concerned enough about this erosion of the concept to convene a special session at a UN conference. The Keystone Cops restored the original concept to intellectual rigor by redefining and stabilizing it. The new definition was as such:

[W]e define a keystone species as one whose impact on its community or ecosystem is large, and disproportionately large relative to its abundance.

Challenges in the Quest for Keystones. Mary E. Power, David Tilman, James A. Estes, Bruce A. Menge, William J. Bond, L. Scott Mills, Gretchen Daily, Juan Carlos Castilla, Jane Lubchenco and Robert T. Paine. BioScience, Vol. 46, No. 8 (Sep., 1996), pp. 609-620.

(I like to provide links where I can, but sometimes it is impossible.) By 1999, Piraino and Fanelli spoke only of the new, narrower scope of the term:

[T]hose species driving ecosystem processes or energy flows are generally referred as "key" species, but only a few of them are keystones. Putting keystones and key species in the same melting pot ... should be avoided. Therefore, trees and bisons are not keystones, just as the original keystone species identified by Paine was not the dominant mussel, but its starfish predator.

Few ecologists now use the wider, weakened term, but some still complain about its difficulty of application. This article about the ecology of the Chesapeake Bay explains:

An additional problem with these economic approaches is that they require a stable, non-changing predicate set of problems to work. For example, the bioeconomics model is premised on the idea that "the most natural state of nature was balance." ... Although the bioeconomics model has endured, its foundational principle that nature is a "perfectly manageable system of simple, linear, rational order" has not. That premise has been replaced by a much messier picture - [i]nstead of order happily emerging out of chaos, it was chaos that kept boiling up from the darkness, breaking down order" - throwing into sharp relief the shortcomings of that model.... Even with respect to the preservation of biodiversity - the only ecological imperative and management goal most ecologists can agree to - there is uncertainty. For example, scientists disagree about which are the "keystone species," the extinction of which "would bring down other species with it, possibly so extensively as to alter the physical structure of the habitat itself."

Hope M. Babcock, Administering the Clean Water Act: Do Regulators Have "Bigger Fish to Fry" When it Comes to Addressing the Practice of Chumming on the Chesapeake Bay?, 21 Tul. Envtl. L.J. 1-50 (2007).

Even though the topstone story was abandoned by ecologists, it is the one chosen for analogy by almost all non-science uses of the keystone species concept. Again a few quotes from the business literature. In The Keystone Advantage, Marco Iansiti and Roy Levien describe the keystone species concept thus:

[T]he literature on biological ecosystems ... suggests that a species that serves as a hub in food webs or other networks of ecosystem interactions, can improve overall chances of survival in the face of change by providing benefits to the ecosystem as a whole. This literature identifies "keystone species" as having specific characteristics that produce such benefits for the ecosystem and its members. Removal of biological keystones can have dramatic cascading effects through the entire ecosystem, while removal of other species, even species involved in many interactions, can have little effect beyond the loss of those connections.

In other words, Iansiti and Livien interpret "keystone" to mean simply "key", and this book was written nearly ten years after the Keystone Cops accomplished their coup. Iansiti and Livien do make this side note:

The ecological literature contains many conflicting definitions of the term 'keystone' and some debate the extent of its relevance.... Its original use was quite narrow ... but current usage sometimes ranges to the indiscriminate; here we use the term in its most neutral and least technical form: a keystone is simply a species that governs most important ecosystem health, often without being a significant portion of the ecosystem itself.

Often without being a significant portion: but not always. Iansiti and Levien go on to apply this version of the concept to business not by talking about "species" interactions, but by talking about keystone strategies that essentially involve being well connnected, as "hubs":

A keystone strategy is an operating strategy that improves the overall health of the ecosystem and, in so doing, benefits the sustained performance of the firm. The central feature of this strategy is its focus on managing external resources, shaping the structure of the external network, and maintaining and harnessing external health....

The successive waves of transformation that have spread through the software industry (starting with the rise of the PC, and followed notably by the rise of the GUI and the rise of the Internet), for example resulted in significant changes in the software ecosystem, but its overall structure, productivity, and diversity have been unhurt, and its keystones, among them Microsoft, IBM, and Sun, have persisted.

