# Is respect objective or subjective

## The subjective complexity

Complexity here, complexity there, complexity everywhere. The term complexity is omnipresent today. Questions are complex, problems, solutions, systems, projects, plans, requirements, markets - everything is now complex. But is that correct when viewed objectively or is it more a question of subjective feelings? Does it make sense to calculate complexity and how important are the results for your perception of complexity?

### Complexity, the, noun, [kɔmplɛksiˈtɛːt]

The shortest form of the definition of the term complexity is probably: “Complexity; the intertwining of many characteristics ”.¹ What does“ complexity ”mean? From how many layers, factors, features does something become complex? For example, if you read a review about DVD players, you will often find reviews on how to use them. Some are intuitive to use, while others are a little more difficult. In practice, you will certainly be able to start any DVD player, no matter how many steps are involved. No matter how difficult or complex the DVD player is to use, you will be able to play the DVD in no time. But can everyone in your family do that too? Probably not. Complexity and the feeling of complexity are therefore person-dependent.

### The personal perception of complexity

Shall we play a little game? It's very simple, but it leads us to a personal perception of complexity. Just take part! The following task: You see an equation laid with matches: 2 + 2 = 5. As far as we know today, this equation is not correct. Move a single matchstick so that the equation is correct again.

The wrong equation: 2 + 2 = 5

Do you have a solution? Was it difficult to find this solution? 3 + 2 = 5. We all know that, of course. Pretty easy to find. Basic arithmetic is part of a knowledge that we can easily access. The correct answer requires not only a correctly applied basic arithmetic, but also visual skills. Where is the "wrong" match? Have you tried to make 2 + 2 = 4? That would of course also be correct, but you would have to move one match and remove another.

So the equation is correct: 3 + 2 = 5

Let's not make the topic more exciting than it is. There is also a second answer, another match that can be moved: 2 + 3 = 5. After you found your first answer, did you stop looking for an alternative solution?

The equation is also correct: 2 + 3 = 5

Let's go a little further in our search for the personal perception of complexity. A new equation: 4 x 8 = 2. Now you can move two matches. Find all possible answers.

Obviously something is wrong here

Moving two matches is a little more complex than moving one like in the first task, but it's not that much harder, is it?

That's true, of course

4 x 2 = 8. You found the first solution quickly, didn't you? Does it make a difference to you that you know there is more than one correct answer?

So it is also true

4 x 3 = 12. This solution is a little different from the previous one, because you don't change two digits as in the first answer, but only change one digit, the 8, and insert a new digit, the 1, so that the result 12 is created. The task for this special solution could also be: Adjust the equation, move two matches, but only change one existing digit. Even a simple task sounds pretty complex.

Also a correct solution

4 x 0 = 0. We now know the principle. And that makes the answers easier. Once a first solution has been found and this can be reproduced in an adapted manner, we will come to further results more easily and quickly. It is probably not for nothing that "every beginning is difficult."

And of course this equation is also true

1 x 8 = 8. The fourth solution. That's it. How difficult was the task for you? It's just a game, of course, with no pressure, no spectators, no stopwatch. Would it have made any difference to you if you had known beforehand that there were four solutions? Does knowing the number of possibilities increase the personally perceived complexity? At what number of opportunities would you stop playing the game?

There can be no generally valid definition of a perceived complexity. If you do such brain teasers a lot, then the two tasks are probably not complex for you. Once you have internalized the principle, it is easier to find solutions. But whether you find a task, a question, a game or a system complex depends on you. And in detail:

- Your understanding - did you fully understand the task in all its facets?
- of your skills - how could you correct an equation if you don't know the basic arithmetic operations?
- from your experience - do you already know the task, do you know what works well or not so well?

### Calculating the complexity

You might be surprised, but complexity can be measured and calculated. The term “variety” is often used here as a measure of complexity. The term itself stands for “manifold”. At the same time, however, one difficulty of the term lies in the diversity of the interpretation. In anatomy, we speak of variety, i.e. the deviation from the norm in the construction, size or shape of an organ, as in mineralogy in relation to the formation of a mineral (color, size, habit) or in cybernetics. Cybernetics looks at the possibilities of cause and effect in systems.

Let's approach the computation of complexity for a simple, non-complex system: a flashlight. A working flashlight has two states: "On" and "Off". How many states can 5 flashlights have in common if we assume that every flashlight can be "On" or "Off"? Well, we could count: Flashlight 1 is “On”, the other four flashlights are “Off”. Flashlight 2 is "On", the rest is "Off". The first two flashlights are “On”, the other “Off”. We could do that with all flashlights and all combinations. Anyone who remembers combinatorics in mathematics class would simply have the task with 2^{5 }= 32 solved.

Such a calculation turns complexity into a real, objective quantity. How many states can 25 flashlights have in common? 2^{25 }= 33,554,432. Although there are "only" 25 flashlights with two states each, the amount is impressive. But what does this number bring you? Is it important for you to know the number of possible moves in chess in order to judge that chess is a very complex board game? Do you find it appealing that chess games always turn out differently or do the rules, the openings with the most varied of strategies, the middlegame and the endgame seem difficult, lengthy, complex to you? There are 32 pieces in chess and obviously the number of possible moves is very large. A source² on the Internet speaks of 10^{155}. That would be a 10 with 155 zeros. Objectively speaking, chess is therefore very complex. Whether you see this as a problem, however, depends on your personal perception and assessment.

### Conclusion

The more features systems have, the more complex they are. Even if there is an objective, predictable complexity in systems, it depends on you how you classify the result and perceive the complexity yourself. A dual state flashlight is not complex. But if you are wondering how the battery of the flashlight works, what parts a battery ideally consists of, how the toggle switch works and how high the consumption is in watts, then the flashlight as such doesn't seem so simple anymore. The operation remains simple, but the assessment of the system depends on the point of view. So complexity is above all subjective.

PS: I will be playing the matchstick puzzle with a friend's 6 year old daughter next weekend. I'm curious how easy it will be for her.

Hints:

[1] Definition of “complexity” in the Duden, Bibliographisches Institut GmbH

[2] Fredmund Malik: Complexity - what is it? Cwarel Isaf Institute

We are happy to take part in the PM Camp Berlin blog parade on the subject of complexity. The PM Camp will take place from September 10th to 12th, 2015 in Humboldt University Berlin. You can find information about the PM Camp here at microTOOL or directly from the organizer.

Michael Schenkel believes in useful tools, that support users in their work and that provide a common working environment for all types of roles in a project. He became a member of the microTOOL family more than fifteen years ago and took over the position of head of marketing for about half a decade. In October 2017, he moved on to a new adventure and we wish him all the best on this new path.

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