The magic numbers 1, 3 and 7

In this guest article, Carsten Pitz closes the circle to his previous publications at SE-Trends. Among other things, he describes the dangers of dealing with more than one topic at the same time and the limitations of the human brain and how to deal with them. What does this have to do with systems engineering? Only if you take these principles into account can you break down systems in a meaningful way. Enjoy reading.

Guest article by Carsten Pitz

In the third and final part of my introduction, I take the opportunity to bore readers with my personal attitude to the magic numbers 1, 3 and 7. My following guest contributions - a promise is a promise - will then go into medias res.

The reason why I have divided my presentation into 3 parts and the middle part for the most challenging topic as soon as it is the number 3's turn.

What makes the numbers 1, 3 and 7 magical?

All of the three numbers 1, 3 and 7 are boundaries, are frequently disregarded cognitive boundaries of people. The short story "The emperors' old clothes" from C.A.R. Hoare in connection with my experiences with the programming languages ALGOL and Oberon. (Of course, the story is not to be confused with the children's fairy tale about the new dresses.)

ALGOL disregards the cognitive limits of people, Oberon Please note this. ALGOL is extremely difficult to learn. So difficult, in fact, that Niklaus Wirth designed Pascal as a teaching language to introduce ALGOL programming. Even after using ALGOL for a long time, I still had to look up the syntax of rarely used language elements. In contrast, I internalized the syntax of Oberon within a single day.

To put it briefly, the message behind the short story is: You can not implement, what you do not understand.

You can not implement, what you do not understand (C.A.R. Hoare) [tweetthis]You can not implement, what you do not understand (C.A.R. Hoare)[/tweetthis]

And that's exactly what this third part of my short introduction is about: How do I make things understandable to others?

The number 1

There are many sayings about this number. We Germans say "One thing at a time", the Anglo-Saxons say "One idea at a time". People are familiar with the cognitive limit expressed by the number 1. A person can only grasp or process one set of topics at a time.

In my presentation, I dealt with three topics: Object orientation, Papyrus and the magic numbers. The three topics are too different to be grouped together. In addition, summarizing them would have disregarded other cognitive boundaries of people.

The number 3

"All good things come in threes" says the German saying. Nice, but what does this mean? Let's just take a look around:

• In ikebana (Japanese 生け花 also いけばな, literally "living flowers"), 3 elements are often placed in relation to each other. The number 3 also occurs frequently in the plant kingdom itself.
• Steve Jobs always presented exactly 3 products, even when he only presented the iPhone
• Abbreviations with 3 letters are particularly popular (e.g. UML ;-))

For me, the number 3 has the following two aspects: Firstly, an arrangement of 3 is generally perceived as aesthetic and beautiful; secondly, people can choose ad hoc between 3 options, on instinct, so to speak. Two options are usually perceived as too few choices, from four onwards, catalogs of criteria become necessary.

But I often hear the objection: "What the hell does our business have to do with aesthetics?". Well, people are more willing to look at something beautiful than something ugly. Beautiful things attract more attention. More time is invested in beautiful things.

I promised to explain here why I put the most complex topic in the middle, if possible. On the one hand, this is good for the narrative arc. On the other hand, the audience is already awake in the middle but not yet tired. Accordingly, I put the simplest theme at the end, if possible.

The number 7

I use the number 7 in the meaning of the Miller number. To summarize briefly: A person can only hold about seven units of information in their short-term memory at any one time, and this cannot be changed by training. That's why I also had XING group "Better presentations" written:

If I create a concept that has more than three hierarchy levels or more than seven elements per self-contained, atomic component (=diagram)
then the concept is for the garbage can and it's back to square one

This post expresses quite succinctly my use of limits 3 and 7.

In the cited discussion, Peter Claus Lamprecht even sets 4 (instead of 7) as the limit. In my experience, however, we can certainly work with 7 as the limit in systems engineering.

Now the question for the final spurt: "How do I achieve this?"

Divide And Impera

"Divide and conquer" - as old as this principle is, it is often forgotten. In systems engineering, this can be realized in two ways:

Interfaces are an important tool for breaking them down. These should always be modeled from the provider's perspective. For this purpose, they can be broken down by role (e.g. administrator, producer, consumer, user). If necessary, they can also be broken down according to other criteria, e.g. administrator + life cycle (initialization, maintenance) and producer + action (port open/close, object send).

Subsystems are another tool for breaking things down. Systems that are too large should be split up, or the task of the subsystem should be reconsidered and redefined if necessary.

Systems and subsystems should be structured hierarchically (across as many levels as necessary). To this end, self-contained subtasks are separated out by forming subsystems and defining (internal) interfaces.

I say thank you

Many thanks to everyone who has followed me this far.

We are currently planning to address the topics of Century Support (long-term maintainability), traceability, and the modeling of business requirements. I'd love to hear your feedback in the comments section!

Picture: Unsplash / Marvin Ronsdorf