Abstract
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.
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Notes
- 1.
As Drew McDermott writes in the Cambridge Handbook of Consciousness (McDermott 2007), it is as if Hofstadter “wants to invent a new, playful style of argumentation, in which concepts are broken up and tossed together into so many configurations that the original question one might have asked get shunted aside”.
- 2.
Although the recruitment behaviour of real ants is more complex than the behaviour in SDS, both are population-based and find their optima via agents communicating with each other.
- 3.
The rigorous proof is not based on this left-right consideration: “this would involve getting into the quite complex notion of orientation, which is not needed for our proof” (Gale 1979).
- 4.
Group size \(=\, g\, =\) (board area DIV 2) + 1.
- 5.
A process isomorphic to asynchronous passive recruitment SDS (De Meyer 2003).
- 6.
A ‘game tree’ is a directed graph whose nodes are positions in a game and whose edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing all possible moves from each position; a n-ply game tree describes all possible move/counter-move combinations to a depth of n moves.
- 7.
This assumption is not necessarily a good one due to the distinction between random play and optimal play – see analysis of standard Monte-Carlo methods (and MCSDS) in Sect. 22.3.4.
- 8.
The term was coined by Levins in Levins (1969) to describe the dynamics of interacting populations of social insects.
- 9.
The initial motivation for the work on SDST was to extend the applicability of Stochastic Diffusion Search (SDS) to more complex search spaces, and combinatorial games were chosen as a first study case. Then, Monte-Carlo Tree Search (MCTS) came naturally as a good framework for several reasons. First, MCTS does not rely on domain knowledge but rather on a large number random game simulations and the notion of random game simulation fits well with the concept of partial evaluation in SDS. Second, the strength of MCTS relies on the tree policy balancing between exploration of the search space and exploitation of the promising solutions and SDS is a metaheuristic precisely conceived to solve this “exploration-exploitation dilemma” in the management of the computational resources. Finally, MCTS has proven very successful in a wide range of problems – not only game playing – and is still under active study.
- 10.
Ant Colony Optimisation also shares this property
- 11.
This property is due to the partial evaluation of solutions: in the case of string matching for example, as discussed by Nasuto (1999), the position of the solution after convergence is indicated by the formation of a cluster of agents, possibly dynamically fluctuating; in the case of a partial match, agents will keep exploring the text while the cluster will globally stay on the best match.
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Acknowledgements
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.
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Bishop, J.M., Nasuto, S.J., Tanay, T., Roesch, E.B., Spencer, M.C. (2016). HeX and the Single Anthill: Playing Games with Aunt Hillary. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_22
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