 We can study symbol manipulation in general on an abstract level, without any semantic implications. Such a theory was published by Alan Turing (1912–1954). Turing developed a general theory of computing focusing on the actual operations on symbols a mathematician performs (Turing 1936). For him a computer was an abstraction of a real mathematician sitting behind a desk, receiving problems written down on an in-tray (the inut), solving them according to fixed rules (the process) and leaving them to be picked up in an out-tray (the output). 