Biopsychological foundations of geometric cognition

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Mateusz Hohol

Abstract

In this review-paper, I focus on biopsychological foundations of geometric cognition. Starting from the Kant’s views on mathematics, I attempt to show that contemporary cognitive scientists, alike the famous philosopher, recognize mutual relationships of visuospatial processing and geometric cognition. What I defend is a claim that Tinbergen’s explanatory questions are the most fruitful tool for explaining our “hardwired,” and thus shared with other animals, Euclidean intuitions, which manifest themselves in spatial navigation and shape recognition. I claim, however, that these “hardwired intuitions” cannot capture full-blooded Euclidean geometry, which demands practice with cultural artifacts in various time-scales.

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Proceedings of the PAU Commission on the Philosophy of Science

References

Amalric, M., Wang, L., Pica, P., Figueira, S., Sigman, M., Dehaene, S. (2017). The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers. PLoS Computational Biology, 13(1), e1005273–31. http://doi.org/10.1371/journal.pcbi.1005273

Ammassari-Teule, M., Tozzi, A., Rossi-Arnaud, C., Save, E., Thinus-Blanc, C. (1995). Reactions to spatial and nonspatial change in two inbred strains of mice: Further evidence supporting the hippocampal dysfunction hypothesis in the DBA/2 strain. Psychobiology, 23(4), 284–289. http://doi.org/10.3758/BF03333075

Bateson, P., Laland, K. N. (2013). Tinbergen's four questions: an appreciation and an update. Trends in Ecology & Evolution, 28(12), 712–718. http://doi.org/10.1016/j.tree.2013.09.013

Beaulac, G. (2014). Back to the Fodor-modules: The modularity of mind revisited. Proceedings of the Annual Meeting of the Cognitive Science Society, 36, 1904–1910.

Bechtel, W. (2008). Mental mechanisms: Philosophical perspectives on cognitive neuroscience. New York: Routledge.

Bechtel, W. (2016). Investigating neural representations: the tale of place cells. Synthese, 193(5), 1287–1321. http://doi.org/10.1007/s11229-014-0480-8

Brouwer, L. E. J. (1975). Philosophy and foundations of mathematics: L.E.J. Brouwer collected works. (A. Heyting, red.). New York: Elsevier.

Carey, S., Spelke, E. S. (1996). Science and core knowledge. Philosophy of Science, 63(4), 515–533. http://doi.org/10.1086/289971

Cartwright, B. A., Collett, T. S. (1983). Landmark learning in bees. Journal of Comparative Physiology a: Sensory, Neural, and Behavioral Physiology, 151(4), 521–543. http://doi.org/10.1007/BF00605469

Cheng, K. (1986). A purely geometric module in the rat's spatial representation. Cognition, 23(2), 149–178. http://doi.org/10.1016/0010-0277(86)90041-7

Cheng, K. (2008). Whither geometry? Troubles of the geometric module. Trends in Cognitive Sciences, 12(9), 355–361. http://doi.org/10.1016/j.tics.2008.06.004

Cheng, K., Newcombe, N. S. (2005). Is there a geometric module for spatial orientation? Squaring theory and evidence. Psychonomic Bulletin & Review, 12(1), 1–23. http://doi.org/10.3758/BF03196346

Cheng, K., Huttenlocher, J., Newcombe, N. S. (2013). 25 years of research on the use of geometry in spatial reorientation: a current theoretical perspective. Psychonomic Bulletin & Review, 20(6), 1033–1054. http://doi.org/10.3758/s13423-013-0416-1

Clark, A. (2006). Language, embodiment, and the cognitive niche. Trends in Cognitive Sciences, 10(8), 370–374. http://doi.org/10.1016/j.tics.2006.06.012

Cooper, L. A., Shepard, R. N. (1973). Chronometric studies of the rotation of mental images. W: W. G. Chase (red.), Visual Information Processing: Proceedings (ss. 75–176). New York: Academic Press.

