Expertise required for reading:

What you’ll read:

  1. How complex systems are explained as they were wizardry
  2. What really means that “they are not the sum of their parts”
  3. A simple (and clear) explanation of the property of emergence

If you ever looked for information about complex systems, surely you came across someone claiming that complex systems “are not just the sum of their parts,” or that “you cannot understand a complex system just by studying its fundamental components.” This type of expression sounds really interesting and fascinating, and probably this is why it is so widely employed. Unfortunately, it also brings very little meaning to the poor listener which is usually left with a series of confusing images and empty explanations.

This type of communication is not something new. Indeed, it is typical of magic and poetry; where you want to communicate to the soul of a person, not to her mind. Unfortunately, this approach does not match well with science. In science, we want to be 100% clear about what we mean, and the listener should be able to understand it. Otherwise, science communication is just a low-quality version of Hollywood movies, where you can hear the scientist blabbing out of context that “is time to get rid of Fourier transform and start using applied quantum mechanics” (the Transformers movie appeared to produce strokes even in the strongest signal analyst).

Of course, I am aware that most people are not experts in complex systems. Meaning that we cannot just throw equations and graphs and expect everyone to understand. So, today we are not just going to see one of the most peculiar aspects of complex systems (aka emergence). Today we are also going to explain it in a way that is (hopefully) clear for everyone.

“The sum of its parts”

When I first heard the expression “the sum of its parts”, my mind was immediately brought to the concept of addition. I thought that, in some weird way, a complex system was something for which 2 + 2 does not equal 4. And some people actually use this concept for stressing the peculiarity of complex systems. But does this make any sense? Are we studying physical systems that violate standard arithmetic rules?

Now, if you know some math you are probably smiling, as you know that in mathematics 2 + 2 = 100 is perfectly fine (if the right term is using binary representation). Another classic example of these violations is clock-math. Indeed, in a clock 10 + 3 = 1, as if it is three hours after 10 it means that now it is 1 o’clock.

However, all of this feels more like a trick than a real explanation. Indeed, we are just changing representation (e.g. in binary 100 is just the symbol for 4 units of something; i.e. what normal people call “four”). This feels like declaring that you can eat a table, but just because you replaced the word “apple” with the word “table.”

So, all this mess with complex systems is just because someone is replacing the key concept with something else?
To answer as a popular meme of these days, I would say that the answer is yes, but also actually no.

The fireman’s secret

A good (and common!) example for understanding complex systems is the bucket brigade. Indeed, if you have 10 firemen with 10 buckets in front of a house on fire, you can just tell them to run back and forth to throw water at the house. However, a more efficient way is just to line them up in what in a human chain where each one passes the bucket to the next one.

Here I like to stress that the first task can be accomplished with any number of people (even just one), while the second option makes sense only if we have enough people to actually form the chain. Is this enough to explain the mystical power of complex systems? Yes, if we focus on the right thing.

What is “emergence”

People usually claim that the bucket brigade is an emergent feature of firemen which is “not contained in the single fireman.” From this, they also claim that studying a single fireman would be useless, as the single entity does not have the emergent property (and so you cannot study it).

However, when a person is passing the bucket to her neighbor is using her own arms and her own free will (if you suppose free will exists). Her skin is still the same, her eyes do not change color and her memories are still in her brain. So, what’s up with these complex systems? Why do we say that it does not make sense to study the single individual/component?

The trick is here: if you study a person in isolation, you can focus on her past, her face, her whatever… And maybe, if you study her well enough, you can come up with the idea that placing several of them one next to each other can create a bucket brigade. And this is the secret of complex systems: the link between them.

Let me stress it out better. When people are in isolation, they do not exhibit bucket-brigade-like behavior. This does not mean that they have to undergo some kind of mystical transformation. Or that when summed up together they produce some magical flow of chakra things. The problem is that in isolation you cannot observe their link. You cannot study how they interact, which is the key to some behaviors. Of course, you can use your imagination (and this has been done a lot in science!) but if you can directly see the weird way the components interact is so much easier.

For example, I am pretty sure nor even J.K. Rowling, just by looking at a bird will come up with a peculiar dynamics as bird flocking!

Is that… magic?

So, yes, someway we could say that a bucket-brigade is more than the sum of the single people. However, I prefer to avoid this kind of slogans which convey a lot of emotions (at least for the standard of an empty scientist as me) but very little meaning.

Instead, I would try to explain that some phenomena can be observed only by looking at the interaction of some components. So studying them only in isolation would most likely be a waste of time. I know that this does not sound super fancy and catchy, but unfortunately, this is just science.