For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the message was lost.
For want of a message the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.
For Want of a Nail
Minor changes in initial conditions can cause dramatically different future outcomes in complex systems.
I know that sounds boring as heck but bear with me a moment...
What is a complex system?
Complex systems contain too many interrelated variables to allow formation of precise (or sometimes even imprecise) rules describing expected behavior.
One complex system you may be familiar with is your self - other complex systems include; weather, ecosystems, pandemics and traffic flow.
Complex and complicated systems are not the same. A complicated system may contain many interrelated variables but the interaction of those variables is understandable and predictable. This is why we can build complicated systems ranging from automobiles to global positioning systems.
Trying to stay out of the weeds here - but there's a distinction between complexity theory and chaos theory. Chaos theory may be thought of as a subset of complexity theory, but we'll leave that aside for this essay because it's not particularly important in making what I think may be my point ;-)
If these sorts of things interest you BBC Radio 4 has a podcast on Complexity and one on Chaos Theory with some experts.
You may have heard of the so-called butterfly effect where a butterfly flapping it's wings at some distant place and time sets off a series of events that has effects on a tornado at some future time. This idea comes from the work of the American mathematician, meteorologist and founder of chaos theory - Edward Norton Lorenz.
That ecosystems and pandemics are complex would seem to be self-evident if we consider all the unintended consequences of humankind's actions on our planet and our health. If you are not aware of those unintended consequences - congratulations on making it to Earth-2. Also make sure you actually are living on another planet and not just watching too much Fox news or counting on the Wall Street Journal for the straight skinny...cause otherwise you may be in for some unpleasant surprises when old Ma Nature opens up a can of whoop ass to show you how much she doesn't care.
Where was I? Where am I?
The final example of a complex system is traffic flow. If you live in an area where there are a lot of traffic jams on the highway you may have asked yourself - why is traffic slowed down for no apparent reason? There may have been some initial condition - an accident or breakdown, that is long gone - but traffic flow is still stop and go.
Because many drivers are alternately applying their brake pedal and then gas pedal to try to maintain the closest distance possible to the car in front of them, apparently thinking that this will get them to their destination faster. Because they are following so closely they have to use the illumination of the brake-lights on the car in front of them as a signal to apply their car's brakes. After braking, they then accelerate to retain the minimum separation and the process repeats over and over - which contributes to the turbulent (as opposed to smooth) flow of traffic. You can experiment with eliminating the herky-jerky by maintaining multiple car lengths between you and the car in front of you. This smooths out traffic and allows everyone to get where they are going faster, but may also cause varying degrees of road rage...so be careful.
Perhaps the most important example of varying initial conditions, in a complex system, causing dramatically different future effects is in the area of raising and educating the complex systems we call children.
People who have had a teacher, coach, friend or parent who did some small thing(s) in their early life that made a huge positive difference in their later life are living examples.