I was once told that life is more like a vending machine than a restaurant—you have to pay first before you can receive anything. In the context of this article, I would also imagine life as a vast building with nearly infinite rooms and interconnected doors, yet we can never return to the same room even once—echoing Heraclitus’s notion of panta rhei (“everything flows”). Everything moves on, though in many cases the human mind resists doing so.

Before anything else, let me begin by introducing the idea of “modes of thinking” and what it means. A mode of thinking is a powerful concept, best understood as the general state or lens through which we see the world, and one we must learn to mold and adjust. To overcome our circumstances, we might need to shift into a new mode of thinking, often by elevating our thoughts and perspective, so that we can look at the world again with “new eyes”. In this sense, I would place this approach in contrast to wishful or passive thinking. One has to actively guide and calibrate their mode of thinking to find the “eyes” that align with what is required. Confronted with feelings of longing and nostalgia after my journey, I returned to this idea and arrived at a specific case, which I have termed “Segmentation.”

You see, we humans are not very good at dealing with discontinuity or major change. As a result, the end of a trip, journey, or more broadly a phase in life can feel too confronting, and returning to a different, more ordinary phase may become overwhelming. One can be overtaken by feelings of longing and nostalgia, and may effectively begin to live in the past instead of moving on and being present. You might feel helpless, trapped in a net, not knowing how to escape.

Being affected by such a state myself, I eventually realized that, while it may seem to make sense, it does not truly align with the fundamental nature and texture of reality. While we cannot know this reality fully, over time we can develop a better understanding of what it is and what it is not. While events and their consequences are, of course, temporally linked, the emotional comparison of life’s events appears to be a purely human practice, one that does not carry any inherent or objective meaning. The texture of life seems far more inherently segmented, composed of a vast series of chapters. Like an immense building with countless rooms—each with a one-time entrance and exit—we pass through them in time, visiting each only once before moving on.

Segmentation is a mode of thinking that realizes this and views life’s challenges as separate segments that require equal care, without dwelling excessively on the past—whether failures or successes. What matters is that one successfully completes these chapters going forward—for example, by enjoying one’s journey, not making major mistakes, and most importantly returning safely to one’s family—while also broadening one’s vision and abilities for future chapters.

It is therefore a choice, and a poor one, to remain stuck in feelings of nostalgia, comparison, and longing, as this means losing out on all future chapters and rooms. There is only learning and moving on.

Dark Night of the Soul

At a certain point in the past I stumbled upon the term ‘Dark Night of the Soul’. The Dark Night of the Soul describes a profound inner, spiritual struggle or existential disorientation, originating from the 16th‑century Spanish mystic John of the Cross. It is a defining experience in which a person feels lost and stripped of certainty, marked by intense confusion and radical doubt. At the same time, it is a moment of unavoidable confrontation that can make or break, and can open a path to deep inner transformation. It is exactly a process that shifts focus from performance to meaning.

Illustration in the setting of ‘Blood Sport’ (1988)

I want to illustrate this concept and corresponding ideas through the lens of Bloodsport, as it unfolds in a high stakes environment in which doubt slowly creeps into the resolve of an otherwise self-assured protagonist.

The film tells the story of Frank Dux, portrayed by Jean-Claude Van Damme, who competes in the Kumite—an underground martial arts tournament held in Hong Kong. While Frank is a self-assured fighter who easily wins his early matches, his close friend is brutally injured in a tournament fight by the antagonist, Chong Li—an event that introduces growing doubt into Frank’s mindset. This tension culminates in the climactic final fight between Frank and Chong Li, during which Chong Li cheats and blinds Frank.

For me, this is the vital moment in the movie. It introduces a spiritual turn and a discontinuity of the kind I referred to — one that even showed in tone and performance, as Van Damme’s previously unconvincing acting suddenly becomes focused and intense. It was a shift I initially struggled to fully grasp, but I later realized that it is, in fact, a well-depicted cinematic Dark Night of the Soul.

