Figure 1.

Two stages in the history of a hypothetical language, illustrating the notion of economy as a geometric property of sound systems. Four idealized articulatory parameters are shown: place of articulation ([b], [p], [f], and [m] are made with constriction at the lips, while [s] and [z] are made by placing the tongue just above and behind the upper teeth); voicing ([b], [m], and [z] are made with vibration of the vocal cords, while [f] and [s] are without); nasal vs. oral airflow ([m] is made with the velum lowered so that air passes through the nose, while the other sounds are made with the velum raised, allowing airflow only in the mouth); and stop vs. fricative constriction ([b], [p], and [m] are made by totally blocking the flow of air through the mouth, while [f], [s], and [z] allow air to pass through a narrow opening and create noise). At Stage 1, the hypothetical language loses [m], increasing economy by eliminating one of the articulatory degrees of freedom of the inventory. At Stage 2, the language gains [z], increasing economy by making more use of the three remaining dimensions. The hypercube shown is a graph where the edges marked are between pairs of sounds of distance one in an idealized binary articulatory space. The remaining unsaturated edges of the interior and exterior cubes have also been added for clarity.