# What is Complexity: Part 1

A while ago, I noted that one of the subjects I’ve been exploring this year is that of Complexity.  I’ve read a number of books on the subject, and the first thing I’ve learned is that there is no commonly agreed definition of Complexity itself!  It’s a very wide ranging, interdisciplinary field.  Wikipedia has an excellent article on it, and I encourage you to check out the accompanying chart because it will give you a good overview of all the different areas included under the heading of Complexity!

So, as I’ve said, I’ve read several books now, and Deep Simplicity: Bringing Order to Chaos and Complexity by John Gribbin is one of the better overviews of the field.  I first encountered Gribbin’s books twenty years ago with his “In Search Of” titles, and I knew he was a skilled writer that can take a complex subject and make it so non-experts can understand without “dumbing down” the material, and he again accomplishes this in Deep Simplicity.

Gribbin begins with a short history that takes the reader from the early days of science and the Greeks to the beginning of the Twentieth Century, covering the development of Physics, Calculus, and Chemistry and how these lead to laws that could describe the world, as well as the phenomenon of Entropy – some processes don’t run in reverse spontaneously, unless you add energy to the system.  Unfortunately, adding energy to a closed system increases the entropy outside the closed system (i.e., the Universe!) and so entropy always increases.

He then moves on to a discussion of Chaos Theory.  Basically, the idea of chaos is this:  Given a system, very small changes in the starting conditions can lead to very large changes in the outcome.  For example, if you take two planets and calculate their orbits around each other, you will end up with a reasonably accurate systems if you run it forward a few hundred years.  If you add a third planet, however, there is no way to tell where the system will end up.  A more well known version is the so-called “Butterfly Effect” of the weather.  Forecasters can be reasonably accurate a few days ahead, but anything past a week is simply too complex to forecast accurately.  (Note that Anthropogenic Global Warming advocates insist that climate can be predicted 50 years in advance…)

Gribbin then talks about one of the most well-known equations in chaos theory:  the Logistic Equation, which discusses how population changes over time.  Gribbin uses this to demonstrate some common properties of Chaos.  In addition to the “sensitive dependence on initial conditions” noted above, Chaos curves split – a process called bifurcation – and then countinue to double until they hit a point where their behavior becomes (what else) “chaotic.”  I am very much oversimplifying here, but this is a deep subject and it’s hard to cover in a blog post what Gribbins uses an entire book to try to do!  Gribbin also covers cellular automata and fractals as examples of complex behavior arising from simple conditions.

One key item to note is that a completely chaotic system is not complex, and neither is a simple system.  Complexity lies somewhere in the middle.

Having laid this foundation, Gribbins now describes Complexity Theory.  He shows how complex behavior can arise in a system with two plates with a thin layer of liquid between them – add heat, and convection cells arise (rotating strips of water).  Add more heat, and eventually you get chaotic behavior, but in between equilibrium and chaos is the complex region with the convection cells.  You can also see this with your faucet – when it’s off, you have equilibrium.  Turn it on a little, you get a smooth stream of water.  A little more, and the water starts getting complex with twists.  On all the way, and it’s chaotic.

Gribbins also covers the concept of self-similarity – take a coastline, for example.  When you see it from space, it has a jagged appearance.  From the air, a mile up, still jagged, but on a smaller scale.  Walking along it, still jagged.  And so on.  Whatever scale you view it at, it’s still jagged and looks the same.  You can never really find the exact length of coastline because you can always reduce the scale and make it longer.  (Those of you with a Calculus background: It does approach a limit, of course, but I’ll save that for another day!)  In addition Gribbin talks about power laws – where the distribution on a graph follows a curve.  An example is the population of U.S. cities – New York City is obviously the largest, but the next largest comes in at about one-half of New York’s size.  And the third largest is about one-half of the second…and so on.  Power laws, surprisingly, can be found in many places in nature – complexity theory is exploring why.  Gribbins than describes network theory and how the dynamics of a system can be described by it.

Now, Gribbins gets to his objective, which is to show how complexity can be used to discover the properties of living systems.  It shows how a species can change through time based on outside influences, as well as how the operations inside a cell can be described by complexity and network theory.  In his final chapter, Gribbins talks about how this all relates to Gaia theory (Note:  Gribbins sees this as describing a COMPLEX SYSTEM, not as the earth being a living goddess or even one living creature).

Overall, the book was decent introduction to complexity, chaos, and networks and how they can apply to many areas.  This book was a little too focused on the biological end, though, and I think that Melanie Mitchell’s book Complexity: A Guided Tour is a better overview for that reason.  But Gribbins is very good at taking a “complex” subject and making it easy for the layperson to understand.

Note:  If you’re a Christian like me, the book is still worth a read.  Even if you don’t subscribe to macroevolutionary theory or the Theory of Evolution by Natural Selection, you can still get quite a bit out of this book, and I think it has a lot to say about microevolution!