Complexity

The theory

Some of my readers come from rather academic backgrounds, and make comments that sound like "Jabberwockies and slithy-toves are irrelevant!" (This seems to be the most usual type of communication from a university professor, as far as I can tell). A bit of googling is usually needed to understand what is their pet peeve, which may or may not have something to do with what you were talking about. I recently got one of those, and it got me thinking about something I've been wanting to post about for a while, and dreading at the same time. Complexity.

Complexity is one of the key concepts when you talk about systems. But it's difficult to talk about it because it's... well, complex. There are many definitions of complexity, and one of the most common says that a system is complex if it has emergent behaviour, in other words, it does things you wouldn't have guessed if somebody just told you about its parts and how they are put together. I don't like very much that definition because it's almost like saying: "A system is complex if you find it hard to understand" and that is really saying more about your intelligence than about the system. For example, you can tell the physics of the sea surface are more complex than the physics of the surface of a small lake, because the sea has waves and tides. Waves and tides are emergent behaviour that shows only in large bodies of water.

Another definition, that I like more, says that a system is complex if it's highly structured, in other words, if you can recognize a lot of clear patterns and configurations inside it. Highly structured systems almost always have emergent behaviour, so the two definitions are for most purposes equivalent. For example, a plant is definitely more complex than a rock, it has many more structures, configurations and all sorts of stuff going on inside it. It also has plenty of emergent behaviour: it grows, turns its leaves towards the light, etc. If you had never seen a plant in your life you wouldn't have guessed it could do that in a million years.

The most rigurous definitions, loved by mathematicians and people so brainy that they wish there was a quicker way of speaking formulas, use formulas that translated to plain English mean: a system is complex if it would take you a long time to describe it, when you describe it in the simplest possible terms. That has a bit of both of the other definitions: highly structured systems and anything that has emergent behaviour are going to be difficult to describe. For example, it would be much more complicated to describe a plant than it is to describe a rock. But for us plain mortals this definition sounds more "fuzzy", even though mathematically it isn't fuzzy at all, so I recommend that you stay with the idea that a complex system is something with a lot of different complicated patterns in it.

Complex is often confused with complicated, but they are different ideas. A complicated system has a lot of different parts, but the structure may be very simple. Complicated systems are a challenge to your memory and patience, complex systems are a challenge to your intelligence - often a challenge you will fail. A city is complex and complicated; beehives are complex but not too complicated; the people on a beach (that don't interact much with each other) and the sand and pebbles on the beach are simple systems; chess games and many gardens are complicated, but not very complex.

Whenever you are looking at any system, try to estimate how complex it is. The following are good signs that the system is complex:

• The system has a memory. It behaves differently depending on what has happened in the past. A plant has some memory, a rock doesn't.
• The system is nested. You can see that the parts it's made of have smaller parts inside them. A plant has leaves, roots, etc, that are made up of cells, that have a lot of interesting bits inside them called organelles.
• The system has a structured network. By this I mean that connections in the system make a network where some nodes are very highly connected while most of them aren't. In a forest, certain plants are eaten by lots of animals, while some are eaten only by a few. That's part of what makes a forest complex.
• You see the butterfly effect in action. The name of the butterfly effect comes from a saying about complex systems, "a butterfly beating its wings in Brazil could cause a hurricane in the Gulf of Mexico a couple of months later". In complex systems, a small change can cause a huge difference in future behaviour. For example, some tiny vibrations in the air made by a small speaker make a sound that a little girl hears as: "Get lost." The girl starts crying, runs away and shortly afterwards she's well and truly lost. This could be followed by even bigger consequences.
• The system has lots of feedback. "Feedback" means that the result of an event has an influence in the chances of it happening again. For example, you get angry at somebody and you shout at them. Depending on how much this person loves you and their personality, this will reduce or increase the chances that this person does again what made you angry. What's unlikely is that they are completely indifferent. People give feedback to each other all the time, though sometimes they get positive and negative feedback mixed up.
• You have trouble to understand what's going on. This almost guarantees that the system is complex.

The practice

Experiment 1

Think of an organization you are part of (it could be your place of work or a voluntary organization you take part in). Ask the following questions:

• Is the internal structure simple, complex or complicated?
  
• Have you seen the organization behaving in a way unexpectectly well coordinated?
  
• Does it keep good records?
  
• Does it have subgroups within groups?
  
• What is the internal network like?
  
• Is it possible to make big permanent changes by starting small?
  
• Is there lots of feedback?

This should give you a feeling for how complex it is.

An organization that is too simple is just disorganized. Working inside it feels like walking through treacle: a lot of the time you feel like you can't get anywhere.

It's uncommon that an organization is too complex, but nowadays it happens more and more, mostly thanks to modern information and comms technology. You can tell it is if it seems to be taxing your brain a lot just to do the common things that you are supposed to do all the time, and you can't keep up with the speed that things are changing.

Experiment 2

Go to the nearest garden to where you live. It could be a park or a vegetable garden, it doesn't matter.

• Does it look simple, complex or just complicated?
• Is there anything in it that surprises you?
• How does it change with the seasons? Does it go round the same cycle every year, or do you see changes each year?
• How do changes start? Do they start small, or are they complete overhauls?
  
• What patterns can you see in the way different plants are situated?
• What interactions do you notice between plants? Are there many of them or few?
• How long do you think it would keep its character if there were no gardeners?
  
• Do these observations tell you something about what kind of training the gardeners had?