The Paradox of Simplicity

It’s hard to look at something familiar and see it in a new way. But that is what we often must do when we work with the same material over and over again. Musicians use the same 12 notes. Artists use the same forms of composition. Painters use the same primary colors as the source of other colors. Comedians use the same joke structures.

One way to jump-start the creative process is to recognize the relationship between simple and complex elements.

If you have ever visited LEGOLAND, you may have seen a display that asked the question, How many different ways are there to assemble six LEGO bricks that have eight studs (the standard rectangular LEGO brick)? The answer may be surprising – a whopping 103 million different ways!

LEGO patent

The reason there are so many ways to combine six LEGO bricks is, the LEGO brick is very simple. Its simplicity makes it simple to work with and simple to adapt. If it were more complex, it would be less adaptable, and would be more limited in its usage.

Let’s look at it from a different perspective. Instead of starting with the building blocks and seeing how they could be assembled, let’s instead look at an assembled object and then see how it could be deconstructed. For example, let’s look at a simple drawing of a stick figure.

Let’s divide this stick figure into its head and body. If we were trying to describe how these elements fit together, it would be pretty simple: the head connects to the top of the body.

Looking at the body, we see that it is made up of different elements, including the torso, arms and legs, and we can further separate each of these elements from the others. The body as a whole is more complex than each of the elements that comprise the body. 

If we wanted to describe how each of these stick-figure elements fit together it would still be pretty simple (it is just a stick figure after all), but we would need to create more instructions. We couldn’t just say, “the head connects to the body.” Now we would say, “The head, arms and legs connect to each other by connecting to the torso.” But even with these simple elements and simple instructions, different people assembling these parts would produce somewhat different versions of our stick figure.

What can we observe from this exercise? The relationship of the head to the body is simple. The relationship of the head to each of the simple elements of the body is more complex.

To generalize, the more complex the elements, the simpler their relationship. The simpler the elements, the more complex their relationship. Stated more succinctly, the simplicity of the relationship is inversely proportional to the simplicity of its parts.

Back to LEGOLAND, the eight-stud brick is very simple, and so the relationship of six bricks is very complex. The number of possible ways to combine them makes your head spin.

Math professor Soren Eilers visited LEGOLAND with his daughter and wondered how they had calculated that number, 103 million. Recognizing a mathematical challenge, he set out to calculate it himself. As it turns out, he discovered that LEGOS’ own number was far too small. He established that there are, in fact, 915,103,765 different ways to combine six simple LEGO bricks.

Why, you may ask, is this relevant? It is relevant because, when we are actively searching for breakthroughs in our work, we can deconstruct our work into its elements and their relationships. Knowing there is a trade-off between element-complexity and relationship-complexity, we can choose to keep one aspect simple. And suddenly, our task is less difficult.

Going back to our stick figure, if we choose to keep the relationships simple, we can switch heads and keep the same body, or switch bodies and keep the same head. Alternatively, if we wanted to break the stick figure into simpler elements (head, torso, arms and legs), we suddenly have a lot more ways to combine them. We could overlap them at different angles, omit one or more elements, stretch or squash them, rearrange them, or relate them to each other in any number of ways.

The paradox is this: the more we simplify, the more complexity become available.