Skip to main content
SpringerLink
Log in

Categorisation as Topographic Mapping between Uncorrelated Spaces

  • Chapter
Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7070))

Abstract

In this paper, I propose a neurophysiologically plausible account for the evolution of arbitrary, categorical mental relationships. Topographic, or structure-preserving, mappings are widespread within animal brains. If they can be shown to generate behaviours in simulation, it is plausible that they are responsible for them in vivo. One behaviour has puzzled philosophers, psychologists and linguists alike: the categorical nature of language and its arbitrary associations between categories of form and meaning. I show here that arbitrary categorical relationships can arise when a topographic mapping is developed between continuous, but uncorrelated activation spaces. This is shown first by simulation, then identified in humans with synaesthesia. The independence of form and meaning as sensory or conceptual spaces automatically results in a categorial structure being imposed on each, as our brains attempt to link the spaces with topographic maps. This result suggests a neurophysiologically plausible explanation of categorisation in language.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, D.L., Horton, J.C.: Ocular dominance columns: Enigmas and challenges. The Neuroscientist 15(1), 62–77 (2009)

    Article  Google Scholar 

  2. Bargary, G., Mitchell, K.J.: Synaesthesia and cortical connectivity. Trends in Neurosciences 31(7), 335–342 (2008)

    Article  Google Scholar 

  3. Bickerton, D.: King of the sea, 1st edn. Random House (1979)

    Google Scholar 

  4. Borovsky, A., Elman, J.: Language input and semantic categories: A relation between cognition and early word learning. Journal of Child Language 33(04), 759–790 (2006)

    Article  Google Scholar 

  5. Carnap, R.: Logical Foundations of Probability. University of Chicago Press, Chicago (1950)

    MATH  Google Scholar 

  6. Ellison, T.M.: Induction and inherent similarity. In: Similarity and Categorization, pp. 29–50. Oxford University Press (2001)

    Google Scholar 

  7. Goodhill, G.J.: Topography and ocular dominance: a model exploring positive correlations. Biological Cybernetics 69(2), 109–118 (1993); PMID: 8373882

    Google Scholar 

  8. Goodhill, G.J., Sejnowski, T.J.: A unifying objective function for topographic mappings. Neural Computation 9(6), 1291–1303 (1997)

    Article  Google Scholar 

  9. Greenlee, M.W.: Human cortical areas underlying the perception of optic flow: brain imaging studies. International Review of Neurobiology 44, 269–292 (2000)

    Article  Google Scholar 

  10. Harrison, J.E., Baron-Cohen, S.: Synaesthesia: Classic and Contemporary Readings. Wiley-Blackwell (January 1997)

    Google Scholar 

  11. Hlutk, P., Solodkin, A., Gullapalli, R.P., Noll, D.C., Small, S.L.: Somatotopy in human primary motor and somatosensory hand representations revisited. Cerebral Cortex 11(4), 312–321 (2001)

    Article  Google Scholar 

  12. Hubel, D.H., Wiesel, T.N.: Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. The Journal of Physiology 160(1), 106–154 (1962) PMID: 14449617 PMCID: 1359523

    Google Scholar 

  13. Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture of monkey striate cortex. The Journal of Physiology 195(1), 215–243 (1968)

    Google Scholar 

  14. Ide, C., Fraser, S., Meyer, R.: Eye dominance columns from an isogenic double-nasal frog eye. Science 221(4607), 293–295 (1983)

    Google Scholar 

  15. Langers, D.R.M., Backes, W.H., van Dijk, P.: Spectrotemporal features of the auditory cortex: the activation in response to dynamic ripples. NeuroImage 20(1), 265–275 (2003) PMID: 14527587

    Google Scholar 

  16. Le Vay, S., Wiesel, T.N., Hubel, D.H.: The development of ocular dominance columns in normal and visually deprived monkeys. The Journal of Comparative Neurology 191(1), 1–51 (1980)

    Article  Google Scholar 

  17. Majid, A., Boster, J.S., Bowerman, M.: The cross-linguistic categorization of everyday events: A study of cutting and breaking. Cognition 109(2), 235–250 (2008)

