One of the hardest things to explain is why complex systems are actually different from simple systems.
We define the complexity profile as the amount of information necessary to represent a system as a function of scale.
The complexity at the finest scales is finite because of quantum uncertainty and is equal to a universal constant, 1/k B ln(2), times the entropy for a system in equilibrium, where k B is Boltzmann’s constant.
According to the complexity profile, each piece of information about a system has a size — the largest scale at which we can begin to detect that piece of information.
This also means that systems that look different on a microscopic scale may not look different at the macroscopic scale, and their mathematical descriptions become the same.
The result is that these two seemingly different types of systems map mathematically onto each other.
Scientists use the normal distribution for many different biological and social systems.
Even though the specific systems are very different, the dependencies that give rise to their behaviors, and the behaviors themselves, are related mathematically.
The mathematical representation of one system at a particular scale may correspond to the behavior of other systems despite different underlying components.
Source: Why Complexity is Different
Originally published at Cogly.
