HeX and the Single Anthill: Playing Games with Aunt Hillary

  • J. M. BishopEmail author
  • S. J. Nasuto
  • T. Tanay
  • E. B. Roesch
  • M. C. Spencer
Part of the Synthese Library book series (SYLI, volume 376)


In a reflective and richly entertaining piece from 1979, Doug Hofstadter playfully imagined a conversation between ‘Achilles’ and an anthill (the eponymous ‘Aunt Hillary’), in which he famously explored many ideas and themes related to cognition and consciousness. For Hofstadter, the anthill is able to carry on a conversation because the ants that compose it play roughly the same role that neurons play in human languaging; unfortunately, Hofstadter’s work is notably short on detail suggesting how this magic might be achieved. Conversely in this paper – finally reifying Hofstadter’s imagination – we demonstrate how populations of simple ant-like creatures can be organised to solve complex problems; problems that involve the use of forward planning and strategy. Specifically we will demonstrate that populations of such creatures can be configured to play a strategically strong – though tactically weak – game of HeX (a complex strategic game). We subsequently demonstrate how tactical play can be improved by introducing a form of forward planning instantiated via multiple populations of agents; a technique that can be compared to the dynamics of interacting populations of social insects via the concept of meta-population. In this way although, pace Hofstadter, we do not establish that a meta-population of ants could actually hold a conversation with Achilles, we do successfully introduce Aunt Hillary to the complex, seductive charms of HeX.


Douglas Hofstadter Consciousness Meta-population Emergence Swarm intelligence Stochastic diffusion search 



The central argument presented herein was developed under the aegis of Templeton project 21853, Cognition as Communication and Interaction. The initial development of SDST was extracted from the unpublished MSC Dissertation from Tanay (2012) and from Tanay et al. (2013). This work was originally presented by Bishop at the PT-AI conference St. Antony’s College, Oxford, 22nd-23rd September, 2013.