Similarly, keystone species often displace or hold in check other species that would otherwise dominate the system ... This is what the IBM-Microsoft-Intel ecosystem achieved with respect to Apple.

None of these software giants could in any way be called a keystone species by its original or current definition. Not only are they large in all possible biomass equivalents, but their importance to the system is easy to see up front.

Here is another example, from James F. Moore's The Death of Competition:

Recent work in community ecology has dwelled on topics like "keystone" species, the most critical of the species in an ecosystem.... Wal-Mart is not just another business within its environment, and it should not expect to be treated as one.... Wal-Mart hardly has a choice about taking up this mantle. It has become a keystone species -- and the center of one of the most important ecosystems on its continent.

Again one of the largest companies in the world is given as an example of a keystone species. Similarly, Stephan Gothlich and Hagen Wenzek say:

The keystone strategy derived from the business ecosystem model poses a feasible alternative to aggressive dominator behaviour with reasonable prospects of success since they nourish diversity and reduce the dangers of ecosystem-wide spread of failures and contagion.

What this seems to say is that the big guys can still be keystones, as long as they play nice. And again, from a paper by Ivan Matutinovic:

[T]he number of firms in an economy that have a large number of incoming links (suppliers) or outgoing links (buyers) will be relatively small. These firms, which Albert Barabasi (2002) termed "hubs," are in fact analogous to keystone  species in ecosystems and they play a special role in the stability of an economic network. They can be found among top Fortune 500 manufacturing firms, and a myriad of medium and small businesses depend on their operation.

I. Matutinovic, 2005. "The Microeconomic Foundations of Business Cycles: From Institutions to Autocatalytic Networks." Journal of Economic Issues, Vol 39, No.4., 867-898.

In the business literature, it appears to me that the keystone species concept has been appropriated almost as an apologia for the dominance of currently dominant firms. In the same way as the concept was widened to promote economic or cultural favorites among biological species, it has been used to promote dominators in the business world. It is not unreasonable to help metaphors travel from one world of inquiry from another; but choosing only one meaning and failing to mention others, especially when the others have a greater consensus in the original field, seems disingenuous.

A better candidate for a keystone species might be the one in this story (and thanks to my husband for thinking of it). From a 1995 industry report on semiconductor manufacturing:

A recent example illustrates the problems that can arise when diverse sources are not available for critical materials. One Japanese company, Sumitomo Chemical, provides over 50 percent of the world requirements for epoxy resin, which is used in semiconductor manufacturing. Over 90 percent of the world requirement for epoxy resin is supplied by Japanese companies. A July 1993 explosion within the Sumitomo plant curtailed production, and as a result has slowed several semiconductor manufacturing plants that rely on this source of resin. A shortage (real or imaginary) of DRAMs has resulted, and the price of these chips has escalated to as much as 150 percent of the price just prior to the explosion.

And from an interview with an official of the Atari corporation around the same time:

[T]he increases in RAM prices were pretty artificial anyway. There was a report that a major factory was destroyed in an earthquake in Japan, but that turned out to be an epoxy factory...not a chip site. And ... we have benefitted from Apple's problems. As a result of their sales slump, they have cancelled some huge orders for parts (like DRAM), which naturally made the product available to other companies!

This epoxy company was a perfect example of a true keystone species in the semiconductor ecosystem at that time, both because of its impact on the industry and because of the difficulty in identifying it as a keystone species beforehand. (Note that I say "was" because keystone status is not a fixed atttribute of a species. It is more a property of the entire ecosystem, and it can change at any moment. A keystone species is less like a constant force and more like one of those times when the astronomers tell everybody to rush outside in the middle of the night and have a look at how Mars and Venus are lining up next to the archer's knee. If that ever happens.) The uncertainty apparent in the "increases were artificial" claim is also indicative of a possible keystone species: generally speaking, if the role of such a species is easy for all to see (for example if it represents a "hub") it is not likely to be a true keystone. Note also the reference to Apple, which indicates it was acting as a dominator, with a slump in its sales (presumably not a huge one) overwhelming smaller trends.

