...both inspiration and challenge to his work on computing machines. And he attempted to bring a characteristically basic approach to both the physical and the mental, those two irksome companions of the philosopher of mind. Here is Jaegwon Kim (in Physicalism, or Something Near Enough, Princeton, 2005) setting out the problem:
"...The problem of mental causation is solvable only if mentality is physically reducible; however, phenomenal consciousness resists physical reduction, putting its causal efﬁcacy in peril."
How can mentality have a causal role in a world that is fundamentally physical? And what about "overdetermination" — the problem of phenomena having both mental and physical causes?
The most that most philosophers of mind can agree on is a degree of supervenient of mental properties on physical ones.Turing in 1948 came up with his "unorganised machines" which provided a neural net model alternative to the better known predecessor of Warren McCulloch and Walter Pitts.
Christof Teuscher gives an account of the innovative nature of "Turing's Connectionism" in his book of that name. Connectionist models have provided the basis for a large research ﬁeld, and exhibited interesting features in keeping with what one might expect from the human brain. Paul Smolensky, for instance, talks in his 1988 paper On the proper treatment of connectionism of a possible challenge to "the strong construal of Church's Thesis as the claim that the class of well-deﬁned computations is exhausted by those of Turing machines".
2012 marks the centenary of Alan Turing's birth. Image credit: Guy Erwood/Shutterstock
9. The Turing Test and AI
At the other end of the scale we have Turing's famous 1950 paper in Mind astutely narrowing down what one can sensibly say about human intelligence, and discussing in some detail his observer-based test for a thinking machine. The resulting "Turing Test" still dominates people' thinking on the issue. The paper joins the other two most cited papers of Turing. One of these is the 1936 paper of course, which many might expect to be the most frequently cited of his papers. But no...
10. How Nature Computes
To the surprise of those outside of biology and medicine, the most cited of Turing's papers is the ﬁnal 1952 The Chemical Basis of Morphogenesis. And in many ways this is one of his most original and maybe visionary foray into the world of computation.
He was not to know that the mathematics of sunﬂowers and patterns on animal coats would connect up with today's recognition of the importance of emergence, and throw light on a whole range of intractable foundational questions across a wide range of research areas in science and the humanities.
Computationally simple rules, connectivity, emergent forms at the edge of computability, and deﬁnable in terms of the rules, just like Turing's patterns. Turing's coherence of vision, at the end of his short life, giving us morphogenesis — inhabiting the same fractal world as the Mandelbrot set; the same computational world as the halting problem for the universal Turing machine; the same large scale structure as found in the observable universe; and perhaps the key to Kim's world of supervenience.
11. The Alan Turing Year
So, what will we be celebrating in 2012? Above all, it should be the continued inﬂuence of the Turing vision on some of the most important research directions today.
Turing had a very down-to-earth grasp of the what-makes-the-world-tick, combined with a brilliant grasp of abstract structures.
Turing had an amazing instinct for recognising big questions about how the world works. He was like another famous 20th century scientist, Paul Dirac, in having a very down-to-earth grasp of the what-makes-the-world-tick, combined with a brilliant grasp of abstract structures.
Turing's work on the nature of computation has deﬁned the computer revolution that has changed our world. And his groundbreaking explorations of processes beyond what a computer can handle look likely to provide key elements of the next trans-computer developments.
We should celebrate how Turing combined the practical and the visionary, and gave us both technological breakthroughs and a continuing sense of the mystery of what lies beyond.
This article originally appeared as Pushing Back the Incomputable — Turing's Ten Big Ideas (PDF) in the Asia Pacific Mathematics Newsletter.
S Barry Cooper is Professor of Mathematical Logic at the University of Leeds. He is president of the association Computability in Europe and a Managing Editor of the journal Computability. He is currently Chair of the Turing Centenary Committee and Co-Chair of the Turing Centenary Conference in Cambridge in June 2012. The 2nd edition of his book Computability Theory is due out in early 2012. He is editing with Turing’s biographer Andrew Hodges The Once and Future Turing for Cambridge University Press.
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