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Chaotic Social Networks

2009 October 11

From Susan Boyle to the Iranian election, online Social Media has had an enormous effect on society.  Web driven Social Networks can make Gods out of mortals; influence world leaders and slay mighty brands with startling speed.

Moreover, this all seems to happen unpredictably, almost violently as if an entire placid lake immediately erupts into an enormous geyser, irregularly but repeatedly.

What makes Social Media so different from anything we’ve seen before?  The answer is Chaos.

The chaotic nature of networks can be frustrating, because it confounds the linear, correlated way we have learned to look at the world.  However, as I think you’ll see, it’s worth a little effort.  Chaos is why Social Networks can grow so quickly and why they confound conventional business thinking.

As publishers, marketers and users, we can benefit greatly if we understand how to make some order out of chaotic Social Networks.

Certainty Models

We use mathematical models all of the time.  For instance: 2+2=4 not only holds for a particular situation, but is a universal rule that holds true for greater quantities, such as 2000 + 2000 = 4000.  We use the model because it accurately describes the world we live in and saves us a lot of time counting things one by one.

A slightly more complicated model is called a linear model and we use that quite often too.  For instance, if we are driving, we can make note of how far we have gone at different times.  Then we can calculate an average rate and make a reasonable guess where we were at any given time during our trip, not just when we took our measurements.

These are simple models and describe things we are relatively certain about.  However, we can also construct models to describe uncertainty.  Unfortunately, they are non-linear, which makes them more complicated than the simple ones I just described.

Randomness vs. Chaos

Randomness is actually fairly predictable, but somewhat unnatural and uncommon.  It is the math of statistics and we use it quite often even if we are not aware that we are doing it.

For instance, when we say we expect things to “average out,” we are using statistics and a random model.  What we are saying, in effect, is that we expect some variation in our lives, but we expected that variation to be centered on a fixed value.  It’s a comforting concept.

Chaos, on the other hand, is neither linear nor centered. It is turbulent as well as uncertain.  I realize a bit of explanation is required.  Here are two examples:

Rolling dice is Random: For rolling dice or flipping coins we can expect the distribution to be “normal” (in the mathematical sense).  We also know randomness as the bell shaped curve that your teacher used as an excuse to fail you in school.  People who probably didn’t fail many tests in school call this kind of graph a Gaussian or Normal distribution.

Passing someone on the street is Chaotic: Some elements are Random and can be expected to be distributed normally – as when you and your neighbor haphazardly alter your dog walking times each morning.

However, there are also people who are lost, people from out of town, criminals casing your home, etc. This makes who you see on the street so unpredictable and un-centered (and why we can be so surprised by who we run into).

Chaos is much more violent than randomness and lends itself to clustering more than randomness does.  Values do not average out.  Mathematicians describe chaos as both dynamic and non-linear, meaning that it changes and it’s hard to predict how.

Randomness is like a child, filling in the blanks haphazardly, while Chaos is like a felon robbing a few banks and then retreating to the relative tranquility of his hideout only to return, get drunk and break some windows.

While there is no honor among thieves, our mathematical felons are nice enough to follow at least some rules.  We call these rules “Power Laws,” and just like on detective shows, we can use these basic principles to infer the behavior of our chaotic felons.

Power Laws

While Randomness is governed by bell shapes curves, Chaos is ruled by power laws.  These are distributions that scale proportionately creating long-tailed graphs that Chris Anderson made famous in his book.  Power laws are very useful for lots of reasons, but for our purposes they are most valuable in describing that lovable, chaotic rogue we call “Social Networks.”

Long well known in Physics, power laws have a rich history.

At the turn of the century, Vilfredo Pareto noticed that income distributions followed a simple rule where roughly the richest 20% of the population owned approximately 80% of the wealth.  “Pareto’s law” was soon found to apply to a variety of business factors as well.  It has since become standard fare at marketing and sales seminars, albeit redubbed the “80/20 rule.”

The concept spread to the social sciences when in 1949 George Zipf noticed that word distributions in texts also followed a power law.  Since then, the power law distributions have been found to describe population densities, river systems, electrical grids, sizes of religious congregations and even how many sexual partners people have. (I assume that the last two are not related.)

Another interesting point about power laws is that they are “fractal,” which means that the pattern repeats endlessly.  Every long tail is, in effect, made up of smaller long tails.

Benoit Mandelbrot, Fractals and Chaos

Benoit Mandelbrot thought that infinite complexity could be described by simple rules.  Working out of IBM’s research center, he became intrigued by the idea that by repeating shapes according to set rule you could approximate complex systems such as financial markets.

Despite the vilification he suffered from his contemporaries, it is now recognized that Mandelbrot was pioneering the field of Fractal Geometry and his Mandelbrot Sets became pop icons. He introduced the idea that ordered patterns could repeat themselves in disordered ways. (See the video with horrible music below.)

Later, Mandelbrot was somewhat redeemed by the emergence of Chaos Theory.  A young researcher named Edward Lorenz was studying methods of predicting the weather and made a miniscule decimal error.  He was shocked when he realized that a small change in initial conditions could make a huge difference in end results.  He called this phenomenon the “Butterfly effect.”

