I use the previous phrase often and in many circumstances. While it seems redundant, trivial, and self-descriptive in an obvious way, the connotation that I have when I use it is that people often recognize that systems are complex in the inner workings and/or relationships with things other than themselves, but that they don’t really understand what it means for something to have complex relationships. For example: you recognize that a car is a complex mechanical object, but you don’t really have any idea what it means for it to be complex, nor how complex it is; Complex is often a trivially useless descriptor.

My connotation in saying that complex systems are complex is that there are profound things about such systems that are not currently understood (by anybody, even, in the example above, a skilled auto mechanic), and, in some stronger and very important cases, things about such systems that cannot ever be understood.

In introductory physics, you solve a lot of problems having to do with ropes falling off of tables and objects accelerating from rest. You might even do a fun momentum problem in which a running back collides with a linebacker. But do you ever do problems with more than two objects interacting? No. That’s a many-body problem and it is saved for physics majors to tackle in mechanics or advanced mechanics. But how many bodies constitute solvable problems versus very hard or impossible problems?

Here’s an apocryphal story of Daniel Patrick Moynihan asking a Harvard chemist this question. (also, see here.)

A while back, one of Harvard’s great chemists was discoursing on what he called the “many-body problem,” a condition in which the number of variables interacting with one another in any given situation makes that situation extraordinarily complicated and difficult to fathom. I asked in what range of numbers this “many-body problem” begins. A somewhat suspicious glance was returned. Did I really not know? Apparently not. “Three,” he replied.

In the physical sciences, complexity starts at around 3 interacting objects. I always maintain that any system that involves humans is complex. Why? Because humans don’t even understand how themselves, let alone how one human interacts with any number of other humans. We don’t understand our own behavior; sociologists don’t understand our behavior, psychologists don’t understand our behavior, and certainly politicians don’t. We don’t know what policies will work in advance, and it’s rare, and we’re exceptionally lucky if we even can collect the data to understand what policies have worked a posteriori.

-JD Cross