The Outside Perspective

Take a look at some of the massively complex systems at play in the world (economies, politics, social groups), and you’ll consistently observe two fascinating patterns. First, we (humans) who are outside the systems tend to oversimplify what is happening within them. And second, on close analysis, many of these systems do seem to have more structure and order and alignment than we’d expect.

Let’s start with the first realization.

From the outside in, we regularly try to make sense of complex systems in simplistic ways. One psychological technique for doing so: anthropomorphizing.

We refer to countries by their leadership, or to companies or political parties as though they were people instead of simply being made up of people. We draw conclusions about their actions as we might about human beings. We develop affinities to brands as we might to significant others. We hold grudges against identities, not the things comprising those identities.

And yet, this heuristic is a manifestation of a more general strategy. Even though complex systems are—by definition—complex, we somehow derive a lot of information by watching what happens at their perimeters.

The Calculus of Closed Surfaces

Of course, my mind goes to math. There is a beautiful theorem in vector calculus called Stokes’ Theorem. Don’t worry, I won’t get too technical. But I will show it here just to exhibit its succinctness:

In one sentence, here’s what Stokes’ Theorem says: If you draw a boundary around a system, and you measure what is happening at the boundary, you can understand the aggregate effect of what is happening within the system. In that scary-looking equation above, the right side just means “what’s at the boundary”, and the left side stands for “how everything inside is moving.”

Inside of a mathematical system, at every single point, you can measure something called curl. There’s a great political analogy to draw here. Curl is the measure of how much things at a point are spinning clockwise or counter-clockwise. Politically, this is analogous to individuals in a group pushing agendas to the left or to the right.

The motion at the boundary (i.e. the direction the system appears to be moving from the outside) is exactly equal to the total sum of the curl inside of it.

In our political analogy, the stance of a political party is (in theory) equal to the aggregate liberalism or conservatism of its members. The actions of a country (from the perspective of foreigners) represent the aggregate will of its citizens.

Magnets

Except this isn’t ever true in reality. And that is because there is a fundamental difference between the calculus of vectors and the calculus of human beings. Vectors operate independently of each other (this fact is indeed the entire basis of the vector mathematics). People, on the other hand, have immense influence on one another.

And that brings us to the second point I outlined at the top, which is the way that these complex systems, with all their many parts wiggling around freely, still adopt some kind of order in the aggregate.

Perhaps a better way to think about a holistic system, from the outside in, is as a magnetized object.

Here’s one of the many amazing things about magnets. Say I have a system (or a company, or a country, or a political party) and I want all of its components to be aligned (or to support a business decision, or a foreign policy strategy, or a political candidate).

I don’t need to orient every one of the components in the system. I just need to find the bigger ones and magnetize those:

And the magnetic forces will ripple through to the smaller ones, until they’re all aligned:

Or, alternatively, I could magnetize several of the smaller ones and have their aggregate effect impact the larger ones.

The results are the same, which is that once this trickling effect is completed, the group appears homogenous.

Synchronization

The brilliant mathematician and writer Steven Strogatz published a book in 2003 called Sync: The Emerging Science of Spontaneous Order. It explores the math and science behind how enormously complex systems get synchronized without the need for any top down decision making.

For example: Electrons in semiconductors that, from the outside, appear to be a single stream of electricity. Fireflies and their flashing lights that, from the outside, appear to be responding to an orchestral conductor. Pacemaker cells that, from the outside, yield a single consistent heartbeat.

All of these are made up of many (as many as trillions) component parts pushing and pulling, doing their own thing, resulting in astonishing emergent behavior.

Examples extend well beyond those mentioned in Strogatz’s book: Members of a political party who, from the outside, somehow rally around a single candidate. Employees of a company who, from the outside, are fully bought into decision making. Citizens of a country who, from the outside, take unified action, adopt a sense of identify, believe in a distinction between us and them.

And despite the ubiquity of these phenomena, they’re quite counterintuitive when you think about them. As much as things can be a mess sometimes, it’s surprising that the world still manages to work as neatly as it does.

“We're accustomed to thinking in terms of centralized control, clear chains of command, the straightforward logic of cause and effect,” Strogatz writes in his book. “But in huge, interconnected systems, where every player ultimately affects every other, our standard ways of thinking fall apart.”