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“The goal before us is to understand complexity. To achieve that, we must move beyond structure and topology and start focusing on the dynamics that take place along the links.” Linked, p. 225

Dynamics really has two meanings. The first meaning is what we might call dynamics of the network. In this sense of the word, dynamics refers to the evolving structure of the network itself, the making and breaking of network ties. ... A dynamical view of networks, claims that existing structure can only be properly understood in terms of the nature of the processes that led to it.
The second meaning, is what we might call dynamics on the network. From this perspective, we can imagine the network as a fixed substrate linking a population of individuals, but now the individuals are doing something — the outcome of which is influenced by what their neighbors are doing and, therefore, the structure of the network. ... In the real world, both kinds of dynamics are going on all the time. ... The structure of the network could change, but so could the pattern of activity on the network.” Six Degrees p. 54-55

Equilibrium means nothing changes; stability means slight disturbances die out.” Sync p. 60-63

“By viewing networks as dynamical systems that change continuously over time, the scale-free model embodies a new modelling philosophy. ... Our goals have shifted from describing the topology to understanding the mechanisms that shape network evolution ... understanding that structure and network evolution [can’t] be divorced from one another. ... Networks are not en route from a random to an ordered state. neither are they at the edge of randomness and chaos. Rather, the scale-free topology is evidence of organising principles acting at each stage of the network formation process.” Linked, p. 90-91

“We find that real networks are governed by two laws: growth and preferential attachment.” Linked, p. 86

“The expansion of the network means that the early nodes have more time than the latecomers to acquire links. Thus growth offers a clear advantage to the senior nodes, making them the richest in links. Seniority, however, is not sufficient to explain the power laws. Hubs require the help of the second law, preferential attachment. Because new nodes prefer to link to the more connected nodes, early nodes with more links will be selected more often and will grow faster than their younger and less connected peers. Thus preferential attachment induces a rich-get-richer phenomenon that helps the more connected nodes grab a disproportionate large number of links at the expense of the latecomers.” Linked, p. 87-88

Preferential attachment makes an additional statement about the way the world works: small differences in ability or even purely random fluctuations can get locked in and lead to very large inequalities over time.” Six Degrees p. 109

“Even if every trace of racism were to vanish tomorrow, there may still be a natural tendency for races to separate, much like oil and water. Social realities are fashioned not only by the desires of people, but also by the action of blind and more or less mechanical forces — in this case forces that can amplify slight and seemingly harmless personal preferences into dramatic and troubling consequences.” Nexus, p. 186

“Whenever limitations or costs eventually come into play to impede the richest getting still richer, then a small-world network becomes more egalitarian. ... On the one hand, the rich-get-richer mechanism leads inevitably to small-world networks, as if they were dictated by an architectural law of nature. Nevertheless, limitations and constraints sometimes get in the way and leave their telltale traces on the final form. Still, the similarities between the two kinds of networks are probably more important than the differences. The small-world character persists in either case.” Nexus, p. 125-126

“The model offers a general message: encouraging exchange between people, with other things being equal will tend to distribute wealth more equitably. [They] found greater equality whenever they boosted the flow of wealth along the links or increased the number of such links. Alternatively, stirring up the wildness and unpredictability of investment returns worked in the opposite direction, which is not surprising as it boosts the influence of the rich-get-richer phenomenon.” Nexus, p. 193

This suggests that so-called therapeutic approaches like ‘shaking the tree’ or ‘messing up a problem’ may be counter productive.

“A significant fraction of nodes can be randomly removed from any scale-free network without its breaking apart. This resilience to errors is an inherent property of their topology. ... In scale-free networks, failures predominantly affect the numerous small nodes. Thus, these networks do not break apart under failures. The accidental removal of a single hub will not be fatal either, since the continuous hierarchy of several large hubs will maintain the network’s integrity. Topological robustness is thus rooted in the structural unevenness of scale-free networks. ... [However] the removal of a few hubs [can break a network] into tiny, hopelessly isolated pieces. ... Hidden within their structure, scale-free networks harbor an unsuspected Achilles’ heel, coupling a robustness against failures with vulnerability to attack. ... Several of the largest hubs must be simultaneously removed to crush them. This often requires taking out as many as 5 to 15 percent of all hubs at the same time.” Linked, p. 113-118

