During the Renaissance, the five senses were understood to form a hierarchical system from the highest sense of vision down to touch. Vision was correlated to fire and light, hearing to air, smell to vapour, taste to water, and touch to earth.
Perhaps the human fascination with fire stems from the totality of its sensory stimulation. The fire gives a flickering and glowing light, ever moving, ever changing. It crackles and hisses and fills the room with the smells of smoke and wood and perhaps even food. It penetrates us with its warmth. Every sense is stimulated and all of their associated modes of perception, such as memory and an awareness of time, are also brought into play, focused on the one experience of the fire. Together they create such an intense feeling of reality, of the "here and nowness" of the moment, that the fire becomes completely captivating.
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.