Design, it seems, is not only becoming more methodical but also more scientific. This is not surprising. Design as a discipline has moved from “product beautification” to being a central part of product development. It has incorporated methodologies from human-computer interaction, sociology, and anthropology as well as advertising and management. And with the rise of design thinking, a wider range of professional disciplines are using creative methods.
I don’t want to criticize design methodologies. But against the backdrop of an overly structured design process, it is important to remind our community that there is one fundamental aspect to design that cannot be formalized in a methodology. And that is intuition.
Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.
In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.