Another potential keystone-species pattern might be that of the threatening helium crisis (yes, this is from my husband again, it's not my area). Apparently we are close to using up the helium that has built up on the earth over 4.5 billion years. According to a 2008 article on ScienceDaily.com:

Helium plays a role in nuclear magnetic resonance, mass spectroscopy, welding, fiber optics and computer microchip production, among other technological applications. NASA uses large amounts annually to pressurize space shuttle fuel tanks.

 The article quotes Lee Sobotka, a professor of chemistry and physics at Washington University in St. Louis:

"Helium is non-renewable and irreplaceable. Its properties are unique and unlike hydrocarbon fuels (natural gas or oil), there are no biosynthetic ways to make an alternative to helium. All should make better efforts to recycle it.... Up to now, the issue often hasn't risen to the level that it's important. It's a problem for the next generation of scientists. But it's incumbent upon us to have a vision, and tell it like it is — a resource that is more strictly non-renewable than either oil or gas."

To me at least, the business use of the keystone species concept seems remarkably similar to the underbutterfly pattern. True, the choice of the story's hero is the opposite: instead of the underdog, the top dog is championed. But the real champion in both of these second stories is certainty. The danger in repurposing the keystone story in this way is that real dangers like running out of critical non-renewable resources get swept aside.

The steadfast climber and the easy roller

Adaptive landscape

Still with me? I have one more pattern to place before you.

I first encountered Sewall Wright's adaptive landcape metaphor in college, and as a visual thinker I found it useful right away. Even though the metaphor is severely limited, many evolutionary theorists use it a visual shorthand for thinking about genetic change. The way the metaphor works is this. Populations are located in X and Y dimensions to describe their genetic makeup (in a radically simplified way). They exist on a landscape where the height of each point describes the fitness of the population with that particular XY combination of genetic variables.

Fitness may depend on many things: unalterable aspects of the environment, such as changing climate patterns; impacts of the population on its environment, such as the effect of beaver dams on the surrounding ecosystem; and epistatic relationships between variables, such that their co-occurrence either enhances or reduces their combined fitness. To put it more plainly, the landscape doesn't sit still. It reacts to changes in the population itself. So most people think of the adaptive landscape as "rubbery" and the locations of peaks as constantly changing.

Some speak of the "struggle" of a population making its way up to an "adaptive peak" on the landscape, but this is metaphorical as well. The struggle really just means that those closer to the peak have greater fitness, and we know they have greater fitness because ... they didn't die before they reproduced. Hence the struggle of all individuals to survive and reproduce is multiplied as the population as a whole endeavors to pass on its genes. Mutations provide the benefit of a "random walk" near the population's current location. Deleterious mutations are harmful and die out, but advantageous ones lead to increased fitness, which moves the population up the slope. But most mutations are small hops, so populations can easily get "stranded" on lower-fitness peaks because the valleys between peaks represent such low fitness that rarely will any population be able to cross them without dying out entirely. Generally the more rugged the landscape the more peaks will be available, and the more likely populations will be able to make the small jumps required to reach optimality. For a while.

When I used to think of the adaptive landscape, it made sense to link its peaks with the struggle of individual organisms to survive and reproduce. (That it is a struggle is not a controversial claim: just watch some nature videos. I watch a lot of these with my son. Every time I say, "Oh, the poor wildebeest," he says, "But the lioness has to feed her cubs!" We've taken to calling the most recent BBC series, Life, its opposite, as in, want to watch another episode of "Death"?) I even found support in my Catholic upbringing for the adaptive landscape: Yea, though I walk through the valley of the shadow of death, I will fear no evil. The adaptive landscape also conveyed a useful sense of uncertainty: a population at a peak would have an equal probability of descent in any direction.

When I returned to complexity through the organizational door, I was amazed to find people talking about "fitness landscapes" but referring to something quite different from what I was used to. They drew landscapes without peaks but with deep "wells" and "basins of attraction." For years I avoided the issue by avoiding the fitness term and calling the new things complexity landscapes, or just landscapes. But recently I finally scratched the itch to find out what caused this flip. And wouldn't you know it, it is a pattern very similar to the two patterns I mentioned above.

