In the 1960s, the designer Robert Propst worked with the Herman Miller company to produce “The Action Office”, a stylish system of open-plan office furniture that allowed workers to sit, stand, move around and configure the space as they wished.
Propst then watched in horror as his ideas were corrupted into cheap modular dividers, and then to cubicle farms or, as Propst described them, “barren, rathole places”. Managers had squeezed the style and the space out of the action office, but above all they had squeezed the ability of workers to make choices about the place where they spent much of their waking lives.
...It should be easy for the office to provide a vastly superior working environment to the home, because it is designed and equipped with work in mind. Few people can afford the space for a well-designed, well-specified home office. Many are reduced to perching on a bed or coffee table. And yet at home, nobody will rearrange the posters on your wall, and nobody will sneer about your “dog pictures, or whatever”. That seems trivial, but it is not.
The brick is one of those old technologies, like the wheel or paper, that seem to be basically unimprovable. ‘The shapes and sizes of bricks do not differ greatly wherever they are made,’ writes Edward Dobson in the fourteenth edition of his Rudimentary Treatise on the Manufacture of Bricks and Tiles. There’s a simple reason for the size: it has to fit in a human hand. As for the shape, building is much more straightforward if the width is half the length.
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.