complexity

[scruffy]

How do you "measure" complexity?

No one seems to know.

One of the most obvious places to start looking, is computer programming. How complex is a program, or a subroutine, or a few lines of code?

Cyclomatic complexity - Wikipedia

en.wikipedia.org

What exactly IS complexity? If I stuff a few more protons and electrons into a volume of space, does that mean it gets more complex?

How about information? Does more information mean more complexity? Does more complexity mean more information?

Here is a method that seems to increase complexity while keeping entropy constant.

https://www.researchgate.net/publication/227277862_Measure-theoretic_complexity_of_ergodic_systems

 

[scruffy]

Here's my take:

In a static system, nodes x paths

In a dynamic system,

integral (cover(node x) * sigma (path(I) * probability (I)) dx),

which basically means, the sum of all contributions from all paths between all nodes

a node, in this case, is defined as a union of intervals - which allows for geometry, like lattices and so on

a node, loosely speaking, is an object

and a path, loosely speaking, is a relationship between objects

so your complexity is number of objects * number of paths, plus whatever additional complexity is introduced and supported by the dynamics

In quantum physics, dynamics become probabilities in a complex Hilbert space, complex being the operative word. "Additional complexity" is only that which has no real component, because all the real components go along the paths that are already accounted for.