The explanation is that the field of physics also happens to use a landscape metaphor. It refers to energy and is called the free-energy or potential energy function, and physicists speak (variously) of potential energy surfaces and free-energy landscapes. The X and Y dimensions are similar in that they describe variables of interest, here of materials rather than populations. The height dimension in these landscapes is free energy, or energy available to do work and not lost to entropy (the light coming out of a light bulb, for example, rather than the heat -- unless you are after the heat, of course). Physicists use these landscapes to talk about optimization of processes so that the deepest wells of high entropy and low free energy can be avoided.

Stuart Kauffman may have been the first to consider the link between adaptive and free-energy landscapes in his book The Origins of Order:

The flow of an adapting population on rugged landscapes under the drives of mutation and selection is closely analagous to a physical system, such as spin-glass at a fixed finite temperature. These analogies are important because ideas from statistical physics are likely to prove generally useful in population-flow problems.... [At zero degrees] K, a spin-glass walks to a local energy minimum via fitter (lower-energy) one-mutant neighbors.... At a fixed temperature, a system with two quadratic potential wells separated by an energy barrier typically shows an exponential escape from the higher-energy to the lower-energy well.... In spin-glasses with complex potential energy landscapes, slow relaxation is manifest by a multiplicity of time scales of exploration of ever larger regions of configuration space. The parallels to population flow on rugged landscapes are clear.

The argument Kauffman seems to make is that three forces can be considered analogous: the force of natural selection; the increase in entropy specified by the second law of thermodynamics; and the force of gravity. The force of natural selection can be seen as similar to decay or gravity; thus picturing selection as the descent into a well or "basin of attraction" makes some sense. However, this is a confusing mixture of analogies. Increased fitness doesn't usually link with increased entropy, to begin with, life being considered at least partially an anti-entropic phenomenon. On the other hand, biological mechanisms such as mutation, sex, phenotypic variation, and genetically stable allele mixtures could all be seen as entropic processes. So it's not a clear mapping to begin with.

You could argue that whether selection is enough like gravity that increasing fitness can be portrayed going downward depends on your point of view. If you are looking at evolution as a whole, populations that don't move toward greater fitness don't figure in the equation, because they aren't around to complain. But if you are considering a particular population, even though natural selection does exert a constant force, so do genetic drift, gene flow and mutation. From the local point of view, populations are not so much drawn inexorably downhill by gravity alone as they are pulled in many directions at once. (Though I suppose friction might stand in for drift...) What bothers me is that translations of evolutionary theory to other spheres, such as the business world, are rarely about evolution as a whole. They are almost always about particular populations, meaning particular firms.

This is where I think the pattern I'm seeing fits with the other two patterns I've mentioned so far. Selection seen as rolling into a pit, or what I've come to call the "easy roller" story, is the second story of the adaptive landscape. When fitness rolls down into a well, selection appears not only more powerful than other evolutionary forces but more certain as well. Instead of a ball balanced precariously on a peak and facing a multiplication of possibilities heading in all directions, a ball near a well faces a collapse of possibilities to one still small point. To be fair, I don't think all the blame for this falls on Stuart Kauffman. He merely pointed out the similarity of the two systems and probably did not intend for everyone to flip the adaptive landscape as a result. Still, he did seem to set the ball rolling.

The thing I've noticed most in descriptions of the "fitness" landscape (nobody talks about the adaptive landscape anymore) is that the flipping is mentioned in a nonchalant, couldn't-possibly-matter way. I find this amazing, since height-value relationships are so strong in human communication. Didn't everybody read Metaphors We Live By? Here is an example explanation of the landscape flip from the Principia Cybernetica Web:

It is unfortunate that the convention in physics sees systems as striving to minimize a potential function, whereas the convention in biology sees systems as striving to maximize a fitness function. Although this tends to be confusing, the two types of representation are equivalent apart from an inversion of the sign of the function.

But an "inversion in the sign of the function," when people are thinking about the function, is not equivalent: it is quite different. This blog post has a useful visual explanation of the flip, but the author interprets the flip as useful, an argument with which I disagree. The post says holes seem more difficult to get out of; but if we remember what decreased fitness means -- death -- it's perfectly easy to perceive the danger in leaving a peak. I keep thinking of the sayings "it's as easy as falling off a log" and "it's lonely at the top."

