S is for Simple Rules

Consider the following: schooling fish, roundabouts, segregation, and human consciousness are all examples of the same fundamental property of the world.  It may seem crazy to suggest that roundabouts may be interesting in some sense, but bear with me.

The property in question, and this week’s topic, is emergence.  In each case individual entities, by following simple rules, can create complex patterns of behaviour.  What makes these patterns special is that they can’t be predicted based on the simple rules alone.

Swarms

If you’ve ever seen a murmuration of starlings, you have probably found yourself wondering how that many birds (upwards of 100,000) can all fly so quickly in such close proximity without hitting each other.  For those of you uninterested in ornithology (the study of birds), there are also plenty of examples of swarms in entomology (the study of insects) and ichthyology (the study of fish), and even chiropterology (study of bats).

Image by SteveD
Image by SteveD

In each case, the animals are unaware (and frankly, uncaring) of the beautiful shapes their swarms make.  They aren’t even trying to swarm.  They are trying to survive and their instinct tells them to follow a few simple rules.  Since the advent of computers, scientists have been trying to find out what those rules are.

One of the most famous computational models of swarming behaviour was proposed by Craig Reynolds in 1986.  In his Boids program, simulated birds had to follow three rules:

  1. Separation: Don’t crash (steer away from nearby boids).
  2. Alignment: Get with the program (steer towards the average heading of nearby boids)
  3. Cohesion: Don’t get lost (steer towards the average location of nearby boids)

This model is actually a really good model for the behaviour we observe in birds and fish.  Recent studies have also shown this alignment rule is especially important for bats.

Locusts, on the other hand, seem to have a much simpler set of rules.  Locusts just want to avoid getting their backsides eaten.  When approached from behind, locusts will tend to fly forward for fear of cannibalism.  This creates an overall tendency to move forward and can lead to giant swarms.

Image by CSIRO
Image by CSIRO

Roundabouts

If you’ve ever been to Swindon (and, from what I hear, you’re not missing much if you haven’t), you might have come across quite possibly the most offensive piece of civil engineering in the UK.

That's right.  A giant roundabout.  Image in the public domain
That’s right. A giant roundabout. Image in the public domain

As a North American, I cringe at the thought of even a tiny roundabout but Swindonians apparently hate everything that is good in this world.

They built the Magic Roundabout.  A terrifying series of 6 small roundabouts encircling a larger roundabout that goes the other way.  If that sounds confusing, it’s because it is.

Hell for North Americans.  Image from the BBC
Hell for North Americans. Image from the BBC

The more confusing part, however, is that hundreds of thousands of cars pass through it while there is certainly a lot of anxiety about it, there have been only 14 major accidents in 25 years.  The vast majority of people pass through fine, despite there being 5 different entry and exit points and many conflict points (places where streams of traffic cross).  This happens because of a few simple rules:

  1. Follow the lines
  2. Give way to cars coming from the right
  3. Drive to where you want to go
  4. Don’t crash

Apparently it’s actually an effective way to move cars through an intersection, but my North American sensibilities just can’t handle it.

For more information on this piece of crazy road engineering, visit this explanatory page and watch this video.

Segregation

Choosing who you associate with based on a singular trait has been known to lead to a lot of issues in the past.  As a dog person, I’ve lost a lot of friends to cats (and their parasites).  Despite my friendly demeanour and my ability to put up with a fairly large proportion of cat-lovers in my immediate vicinity, at a certain point I start to feel uncomfortable and want more fellow dog-lovers.

Tensions flare.  Image by Peretz Partensky
Tensions flare. Image by Peretz Partensky

In 1971, Thomas Schelling set out to model this behaviour and came out with a somewhat surprising and scary result.  Even when people are fine with being in the minority, if they are dissatisfied when surrounded by a large majority of “others”, they will tend towards segregation.  The model followed a few simple rules:

  1. If you are surrounded by a certain percentage (e.g. 30%) of similar people, you are satisfied
  2. If you are surrounded by a certain percentage of different people (e.g. 70%), you are dissatisfied
  3. If you are dissatisfied, move to somewhere where you are satisfied.

Within a few rounds, there is very little diversity left as people tend to move towards those who are similar.  This, despite the fact that no individual is saying they outright dislike the other group or couldn’t live with members of the other group.  This model helps to explain why segregation is so hard to eliminate.

Interestingly, this tendency towards segregation can be reversed if a maximum of similar people rule is added:

4. If you are surrounded by a certain percentage of similar people (e.g. 90%) you are dissatisfied

Again, complex patterns and simple rules.

To learn more about the model, go here.

Conciousness

There are approximately 100 billion neurons in an adult human brain.  These neurons are connected in intricate ways to create an estimated 100 trillion connections.

Now that's a lot of connections!  Image from Wikimedia
Now that’s an impressive set of connections! Image from Wikimedia

Somehow (and to be honest we’re not really sure how yet), these connections lead to all of our brains’ activities from thought to imagination and memory.  The abilities of the system (the brain) couldn’t possibly be known from the rules that neurons abide by.  All that a neuron does is pass on its signal according to a set of rules.  We still don’t know what those rules are.

We do know that when a neuron is activated (whether by electrical or chemical stimulation), it activates other neurons.  The precise number and location of these other neurons is still a big mystery in neuroscience, but it must be activating both nearby neurons and neurons on the other side of the brain.  This dual activation of long- and short-distance connections is what creates the sustained patterns we observe in fMRI scans.

Human Connectome Project
The Human Connectome Project, kind of like the Human Genome Project before it, is setting out to map all of the brain’s 100 trillion connections to better understand how it works.  Image by Xavier Gigandet et al.

While I don’t mean to suggest that everything in life can be boiled down to simple rules, I think it’s pretty incredible the patterns that emerge from individual actors all playing their parts.

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