Abstract
The decision to remember Alan Mathison Turing in the anniversary of his birth in a conference dedicated to “Mathematics and Culture” is quite appropriate, since Turing’s vision has determined some of the most important social and cultural changes of the these one hundred years, especially in the last part of the century we have lived through, and he was not going to see due to his untimely death.
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Notes
- 1.
Not the halt problem, the original Turing’s machines never halt; the problem has been formulated and proved undecidable by Martin Davis (1958) in relation to the modern presentation of Turing machine given by S. C. Kleene (1952).
- 2.
To von Neumann are due the specification of the measure of byte, the buffer, the flow charts.
- 3.
Some of Turing’s papers were classified and became known only in the nineties and later.
- 4.
Langley P., Simon H., Bradshaw G., Zytkow J.: Scientific Discovery: An Account of the Creative Process. MIT Press, Cambridge MA (1986).
- 5.
Aiken H.: The Future of Automatic Computing Machinery. Elektronische Rechenanlage und Informationsverarbeitung (1956), n. 33. Aiken had built Harvard Mark I, a joint enterprise of Harvard University and IBM.
- 6.
Turing, 1950.
- 7.
He rediscovered independently the central limit theorem.
- 8.
He introduced for example the so called LU decomposition of a matrix in two triangular matrices.
- 9.
Group theory and almost periodic functions were the areas mentioned in his application for a Princeton scholarship in 1936.
- 10.
In the march 2012 issue of Nature Genetics it has been confirmed the discovery of two excitation and inhibition morphogenes, included in his model.
- 11.
So it has been surmised: Toulmin S.: The New York Review of Books, January 19), p. 3 (1984).
- 12.
Clark A.C.: 2001: A Space Odyssey. New American Library (1968).
- 13.
Weizenbaum J.: ELIZA — A computer program for the study of natural language communication between man and machine. Communications ACM, 9, pp. 36–45 (1966). This was actually anticipated in 1948 by Turing, who observed that in order to ascertain the presence of consciousness in an interlocutor one should conduct a roundabout dialogue on subjects indirectly related to an argument, making connections and associations by means of literary images, analogies, metaphors.
- 14.
We prefer to mention only the sin, not the sinners.
- 15.
See for example Searle J.R.: Minds, Brains and Programs. Behavioral and Brain Sciences, 3, pp. 417–58 (1980).
- 16.
The transcript has been published in Italian with the permit of Turing’s estate curators in: Sistemi Intelligenti X(1), pp. 27–40 (1998).
- 17.
In the Lecture at the London Mathematical Society.
- 18.
He goes on observing that the scientist does not proceed from facts to facts, but is often guided by unproved conjectures: “Conjectures are of great importance since they suggest useful lines of research”.
- 19.
Tremolada L.: “Se il telefono ha il senso dell’umorismo”. Il sole24ore, January 2012, p. 49.
- 20.
See among others, Meo A.R.: Guida alla Metrologia. Supplement to Qualità, n. 4, 1995.
- 21.
Though some statements seem to express the opposite direction: “We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions”.
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Lolli, G. (2013). Alan M. Turing (1912–1954). In: Emmer, M. (eds) Imagine Math 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2889-0_26
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