One of the key concepts in computing nowadays is that of a programming language, a name for a tool that facilitates the communication of a task at hand to the computing machine. Juxtaposing translations between two natural languages and translations from a natural language into some kind of a code or language understandable to the computer reveals the power of the computer as well as its limits. These limits are closely connected to the possibility of reducing human thinking to that which can be communicated through the language of mathematics. The language of mathematics as a concept is much older than electronic computers. In comparing a computer with a brain, John von Neumann made a clear distinction between the language of the brain and the language of mathematics. The use of the termmachine language seems to have been stimulated by the use of the termlanguage in symbolic logic.