Gauging Risk with the Risk Watch

  • 05 October, 2016
  • Amsterdam Security TU Delft

Blog: Max Mendel, TU Delft Safety and Security Institute


Gauges are everywhere. They express an abstract quantity that is hard to gauge with the eye, into a distance that is easy to gauge with the eye. For example, temperature is hard to gauge, but a thermometer makes this easy by expressing it as the height of a mercury column. Likewise, your car’s fuel level or speed is hard to gauge directly, but your car has effective gauges that urn these quantities into easy to read-off distances that the dial traverses against the back plate.

Risk is an abstract quantity and the benefits of a practical risk gauge are obvious. Such a gauge could be implemented on a smart phone, a watch, or a dashboard of a vehicle to display the risk you are facing while going about your business. Or it could be built into the control of an autonomous vehicle to avoid collision automatically.

At TU Delft’s Safety and Security Institute, we are developing a practical risk gauge that we call the Risk Watch. Figure 1 shows an artistic rendering of the risk watch’s back plate by M.C. Escher. The mathematical theory underlying the risk watch is called Hyperbolic Geometry and Escher’s work was inspired by geometers working in his day on this subject from a purely mathematical perspective.

Amsterdam Security

How do you read the risk watch? You read it like you would read a map of the earth. Indeed, navigating the risk world with the risk watch is like navigating the earth with your typical Mercator map. The issue of scaling illustrates this nicely. In the real world of risk, all the devils and angels are equally risky, but on the risk watch they appear to decrease in size towards the rim, the bankruptcy or fatal horizon, where they disappear altogether. Compare this with a map of the earth. There the scale also changes, but it is in the opposite sense getting larger as you move away from the equator towards a poles (Greenland looks huge compared to Ecuador!). This contrasts the unusual hyperbolic nature of risk to the roundness of the earth. It has to be this way, though. On earth, if you travel far away enough you end up returning to where you started, but in the risk world this is quite the opposite. Otherwise a viable strategy for reducing risk would be to take on more!

In fact, risk doesn’t even live in a flat world (or Euclidean world as geometers like to say). In a flat world, it’s just as hard to come back as it is to go. That’s our experience for small distances on the earth, but as soon as people began to travel far in the age of exploration it became clear that this assumption was not valid anymore. And so it is for risk. For small amount of risk, recovering is no harder than it was to get you in trouble. However, for large amounts of risk, the error becomes significant and there is a point where you disappear altogether. We live in a world with larger and larger risks (think credit crisis, terrorism, cyber risks) and the need for an accurate map to navigate the risk world is comparable to the need to create accurate maps of the earth for the age of exploration five hundred years ago.

A simple finance example illustrates the general case. If you have €1000 and you lose 1% and then gain 1%, you are basically back to where you started. However, when you lose 50% and then gain 50% you are only at €750; now you need a gain of 100% to get even. It keeps getting harder to recover as the losses increase until after a loss of 100% you cannot recover at all anymore. You have arrived at the horizon of death! The rim of the risk watch.

There are many more aspects to the risk watch than I can sketch in this article. Notice, though, that it is a 2D gauge, rather than the usual 1D gauges. You can think of it perhaps as a regular watch with a centered dial that can change length continuously from 0 to the radius where it hits the rim; a sort of extension of your regular watch, which only has two fixed dials. That’s one reason we call it the risk watch.


Amsterdam Security

Although it may seem unusual, these type of displays are used in engineering, in particular by electrical engineers designing microchips who call it a Smith Chart (see Figure 2). This is an important observation for engineers like us, because it indicates that the concepts and methods used in electrical engineering for circuit analysis can be exploited for risk analysis and that the risk watch is easily understandable to engineers designing devices like automated vehicles or traffic control systems.

Noot voor de redactie / niet voor publicatie:
Voor meer informatie kunt u contact opnemen met:

Alice Muurlink, Communication Manager

+31(0)6 246 85 555

Share this article

Latest Video

All videos »