Problem solving is at the core of human intelligence, and is arguably the reason that as a species we’ve thrived so much. Whenever there is a difference between our goal state (where we want to be) and our initial state (where we are), we can intelligently perform operations that get us farther away from our initial state and closer to our goal state. However, that is not enough — we do so while making sure that we aren’t detrimental to our ability of solving other problems. One way to cook a meal is by burning down the house, however we are intelligent enough to solve our problems by recognizing and acknowledging the constraints. This is the same intelligence we are trying to produce in our machines lately, and is the same intelligence that enables us to carry even the most simplest of tasks like walking.

However, the problem is that problems don’t form a uniform class because not all problems are well-formulated. Some problems are ill-defined, which means it’s incredibly hard to come up with a solution directly. However, with some restructuring and redefining of the problem, we can convert an ill-defined problem into a well-defined problem. This requires what cognitive scientists call insight. Insight is at the heart of problem solving because many problems we face in our everyday life aren’t really well-defined, and once we reach a good problem formulation, solving it is really straightforward. The truth is, we understand very little about the mathematical functioning of how insight actually works. What we do know, however, is how we can enhance it, to ultimately enhance our problem solving capacity. Insight involves paying attention to the right things. Then, you might ask, what really is attention? Attention has four directions: transparent, opaque, featural, gestalt. Let’s look at the first two directions first.

The idea is to think of our awareness as our vision: we can look through our glasses, but we can also look at our glasses. In the same way, when we’re hitting a hammer on the nail, we are focally aware of the hammer hitting the nail through our fingers and arm. However, if we wish to, we can instead choose to redirect our attention so that we’re focally aware of the swinging motion of our arm through the hammer hitting the nail and the fingers gripping it. This hopefully builds the concept of attention as layers through which we are aware — we can be aware through something (make it transparent) to be aware of something else (make it opaque). This applies to problem solving because often we look through our formulation of the problem to solve it because we feel we have an idea of how to solve it. However, sometimes we need to transform our transparent formulation, and make it opaque to look at how we are formulating the problem. Often what we consider a calculus problem, can turn out to be a trigonometry problem. What we might consider a manufacturing problem, could turn out to be quality control problem. We need to be able to switch between transparency and opacity to sometimes look through our formulation of a problem, and sometimes look at the formulation of our problem, to actually be able to solve it.

Now let’s look at the next two directions: featural and gestalt. It turns out that the left hemisphere of our brain is really good at looking in the details, while the right hemisphere of our brain is really good at looking at the larger picture. When we look into the details, we are looking at specific features. However, the concept of gestalt builds on the idea that the whole is greater than the sum of its parts. Consider two sentences, “Ron slapped Harry” and “Harry slapped Ron”. Both the sentences are the same if we look at the features alone, i.e. words; however, it is the way they are organized together that the meaning of the features is shaped. So, sometimes we need to look at the details to solve a problem (featural level), while sometimes we need to be looking at the larger picture (gestalt level).

So it turns out that insight is the ability to dynamically switch between the featural and opaque direction to the gestalt and transparent direction. If we keep looking at the features, we get fixated into one formulation and cannot solve the problem. If we keep looking the bigger picture, we get choked with making sense of everything. We need to dynamically go from one of these configurations to the other. The ultimate way to do so is the ultimate way to do anything: practice. How? That is what this article is actually about.

What is the extreme end of the feautral and opaque direction? Instead of looking through your awareness at the world, we move back and look at our awareness, and instead of trying to find meaning through things or looking at the larger picture, we dive really deep into our awareness and focus on some deep feature. This process, is the formal definition of meditation. We focus on our awareness and our thoughts, and we try to turn our thoughts into some feature like our breath. We stop trying to make sense of the larger world around us, and we stop trying to look through the glasses of our awareness. We internalize our attention completely.

However, from our journey so far, you might’ve guessed — that’s not it. Meditation is just one half of the coin, we need to go to the other extreme to truly practice our attention. The other extreme involves looking through are awareness, and looking through everything around us to find some greater meaning or the bigger picture. We call this contemplation. This involves thinking about the meaning of life, purpose of the world, and of what role you play in the universe. It involves scaling out to an extreme, and think about things that others call “too philosophical”. Who are you really? What is reality? This is just as important as meditation is.

I believe that in the modern era we have placed tremendous importance on meditation, and we confuse mindfulness with just meditation. In fact, mindfulness is a combination of meditation and contemplation to take to both extremes of our cognition. This not only practices our attention, and drastically improves our ability to solve problems of all sorts, but also has a variety of proven physical and mental health advantages. Any “successful” or “intelligent” person either knowingly or unknowingly engages himself in this activity, and that is the ultimate way to enhance your problem solving! So now you know what you need to regularly and wholeheartedly do!

Note: As always, this article is greatly inspired by the lectures of Professor Vervaeke at the University of Toronto.