At this point a few second-story examples from other fields are in order. From The Edge of Organization by Russ Marion:

According to Kauffman, the evolution of coevolution can be visualized from yet another perspective. Envision the fitness landscape turned upside down; now instead of peaks there are holes. What you get is called a potential energy landscape by physicists.... In a coevolving system of potential energy landscapes, actors perturb each other's landscapes and knock each other out of their holes. Imagine marbles on a vibrating potential surface. Typically they will pop in and out of holes, but as they work their way into ever deeper holes it gets increasingly difficult to pop them out. Eventually marbles find a hole so deep that the vibrations no longer dislodge them. Similarly, actors on coevolving landscapes are not allowed to rest on their laurels. They perturb one another; new actors enter the stage and existing ones leave it; and in the process, actors work themselves into deeper and deeper holes (or onto higher and higher peaks, if you're still imagining a fitness landscape).

Now let me rewrite the last part of that paragraph, but with peaks instead of wells:

In a coevolving system of adaptive landscapes, actors perturb each other's landscapes and knock each other off their adaptive peaks. Imagine marbles on a vibrating potential surface. Typically they will climb up to peaks and fall down again, but as they work their way into ever fitter peaks it gets increasingly difficult to leave them. Eventually marbles find a peak so high that the vibrations no longer dislodge them. Similarly, actors on coevolving landscapes are not allowed to rest on their laurels. They perturb one another; new actors enter the stage and existing ones leave it; and in the process, actors work themselves onto higher and higher adaptive peaks.

I see a few differences in these two mirrored descriptions of coevolution.

1. Coevolving species don't just knock each other off adaptive peaks: sometimes they give each other boosts.
2. A population that climbs to an adaptive peak is not just as likely to fall down again, because that means decreased survival. In fact, once a population attains an adaptive peak, no matter how small, it is difficult to move from it because of all that messy death around it.
3. No population is ever on a peak so high that vibrations can no longer dislodge it. Environmental catastrophe, mass migration, parasitism, disease, the list goes on and on. No adaptive peak can ever be entirely stable, but those deep wells certainly appear to be.
4. It is not true that the process of coevolution causes actors to work themselves onto higher and higher adaptive peaks. The best that can be said is that things change because of coevolution, and whether the change is adaptive or maladaptive depends on context and history.

Flipping the adaptive landscape upside-down opens the door to a different set of explanations about evolution, one that tends toward increased certainty and increased teleology, like when people say that a species evolved in some way "in order to" do something. But that's not how evolution works. All natural selection means is that in the story of any population, some organisms lived to reproduce and some died first, and the ones that lived were more likely to live, and we can see that because they ... lived. There is no purpose or goal or direction or gravity to it. It's all retrospective.

Here is a telling snippet from an online forum discussing the upside-down flip:

I'm not sure why Wright chose to describe 'fitness landscapes' upside-down from the physicist's convention.  Probably because the usual metaphor of evolution has species arising in the slime and progressing uphill.

Sewall Wright published his adaptive landscape metaphor in the 1930s, but the earliest mention I can find of free-energy or potential-energy landscapes is in the 1980s. (Please do correct me if I'm wrong.) When one metaphor predates another but is seen as "upside-down" from it, that is usually a strong indicator of cultural forces at work. Of course it is possible that a view of evolution as progress was behind the peaks in the adaptive landscape, but because up and down mean so many things, that doesn't mean it is the only impact.

One more and then I'm really done, I promise. This is from The Quark and the Jaguar by Murray Gell-Mann:

Biologists conventionally represent fitness as increasing with increasing height, so that maxima of fitness correspond to the tops of hills and minima to the bottom of pits; however, I shall use the reverse convention, which is customary in many other fields, and turn the whole picture upside-down.

Gell-Mann then gets into the difficulties of this flip, seemingly without realizing it:

If the effect of evolution were always to move steadily downhill -- always to improve fitness -- then the genotype would be likely to get stuck at the bottom of a shallow depression and have no opportunity to reach the deep holes nearby that correspond to much greater fitness. At the very least, the genotype must be moving in a more complicated manner than just sliding downhill.

That is precisely the problem with flipping the landscape: that when you do so, things that are in reality very complicated seem simple, and certain.

