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.

**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.