As the word spread, scientists were finding similar patterns in lots of places, from the ways metals magnetized to the way pacemaker cells in the heart stay constant for decades and suddenly, like, our window breaking felon, go wildly out of phase (which, by the way, is how my father suddenly died one morning).

Chaos caught on and became an exciting field for bright young scientists.  One of them was a young Marshal Scholar named Steven Strogatz who went on to teach at Cornell. There he took on a talented PhD candidate named Duncan Watts. It was they who gave the world its first look at how Social Networks work.

(See The Forces that Drive Social Networks)

Which Brings Us Back to Social Networks

Although Watts and Strogatz wrote the seminal paper on network theory, ironically, it was the rival team of Barabasi and Albert at Notre Dame who realized that networks follow the chaotic power law distribution that is now widely referred to as the Long Tail.

When viewed through the prism of Chaos, Social Networks can now be seen in a new light:

Long tail: Everybody is equally small and there is a low rumble of activity.  Lots of chatter, but not much going on (the felon in his hideout, presumably chatting and playing cards).

Short head: In this area of the network giants roam.  They wield enormous power and drive the network.  When they decide to act, the earth shakes! (The felon going back to his bank robbing, window breaking ways.)

An important point is that the two regions are interdependent.  In actuality, they are two sides of the same coin.  They reinforce each other.  There can be very little action within the network without the heavily connected hubs in the short head.  Moreover, the strength of the network is really a function of the length of the long tail.

Chaos Yields Practical Insights for Social Media

While the complexity of chaos can be daunting, understanding the chaotic nature of networks is critical to understanding what drives them.

Recognition is the primary growth driver for Social Networks: Allowing people to be recognized is not only a primary driver within the network, but also for growth of the network.  The “giants” in the short head and the masses in the long tail are mutually reinforcing. Many social networks fail because they don’t do enough to encourage people to promote themselves.  There is no such thing as an egalitarian network.

Growth favors Giants: Because networks are scaled, new members benefit the most connected ones disproportionately.  This insight should put the bias against “newbies” in MMO games into a new light.  Only weak players are diminished by new entrants.  Strong players benefit.

Social Networks are Local and Global: Like Mandelbrot Sets, Social Networks are fractal.  The patterns repeat.  In effect, the Long Tail is made up of Long Tails, each guided by the same Power Law equation on a different scale.  There is no reason for Social networks to dilute as they grow if they maintain local cohesiveness.

Professionals depend on Amateurs: While professional media people tend to be derisive of amateurs, in a networked world they depend on them.  In effect, large media operations depend on the very bloggers and twitters that they love to hate (and vice versa).

In the same way that politicians depend on voters and corporations depend on consumers, media organizations today have to recruit and organize their audiences, not just broadcast to them. A mutual respect needs to form for both to use the network effectively.

We still have a lot to learn about Chaos and even the little we do know is far more than I can do justice here.  However, one thing is clear:  Social Media is no fad.  It will continue to grow, surprise, delight and even sometimes horrify us.

– Greg

18 Responses leave one →
  1. Stuart Nicholson permalink
    October 11, 2009

    now youve really done my head in, Greg!

  2. October 11, 2009


    No. That was Russia:-)))

    Sure you don’t want to weigh in about ROI?

    – Greg

  3. Olena permalink
    October 13, 2009

    Greg, great theme to discuss!
    Every day think about how chaotic social networks become. Especially it’s visible to big corporations.
    No matter if they have official blog, or fan page, or maybe are not officially registered within any of social networks. Anyway, news, rumors spread faster than speed of light within social networks and no one can control them. That’s why big companies have started social media marketing devision/departments, that monitor what news about their company appear in social networks..
    GM is a good example on how a company should respond to critics , negative or even neutral information that appears in social media.
    GM representative contacted David Meerman Scott within few hours after the blog post “Attention GM: Here are the top 5 marketing ideas for your reinvention” appeared. (see post at )
    Of course, not all the organisations, esp. smaller ones have resources to monitor enormous, chaotic social networks , blogs etc.etc. with a lot of people being laid off sometimes marketing person has to be two in one.
    That’s why companies have to pay more attention to their reputation (and internal PR too). Because the luxury of chaotically growing social networks, may sometimes be not affordable.
    Moral: Bad news and rumors spread faster than good news.