Unpopular stories

So, we have looked at three patterns in the interpretation of significant findings from the fields of complexity and chaos. The effect of each interpretation, though probably not its intent, is to increase certainty, or one might almost say provide comfort, in the face of unpredictability. And each interpretation, though at its strongest outside science, is also present in those directly confronting the face of complexity. Taken together, these interpretations present a picture to me of people holding up a screen to filter the truth to better fit what they can handle. They seem to be saying: "We are not ready to go there yet."

When I started researching this issue, I kept recalling a particular experience. It was one I had shortly after re-entering the complexity field through organizational narrative. Around the turn of the last century (I've always wanted to say that) I went to a systems thinking conference. It was exciting, as all conferences are. I watched the devotees chanting the mantras uttered by the keynote speakers; I learned the insider vocabulary; I free-associated at the dinners; I enjoyed the heady talks during our walks back to the hotel afterward. It was fun. On one particular day of the conference, I remember sitting in a room with about eight or ten other people, in a circle. We were all given a handout with a systems thinking flow diagram on it. On the diagram was a circle made out of two semicircular arrows connecting two boxes. One box was labeled "productive collaboration." (Or ... productive something. I've looked back through my papers and can't find it. I think it was collaboration.) The other box was blank. We were all asked to take a few minutes to sit quietly and write something in the other box. I wrote "unproductive collaboration."

After the few minutes, we went around the circle, and everyone showed their diagram to the group. I was amazed to discover that every other person had filled in the other square with something people could do to create productive collaboration. The boxes said things like "foster better communication skills" and "listen more" and "create productive dialogue." When we got around to me, I showed my diagram. There was dead silence. I felt a sense of  -- well, have you ever heard about what happens in an Amish community when people do things they are not supposed to? The community ostracizes them? I felt like that. There was a strong sense that the group ... sort of wanted me to go away. They didn't want to hear the story I told. They wanted to hear their story, where complex systems respond to the earnest efforts of good people. The story where the underbutterflies flap their wings in the dappled light of the fractal forest and change the world.

I was actually pretty happy with my diagram. I'm the proud owner of many and varied mistakes, and I've collected abundant evidence that unproductive -- well, anything -- can lead to more productive anything. I even have made up lots of cute aphorisms around it. Now that I'm finished, I'm ready to start. If you want to be patient, just wait a while and you will be. Forgiveness is a gift you give yourself. Happiness is a decision. Giving up has power. And so on. It seems to me to be a fundamental property of life itself: you have to go down to go up.

I've always remembered the day I encountered this strange, stony reception when I've thought about complexity and chaos. The people at this conference couldn't stop talking about fractals and bifurcations and flocks and "order for free" and all the lovely things we are supposed to get from complexity and chaos. But they didn't want the uncertainty part. (Note: I do not intend to disparage systems thinking itself by this story. What happened that day was not necessarily a reflection on the conference itself; it might have just been the mood in the room.)

If you think about it, this is not at all surprising. We have been conditioned since an early age to believe in this equation:

uncertainty + science = certainty

When we meet an equation like this:

uncertainty + science = more uncertainty

We react, and a second story arises. That can't be right. There must be another explanation. That's what Edward Lorenz said when his computer generated a new weather system based on what he thought were the same inputs. He called in the hardware engineers to find the broken vacuum tube.

This article on the underbutterfly effect says it well:

Pop culture references to the butterfly effect may be bad physics, but they're a good barometer of how the public thinks about science. They expose the growing chasm between what the public expects from scientific research - that is, a series of ever more precise answers about the world we live in - and the realms of uncertainty into which modern science is taking us.... It speaks to our larger expectation that the world should be comprehensible - that everything happens for a reason, and that we can pinpoint all those reasons, however small they may be.... "People grasp that small things can make a big difference," [a quoted scientist] says. "But they make errors about the physical world. People want to attach a specific cause to events, and can't accept the randomness of the world."

I had my own little experience with first and second stories about complexity. My master's thesis showed mixtures of "smart" and "dumb" simulated foragers to be more adaptive (in some circumstances) than a pure population of "smart" foragers. (To sum up the thesis in seven words: nobody goes there anymore, it's too crowded.) When I first showed the results of the simulation to my advisor, his reaction was like Lorenz's. "Oh," he said, "must be a bug in your code. Let me see, I'll fix it." He couldn't. It was a bug in science. Seeing that bug for myself was a turning point in my life. The funny thing is that I got the idea for asking the question (what would happen if everybody knew everything?) while I was lying incapacitated by a back injury for weeks, staring at the ceiling and thinking about foraging theory and complexity. Unproductive collaboration.