“Any hub or connector species has a huge number of links to other species. As a result, most of these links will be weak links; the two species interact infrequently. ... The consequences of removing just one connector species can be especially dramatic, as a huge number of weak stabilizing links goes with it. Ecologists have long talked about ‘keystone’ species, crucial organisms the removal of which might bring the web of life tumbling down like a house of cards. ... Ecologists have] found that the highly connected keystones were often inconspicuous organisms in the middle of the food chain or were sometimes basic plants at the very bottom of the web. In other cases, they were major predators. There appear to be no hard and fast rules for determining which kind of species are likely to be keystones. Identifying keystones means studying the network architecture and seeing which species are the connectors, the lynchpins of the living fabric.” Nexus, p. 151-154

Weak links between species act to take the wind out of dangerous fluctuations. They are the natural pressure valves of ecological communities.” Nexus, p. 150

In small worlds, weak links are both change-propagating and change-restraining. They increase the chance of interacting with more 'distant' (not alike) nodes. This is particularly important at a time of crisis when, by definition, business-as-usual is not an option. Weak ties increase stability but this in turn works against radical change. At the same time, it is these same weak ties that propagate a change/failure/disease throughout the network.



“Having an interconnected system really makes for a more efficient use of our natural resources and keeps the cost down, but it means when something goes wrong, it can cascade through the system A property of complex networks is their vulnerability due to interconnectivity. ... In general, natural systems have a unique ability to survive in a wide range of conditions. Although internal failures can affect their behavior, they often sustain their basic functions under very high error rates. This is in stark contrast to most products of human design, in which the breakdown of a single component often handicaps the whole device.” Linked, p. 110-111

“[In] interacting systems ranging from forest fires to mass extinctions ... the individual element is subjected to increasing pressure, builds up towards a threshold, then suddenly relieves its stress and spreads it to others, potentially triggering a domino effect.” Sync p. 31

“The 1996 blackout is a typical example of a cascading failure. When a network acts as a transportation system, a local failure shifts loads or responsibilities to other nodes. If the extra load is negligible, it can be seamlessly absorbed by the rest of the system, and the failure remains effectively unnoticed. If the extra load is too much for the neighboring nodes to carry, they will either tip or again redistribute the load to their neighbors. Either way, we are faced with a cascading event. ... Simulations indicate that most cascades are not instantaneous: failures can go unnoticed for a long time before starting a landslide. Attempting to decrease the frequency of such cascades has inevitable consequences, however, as those cascades that do succeed are then more disruptive. ... Topological robustness is a structural feature of networks. Cascading failures, however, are a dynamic property of complex systems. ... The results of the research forced us to acknowledge that topology, robustness, and vulnerability cannot be fully separated from one another.” Linked, p. 119-122

“The [blackout] cascading failure that struck the West on August 10, 1996, was not a sequence of independent random events that simply aggregated to the point of a crisis.  Rather, the initial failure made subsequent failures more likely, and once they occurred, that made further failures more likely still, and so on.  ... Perhaps the most perturbing aspect of cascading failures is that by installing protective relays on the power generators, by reducing, in effect, the possibility that individual elements of the system would suffer serious damage — the designers had inadvertently made the system as a whole more likely to suffer precisely the kind of global meltdown that occurred.”  Six Degrees p. 23-24

“There are three ways in which cascades can be forbidden. The first one is obvious: if everyone’s threshold is too high, no one will ever change and the system will remain stable regardless of how it is connected. Even when this is not the case, cascades can still be forbidden by the network itself, in two ways: either it is not well connected enough or (and this is the surprising part) it is too well connected.
    Networks that are not connected enough, therefore, prohibit global cascades because the cascade has no way of jumping from one vulnerable cluster to another. And networks that are too highly connected prohibit cascades also, but for a different reason: they are locked into a kind of stasis, each node constraining the influence of any other and being constrained itself. In social contagion, a system will only experience global cascades if it strikes a trade-off between local stability and global connectivity.” Six Degrees p. 237 & 241

The too connected scenario is a classic description of a binding pattern.

“Only when a disease reaches a shortcut does it start to display the worst-case, random mixing behavior. Epidemics in a small-world network have to survive first through a slow-growth phase, during which they are most vulnerable. And the lower the density of shortcuts, the longer this slow-growth phase will last.” Six Degrees p. 181

While there is a good chance of preventing a full-scale epidemic during the slow-growth phase, when change is the intention, newness and difference will need to be nurtured through the slow-growth phase.

This finding may also support the notion of (i) Spending time at the beginning of a session to develop the links/relationships in a Metaphor Landscape as this will likely increase the density of shortcuts, thereby shortening the slow-growth phase and (ii) Taking your time at the beginning of the Maturing Changes phase to allow for the completion of the slow-growth phase.