The blinding leads to profound disorientation. After a moment of intense struggle, as one can see in the included image, he is able to find composure and calmness through the recollection of his training, which included sessions practiced blindfolded, and goes on to win decisively. It is a movie, after all.

The Dualism of Achievement and Meaning

While doubt in our abilities is common, doubting meaning is rare. This is largely because we are usually healthy and functioning, which naturally places our focus on external goals such as competition. There is a silent assumption that our well-being and stability are guaranteed. But when our bodies or minds are impaired—through illness, injury, or other challenges—the focus shifts. Concerns turn toward recovery, reflection, or even spiritual considerations. In this context, regaining orientation, coordination, and resolve becomes the true achievement, and one could argue that everything beyond this point is a bonus. The real win for Frank, if you ask me, is precisely this, not the tournament title.

It only makes sense to doubt you models and preparation

The movie actually offers more than just a vivid depiction of this concept, which is why it remains a classic for martial arts enthusiasts. What made it especially interesting at the time was that it appeared in an era without any clear consensus on what constituted the most effective fighting method — was it karate, kickboxing, or kung fu? This was before organizations like the UFC staged real tournaments to get an answer to this question. In terms of Model Thinking, people were essentially asking what the best “model” of fighting was — a logical and very practical question, since martial artists wanted to train in the most effective style. In this light, all the martial artists in the movie can be seen as embodiments of particular models: specific fighting schools and their underlying philosophies.

Through this lens one can also meaningfully approach the question when doubt makes sense. In this context it only makes sense for the fighters to doubt their model and preparation as the rest is uncontrollable uncertainty anyway. One either believes in this, and competes, or otherwise does not. You see, in a competitive and complex environment one can’t have total information on what the best model is and how other participants will strategize and execute their strategy.

Therefore, in a competitive setting, it makes sense to critically examine and doubt one’s model and preparation beforehand. But once the moment of execution arrives, commitment is required and doubt must disappear, as it will be of no value and only be detrimental. Eliminating meaningless doubt is not straightforward, but it is an essential part of competition.

Doubt the doubt

As one can see, doubt is a logical companion of ambition, but only meaningful when it concerns one’s models and preparation. If one is properly prepared and employs adequate models, one should let go of the doubt and simply follow the path and execute, as everything else is meaningless and a burden.

Certain skills, like more rigorous modes of thinking, are indeed hard to develop and require considerable practice. Others, however, come down mostly to a matter of willingness.

In this post, I want to focus on an example of the second type and show that real progress here is often not mystical—it comes from straightforward actions. For instance, by consistently speaking up about what you want and looking out for your own interests.

Being unassertive, too nice, or unable to say “no” is a core issue many people face and one that can have detrimental consequences, as there will always be people who take advantage of it. This dynamic shows up even in close relationships, including friendships and marriages. After all, who wouldn’t prefer someone who always goes along? At the same time the solution is remarkably simple, though initially hard to execute: Just (learn to) speak up about what you want!

There are many reasons why assertiveness can feel difficult, especially for kind and empathetic people. They may be conflict-averse, or they care deeply about others’ feelings and don’t want to hurt others. As a result, they often avoid confrontation. What this means, however, is that they have effectively made other people the reference point for their own decisions and actions. This way of thinking is ultimately nonsensical and, in practice, often rewards and sustains poor or even toxic behaviour.

Seen more broadly, clear and honest feedback is not about confrontation, but about mature and responsible communication. Addressing behaviour that pushes you against what you want provides necessary feedback, establishes healthy limits, and can help others reflect on how they relate to the people around them. So while we often focus on the individual discomfort involved in speaking up, this kind of communication serves a much broader educational role and contributes to a healthier overall culture.

As you can see, simply speaking out about what you want can be very impactful; it will benefit you, and it can also create a much more honest and healthy dynamic that benefits others. So from now on, choose to be a mature, responsible, and assertive person and speak out about what YOU want!