A generation, or two or three, to sink in

If people tell second stories about complexity because we aren't ready for the first stories,  I think our children are ready. In many of my narrative projects I ask people to rate the predictability of events in stories -- it's useful to map perceptions of stability and instability across conceptual space. I've noticed a pattern across several projects that older people are more likely to associate instability with negative outcomes in stories. Younger people are more likely to mark stories as both unstable and positive.

I was thinking about all this the other day while playing with my son, and two things happened that gave me food for thought. The first was that we watched the movie Clifford's Really Big Movie. It's a great movie, and it's in our pantheon now and will probably be watched many more times. One of my favorite parts of the movie is this lovely song, which my six-year-old understood and liked immediately. It goes, in part:

You've gotta get lost if you wanna get found
Gotta wind up to get unwound
Things only look up from down below
And I can't come home until I go

It only gets better after it gets worse
Happy ever after needs a scary part first
You've gotta fall off to get back on
And I can't come home until I'm gone

Doesn't that sound exactly like my productive-unproductive diagram that nobody wanted to see? And doesn't it sound exactly like the uncertainty of the butterfly, the keystone species and the steadfast climber? Why is it that such a piece of wisdom (and it is) fits perfectly into a children's movie but cannot enter into the things adults write for adults about big serious adult things? Is this not a problem?

I wonder if a true appreciation of complexity and chaos needs a new generation to really sink in. One my my husband's favorite books is Voyage to Yesteryear by James P. Hogan. In it, a ship filled with children travels to a new planet, and once there they create an entirely new society, with new expectations (mainly of a gift-based economy). When people from the parent planet arrive years later, the cultures clash. The Wikipedia page about the novel explains its motivation:

The inspiration for the novel was the contention that the ongoing conflict in Northern Ireland had no immediate practical solution, and could only be solved if the children of one generation were somehow separated from their parents, and hence did not learn any of their prejudices.

I don't much like that "separated from their parents" bit, but still, sometimes the really big ideas do need some time to sink in. I think we're on generation two on complexity and chaos, so maybe we need a few more.

Who are these stories for?

My second child-derived insight related to complexity revolved around the island of Sodor. For those who don't know, Sodor is where Thomas the Tank Engine lives. It is a strange world. The train engines are all alive, but they are bought, named, sold, and even killed at the whim of their human overlords, chief of which is Sir Topham Hatt. Many of the plots of the Thomas series (and there are hundreds) revolve around elaborate reward and punishment structures set up by Sir Topham Hatt and other humans. Engines who behave receive booming accolades and new coats of paint, which evidently is like loads of money would be to us. Engines who misbehave are shut up in their sheds and abandoned, or worse, labeled "unuseful" and sent to the dreaded smelter. In all of the Thomas stories I have seen and read, nobody is actually melted down, and Sir Topham Hatt hotly denies any such thing, but there are many stories of old trains narrowly avoiding forced euthanasia, and certainly the pervasive fear of the smelter must be based on something. There are many other fascinating sociological aspects of the Thomas series (such as the clear upper-class and lower-class facial characteristics and behaviors evident in the different engines -- take a look at the straight versus snub noses), but those are less relevant to the matter at hand.

So the other day we were discussing this system of institutionalized slavery, as we often do, and we had generated a story in which the engines had staged a cleverly conceived coup when Sir Topham Hatt was away on one of his many holidays. The engines set up an alternative system where each engine had perfect autonomy and could decide whether it wanted to shunt cars, pull coaches, or deliver cargo that day. All the engines conferred regularly as to how to meet the demands of the railway customers together. New coats of paint were administered by a self-painting system in which engines could simply chuff in whenever they felt the need. Shed doors were controllable solely by the occupants. The smelter was itself melted down and transformed into a recycling center, and never again would an old engine face the fear of death from unnatural causes. The engines welcomed Sir Topham Hatt back and offered him an advisory sinecure, which he gratefully and humbly assumed (bless him).