“In scale-free networks even if a [computer] virus is not very contagious, it spreads and persists.  Defying all wisdom accumulated during five decades of diffusion studies, viruses travelling in scale-free networks are practically unstoppable. The source of this unexpected behavior lies in the uneven topology. Scale-free networks are dominated by hubs. Because each hub is linked to a very large number of other [nodes], it has a high chance of being [re-]infected by one of them. Once infected, a hub can pass on the virus to all the other [nodes] it is linked to. Thus highly linked hubs offer a unique means by which viruses persist and spread. ”  Linked, p. 135

This maybe one way to explain why ‘relapse’ after an apparently successful relief from depression or anxiety is not uncommon. If an unproductive thought (a ‘thought virus’ as Robert Dilts calls them) survives somewhere on the network it has a good chance of eventually re-infecting nodes that have become virus-free. Of course, the source of the thought virus may be outside the client.

This metaphor suggests that, rather than attempting to the eliminate all negative thoughts, it maybe wiser to establish a way of handling them when they occur, i.e. building up an immunity.

“It is not necessarily good ideas that spread — just infectious ones.  ... the infectious movement of desires and ideas from mind to mind is even the basis of a new theory of advertising known as ‘permission marketing’.” Nexus, p. 160

A more pleasant but less sticky name than ‘viral marketing’.

“[During] an information cascade individuals in populations essentially stop behaving like individuals and start to act more like a coherent mass. Sometimes information cascades occur rapidly [as when a market bubble burst]. And sometimes they happen slowly — new societal norms, like racial equality, woman’s suffrage, and tolerance of homosexuality, for example, can take generations to become [almost] universal. What all information cascades have in common, however, is that once one commences, it becomes self-perpetuating; that is, it picks up new adherents largely based on the strength of having attracted previous ones. Hence, an initial shock can propagate through a very large system, even if the shock itself is small.
    Because they are often of a spectacular or consequential nature, cascades tend to make newsworthy events. This disguises the fact that cascades actually happen rather rarely.” Six Degrees p. 205-65

“One of the most intriguing features of the cascade problem was how most of the time the system is completely stable even in the face of frequent external shocks. But once in a while, for reasons that are never obvious beforehand, one such shock gets blown out of all proportion in the form of a cascade.
    And the key to a [social] cascade is that when making decisions about how to act or what to buy, individuals are influenced not only by their own pasts, perceptions, and prejudices but also but each other
    It seemed clear that contagion in a network was every bit as central to the outbreak of cooperation or the bursting of a market bubble as it is to an epidemic of disease. It just wasn’t the same kind of contagion. This is important because typically when we talk about social contagion problems, we use the language of disease. Thus we speak of ideas as infectious, crime waves as epidemics, and market safeguards as building immunity against financial distress, But the metaphors can be misleading because they suggest that ideas spread from person to person in the same way that diseases do — that all kinds of contagion are essentially the same. They are not. ... Social contagion is a highly contingent process.” Six degrees p. 220-224

Social contagion is even more counterintuitive than biological contagion, because the impact of one person’s actions on another depends on what other influences the latter has been exposed to. The spread of ideas, unlike the spread of disease, requires a trade-off between cohesion within groups [clustering enables local reinforcement] and connectivity across them. A node can be vulnerable in one of two ways: either because it has a low threshold (thus, a predisposition to change); or because it possesses only a few neighbours, each of which thereby exert significant influence.” Six Degrees pp. 231-3

Not only is timing of the introduction of an innovation important, so is where it is introduced. So when in the Maturing Changes phase you enquire if a change to one symbol has spread to another symbol (And when X, what happens to Y?) it may be prudent to start with the ‘closest’ and most similar symbols.

“The presence of a wide range of personal thresholds in a population tends to increase the chance of new ideas or products catching on considerably.
    The term innovators can be used to refer not only to individuals who introduce new devices but also to advocates of new ideas, or more generally still, any small shock that disturbs a previously quiescent system. Early adopters are simply members of a population who are the first to be influenced by an external stimulus [innovator]. ... Obviously the more early adopters there are in the population, the more likely a particular innovation is to spread. And the larger the connected cluster of early adopters in which the innovation lands, the farther it will spread.” p. 227, p. 232-235 Six Degrees

“The Pfizer study [‘How Physicians Adopt a New Drug’] demonstrated that innovations spread from innovators to hubs.  The hubs in turn send the information out along their numerous links, reaching most people within a given social or professional network. ... Conversion [of hubs] is the key to launching an idea or an innovation.  If the hubs resist a product, they form such an impenetrable and influential wall that the innovation can only fail.  If they accept it, they influence a very large number of people.”  Linked, p. 129-130

Thus in a small-word network you don’t need to influence to a hub directly.  Change in an early adopter connected to a hub may do just as well.
    But how do you tell which symbols are the early adopters? And when a Metaphor Landscape is not changing, under what conditions would an innovation be above the personal threshold of an early adopter; and that early adopter (i) is able to influence a neighbour and (ii) is not overly influenced by its neighbours?
    Of course, sometimes the problem is that some nodes change too easily.

