Turing Centenary Research Proj.


More than any other figure, Turing has left a coherent scientific agenda related to many of the 'Big Questions' concerning the relationship between the human mind, mechanism in nature, and the mathematics required to clarify and answer these questions. The very breadth and fundamental nature of Turing's impact makes the centenary celebration a hugely opportune period in which to reassert the role of basic thinking in relation to deep and intractable problems facing science.

'The Turing Centenary Research Project - Mind, Mechanism and Mathematics', supported by a major grant from the John Templeton Foundation, arises from the above-mentioned scientific agenda, and involves researchers still within ten years of receiving their Ph.D. previous to winning their awards. The researchers on this 3-year research project are the eight winners (listed below) of the 'Mind, Mechanism and Mathematics' competition. Five of the winners are designated JTF 'Turing Research Fellows'; and three of the awards are for JTF 'Turing Research Scholars' in the 16 to 25 age-group, coming under the JTF Exceptional Cognitive Talent and Genius programme.

The grant holder and Project Leader is the Turing Centenary Advisory Committee Chairman, Professor S Barry Cooper from the University of Leeds.

The competition was organised in conjunction with the major Alan Turing Centenary Conference, held June 22-25, 2012, at the Manchester City Hall and the University of Manchester.

The award winners were duly honoured on the June 23, 2012 centenary of Turing's birth with a presentation of certificates on behalf of the Lord Mayor of Manchester. On this occasion, two of the Turing Research Fellows - Mark Braverman and Paul Grant - gave 30 minute conference talks on their work. This meeting, also funded by the JTF, was organised by Professors Andrei Voronkov and Matthias Baaz.

The first Project Workshop was held in Milan, June 30, 2013, in conjunction with the international conference Computability in Europe (CiE 2013): Logic, Algorithms, Applications

The 2nd Project Workshop is being held at Columbia University, New York, May 12-13, 2014.

The Project Team:
Team Leader

S. Barry Cooper (University of Leeds)
is Professor of Mathematics at the University of Leeds. Author and editor of numerous books, including Computability Theory, New Computational Paradigms, Computability in Context, and Alan Turing - His Work and Impact, he is he is a leading advocate of multidisciplinary research at the interface between incomputability and real world computability. Chair of the Turing Centenary Advisory Committee, which coordinated the international Turing Centenary celebrations, he is President of the Association Computability in Europe, which is responsible for the largest computability-themed international conference series, and chairs the Editorial Board of its Springer book series Theory and Applications of Computability. He is a member of the Board of Advisors of the John Templeton Foundation.

Turing Research Fellows and Scholars

Mark Braverman (Princeton University)
Mark Braverman is an assistant professor of computer science at Princeton University. His main interests lie in the theory of computation and its applications in the natural and social sciences. He received his PhD from the University of Toronto in 2008 under the supervision of Stephen Cook. [Turing Fellow]
Stephanie Dick (Harvard University)
Stephanie Dick is a doctoral candidate in the Department of History of Science at Harvard University, under the supervision of Prof. Peter Galison. Her dissertation is a historical exploration of attempts to automate mathematical reasoning and theorem proving after the advent of digital computing. She aims to recover and reconstruct the interactions between theory, practice, and technology in historical understandings of mind, computing, and mathematics. [Turing Fellow]
David Gamez (University of Sussex)
David Gamez holds PhDs in both philosophy and computer science. His cross-disciplinary research uses philosophy and neural modelling to explore how a science of the mind can be developed based on mathematical theories. Between 2009 and 2012 he was at Imperial College London, where he worked on brain-inspired neural networks and robotics and investigated new algorithms for making predictions about consciousness. He is currently a Research Fellow at the Sackler Centre for Consciousness Science, University of Sussex. [Turing Fellow]
Paul Grant (University of Cambridge)
Paul Grant is a postdoctoral fellow in the Department of Plant Sciences at the University of Cambridge. He currently works on synthetic pattern-forming genetic circuits in microbes but his background is in developmental biology, having written his doctoral dissertation at the University of Washington on neuron migration in zebrafish. He is originally from Northern New York and maybe plans to pursue an academic career back in the States. [Turing Fellow]
Noam Greenberg (Victoria University of Wellington)
I am a mathematician, interested in mathematical logic and in particular in computability and set theory. I am interested in how diverse notions such as randomness or algebraic structure, or generalisations to large domains, influence our understanding of the notion of computation. I work at Victoria University of Wellington, New Zealand; I received a Ph.D. from Cornell University and a B.Sc. from the Hebrew University of Jerusalem. [Turing Fellow]
Rutger Kuyper (Radboud University Nijmegen)
My name is Rutger Kuyper and I am a PhD candidate at the RadboudUniversity Nijmegen in the Netherlands. I am currently researching probability logic, in which mathematical logic (the subfield of mathematics in which logical reasoning is investigated) is combined with probabilistic, inductive reasoning. [Turing Scholar]
Andrew Marks (Caltech)
I recently finished a Ph.D under the supervision of Theodore Slaman at UC Berkeley. I am currently a postdoctoral fellow at Caltech. [Turing Scholar]
Simon Martiel (University of Nice-Sophia Antipolis)
I am starting a PhD in the University of Nice-Sophia Antipolis in France supervised by Bruno Martin and Pablo Arrighi. I am interested in the links between abstract notions in Computational Model Theory such as model complexity or intrinsic universality and Theoretical Physics, trying to answer the question: How does nature compute itself? [Turing Scholar]
Rebecca Schulman (Johns Hopkins University)
Rebecca Schulman is an assistant professor of chemical and biomolecular engineering and computer science at Johns Hopkins University. Her group is working to learn how to program molecules to assemble complex patterns and structures that can learn and adapt. [Turing Fellow]