  1. Abramson, B. (1990). Expected-outcome: A general model of static evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(2), 182–193.CrossRefGoogle Scholar
  2. Aleksander, I., & Stonham, T. (1979). Guide to pattern recognition using random-access memories. IEE Journal on Computers and Digital Techniques, 2(1), 29–40.CrossRefGoogle Scholar
  3. Beattie, P., & Bishop, J. (1998). Self-localisation in the ‘SENARIO’ autonomous wheelchair. Journal of Intelligent & Robotic Systems, 22(3), 255–267.CrossRefGoogle Scholar
  4. Bishop, J. (1989). Stochastic searching networks. In First IEE International Conference on Artificial Neural Networks, 1989 (Conf. Publ. No. 313) (pp. 329–331). IET.Google Scholar
  5. Bishop, J. (1992). The stochastic search network. In R. Linggard, D. Myers, & C. Nightingale (Eds.), Neural networks for images, speech, and natural language (pp. 370–387). London/New York: Chapman & Hall.CrossRefGoogle Scholar
  6. Bonabeau, E., Dorigo, M., & Theraulaz, G. (2000). Inspiration for optimization from social insect behaviour. Nature, 406, 3942.CrossRefGoogle Scholar
  7. Browne, C., Powley, E., Whitehouse, D., Lucas, S., Cowling, P., Rohlfshagen, P., Tavener, S., Perez, D., Samothrakis, S., & Colton, S. (2012). A survey of monte carlo tree search methods. IEEE Transactions on Computational Intelligence and AI in Games, 4(1), 1–43.CrossRefGoogle Scholar
  8. Chaslot, G., Bakkes, S., Szita, I., & Spronck, P. (2008). Monte-carlo tree search: A new framework for game ai. In Proceedings of the Fourth Artificial Intelligence and Interactive Digital Entertainment Conference, Palo Alto (pp. 216–217).Google Scholar
  9. De Meyer, K. (2003). Foundations of stochastic diffusion search. Ph.D. thesis, University of Reading.Google Scholar
  10. De Meyer, K., Bishop, J., & Nasuto, S. (2000). Attention through self-synchronisation in the spiking neuron stochastic diffusion network. Consciousness and Cognition, 9(2), 81–81.Google Scholar
  11. De Meyer, K., Nasuto, S., & Bishop, J. (2006) Stochastic diffusion optimisation: The application of partial function evaluation and stochastic recruitment in swarm intelligence optimisation. In A. Abraham, C. Grosam, & V. Ramos (Eds.), Swarm intelligence and data mining (Vol. 2). Berlin/New York: Springer.Google Scholar
  12. Dorigo, M (1992). Optimization, learning and natural algorithms. Ph.D. thesis, Milano: Politecnico di Italy.Google Scholar
  13. Dorigo, M., Maniezzo, V., Colorni, A., Dorigo, M., Dorigo, M., Maniezzo, V., Maniezzo, V., Colorni, A., & Colorni, A. (1991). Positive feedback as a search strategy. Technical report (Technical Report No. 91-016), Politecnico di Milano.Google Scholar
  14. Gale, D. (1979). The game of hex and the Brouwer fixed-point theorem. The American Mathematical Monthly, 86(10), 818–827.CrossRefGoogle Scholar
  15. Goodman, L. J., & Fisher, R. C. (1979). The behaviour and physiology of bees. Oxon: CAB International.Google Scholar
  16. Grech-Cini, H., & McKee, G. (1993). Locating the mouth region in images of human faces. In Sensor fusion VI (SPIE-the international society for optical engineering, Vol. 2059). Bellingham: Society of Photo-optical Instrumentation Engineers.Google Scholar
  17. Hart, S. (1992). Games in extensive and strategic forms. Handbook of Game Theory with Economic Applications, 1, 19–40.CrossRefGoogle Scholar
  18. Hofstadter, D. (1979). Godel, escher, bach: An eternal golden braid. New York: Basic Books.Google Scholar
  19. Holldobler, B., & Wilson, E. O. (1990) The ants. Cambridge: Springer.CrossRefGoogle Scholar
  20. Kennedy J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks (IV) (pp. 1942–1948).Google Scholar
  21. Kennedy, J. F., Eberhart, R. C., & Shi, Y. (2001). Swarm intelligence. San Francisco/London: Morgan Kaufmann.Google Scholar
  22. Kocsis, L., & Szepesvári, C. (2006). Bandit based Monte-Carlo planning. In Machine Learning: ECML 2006 (pp. 282–293).Google Scholar
  23. Levins, R. (1969). Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the ESA, 15(3), 237–240.Google Scholar
  24. McDermott, D. (2007) Xartificial intelligence and consciousness. In M. Moscovitch, P. D. Zelazo,& E. Thompson (Eds.), The Cambridge handbook of consciousness. Cambridge/New York: Cambridge University Press.Google Scholar
  25. Metropolis, N., & Ulam, S. (1949). The monte carlo method. Journal of the American Statistical Association, 44(247), 335–341. doi:10.1080/01621459.1949.10483310. PMID: 18139350CrossRefGoogle Scholar
  26. Moglich, M., Maschwitz, U., & Holldobler, B. (1974). Tandem calling: A new kind of signal in ant communication. Science, 186(4168), 1046–1047.CrossRefGoogle Scholar
  27. Nasuto, S. (1999). Resource allocation analysis of the stochastic diffusion search. Ph.D. thesis, University of Reading.Google Scholar
  28. Nasuto, S., & Bishop, J. (1998). Neural stochastic diffusion search network-a theoretical solution to the binding problem. In Proceedings of ASSC2, Bremen (Vol. 19).Google Scholar
  29. Nasuto, S., & Bishop, M. (1999). Convergence analysis of stochastic diffusion search. Parallel Algorithms and Applications, 14(2), 89–107.CrossRefGoogle Scholar
  30. Nasuto, S., Bishop, J., & Lauria, S. (1998). Time complexity analysis of the stochastic diffusion search. Neural Computation, 98.Google Scholar
  31. Nasuto, S., Bishop, J., & De Meyer, K. (2009). Communicating neurons: A connectionist spiking neuron implementation of stochastic diffusion search. Neurocomputing, 72(4), 704–712.CrossRefGoogle Scholar
  32. Seeley, T. D. (1995). The wisdom of the Hive. Cambridge: Harvard University Press.Google Scholar
  33. Tanay, T. (2012). Game-tree exploration using stochastic diffusion search. Technical report, goldsmiths, University of London.Google Scholar
  34. Tanay, T., Bishop, J., Nasuto, S., Roesch E. B., & Spencer, M. (2013). Stochastic diffusion search applied to trees: A swarm intelligence heuristic performing monte-carlo tree search. In Proceedings of the AISB 2013: Computing and Philosophy Symposium,‘What is Computation?’, Exeter.Google Scholar
  35. Whitaker, R., & Hurley, S. (2002). An agent based approach to site selection for wireless networks. In Proceedings of the 2002 ACM Symposium on Applied Computing, Madrid (pp. 574–577). ACM.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • J. M. Bishop
    • 1
    Email author
  • S. J. Nasuto
    • 2
  • T. Tanay
    • 1
  • E. B. Roesch
    • 2
  • M. C. Spencer
    • 2
  1. 1.GoldsmithsUniversity of LondonLondonUK
  2. 2.University of ReadingReadingUK

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