Complex problems are those that cannot be conceptualized or approximated.

A useful analogue for this is to consider a four dimensional object. Humans only see in three dimensions. If presented with a four dimensional object, we would only see aspects of the object in a perspective bounded by three dimensions. This would become particularly confusing if multiple people were to view the same 4D object from their own perspective. Each would be able to describe the shape, and, insofar as they could describe their own senses, they would have an absolutely correct accounting of what they saw—but it may massively differ from what another observer sees. The problem in this case, is that both of the observers can be totally “correct” relative to their three-space commentary.

Even if a single observer stared at the 4D object from all available 3D perspectives, they still wouldn’t have an accurate grasp of the shape because they lack the additional dimension of perspective in which to see true four-space shape. Most people, when they learn about 4D shapes, have to think their way through them by applying rules such as number of lines intersecting at a vertices, but it is very hard (probably impossible) for 3d based minds to intuit 4D shapes.

Something similar happens when people consider complex problems. First, it seems entirely possible to problems can exist with dimensions that we cannot perceive. Furthermore, complex problems tend to create conflicting commentary because the nature of the problem is that viewed from differing perspectives, you will get entirely accurate — and entirely conflicting — information.

Consider the hypercube presented below. Rotating on a single axis, I show three perspectives. Were I to ask which “cube” composed of 8 points and six sides is at the center, I would expect different answers, depending upon perspective. Each answerer may be absolutely right relative to their own perspective, but wrong as soon as they change perspective.

Just looking at this single shape, it can also appear that the lines change length as the perspective changes, but that is only because you can only see the 3D components of a 4D length vector. Actually, all the lines are the same length. The points of are in a constant 4D relative position to each other with only the observation perspective changing.

Thus complex problems seem to leave open the possibility for multi-dimensional answers. An answer, provided accurately at one perspective, may be inaccurate at another. It may even appear that some willful deception is taking place. The truth is, there are problems that demand more dimensions of analysis than our perspective or perception allow us to handle.

An example of this seems to exist with the behavior of large organizations. Observers can look at a complex organization and take in one aspect with absolute accuracy, while radically mischaracterizing the actual organization. There perspective will conflict with another, and that conflicting perspective — being accurate in itself — will likely engage a passionate defense. Who does not believe their senses? Who could recuse themselves of their insight when drawn from earnest and honest observation?

So it is that many of the people whom I discuss the Air Force, or National politics. They have their own perspective, as valid as mine, and we are both massively incomplete. It is hard to imagine that the nature of the object of your study may exceed your perceptive ability to observe or your cognitive ability to comprehend.