The Big Questions

Turing's work and scientific legacy inhabits a world at the interface between the physical universe and the abstractions of mathematics; between the computational, the predictable, and the uncertainties manifest in human creativity, and in the emergence of form from randomness and chaotic environments; and a world at the interface between science, reason, reductionism and the mysteries of intuition, incomputability, and the failures of foundational thinking.

There are many deep and intractable questions arise in such a context. We list below four main scientific themes around which the research project has been built:

  1. The Mathematics of Emergence: The Mysteries of Morphogenesis

    • Q1. Does emergence exist as something new in nature, and is it something which transcends classical models of computation?
      (Develop a sufficiently fundamental model of emergence to answer this question.)
    • Q2. To what extent do existing models of natural processes accommodate emergent relations?
      (Characterize the mathematical characteristics of such models, and the extent of their representational and recursive capacities.)

    One of the less familiar but most innovative of Turing's contributions was his successful capturing of emergence of various patterns in nature in mathematical equations. This key innovation now forms the basis of an active and important research field for biologists. There are still general questions concerning both the computational content of emergence, of the unifying features extractable from different contexts, and the nature of good mathematical models applicable in different environments. John Holland, in his popular 1998 book on Emergence: From Chaos to Order sets out the extent of our ignorance of the precise mathematical character of emergence:

    "It is unlikely that a topic as complicated as emergence will submit meekly to a concise definition, and I have no such definition to offer."

    Issues of self-organization, emergence of form from chaotic or turbulent environments, non-locality in physics, and the relevance of classical models of computability such as Turing machines, cellular automata, neural nets, among others, are all in need of further investigation. It is hoped that a more coherent and mathematically-based viewpoint will shed light on some of the issues arising under the following three headings.

  2. Possibility of Building a Brain: Intelligent Machines, Practice and Theory

    • Q1. Is there a successful mathematical model of intelligent thought?
      (Develop more basic models, capable of pinning down the exact relationship between the human brain and standard paradigms from classical computability and computer science.)
    • Q2. Is intelligent thought essentially experimental and inexact? Are mistakes an essential aspect of intelligence?
    • Q3. What is the extent of application of the notion of a 'virtual machine'? Is human thinking essentially embodied, and the Turing paradigm of a universal machine inapplicable in this context?

    Turing's seminal role in artificial intelligence - for instance, his formulation of the Turing Test and his interest in connectionist models - has given rise to many different and contrasting approaches to building intelligent machines. There is a basic dichotomy between experimental, ad hoc approaches and more logic-based theoretical ones. There is a general agreement that we need to understand more about the relationship between these, and to obtain a better theoretical grasp of the practicalities, and of the underlying theoretical obstacles. The extent of the challenges facing researchers is summed up by Rodney Brooks, in Nature in 2001:

    "neither AI nor Alife has produced artifacts that could be confused with a living organism for more than an instant."

