In 1937, Alan Turing outlined the details of the Turing machine in a paper investigating the possibilities and limits of machine computation. The machine is an idealized computing device that consists, in its simplest form, of a tape divided up into cells that are processed by an active element called a "head." The cells can be in one of two states. The head moves along the tape, changing the cells from one state to the other and moving either forward or backward according to a set of predetermined instructions. Turing machines can be described with a set of simple mathematical equations that allowed scientists to understand many of the basic properties of digital computing long before the first modern computer was built.