For innovations to spread to early adopters and perhaps a few of the early majority:

“social contagion is largely equivalent to biological contagion because it undergoes the same phase transition that epidemics of disease do. And for the same reason — that network connectivity, rather than the resilience of individual decision makers, is the principal obstacle to a successful cascade ... the cascade propagates until it occupies the vulnerable cluster and then it runs out of places to go.

For the cascade to become global, and the innovation to spread to the early and late majority, the cascade has to cross the chasm, and that’s a different kind of phase transition. Now:

“being simply well connected is less important than being connected to individuals who can be influenced easily ... and whose neighbors have one or more vulnerable neighbors, and so on. So even if you can identify potential early adopters, unless you can view the network, you wont know whether or not they are all connected.
    In other words, the structure of the network can have as great an influence on the success or failure of an innovation as the inherent appeal of the innovation itself. And even [when a cascade is possible] much of an innovation’s fate hangs on random chance. As much as we want to believe that it is the innate quality of an idea or product that determines its subsequent performance, or even the way it is presented, the model suggests that for any wild success, one could always find many deserving attempts that failed to receive more than a tiny fraction of the attention. And in general no one will know which one is which until all the action is over.” pp. 239-244 Six Degrees


“Each node has a certain fitness ... The introduction of fitness does not eliminate growth and preferential attachment, it changes, however, what is considered attractive in a competitive environment.”  Linked, p. 95-96

“Independent of the nature of links and nodes, a network’s behavior and topology are determined by the shape of its fitness distribution.  But even though each system, from the Web to Hollywood, has a unique fitness distribution, all networks fall into one of only two possible categories.  The first category includes all networks in which, despite the fierce competition for links, the scale-free topology survives.  These networks display a fit-get-rich behavior, meaning that the fittest node will inevitably grow to become the biggest hub.  The winner’s lead is never significant, however.  The largest hub is closely followed by a smaller one, which acquires almost as many links as the fittest node.  At any moment we have a hierarchy of nodes whose degree distribution follows a power law.  In networks belonging to the second category, the winner takes all, meaning that the fittest node grabs all links, leaving very little for the rest of the nodes.  Such networks develop a star topology, in which all nodes are connected to a central hub.  In such a hub-and-spokes network there is a huge gap between the lonely hub and everybody else in the system.  A winner-takes-all network is not scale-free.”  Linked, p. 102-103

An examples of a fit-get-rich distribution is that of Web search engines.  Google is the fittest and the biggest, but there are plenty of others that are not far behind.  An example of the winner-takes-all distribution is Microsoft Windows which runs on 86% of personal computers. The second most popular operating system, Mac OS by Apple, has only 5% of the market. Both Google and Apple are examples that the first innovator does not always have the advantage.

“The irregularity of investment return stirs up wealth differences, while transactions of all types between people tend to wipe them out.  The competition between these two forces leads to Pareto’s Law, with a greater or lesser concentration of wealth falling into the hands of a small fraction of people.  The model, however, [suggests] that if the investment irregularities grows sufficiently strong, they can completely overwhelm the natural diffusion of wealth provided by transactions.  In this case, an economy can pass through a sudden and dramatic transition in which the wealth disparities kicked up are simply too pronounced to be adequately tempered by flows between people.  The economy will tip and wealth, instead of being possessed by merely a small minority, will instead ‘condense’ into the pockets of a mere handful of super-rich ‘robber barons’ [cf. winner takes all].  ... It has been estimated, for example, that the richest forty people in Mexico have nearly 30 percent of the money.”  Nexus, p. 195

It seems to us that, in terms of networks, diversity is equivalent to the variety of nodes and choice to the number of links emanating from a node.
    Scale-free networks have a greater range (diversity) of nodes than random, star or latticed networks. However, in social networks, too much diversity makes it impossible for a group or team to function effectively.  The same is true of choice.
    The bottom line? Gregory Bateson noted that attempting to maximise any part, characteristic or value of a system will ultimately become ‘pathological’ when the effects of the maximisation act against the interest of the system as a whole. In particular Bateson was keen to point out that this particularly applies to that part known as ‘conscious purpose’.


