by Gilles Dowek and Samson Abramsky

This Turing centenary marks a point at which we can realize that Alan Turing has become, with the passage of time, a scientific icon whose name is known by people in many countries world-wide, and far beyond the scientific community. This may seem a paradox because the genesis of computability theory, for which Turing is probably best known, was a collective effort, to which the names of Herbrand, Gödel, Church, Post, Kleene, Rosser and Turing are often associated.

There are of course many non-scientific reasons for Alan Turing to be an icon: his short life, martyrdom, significance as a gay political symbol, ... but Turing's fame came firstly within the scientific community, as a founding father of Computer Science. Thus, for example, it was decided by the ACM, in 1966, to name the highest distinction in computer science, the Turing Award, after him. So we must search for the origin of Turing's fame in his scientific achievements.

Alan Turing started his scientific work with one of the most abstract problems in mathematics: the decision problem. And he solved it by introducing an imaginary, mathematical computing machine. This work already shows the originality of Turing’s work: Church independently solved the decision problem at the same time, but Church's approach focused on the concepts of a language and of an algorithm, with their roots in logic and mathematics. Turing, by contrast, introduced a decisive third concept, of a *machine*, thus going beyond logic, and laying the foundations for the nascent discipline of Computer Science. Moreover, his analysis of computability in terms of his notion of machine was so compelling that it was rapidly accepted as definitive; and in the form of the Church-Turing thesis, is still with us today.

Turing continued this work on machines after the war, when he designed a real machine: the Automatic Computing Engine (ACE) for the National Physical Laboratory. While many mathematicians, at that time, saw a water-tight boundary between mathematics and technology, Turing introduced a notion of a machine within mathematics, and moved freely back and forth between computability and computational machinery. While many logicians came close to inventing computer science, only Turing did it.

During the war, many of Turing's contemporaries, under the pressure of history, turned to action. Turing understood that the outcome of the war depended as much on the development of cryptanalysis as on what happened on the battlefield. This led him to join the Government Code and Cypher School in Bletchley Park, where ciphers and codes of several Axis countries, in particular the Enigma and the Lorenz machines, were decrypted. Again, Turing seemed not to pay attention to the boundary that we all customarily see between thought and action.

When Turing became interested in biology and morphogenesis, he modelled the development of living organisms with differential equations, as reaction-diffusion systems, just as one would model an inorganic object. And, when he got interested in intelligence, which many consider to be the sole prerogative of mankind, he got rid of the border between the human and the non-human, to ask under which conditions a computing system could be said to be intelligent, giving a purely behavioural definition of intelligence.

The scientific legacy of Turing is huge: on models of computations (see the paper of Jean-Yves Marion, and that of Jos Baeten, Bas Luttik, and Paul van Tilburg in this issue), on Cryptographic systems (see the paper of Benjamin Grégoire), on morphogenesis (see the paper of Nadia Pisanti), at the border of biology and computation, on systems biology (see the paper of Anna Gambin, Anna Marciniak-Czochra, and Damian Niwinski and that of Claudio Angione, Pietro Liò, and Giuseppe Nicosia), ... But Turing not only left us with this huge scientific legacy, he also showed that borders must be crossed, as an essential part of the scientific endeavour.

Science and technology, thought and action, organic and inorganic, human and non human: we tend to believe that these boundaries are fixed and immutable, but they are really only there to divide our knowledge into small and comfortably familiar pieces. Alan Turing did not pay much attention to these boundaries and, following where his powerful curiosity led, he moved from one area to another, with an amazing intellectual ease and technical facility. He applied methods from one domain to another, candidly asking why these methods should not work, if they had worked somewhere else. He has set an invaluable and inspiring example: go where your ideas lead you, and pay no attention to artificial borders.

Please contact:
Gilles Dowek, Inria, France
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Samson Abramsky, University of Oxford
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Next issue: January 2023
Special theme:
"Cognitive AI & Cobots"
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