Editing Turing machine (section)

===Historical background: computational machinery===
[[Robin Gandy]] (1919–1995)—a student of Alan Turing (1912–1954), and his lifelong friend—traces the lineage of the notion of "calculating machine" back to [[Charles Babbage]] (circa 1834) and actually proposes "Babbage's Thesis":

{{blockquote|''That the whole of development and operations of analysis are now capable of being executed by machinery''.|(italics in Babbage as cited by Gandy, p. 54)}}

Gandy's analysis of Babbage's [[analytical engine]] describes the following five operations (cf. p.&nbsp;52–53):
# The arithmetic functions +, −, ×, where − indicates "proper" subtraction: {{nowrap|''x'' − ''y'' {{=}} 0}} if {{nowrap|''y'' ≥ ''x''}}.
# Any sequence of operations is an operation.
# Iteration of an operation (repeating n times an operation P).
# Conditional iteration (repeating n times an operation P conditional on the "success" of test T).
# Conditional transfer (i.e., conditional "[[goto]]").

Gandy states that "the functions which can be calculated by (1), (2), and (4) are precisely those which are [[Turing computable]]." (p.&nbsp;53). He cites other proposals for "universal calculating machines" including those of [[Percy Ludgate]] (1909), [[Leonardo Torres Quevedo]] (1914),<ref name="LTQ1914es">L. Torres Quevedo. ''Ensayos sobre Automática – Su definicion. Extension teórica de sus aplicaciones,'' Revista de la Academia de Ciencias Exacta, Revista 12, pp. 391–418, 1914.</ref><ref name="LTQ1915fr">Torres Quevedo. L. (1915). [https://diccan.com/dicoport/Torres.htm "Essais sur l'Automatique - Sa définition. Etendue théorique de ses applications"], ''Revue Génerale des Sciences Pures et Appliquées'', vol. 2, pp. 601–611.</ref> [[Maurice d'Ocagne]] (1922), [[Louis Couffignal]] (1933), [[Vannevar Bush]] (1936), [[Howard Aiken]] (1937). However:

{{blockquote|… the emphasis is on programming a fixed iterable sequence of arithmetical operations. The fundamental importance of conditional iteration and conditional transfer for a general theory of calculating machines is not recognized…|Gandy p. 55}}