The beginning of a poem that makes the point that a seemingly
minor event can lead to significant consequences.
For want of a nail, the shoe was lost;
For want of the shoe, the horse was lost;
For want of the horse, the rider was lost;
For want of the rider, the battle was lost;
For want of the battle, the kingdom was lost;
And all for the want of a horseshoe nail
An important caveat is that these chains of causality are only
ever seen in hindsight. Nobody ever lamented, upon seeing his
unshod horse, that the kingdom would eventually fall because of it.
Equally important, yet tending to be overlooked, is that, when we
trace these events backward, starting from
the fall of Rome and finally
ascribing it to a blacksmith oversleeping one morning --
or do we go one step further and blame the visting friend who
kept him up all night drinking mead
-- we are following branches of a tree structure, and we don't notice
that at any point, we could have chosen a different path and ended up
at a totally different conclusion, e.g., that it was all the fault of
a nail protruding from a plank in the deck of a galley that tripped
a slave, causing the ship to burn, u.s.w..
It is also an illustration of the idea underpinning chaos theory,
known as sensitive dependence on initial conditions; the initial
condition being the presence or absence of the horseshoe nail.
We actually see the ramifications of small changes every day. For
example, we're driving along, and the car in the next lane is five
feet ahead of us. Because of that, it is just able to get through
a green light (please excuse the U.S.-centrism), while you stop for
the red. The small difference between your being one foot behind or
five, can then translate into his lead opening up to a mile.
It is sometimes assumed that the effects of the initial change will
be magnified as time goes on; this is the basis of several science fiction
stories that posit a time traveler far in the past performing some
utterly innocuous action, then returning to his starting time to find
the universe totally unrecognizable.
However, it is equally likely (for sufficient values of equal) that
the effects of the two different initial conditions soon merge, and it
turns out to be inconsequential which one actually obtained. For
example, the car with the initial five foot lead may continually pull
farther and farther ahead with each controlled intersection along your
path, or it may be that you'll catch up to it again at the very next
light. (Actually that is more likely if the traffic signals are
synchronized -- though even that is sensitive to whether the
other car is travelling slightly above or
below the speed limit....) Just as it is likely that
the rider bearing the vital news could just have picked a different horse
bearing a full complement of shoes.
The fact that a small change in the initial conditions
may actually not cause a significant difference
down the road then leads to the idea from
dynamic systems of a strange attractor, which is a
complex behavior that a system may exhibit, and to which it
will tend to return even if the initial condition is
changed slightly. (A sufficiently large change, of course, will
lead to different behavior, but often to another
strange attractor with its own range of initial conditions.)