For example, around 30 years ago it was already an advantage to be able to work with tools like Excel and basic software. Today, however, the requirements are much steeper. We need to be able to work with far more sophisticated tools and platforms that are also more dynamic in nature. Especially as change is accelerated by AI, we are forced to adapt more frequently and more thoroughly.

Another example is that of a small retail business. Fifty years ago, there were far fewer considerations: a physical shop, inventory, and local customers. Now in 2026, there is a need for an online shop, a social‑media presence, digital marketing, online reviews, and often integration with various platforms and delivery channels.

In such an environment, the question of when one is future‑ready is not a trivial one, and it is not even clear how we should view and approach the concept of future‑readiness as a whole. Yet again, we can resort to the power of Model Thinking to form a basic and intuitive understanding of this concept, which in turn reveals several additional implications.

The included figure shows the complexity level in our work environment as a function of time. The model is very simple and consists of two lines:

• The complexity level of reality (in red), such as the work environment we have to operate in.

• One’s Problem‑Solving Ability (PSA) (in blue).

Going from 2025 to 2026, we can see that the red line increases, as we should expect new developments, such as technological, geo‑political, and regulatory changes.

We can define the Complexity Gap as:

Complexity Gap = Complexity Level of Reality (red) − Problem‑Solving Ability, PSA (blue).

Ideally, this gap should be negative, as one’s PSA should be above the required level of operation, which implies that one is in control. In the opposite situation, however, one becomes overwhelmed and will gradually lose out to competition.

This model shows that non‑progress means decline: in a situation where one does not develop skills and capabilities, one will increasingly fall behind over time. As a result, future‑readiness corresponds to the ability to consistently keep up with, and remain in control of, rising complexity.

This type of control requires adaptability and deeper forms of understanding: It is not simply a matter of switching to new tools and frameworks, especially when there can be fundamental disruptions in where human value needs to shift in an environment shaped by AI. This, in turn, demands potent and realistic education and development programs that are able to anticipate such changes and carefully prepare people to navigate them.

At the same time, we should also view this model from a different angle. A changing landscape does not only bring threats. It also presents opportunities for the person who is adaptable and future‑ready, as they can move faster, adapt sooner, and outperform less prepared competition.

Just as a football player cannot get very far relying on only one technique, the mind needs multiple techniques to grasp complex topics and concepts. And just as every football player has a different style and set of skills, each person must discover what works best for them. Still, there are certain techniques that are universally useful and provide a solid base.

Building on our visual approach from the previous posts, we want to present a technique called the Wolf Tree, which is based on the first-principles learning approach. The idea is simple: You break something you want to understand down to what it essentially is and start “growing” your understanding by asking the right questions step by step. One person may ask different questions than another and grow the tree mentally in their own way, it doesn’t matter, the most important thing is to keep growing the tree, and eventually it will bear fruit!

I have made a slide to explain how this technique works, as one can see below, and why it is called the Wolf Tree. The Wolf Tree was a pattern I originally constructed because I wanted a very simple, fractal-like image to explain people the idea of fractals. People interestingly seemed more amazed by the process of building the image step by step, so I began using it as a didactic tool.

The example the slide gives is that of electricity, which is actually quite a difficult and tricky concept. It is therefore useful to look at other examples, for instance:

• Democracy:
  (1) It is a governance structure where elected officials govern for a certain period of time.
  (2) The people don’t govern themselves directly but choose representatives.
  (3) A simple mental image I would use is that of people voting for one of two candidates, with some vote percentages. (etc.)

• Internet:
  (1) A network of computers that exchange data.
  (2) The internet is not a thing or a place, it refers to a constantly changing network.
  (3) I imagine computer screens connected by links, like a web.

  (etc.)

• Wolf Tree (making the circle round 🙂):
  (1) It is a simple, fractal-like pattern that can be drawn by following simple rules iteratively.
  (2) It has no direct relation to wolves, the resulting shape simply resembles something wolf-like.
  (3) See drawing.

  (etc.)

