 Extended Turing Machines (ETMs) were invented by Fred Abramson (1971). An ETM is exactly like a standard Turing machine except that, whereas a standard Turing machine stores only a single discrete symbol on each (non-blank) square of its tape (e.g., ‘0’ or ‘1’), a single square of an ETM’s tape can store any desired real number, for example π, or even an uncomputable real number. (The method of storing real numbers on the tape is left unspecified in this purely logical model.)