74 COMMUNICATIONS OF THE ACM | MARCH 2012 | VOL. 55 | NO. 3 review articles ILLUSTRATION BY GERARD DUBOIS DOI:10.1145/2093548.2093569 Embodied and disembodied computing at the Turing Centenary. BY S. BARRY COOPER Turing’s Titanic Machine? So why are questions about the ad- equacy of the Turing model of com- putation 34 so difficult to resolve, so avoided by “normal science,” and so controversial among those who debate the issues? There are both theoretical and mod- eling uncertainties at work here. On the mathematical side, we have a well- developed theory of classical comput- ability—and incomputability—based on the Turing machine model and its oracle-enhanced incarnation. On the other side we have the Internet, ar- tificial intelligence, and nature, with closely related models sometimes termed new computational paradigms. Turing’s universal machine fa- mously “computes” an incomputable object—the halting set of inputs on which its computations terminate— appearing over the years in many dif- ferent guises. But in what sense is such an object computed? Why does it mat- ter? A short answer is that it is comput- ed much as the Mandelbrot set appears on a computer screen. It is computably enumerable. A great deal of research activity is directed at discovering in- computable objects that are not just notational variants of the halting set, and making the incomputable objects we have more accessible and more at home in the real world. Back in the 1950s, John Myhill 22 elegantly brought all known naturally arising incomput- IT IS IN the nature of things that 1912 is generally more remembered for the sinking of the “unsinkable” Titanic than it is for the far more world-changing event: the birth of Alan Mathison Turing in a London nursing home on a Sunday in June of that year. The Turing Centenary presents a timely opportunity for us to remember the startling depth of impact of Turing’s universal machine over the last 75 years. In this brief review I examine challenges to its continued primacy as a model for computation in daily practice and in the wider universe. In doing this, the Titanic analogy is surprisingly useful, even apt from some points of view. It reminds us of the achievements of science and engineering, and its precarious coexistence with the often surprising unpredictability of events in nature. Of course, this is a controversial area, and the arguments are too finely balanced for definitive conclusions. In the end we might decide that, at a basic level, things have not gone that far beyond Turing’s own clarifying constructs and his persistent uncertainties about their adequacy. key insights The demise of Turing’s computational model is still a long way off. Both the modern computing experience, and the natural world we live in, are full of challenges to its universal validity. What we should learn from AI, physics, and computing practice are due respect for “embodied” computation as well as information and process. Theoretical modeling, and engagement with computing realities, are synergetic ingredients of both past and future progress. Turing’s legacy points to exciting possibilities for the unraveling and harnessing of the mysteries of “how the world computes.”