Maybe one latest guideline: The harder a concept, the more questions one would need to ask to grow a proper understanding. This is also when one will start realizing that asking the right questions is a skill in itself, we will reserve this for a next part.

I hope you find this interesting and can bring it to good use, good luck!

Building on the previous post with the Celtic knots, I thought it would be interesting to turn it into a (not particularly strictly ordered) series, so we number this as Part II. The goal is to provide a gentle exploration of the connection between mathematics and art through some fun topics, without getting too much into detail.

Anyone who has tiled a bathroom wall or worked on a jigsaw puzzle is familiar with the concept of tessellation (or tiling). Tessellation is the process of covering a surface with one or more geometric shapes in such a way that:

• There are no gaps left, and

• There is no overlap between the pieces.

While this can be done simply with square tiles, tessellations can also be created in more interesting and less regular ways. Examples of this can be found in the works of Maurits Escher.

We can also consider an additional property of tessellations: aperiodicity. Although aperiodicity is a subtle concept, it means patterns on an infinite plane never repeat when shifted. We have known some time this is possible using multiple tiles. For example, in the 1970s, Roger Penrose introduced Penrose tilings, which cover the plane aperiodically using at least two distinct shapes.

Mathematicians had wondered for a very long time whether a single-tile (monotile) aperiodic tessellation was possible, until this question was finally answered in 2023. Hobby mathematician David Smith discovered the “hat”, which showed this was possible (with reflections). Later, another related shape, called the “spectre” or “vampire”, was discovered, which does not need reflections. These shapes were mathematically proven to satisfy the requirements for aperiodic tiling.

The reason they are referred to as “Einstein” tiles is that “ein Stein” means “one stone” in German (a pun).

An Einstein tessellation can be seen in the image.

(Aperiodic tiling by hats by David Smith, Joseph Samuel Myers, Craig S. Kaplan & Chaim Goodman‑Strauss — CC BY 4.0)

Building on our previous post about observation, we can explore this concept in a fun and practical way to help you draw beautiful patterns.

Examining patterns, especially complicated ones like Celtic knots (see image), can be a great learning experience. A key question to ask is whether one can replicate the pattern independently. Essentially, the challenge is to determine the best model for replication.
To examine this, the mind must oscillate between the details and the overall pattern, as it cannot focus on both simultaneously. Eventually, one can spot an interesting underlying model: Take one element of the pattern, rotate for convenience, extend its lines (as in step 3), and apply some basic logic to reproduce a segment of the design.

Tips:
1. Imagine the white part as a road and the black parts as gaps. The red line represents one boundary of the road—now draw the other boundary first.
2. Remember, the road in tip 1 needs to incorporate a sort of U-turn leading to three additional gaps.

If you need additional tips let us know. Good luck!

Matrix 1 is one of my favourite movies, and my friends and I refer to it often. Recently, I had to think about a quote in connection to how people make decisions, perceive people, and form relationships:

“Have you ever had a dream, Neo, that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world?”

Although the connection to the quote is not directly obvious, someone told me that she thought I came across as a dangerous person, but actually, I was very nice and playful. In some different world, however, we would have never met, which would have been a loss. But also, in this world, there must be many people that we have lost based on our prejudices. How can we know that we meet the people that we truly need or long for? As our decisions guide our lives, in a sense, it is not that different from living in a dream world confined by our beliefs.

This post highlights one core characteristic of an effective didactician (in under 150 words).

In an initial stage, a didactician in a certain setting, such as a team meeting, is not the main actor but the (effective) observer. Or even the (effective) observer who observes the main actor and how the first observers observe. With effective observation we mean being able to distill mechanisms and patterns that succeed or fail, forming a deeper understanding. These observations themselves can be turned into didactic content and used for mentoring and training—transforming insights into scalable learning tools.

In this context, it is important to emphasize that the didactician acts through didactics. Where one competent actor can have impact, impactful didactics can create many competent actors—ten, a hundred, or even millions. This is why we say that addressing large challenges always starts at the level of potent education.