Advertisement

What Sort of Information-Processing Machinery Could Ancient Geometers Have Used?

  • Aaron Sloman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10871)

Abstract

Automated geometry theorem provers start with logic-based formulations of Euclid’s axioms and postulates, and often assume the Cartesian coordinate representation of geometry. That is not how the ancient mathematicians started: for them the axioms and postulates were deep discoveries, not arbitrary postulates. What sorts of reasoning machinery could the ancient mathematicians, and other intelligent species (e.g. crows and squirrels), have used for spatial reasoning? “Diagrams in minds” perhaps? How did natural selection produce such machinery? Which components are shared with other intelligent species? Does the machinery exist at or before birth in humans, and if not how and when does it develop? How are such machines implemented in brains? Could they be implemented as virtual machines on digital computers, and if not what human engineered “Super Turing” mechanisms could replicate what brains do? How are they specified in a genome? Turing’s work on chemical morphogenesis, published shortly before he died suggested to me that he might have been considering such questions. Could deep new answers vindicate Kant’s claim in 1781 that at least some mathematical knowledge is non-empirical, synthetic and necessary? Discussions of mechanisms of consciousness should include ancient mathematical diagrammatic reasoning, and related aspects of everyday intelligence, usually ignored in AI, neuroscience and most discussions of consciousness.

Keywords

Geometrical/topological reasoning Evolution Kant Turing AI 

References

  1. 1.
    Sauvy, J., Sauvy, S.: The Child’s Discovery of Space: From Hopscotch to Mazes an Introduction to Intuitive Topology. Penguin Education, Harmondsworth (1974). Translated from the French by Pam WellszbMATHGoogle Scholar
  2. 2.
    Kant, I.: Critique of Pure Reason. Macmillan, London (1781). Translated (1929) by Norman Kemp SmithGoogle Scholar
  3. 3.
    Piaget, J.: The Child’s Conception of Number. Routledge & Kegan Paul, London (1952)Google Scholar
  4. 4.
    Chappell, J., Sloman, A.: Natural and artificial meta-configured altricial information-processing systems. Int. J. Unconv. Comput. 3(3), 211–239 (2007)Google Scholar
  5. 5.
    McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of AI. In: Meltzer, B., Michie, D., (eds.) Machine Intelligence 4, pp. 463–502. Edinburgh University Press, Edinburgh (1969). http://www-formal.stanford.edu/jmc/mcchay69/mcchay69.html
  6. 6.
    Schmidhuber, J.: Deep learning in neural networks: an overview. Technical report IDSIA-03-14 (2014)Google Scholar
  7. 7.
    Sloman, A.: Diagrams in the mind. In: Anderson, M., Meyer, B., Olivier, P. (eds.) Diagrammatic Representation and Reasoning. Springer, London (2002).  https://doi.org/10.1007/978-1-4471-0109-3_1CrossRefGoogle Scholar
  8. 8.
    Sloman, A.: Predicting affordance changes (alternative ways to deal with uncertainty). Technical report COSY-DP-0702, School of Computer Science, University of Birmingham, Birmingham, UK, November 2007. goo.gl/poNS4J
  9. 9.
    Craik, K.: The Nature of Explanation. CUP, London (1943)Google Scholar
  10. 10.
    Karmiloff-Smith, A.: Beyond Modularity: A Developmental Perspective on Cognitive Science. MIT Press, Cambridge (1992)Google Scholar
  11. 11.
    Turing, A.M.: The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237(237), 37–72 (1952)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The University of BirminghamBirminghamUK

Personalised recommendations