Linearity and Nonlinearity

A Short Primer

Linear things are amazing.  Linear processes can be reliably scaled and are responsible for much of the wonders of the modern world. But linearity isn’t the only thing going on. The nonlinear is afoot as well.  It’s the stuff of virality, of the whole being greater than the sum of its parts—like the combination of chocolate and peanut butter.

Non-Linearity: A property of complex and chaotic systems, characterized by approximation, random behavior, and unpredictability. It is the feature of natural (real world) or other systems which cannot be decomposed into parts (additivity) and reassembled into the same thing (replicability), or do not change in proportion to a change in an input (proportionality).

I didn’t learn about nonlinearity until a few years ago. I wish I’d known sooner. I wish I’d had the language to understand it—since my job was figuratively and literally swimming in nonlinearity. It seems to be a common theme—we want a context full of nonlinearity to act in a linear fashion, and then we get frustrated when it doesn’t. 

Nonlinear processes have always been around (see nursery rhyme), but our interconnected age has sped up the tempo of such events. The trick is to understand when we’re in a linear place, and when we’re in a nonlinear one, and to manage our expectations/conduct accordingly.

Disclaimer: This is a work in progress, trying to integrate some disparate ideas in one location.

All the ways that I have seen to illustrate this order/complexity/chaos spectrum are two dimensional, so I was trying to figure out a way to make it more interesting with a sphere. I really like the Order-Complexity-Chaos depicted as Ice-Water-Steam—I think it captures the main idea well.

The chart is a synthesis of a bunch of different readings on complexity and chaos.  Cynefin framework is depicted on the chart- I don’t have disorder on here, but maybe disorder is in the center of the sphere. Vervaekian ways of knowing (This is an idea from Story Grid, to tie the ways of knowing to domains), and Rumsfeldian “knowns” (I know it’s not Rumsfeld’s thing, but he really brought it into public consciousness when he talked about it in 2002.) Also depicted is the McGilchrist left brain/right brain dichotomy- “the left brain apprehends; the right brain comprehends.” Left brain is used to exploit what we find in the world, the right brain is used to explore it, and we need both to see clearly. Having mode/being mode goes along with that.

Here is a link to the actual power point (because I have sweet gifs of flowing water and steam embedded).