So while we were in the middle of this, I suddenly had a realization. Nobody writes books about complexity for the engines. They write them for Sir Topham Hatt. And Sir Topham Hatt does not want to hear that the science of complexity adds rather than removes uncertainty, or that things will still work if the railway director is demoted to a perfunctory advisor. The people in charge aren't going to buy a book about complexity if it doesn't give them a way to stay in charge.

According to my surely-biased reading, there are three ways the authors of business books about complexity and chaos provide reassurance to those in charge. One is to drain the power out of the major discoveries by highlighting the second stories, which do exist in science and so can be called scientific: the underbutterfly, the topstone, and the easy roller. The first stories can be waved away as "internal disputes" that don't matter.

The second method of making complexity palatable to those in charge is to make it seem magical. That is why the phrase "order for free" is so wildly attractive in these books, and why people love to throw around terms like "strange attractor" and "fitness landscape" and "coevolution" -- because they are magic words of power that seem to promise something for nothing. Even "nonlinear" effects are spoken of mainly for the idea of something small going in and something big (and beneficial to the reader) coming out. I see this rose-colored view of complexity in most (but not all) business writings about complexity. Consider for example the way people talk about coevolution: nearly every treatment of business coevolution I have read has talked about it like nothing can possibly go wrong. But in real coevolution things can and do go horribly wrong at times. It is these sorts of distortions that not only give complexity concepts a bad name (because rarely can such wild claims of magical power be justified) but also spread confusion about the true utility of complexity and chaos based approaches.

And finally, the third and most used tool in the business complexity writer's toolkit is that the sky is falling. You need this, say the business books, because the world has changed in such dramatic ways that you can't possibly survive without it. People who use this tool ramp up the fear quotient by making claims such as that "an organization is a complex adaptive system" -- the implication being, and you had better find out what that means, and quick. But organizations are not complex adaptive systems! More precisely, they are not only complex adaptive systems. An organization is a lot of people. Those people interact with each other in many ways, some of which are complex and emergent, and some of which are not. Organization and self-organization, hierarchy and meshwork are inextricably bound up together in organizations, and saying an organization "is" one without the other is sheer nonsense and is probably meant to entice rather than inform. There are no only-complex social groupings in human life. Every gathering of ten huts has a path through it. Every lunch meeting has a leader. Every subway car has a social structure, if even only for the two minutes the same people are in it. That's what we do. There may be such things as only-complex systems in the lives of social insects, but even there some hierarchy (in the form of central pheromonal control) is usually mixed in.

I don't believe that the writers of business books about complexity are deliberately tricking anyone. Well, mostly not. It's human nature to enlarge upon something that will benefit oneself. We all do it, myself included. But I think the larger force is that most writers of such books don't know how to frame complexity so that it doesn't threaten those in power. They believe that if they write about what they think complexity really means -- the devolution of power -- the only people who will buy the books will be the people on the factory floor, who can't afford books and wouldn't buy them if they could. The writers are in a trap: how do you write about the loss of power to those in power?

My advice, if anyone wanted it, would be this. First, stop saying everything is complex, and start talking about how complexity and hierarchy can work to mutual benefit. I saw a perfect example of this at IBM, which is more like a city than a company. The savvy people at IBM knew how to use the hierarchy and how to use the meshwork, and they knew which to use when and even how to combine them. I wasn't very good at it, but I watched some masters in action. The masters didn't get all excited about the organization as an adaptive monster organism. They knew emergent patterns when they saw them, and they knew the structures of hierarchy when they saw them.

When you don't fear complexity, when you see it as a part of reality but not a "whole new world" dominated by a falling sky, you don't have to muzzle it. The underbutterfly and the topstone and the easy roller can go plague other people. You can take the butterfly and the keystone and the steadfast climber as they come to you, in stride. You can learn to recognize them, deal with them, work with them, and even in time welcome them as old friends. You'll just know better than to hand over your car keys to them.

Well, there you go. I have no idea why I wrote all of this, and I have no idea if it will be of any use to anybody else either. It's just something that seems to need to emerge, after years of thinking and reading about these issues. The other nine stories are likely to be much shorter, which will be to everyone's benefit. Please do alert me to all egregious mistakes here and elsewhere: I'll be counting on them.