“The trouble with systems like the power grid is that they are built up of many components whose individual behavior is reasonably understood, but whose collective behavior, like that of football crowds and stock market investors, can be sometimes orderly and sometimes chaotic, confusing, and even destructive.
    How does individual behavior aggregate to collective behavior?  This is one of the most fundamental and pervasive questions in all of science. ... What makes complex systems complex, is that the parts making up the whole don’t sum up in any simple fashion.  Rather they interact with each other, and in interacting, even quite simple components can generate quite bewildering behavior. ...
    The flip side of complex systems [is that] while knowing the rules that govern the behavior of individuals does not necessarily predict the behavior of the mob, we may be able to predict the same mob behavior without knowing very much at all about the unique personalities and characteristics of the individuals that make it up.
    Sometimes, the interactions of individuals in a large system can generate greater complexity than the individuals themselves display, and sometimes much less.  Either way, the particular manner in which they interact can have profound consequences for the sorts of new phenomena that can emerge at the level of groups, systems, and populations.  In particular, what is it about the patterns of interactions between individuals in a large system that we would pay attention to? No one has the answer yet, but in recent years a group of researchers has been chasing a promising new lead, the science of networks.” Six Degrees p. 23-27

“Individuals have severe limitations imposed on what they can deduce about the world based on what they can observe.  A well-known aphorism contends that all politics is local, but really we should say all experience is local — we only know what we know, and the rest of the world, by definition, lies beyond our radar screen. That’s why the small-world phenomenon is so counterintuitive — it is a global phenomenon, yet individuals are capable only of local measurement.”  Six Degrees p. 83

Weak ties can be thought of as a link between individual- and group-level analysis in that they are created by individuals, but their presence affects the status and performance not just of the individuals who own them, but of the entire group to which they belong.”  Six Degrees p. 49

“The real issue is that there is a big difference between two people being connected by a short path (which is all the small-world network models claim) and their being able to find it. ... The fundamental difficulty being that you are trying to solve a global problem using only local information about the network. ... Finding paths to the right information becomes particularly important in times of crisis or rapid change. ... Cleinberg’s deep insight was that mere shortcuts are not enough for the small-world phenomenon to be of any actual use to locally informed individuals. In order for social conditions to be useful — in the sense of finding anything deliberately — they have to encode information about the underlying social structure.”  Six Degrees p. 136-145

“[When a] system is decentralized, no one has global knowledge.  And that’s what makes the puzzle so challenging: How can the system using a local rule, solve a problem that is fundamentally global in character?  This puzzle captures the essence of what’s called collective computation.  Think of a colony of ants building a nest.  Individually, no ant knows what the colony is supposed to be doing, but together, they act like they have a mind.”  Sync p. 250

Just for fun Penny tompkins and I have summarised some of the above into
‘The Eight Laws of Small-world, Scale-free Marketing’
soon to be available in all good bookshops:
 Law 1 The fit get rich so get very good at what you do.
 Law 2. The rich get richer because of preferential attachment, so give people a small extra reason to attach to you.
 Law 3.
Early nodes acquire more links so be one of the first in some area of specialism and keep doing what you’re doing — the early birds eventually get the worms.
 Law 4. Fitness has to be noticed so work in contexts where your particular skills are visible and keep putting your talent out there — persistence pays. (J K Rowling’s first manuscript was turned down by several publishers.)
 Law 5.
Connectors influence the most so be linked to hubs in your chosen field and be recommendable.
 Law 6.
Six degrees of separation means you can quiet easily get to anyone — providing you find out who you know knows.
 Law 7.
Establish weak ties, you never know where they will lead and when they might come in handy. According to Robert Cialdini in Influence, one good way to do this is to do stuff for other people as it activates the Law of Reciprocity.
 Law 8.
The network decides which cascades go global and which peter out. So don’t take it personally if your idea fails to capture the minds of millions, and even more importantly, don’t take it personally it is succeeds.

James Lawley

James LawleyJames Lawley offers psychotherapiy to individuals and couples, and coaching, research and consultancy to organisations. He is a co-developer of Symbolic Modelling and co-author (with Penny Tompkins) of Metaphors in Mind: Transformation through Symbolic Modelling, (with Marian Way) Insights in Space: How to use Clean Space to solve problems, generate ideas and spark creativity and an Online training in Clean Language and Symbolic Modelling. For a more detailed biography see about us and his blog.

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