    Article  Google Scholar 

  18. Majid, A., Gullberg, M., van Staden, M., Bowerman, M.: How similar are semantic categories in closely related languages? a comparison of cutting and breaking in four germanic languages. Cognitive Linguistics 18(2), 179–194 (2007)

    Google Scholar 

  19. Peirce, C.S., Hartshorne, C., Weiss, P., Burks, A.W.: Collected Papers of Charles Sanders Peirce. Harvard University Press (1931, 1958), http://books.google.com/books?id=G7IzSoUFx1YC

  20. Penfield, W., Boldrey, E.: Somatic motor and sensory representation in the cerebral cortex of man as studied by electrical stimulation. Brain 60(4), 389–443 (1937)

    Article  Google Scholar 

  21. Penfield, W., Rasmussen, T.: The Cerebral Cortex of Man. Macmillian (1950)

    Google Scholar 

  22. Pettigrew, J.D.: Bi-sensory, striped representations: comparative insights from owl and platypus. Journal of Physiology-Paris 98(1-3), 113–124 (2004)

    Article  Google Scholar 

  23. Ramachandran, V., Hubbard, E.: Synaesthesia – a window into perception, thought and language. Journal of Consciousness Studies 8(12), 3–34 (2001)

    Google Scholar 

  24. Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)

    Article  MATH  Google Scholar 

  25. Schluppeck, D., Glimcher, P., Heeger, D.J.: Topographic organization for delayed saccades in human posterior parietal cortex. Journal of Neurophysiology 94(2), 1372–1384 (2005) PMID: 15817644

    Google Scholar 

  26. Schott, G.D.: Penfield’s homunculus: a note on cerebral cartography. Journal of Neurology, Neurosurgery, and Psychiatry 56(4), 329–333 (1993) PMID: 8482950 PMCID: 1014945

    Google Scholar 

  27. Shillcock, R., Kirby, S., McDonald, S., Brew, C.: Filled pauses and their status in the mental lexicon (2001)

    Google Scholar 

  28. Silver, M.A., Kastner, S.: Topographic maps in human frontal and parietal cortex. Trends in Cognitive Sciences 13(11), 488–495 (2009)

    Article  Google Scholar 

  29. Solomonoff, R.J.: A formal theory of inductive inference. Information and Control, 1–22, 224–254 (1964)

    Google Scholar 

  30. Swisher, J.D., Halko, M.A., Merabet, L.B., McMains, S.A., Somers, D.C.: Visual topography of human intraparietal sulcus. The Journal of Neuroscience 27(20), 5326–5337 (2007)

    Article  Google Scholar 

  31. Tamariz, M.: Exploring systematicity between phonological and context-cooccurrence representations of the mental lexicon. The Mental Lexicon 3, 259–278 (2008)

    Article  Google Scholar 

  32. Thivierge, J., Marcus, G.F.: The topographic brain: from neural connectivity to cognition. Trends in Neurosciences 30(6), 251–259 (2007)

    Article  Google Scholar 

  33. Thom, R.: Structural stability and morphogenesis. Addison Wesley Publishing Company (1989)

    Google Scholar 

  34. de Thornley Head, P.: Synaesthesia: Pitch-Colour isomorphism in RGB-Space? Cortex 42(2), 164–174 (2006)

    Article  Google Scholar 

  35. Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11(2), 195–209 (1968)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IO Institute of Linguistics, Australia

    T. Mark Ellison

Authors
  1. T. Mark Ellison
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, Clayton School of Information Technology, Monash University, Bldg. 63, Wellington Road, 3800, Clayton, VIC, Australia

    David L. Dowe

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ellison, T.M. (2013). Categorisation as Topographic Mapping between Uncorrelated Spaces. In: Dowe, D.L. (eds) Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence. Lecture Notes in Computer Science, vol 7070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-44958-1_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-44958-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-44957-4

  • Online ISBN: 978-3-642-44958-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation