Complex vs Complicated

For this first real post of the series, let's look at the terms "complex" and "complicated". In the world of project management, the term "complex" is used more often, whereas in everyday life, "complicated" is favored. But in the end, few people manage to give you a clear difference between the two — at best give you a moderately convincing example, at worst tell you they are synonyms. If we rely on the statistics of a well-known search engine, it's the term "complex" that is the most searched.

Let's start with their etymology.

Etymology

• Complex: From Latin complexus ("embracement", "hug")
• Complicated: From Latin complicare ("to fold", "to roll up")

So, even if the words share the same first 5 letters, their origin is clearly not common. Let's look at their definitions now.

Definitions

Might as well take the language reference that is the Académie française dictionary.

Complex

Qui n’est pas simple, qui est composé d’éléments divers et entremêlés ; compliqué, difficile à comprendre. Source

A good start: the definition of "complex" ("complexe") includes "complicated" ("compliqué"), which shows the words are close to each other. Moreover, it's amusing to see that its definition starts with its antonym "simple". We see there is a notion of a high number of elements and of their interactions, but these interactions are not qualified.

Complicated

Composé de parties plus ou moins nombreuses qui ont entre elles des rapports difficiles à analyser, à saisir ; dont la réalisation ou l’usage est délicat ou difficile. Source Good already, no loop: we don't find the term "complex" in the definition. We find a notion of number of elements, which can, however, be low. We also find the interactions, but there they are properly qualified: they are « difficiles à analyser ».

Shedding light

Complex thus designates a system with multiple elements that interact with each other. No matter whether these interactions are simple or complicated, it's their number that makes it a complex system. I haven't lingered on the end of this word's definition, but it's almost the most interesting part — « difficile à comprendre » — which means that the ins and outs of the system demand a significant cognitive effort to grasp it globally, if that is even possible. The difficulty is often in the complete grasp of the system; we end up with "unknown unknowns". And that's precisely the difference from a complicated system: one interaction not taken into account or unknown, and the result at the end of the chain becomes unpredictable.

Complicated designates a system with few or many elements that have non-trivial interactions. But all the relationships and their difficulties are listed, inventoried, so we have "known unknowns". The end of the definition is also very interesting: a new notion appears there, that of realization or use — we're thus dealing with something more concrete, tangible.

Examples

What better than examples to understand well.

Un bon croquis vaut mieux qu’un long discours. (Napoléon Bonaparte) source

It's for "complex" that I had the most trouble finding a good example.

These flocks of birds, which have something hypnotic about them, are purely complex systems. They are guided only by a few fairly simple rules that one can describe like this:

• Separation: Avoid crowding your neighbors (short-range repulsion)
• Alignment: Head toward the average heading of your neighbors
• Cohesion: Head toward the average position of your neighbors (long-distance attraction)

And yes, with these 3 simple rules, thousands of individuals can coordinate and fly in concert. But birds aren't the only ones to move in groups like that — herds of land animals or schools of fish are governed by the same rules! Moreover, their movements and changes of direction are not random, but directly depend on many factors that aren't necessarily known. Of course, we have some obvious ones, like winds, terrain, predators, but a certain number are not known and are discovered through experience and observation. So we are indeed dealing with a complex system, but not a complicated one. As an anecdote, it has been observed that a movement of only 5% of the individuals was enough to decide the direction of the whole group!

As for a complicated but not complex system, we can include mathematical formulas such as this one:

x²+2(y-0.8*abs(x)0.4)² = 1

Which gives interesting things.

Source

So we do have a system that is complicated because of its resolution, but not complex, because all the unknowns are known and its resolution is not obvious. Moreover, its low number of elements is a good indicator of its simplicity. Careful: "simple" doesn't mean "easy".

FAQ

Is a system exclusively one or the other?

Absolutely not! It's even much more common for it to be both at the same time. The criterion to look at is the number of interactions and their exhaustiveness

Can a complex system be complicated and vice versa?

Yes! The two are often linked, and that's precisely why they are listed as synonyms. But it's not mandatory: a system with many elements and simple interactions cannot qualify as complicated. Likewise, a system with few elements but relationships difficult to solve will be complicated but not complex.

Can a system of one type be transformed into the other?

Absolutely! But to my knowledge, not in all directions. Turning a complex system into a complicated one is quite feasible; for that, empiricism is the best of allies. Knowing that the system contains unknowns, with experience and a posteriori analysis, it is normally possible to discover all these variables we were missing. So we end up with a system of known unknowns — that is, a system that is at worst complicated, at best obvious.

And the antonyms of each, what would they be?

For that I'll rely on the website of the Centre National de Ressource Textuelles et Lexicals, and particularly its antonym search feature. Unsurprisingly, some identical antonyms are found for the 2 terms:

So take your pick.

Benefits

Now that you know the subtleties between these 2 terms, you may be wondering how this is going to help you in your everyday work, beyond using the right term for the right situation. Well, it will let you tackle any type of issue or situation with the most appropriate approach, much faster.

• Complicated problem or situation: get help from an expert; they'll spare you a skills ramp-up and will save time.
• Complex problem or situation: favor people with better reactivity to face the unknowns that would appear without warning (who said agile?). If possible, explore several paths in parallel; moreover, empiricism and short iterations are the best means of learning and de-complexifying the subject. [ref]Thanks to William Bartelett for helping me complete this point. [/ref]

Of course, in real life, it's never black or white, but always a subtle mix of both. It's then up to you to subdivide the problem to better assign the right resources to the right places. If despite your efforts the mix remains inseparable, then create a team in the image of the problem.

Opening up

If you're still not fed up, know that there is a whole conceptual decision-making framework called Cynefin. I'll just tell you that "complex" and "complicated" are two pillar terms of this framework and that a good understanding is essential to approach it. I won't expand any further on the subject, because it is extremely rich and would deserve one or more posts of its own.