# Theory of complexity

In his book Black Swan, the essayist Nicholas Nassim Taleb provides a functional definition of complex domains:

“A complex domain is characterised by the following: there is a great degree of independence between its elements, both temporal (a variable depends on its past changes), horizontal (variables depend on one another), and diagonal (variable A depends on the past history of variable B). As a result of this independence, mechanisms are subjected to positive, reinforcing feedback loops.”

Nate Silver expands on this brief introduction with a more illustrative description in his book The Signal and the Noise:

“The theory of complexity that the late physicist Per Bak and others developed is different from chaos theory, although the two are often lumped together. Instead, the theory suggests that a very simple things can behave in strange and mysterious ways when they interact with one another.

Bak’s favourite example was that of a sandpile on the beach. If you drop another grain of sand onto the pile (…) it can actually do one of three things. Depending on the shape and size of the pile, it might stay more or less where it lands, or it might cascade gently down the small hill towards the bottom of the pile. Or it might do something else: if the pile is too steep, it could destabilise the entire system and trigger a sand avalanche.”

Just imagine the number of different ways that the sandpile could be configured. And just imagine the number of ways the falling grain of sand could hit the pile. Despite being such a simple object (a sandpile) the number of possible interactions between its constituent parts are innumerable. And each potential scenario would have a different result.

But of course a pile of sand containing thousands of irregular grains is complex. An simpler example would be the initial break in a game of pool. 16 spheres on a flat surface. But still, how many times would you have to break until every ball landed in the exact same positions?

These are complex systems.

Whilst Silver is quick to distinguish between complexity and chaos, it’s worth noting that Tim Harford is also keen to make a distinction. In his book Adapt he separates the concepts of complex systems and tightly coupled systems.

To put it simple, complex systems have a lot of possible, hard to predict scenarios. Some will destabilise the entire system, some won’t. Tightly coupled systems are always the latter.