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Practical Complexity

It was a great, spirited conversation about the concept of complexity that led me to wonder what we really know.  Specifically, the conversation was about the idea that we love linear problem solving.  Proverbially, it’s the simplicity of A+B=C.  It’s a simple math equation that anyone who has learned algebra gets.  However, it’s a simplification of the world around us – and one that sometimes gets us into trouble.

Chemical Reactions and Probabilities

Given perfect understanding and infinite time, A+B does, in fact, equal C.  However, the problem is that we rarely understand things perfectly – and we rarely have enough time to allow all of the A+B to happen.  Let’s take a chemistry example in an attempt to make this clear.

We now know that different kinds of atoms have different kinds of properties and propensities to cluster together.  For instance, water is H2O: two hydrogen atoms with one oxygen atom.  If we placed twice as much hydrogen as oxygen in a sealed container, we’d end up with water.  The reaction time is dependent on many things, principally temperature and pressure.

Both of these factors lead to the probability that the correct combination of atoms will collide into one another in a range that causes them to enter the relatively stable relationship we call water.  Too slow, and they’ll bounce off; too fast and they’ll plow through each other without enough magnetic pull to stay together.  Temperature and pressure increase the overall motion of the atoms and their proximity to one another and therefore make the conditions more likely to occur where the factors are just right.

There are a few important aspects here.  First, the reaction isn’t immediate.  It may appear immediate, but it’s not.  Second, we simplify the billions of individual molecule formations of a much larger quantity – say, a cup of water – into a single reaction when it’s not.  Finally, the introduction of other factors may increase or inhibit the reaction.  We call items that accelerate a reaction, but are not consumed by it, “catalysts.”

Reinforcing Loops

Einstein called compounding interest the 8th Wonder of the World.  Even small changes over time create big results.  Consider, for a moment, the idea that you get better by 1% each month.  It’s a tiny change – barely noticeable.  After 10 years of this, how much better would you expect to be?  Mathematically, you’d be 3.3 times as good as when you started.  This is because even at very low rates of increase, these increases compound over time.  The previous result – the increase – is fed back in for the next cycle, so the second month you’re better from the first by not just two percent but slightly more than that (2.01%).

Extended out over long periods of time, this makes some sense.  However, the problem becomes that we rarely think about short periods of time.  Returning to the world of chemistry for a moment, an explosion is a rapid increase in a chemical reaction.  Fire results from heat (energy), oxygen, and fuel.  In an explosion, the cycle time from one set of molecules to the next is very, very quick.  There’s enough heat in the presence of oxygen and fuel that the reaction expands quite quickly.  The output of the prior reaction – fire or explosion – is available for the next cycle.  The result can be catastrophic very quickly.

Balancing Loops

Most of the time, we don’t find explosions, because there are balancing loops that reduce or dampen the impact of the forces that tend to reinforce themselves.  In the case of explosions, the consumption of the fuel eventually depletes it and deprives the reinforcing loop of the conditions of its action.  In the simple example, the results are relatively predictable.  The explosion continues until the conditions of heat, fuel, and oxygen are somehow removed.  Often, the fuel component is exhausted, but sometimes the expansion created by the explosion occurs more rapidly, and the heat (energy) dissipates too quickly.

In many cases, the reinforcing loops are stopped automatically because they reach some limit.

Initial Conditions

Imagine that you’re standing at the Continental Divide in the United States.  On one side of a spot, water rolls down into the Pacific Ocean; on the other side, water will roll down into the Atlantic Ocean.  At the very top of a peak, a very tiny difference in position leads to a very large difference in the water’s final resting place.  (If you’re a teenage boy, you’ll stand at the top and urinate in a sweeping motion to pee in both oceans at the same time.)

A very small difference in initial conditions leads to a very radical difference in the outcomes.  While it’s easy to determine that when we’re at the Continental Divide, it’s much more challenging to determine the places in life where a very small change in initial conditions can have a large impact.  Whether we identify them or not, they’re present everywhere in our everyday life.

Perfect Understanding

Of course, it would be great to have perfect understanding.  If we knew all the places where initial conditions mattered, we could adapt, adjust, and engage in ways that allow us to take advantage of the situation – but we don’t.  In fact, we simplify our world to pretend as if we have a perfect understanding when we often do not.  Let’s come back to water.

You get a glass of water from your faucet and wonder, is it 100% pure water, or are there other things in there as well?  There are, of course, other things in trace amounts.  There’s some chlorine that was used in the treatment process that hasn’t fully broken down yet.  There’s a bit of limestone that was dissolved in the water.  There are probably very tiny amounts of all sorts of things.

You dump the water, turn around, and get some from the refrigerator, thinking that it will be colder anyway.  The filter in the refrigerator has removed some more of the impurities from the water – but it’s still not 100% H2O molecules.  Trace amounts of other stuff still hitch a ride.

Even in our examples here, we’re intentionally ignored the impurities that don’t make much of a difference – at least most of the time.

Applying Probabilities, Time, and Loops

Now, combine these concepts and recognize that there’s a probability of something happening in a given time, that loops drive the continued expansion until a point of collapse or stability, and that our initial conditions that we can’t fully understand can make a big difference in outcomes, and we’ve arrived at complexity.  It’s a place where we can’t predict the outcomes with high degrees of certainty, because there are too many variables and too many components of the situation that we cannot know.  This is what led Lorenz to realize that a butterfly flapping its wings could create a tornado in Texas.  This doesn’t occur in the linear cause-and-effect type way.  Rather, given loops, time, and initial conditions, it’s possible that a small change can lead to a very, very large outcome.

Some would describe this as a non-linear model or a non-proportional result, but I do not.  Ultimately, it is a set of equations and reactions that are all quite linear in nature.  The results of a linear equation need not be proportional – exponents are allowed.  Further, the emergence of the perception of non-linearity is because we fail to recognize both the simplification of many to one – and we fail to recognize the challenges of multiple iterations and the impact of initial conditions.


What we perceive as complexity is often just something complicated that we’ve over-simplified and failed to take into account the components and speed at which the system loops and therefore feeds back on itself.

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