2.5 The Universal Turing Machine (UTM)
The Turing Machine was invented in 1936 by Alan Turing, the Cambridge mathematician whose life and work deciphering Nazi communications generated by Enigma was popularized in the film The Imitation Game, based in turn on the wonderful biography by Andrew Hodges (“Alan Turing: The Enigma.” Princeton University Press (2014) (originally published in 1983)). The Turing Machine is not a physical computer; rather, it is a mathematical description of how a physical computer (as opposed to a human who computes) must work. It is generally accepted that if anything can be computed then it can be done on a Turing Machine.
It’s one thing to know that the Game of Life can support a Turing Machine in principle, but quite another to implement it in practice. In the event, in 2000, Paul Rendell, who was at the time a systems development engineer at Marconi, was the first person to implement a Turing Machine in the Game of Life, as described in his doctoral thesis. Although this machine performed one specific task, namely to duplicate a sequence of “1”s, Rendell future-proofed his design so that it could eventually form the basis of a Universal Turing Machine.
A Universal Turing Machine, often abbreviated as UTM, will simulate any Turing Machine designed to perform a specific task. It does this by using as its input the information that describes the Turing Machine it is going to simulate. It then uses the input data that would have been fed into the original Turing Machine to perform the originally intended task. So, the UTM is, in fact, a programmable computer, where the program is the description of the Turing Machine for the specified task. It should, in theory, be able to simulate any modern computer.
Rendell persevered with his work and, ten years after he had invented the Game of Life’s first Turing Machine, he had upgraded it to a working UTM! The Game of Life UTM is not fast compared with, say, your laptop or the computer controlling your mobile phone – for instance, it takes 18,960 time-steps of the Game of Life to produce just one UTM computer cycle!
A Universal Turing Machine (UTM) implemented on the Game of Life. From: McKenzie, A. (2020). “Reality and Super-Reality: Properties of a Mathematical Multiverse.” Axiomathes 30: 453-478.
