The art of abstraction of models and maps

Modelling of complex systems can be a powerful way to get grip on such systems. Using the model as a digital twin can make it even better. It is important to use models wisely, to define its purpose and to know its limitations. It is instructive to look at the analogy between models and maps.
We got inspiration from a maybe unexpected direction: Lewis Caroll, the author of literature classics such as “Alice in wonderland”.
How? Read on if you want to know.

In our daily lives we, individually and the society as a whole, depend heavily on complex systems that are all around us. Whether it is the public rail system, a medical x-ray system at your local hospital, the electricity grid, or the water management system that secures us from floods, they all share a high level of complexity that those responsible for these systems face every day. And they encounter this in all stages of the lifecycle, whether when designing, operating, maintaining, upgrading, changing or decommissioning (part of) these complex systems.

A very powerful and widely used approach to get a grip on complex systems is the use of models. A model is a simplified representation of the system that helps get our head around the system. It is an abstraction of reality, capturing a limited set of features that are sufficient for a certain purpose. A specific class of models is what is commonly known as a digital twin. In such case the model is regularly, sometimes even continuously, updated with status information of the system it represents.

For instance, if we want to know whether a dyke of certain height will protect us from flooding, we can use a very simple model, reducing the dyke to a wall and reducing the river to a water mass with a smooth surface at the level of the river. The model tells us = that if the wall height exceeds the water level we are safe. However, I would not trust this model, it is to simple and clearly contains too few features to be useful. We should at least somehow include the effect of wind and waves. Maybe also the slope of the dyke and current patterns in the river. At a certain moment, we will have built a useful model that serves our purpose. If we enter into the model the actual water levels, wind speeds, flow speed of the river etc., we can consider the model to be a digital twin.

This same model will be inadequate if we want to know the expected stability of the dyke over time. Then we need to include for instance the materials the dyke is made of, while we may leave out some of other features. In other words, we need a different abstraction. We could fall into the trap of making a model that includes all features and all details we can think of, such that it serves all purposes. In effect, we try to make an exact copy of the complex system. Read on to find out why that is a bad idea and why proper abstraction, which is a skill people need to be trained in, is essential to for a model to be useful and successful.

To understand how abstraction works, and why it is essential for modeling, let’s look at a particular class of models we are all very familiar with: maps.

A map is an abstraction of a geographical situation. Mostly, maps represent an existing situation, but they can also serve as designs of situations that still need to be realized, in the same two ways we just noted about models.

Master story teller Lewis Caroll has explained us brilliantly why abstraction, the art of leaving out (the majority of) details, is essential to end up with useful maps. He does so in this highly entertaining passage from his story “Sylvie and Bruno Concluded” from 1893:

"That's another thing we've learned from your Nation," said Mein Herr, "map-making. But we've carried it much further than you. What do you consider the largest map that would be really useful?"
"About six inches to the mile."
"Only six inches!" exclaimed Mein Herr. "We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!"|
"Have you used it much?" I enquired.
"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well”.

Every map is made with a certain purpose in mind. There are detailed hiking maps, city maps, highway maps, there are sailing maps and geological maps, just to name a few. Each of these could well represent the same area but contain complete different features, and more importantly leave out different details. Everyone understands that going on a hike with a sailing map of the area is not a good idea

The art of making the right abstraction, to know which details to leave and select the few out of many possible features to include is a special skill crucial in mapmaking.

With models, it is no different. Whenever we model a system, whether it is an existing system or a system under design, we have to ask for what purpose we create the model. For instance, if we want to get a feel how well a system can perform a certain task, we will create a functional model, while if we want to know whether it fits in a certain room we will create a spatial model. So, if we hope to answer a certain question we have about a system, the simple statement that a model is available does not give us sufficient information. Just as with mapmaking, recognizing and being able to make the right abstraction for a specific purpose is a crucial skill in modelling.

This holds no less for digital twins. As with maps and models, the digital twin only takes into account the details of the system that are relevant to the purpose for which the digital twin was created. If we hope to use it for a different purpose, the twin may provide us with untrustworthy answers, or no answer at all.

When faced with a complex system one needs to get a grip on it, It is therefore important to realize that for a given system, there is no such thing as the digital twin, just as the map for a certain geographical area, containing all features up to the smallest details, does not exist, as Mein Herr in Lewis Caroll’s story found out the hard way.

I encounter quite often hopeful expectations that the availability of a model or digital twin will solve wicked problems that people or organizations are dealing with. They are bound to be disappointed. Models and digital twins can certainly be powerful aids, but the analogy with map-making has made it for me much easier to ask the right critical questions regarding the purpose and the nature of the digital twin, and whether that matches the needs and expectations. Also, reversely, to manage the expectations and understand to what extent it will help, and where not.

I am curious to know whether the analogy is also insightful to you, and whether it changes the way you look at models and digital twins.

I am greatly indebted to Steve Holt’s presentation at the INCOSE International Symposium 2024 on the importance of conceptual and simple modelling. Steve made the connection with Lewis Caroll’s story. The parallels between modeling and map-making had intrigued me for a long time and his talk gave me the final push to write these thoughts down.

Thanks to my colleagues at TNO-ESI for their very useful comments and suggestions for this text.