    The question of embodiment of intelligent computation is a key one, and is related to the problems surrounding the character of mental causation. As the Brown University philosopher Jaegwon Kim puts it, in relation to the brain, in his book Physicalism, or Something Near Enough (2005):

    "... 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."

    Turing himself refers to the role of mistakes in human intelligence (a feature without a positive role in current machine-hosted computation):

    "if a machine is expected to be infallible, it cannot also be intelligent. There are several theorems which say almost exactly that" (talk to the London Mathematical Society, February 20, 1947, quoted by Andrew Hodges in Alan Turing - the enigma, p.361).

    One will be looking for new thinking in this area, or more insightful unifying of existing knowledge. This is an area in which it is easy to produce speculation detached from clearly formulated models, and there will be an emphasis on rigor, clarity and mathematical content.

  3. Nature of Information: Complexity, Randomness, Hiddenness of Information

    • Q1. To what extent is complexity practically computable?
      (Elucidate the distinctions and identities pertaining to the numerous computational complexity classes.)
    • Q2. How much mathematical randomness occurs in nature?
      (Characterize quantum 'randomness', and answer questions in the mathematical theory relating to information theory, cryptology and physics.)

    This is an area more concerned with practical issues of computation, and the extraction of information from less favorable contexts. The focus is more on what is possible in the way of information processing. Cryptology, where this topic has its origins, has advanced hugely since the time of Turing and his Bletchley Park contemporaries, and there is a rich and developing mathematical theory. There are basic issues of complexity, also going back to the time of Gödel and Turing, where progress depends on solutions to fundamental questions. Turing's own interest in computational efficiency, and by implication complexity of programs, goes back to his work with the 'Turing Bombe' at Bletchley Park in the 1940s. In her article on Computing over the Reals: Where Turing Meets Newton (Notices of the AMS, 2004), Lenore Blum traces Turing's early contribution to the study of complexity in the context of numerical analysis in Rounding-off Errors in Matrix Processes in The Quarterly Journal of Mechanics and Applied Mathematics, vol. I, 1948, pp. 287-308, where she quotes Turing:

    "It is convenient to have a measure of the amount of work involved in a computing process, even though it be a very crude one ... We might, for instance, count the number of additions, subtractions, multiplications, divisions, recordings of numbers, ... "

    There are connections to the fast-developing body of work concerned with randomness and hidden information, and to questions of the extent to which randomness occurs in nature, particularly at the quantum level.

  4. How should we compute? New Models of Logic and Computation

    • Q1. Working at the interface between science and mathematics, how do classical models from logic and computability theory model real-world processes?
      (Develop the mathematical theories of relative computability, and solve long-standing open problems relevant to higher-order features of the real universe.)
    • Q2. What are the inadequacies of classical models, and what are the new computational models which capture more of the essentials of natural and physical computation?
      (Develop new computational models, and identify the extent of their real-world application.)

    This theme would concern the extraction of mathematical models of computation from nature, and the investigation of their theoretical properties, a key concern of Turing himself. Even for those who adhere to classical models, there are still questions relating to modeling and underlying theory. Here is David Deutsch quoted in the New Scientist in 2006:

    "I am sure we will have [conscious computers], I expect they will be purely classical, and I expect that it will be a long time in the future. Significant advances in our philosophical understanding of what consciousness is, will be needed."

    So topics can range from classical Turing analyses of the incomputable, to new computational paradigms in bio-informatics, to quantum or relativistic models from physics. Contributions relating to a wide spectrum of different computational models, both new and established ones, would be welcome. However, both modeling and theory should be motivated by the drive to say something new and fundamental about the nature of computation in the real universe. The real contexts within which the models originate can also be very diverse, but a unifying viewpoint will be encouraged.


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Websites: S. Barry Cooper, with technical assistance from Arnold Beckmann and Tim Hainsworth -

and many thanks to Lourens Thalen and Chatbots.org for the ATY masthead
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