There’s lots of talk of complexity in the world of social programme evaluation with little clarity about what the term means. I thought I’d step back from that and explore ideas of complexity where the definitions are clearer.
One is Kolmogorov complexity:
“the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object.”
For example (mildly edited from the Wikipedia article) compare the following two strings:
abababababababababababababababab
4c1j5b2p0cv4w1x8rx2y39umgw5q85s7
The first string has a short description: “ab 16 times” (11 characters). The second has no description shorter than the text itself (32 characters). So the first string is less complex than the second. (The description of the text or other object would usually be written in a programming language.)
One of the fun things we can do with Kolmogorov complexity is use it to help make sense of emergence – how complex phenomena can emerge at a macro-level from some micro level phenomena in a way that seems difficult to predict from the micro-level.
A prototypical example is how complex patterns emergence from simple rules in Conway’s Game of Life. Game of Life consists of an infinite 2D array of cells. Each cell is either alive or dead. The rules are:
-
- Any ‘on’ cell (at time t-1) with fewer than two ‘on’ neighbours (at t -1) transitions to an ‘off’ state at time t.
- Any ‘on’ cell (t -1) with two or three ‘on’ neighbours (t -1) remains ‘on’ at time t.
- Any ‘on’ cell (t -1) with more than three ‘on’ neighbours (t -1) transitions to an ‘off’ state at time t
- And ‘off’ cell (t -1) with exactly three ‘on’ neighbours (t -1) transitions to an ‘on’ state at time t.
Here’s an example of the complexity that can emerge (from the Wikipedia article on Game of Life):
Looking at the animation above, there’s still an array of cells switching on and off, but simultaneously it looks like there’s some sort of factory of (what are known in the genre as) gliders. The challenge is, how do we define the way this macro-level pattern emerges from the micro-level cells?
Start with Mark Bedau’s (1997, p. 378) definition of a particular kind of emergence known as weak emergence:
Macrostate P of S with microdynamic D is weakly emergent iff P can be derived from D and S‘s external conditions but only by simulation.
This captures the idea that it’s difficult to tell just by inspecting the rules (the microdynamic) that the complex pattern will emerge – you have to setup the rules and run them (whether by computer or using pen and paper) to see. However, Nora Berenstain (2020) points out that this kind of emergence is satisfied by random patternlessness at the macro-level which is generated from but can’t be predicted from the micro-level without simulation. Patternlessness doesn’t seem to be the kind of thing we think of as emerging, argues Berenstain.
Berenstain (2020) adds a condition of algorithmic compressibility – in other words, the Kolmogorov complexity of the macro-level pattern must be smaller than the pattern itself for it to count as emergence. Here’s Berenstain’s combined definition:
“Where system S is composed of micro-level entities having associated micro-states, and where microdynamic D governs the time evolution of S’s microstates, macrostate P of S with microdynamic D is weakly emergent iff P is algorithmically compressible and can be derived from D and S’s external conditions only by simulation.”
Now I wonder what happens if a macrostate is very simple – so simple it cannot be compressed. This is different to incompressibility due to randomness. Also how should we define simulation outside the world of models in reality: does that literally mean observing a complex social system to see what happens? This would lead to interesting consequences for evaluating complex social programmes, e.g., how can data dredging be prevented? What should be in a study plan?
References
Bedau, M. (1997). Weak emergence. Philosophical Perspectives, 11, 375–399.
Berenstain, N. (2020). Strengthening weak emergence. Erkenntnis. Online first.
A lovely video about Game of Life, featuring John Conway
Once you’ve watched that, have a play over here.