A complicated issue, a complex situation. When we use these adjectives we do not ask ourself the question on their exact meaning. Apparently one can be substituted for the other without modifying the sense of the subject. But in fact, it is just what it seems to be. We can then wonder why we have got two terms to express the same thing ? I suggest we take a moment thinking about the nuance between both. Then we shall see the importance which it can have to approach the problem solving.
Complicated / complex : dictionaries add to the confusion.
The usual dictionaries do not help a lot with their definitions of complicated and complex. They consider complicated as a synonym for complex and vice versa. They even go as far as raising the same list of synonyms for both terms.
We have got to look at the antonyms to begin glimpsing the difference between both. The antonyms of complicated are : well-to-do, easy, simple and those of complex : elementary, basic, clear.
But as very often an analogy allows to make better understand the shades of meaning. The most classic one opposes the machine, with its complicated structure, to an alive body with its complex way of functioning.
From my point of view, I would rather compare puzzle and jackstraw to illustrate the difference of meaning between complicated and complex.
Puzzle ou jackstraw?
Pieces of a puzzle are numerous, dissimilar and have a unique location in the composition of the picture. Generally we proceed in a very logical and rigorous way to reconstitute the image : analysis each pieces, classifications them in category (corners, colors …), try of positioning …
If it is too much difficult for us, we can use a model of the image to place the puzzle pieces at the right place (Real puzzle amateurs do refuse to do so !).
It is also interesting to observe that we can build, deconstruct and reconstruct the puzzle infinitely. The final result will always be the same.
For the jackstraws it is quite different. There is also a lot of pieces in the game but once launched they constitute together one complex set. Impossible to know how they hold really together, nor to anticipate what risks to occur if we move one of them. It is moreover all the principle of the game. We have to carefully observe the set and then try and pick up a jackstraw as possible without disturbing the heap. After every unfortunate attempt jackstraws find themselves a new balance at least as much complex, and even more, as the precedent.
Of course it is almost impossible to reproduce the same configuration of set.
What is the avantage of using the right adjective ?
Besides the satisfaction to use the correct word, qualifying appropriately a problem can save you a precious time. Knowing if you face a complicated or a complex problem is key for adopting the right way of reasoning and the method of analysis.
In the front of a complicated issue we know beforehand that with a little of patience, analytical mind and method we shall manage to understand the inner workings of the set. We can begin immediately to unwind the well known methods of analysis and to split the set in understandable subsets according to the proverb : « How to eat an elephant? Piece by piece !»
We apply a progressive process of understanding which rests on the observation and the characterization of every subsets and the definition of their exact function.
On the contrary in front of a complex problem, it makes no sense to rush to the analysis of each single item : we know that it is not the appropriate method. It is better to start considering the interactions subsets keeping an eye to the whole set.
It is not the items themselves, nor their individual role and function, that matter but their faculties of interaction and of fast adaptation for the outside requests.
To be efficient we have to show humility and to accept that our understanding will remain partial whatever we make. On the other hand we should activate all our senses to get the slightest indications which will allow us to encircle better the problem. We have to give up logical reasoning and trust our intuition, raise hypotheses and experiment them.
By the way should you find a solution that works, be happy and not to waste additional time trying to find out why.
Opposing complicated to complex make the above explanations easier. The reality is is less simple. Very often an issue is complicated and complex at the same time. A kind Yin/Yang in the difficulty ! However using the prism puzzle/jackstraw to solve issue can open doors to interesting approaches. I encourage you to try. Enjoy practice !