  4. Roy Reshef permalink
    October 14, 2009

    Very interesting theme, Greg, I fully agree.
    SoMe is Chaos in the straight-forward meaning of the word, I think everyone would agree with that.
    The mathematician in me misses the mathematical argumentation to let SoMe also qualify as a Chaotic phenomenon in the mathematical meaning. Chaos was my passion in the beginning of the 90s, as an undergraduate student. It was then mainly used to describe mathematical and physical phenomena like weather forecasting, fractal geometries of a snow flake and shoreline etc.
    I pretty much missed the theories about social networks in the mid-90s, was too busy developing software at the time. Now SoMe has become my new passion 🙂
    However, mathematical Chaos theory is defined (see your reference to Wikipedia) as “the study of the behavior of certain dynamical systems that may be highly sensitive to initial conditions”. Which parameters of SoMe can we quantify and then measure under which initial conditions (which should be quantified as well)? I have seen various kinds of statistics regarding SoMe (e.g. No. of RTs based on textual analysis of the original tweet; % of men and women using all kinds of SoMe sites etc.). But all of these seem to me rather bleak, not really the quantifiers to measure the impact on society.
    Which leads us to an important question – how can one, at all, measure or determine such an impact? That seems to me a pure subjective decision, which at least in some cases may render such an impact disputable. There are already some “conspiracy theories” that the demonstrations in Iran were masterminded by people or organizations which had interests to set the streets of Tehran on fire; I am not advocating these, I do not know the truth myself – but do we really know what the impact was of the millions (or more) tweets and RTs and profile photos in green on what that happened there?
    To make my long story short, I agree with the direction of your theme, however I believe that quite some work is required – also on the mathematical side – in order to make it a valid statement. I agree that SoMe is Chaos in the sense of the Book of Genesis, if it is also a mathematical Chaos is yet to be proven. I’d be happy to exchange thoughts with you about this.

  5. October 14, 2009


    Thank you very much for your comment.

    While I agree that there are big difference between Social Media and other chaotic phenomenon, I believe that’s mainly a classification issue. Just as weather forecasting is different from fractal geometry, Social Media differs from both.

    My main reason for writing the article was that for all the talk about long-tails, power laws and 80/20 rules, I thought it would be helpful for people to know something about how power laws work and that they are related to other phenomenon.

    As for Political Chaos, this is something i have seen first hand during the Orange Revolution in Ukraine. Isolated griping suddenly transformed into an enormous movement. Just like in Iran, there was much speculation that the whole thing was masterminded by some conspiracy. Often Chaos has the appearance of order.

    Thanks again for sharing your insights.

    – Greg

  6. October 30, 2009

    Hi Greg, This is a deep one. I can’t get my head round Chaos as a theory as I always think of it as existentialist. Power laws on the other hand are predictable and naturally occurring relying on environmental, political or human collusion. In this way the result of what may seem chaotic is in actual fact a hierarchy that influences the mass. Social Networks act as magnets that attract diverse groups of people to one place where natural selection takes place. This results in the formation of ‘tribes’, ‘interest groups’ and ‘communities’ each with it’s own hierarchy of influencers and followers. 10% (or influencers) are responsible for the purchasing behaviour of the other 90%. This is why mobile marketing can be so potent as one can focus on the 10% in a more targeted and relevant manner in order to reach the other 90%. From a creative point of view I would recommend you have a look at “The Art of Looking Sideways” by Alan Fletcher (ex Pentagram) This is his exploration of the workings of the eye, the hand, the brain and the imagination and is a fascinating journey into the order of chaos.
    So until next time, all the best my friend. Gordon

  7. October 30, 2009

    Thanks, Gordon.

    What I think is interesting is that Power Laws and chaos a mathematically the same thing.

    – Greg

  8. October 31, 2009

    Very well written article. I think I will have to read more into the chaos theory.

  9. October 31, 2009


    I can recommend “Chaos” by James Gleik, Sych by Steven Strogatz and The (Mis)Behaviour of Markets by Mandelbrot.

    – Greg

  10. Jim Fox permalink
    November 20, 2009


    This is the first your post that you actually lost for a second or was it Chaos 🙂 But summed betifully in the end with “media recruiting and organizing their audience”

  11. November 25, 2009

    Greg, great summary piece. Certainly the future will be in harnessing the dynamical nature of networks to extract and exploit intelligence. Technologies of the future will need to be “architected” to serve these environments more effectively.

  12. November 25, 2009


    I think you’re right. Real world volatility is much more chaotic than it is random (as the recent financial crises showed). We need to take into account more extreme values.

    – Greg

  13. December 12, 2009

    whenever i hear “chaos theory” i think of jeff goldbloom playing with that water droplet in Jurassic Park. but i digress. your blog is the real deal. i am usually angry that you figured this stuff out before me, but then i’m unbelievably happy that someone else has done the work 😉


  14. December 12, 2009


    To be honest, I do to!

    Thanks for the nice comment and have a great weekend:-)

    – Greg

  15. January 3, 2010

    i like you blog keep up the good work.

  16. January 3, 2010


    Thanks. I’ll try not to disappoint:-)

    – Greg

  17. July 17, 2010

    I find great inspiration in the possibilities afforded us by the neural network of our web connectivity. It seems that we just need to recognize the consistent way our social co-valent bonds can bind us together for mutual benefits, globally.

    My hope is that we use what we don’t know (yet) to discover what we need (now) from what we have learned (then). My suggestion is that to do so we just have to question the answers. So, what’s the best question? (that one of course). Who knows the answer – you do (and I do). The system is not the power – it is the result of power, ours.

    Fractal thought:
    What would it be like if someone grabbed us by our power head and reached down our mental throat and grabbed us by the long-tail – pulled us inside-out ..leaving us exactly the same – only changed – and with a better perspective.? …I’m just sayin’

  18. July 17, 2010

    Thanks for you input, George.

    – Greg

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