Craver, C. F., Darden, L. (2013). In search of mechanisms. Chicago: University of Chicago Press.

Cruse, H., Wehner, R. (2011). No need for a cognitive map: decentralized memory for insect navigation. PLoS Computational Biology, 7(3), e1002009. http://doi.org/10.1371/journal.pcbi.1002009

Dadaczyński, J. (1999). Filozofia matematyki Immanuela Kanta i jej dziedzictwo. Zagadnienia Filozoficzne w Nauce, 24, 26–42.

Dehaene, S. (2011). The number sense (Revised). Oxford: Oxford University Press.

Dehaene, S., Brannon, E. M. (2010). Space, time, and number: a Kantian research program. Trends in Cognitive Sciences, 14(12), 517–519. http://doi.org/10.1016/j.tics.2010.09.009

Dehaene, S., Izard, V., Pica, P., Spelke, E. S. (2006). Core knowledge of geometry in an Amazonian indigne group. Science, 311(5579), 381–384. http://doi.org/10.1126/science.1121739

Dehaene-Lambertz, G., Spelke, E. S. (2015). The infancy of the human brain, 88(1), 93–109. http://doi.org/10.1016/j.neuron.2015.09.026

Dilks, D. D., Julian, J. B., Paunov, A. M., Kanwisher, N. (2013). The occipital place area is causally and selectively involved in scene perception. The Journal of Neuroscience, 33(4), 1331–6a. http://doi.org/10.1523/JNEUROSCI.4081-12.2013

Dillon, M. R., Huang, Y., Spelke, E. S. (2013). Core foundations of abstract geometry. Proceedings of the National Academy of Sciences, 110(35), 14191–14195. http://doi.org/10.1073/pnas.1312640110/-/DCSupplemental

Dove, G. (2014). Thinking in words: Language as an embodied medium of thought. Topics in Cognitive Science, 6(3), 371–389. http://doi.org/10.1111/tops.12102

Fodor, J. A. (1983). The modularity of mind. Cambridge, MA: The MIT Press.

Fyhn, M., Molden, S., Witter, M. P., Moser, E. I., Moser, M.-B. (2014). Spatial representation in the entorhinal cortex. Science, 305, 1258–1264. http://doi.org/10.1126/science.1099901Gallistel, C. (1990). The organization of learning. Cambridge, MA: The MIT Press.

Gee, A. P., Chekhlov, D., Calway, A., Mayol-Cuevas, W. (2008). Discovering higher level structure in visual SLAM. IEEE Transactions on Robotics, 24(5), 980–990. http://doi.org/10.1109/Tro.2008.2004641

Gibson, E. J. (1969). Principles of perceptual learning and development. New York: Appleton Century Crofts.

Glennan, S. (2002). Rethinking Mechanistic Explanation. Philosophy of Science, 69(S3), S342–S353. http://doi.org/10.1086/341857

Gouteux, S., Thinus-Blanc, C., Vauclair, J. (2001). Rhesus monkeys use geometric and nongeometric information during a reorientation task. Journal of Experimental Psychology. General, 130(3), 505–519. http://doi.org/10.1037/0096-3445.130.3.505

Gouteux, S., Vauclair, J., Thinus-Blanc, C. (1999). Reaction to spatial novelty and exploratory strategies in baboons. Animal Learning & Behavior, 27(3), 323–332. http://doi.org/10.3758/bf03199731

Grill-Spector, K., Kourtzi, Z., Kanwisher, N. (2001). The lateral occipital complex and its role in object recognition. Vision Research, 41(10-11), 1409–1422. http://doi.org/10.1016/S0042-6989(01)00073-6

Grobler, A. (2006). Metodologia nauk. Kraków: Aureus-Znak.

Hafting, T., Fyhn, M., Molden, S., Moser, M.-B., Moser, E. I. (2005). Microstructure of a spatial map in the entorhinal cortex. Nature, 436(7052), 801–806. http://doi.org/10.1038/nature03721

Hempel, C. G., Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15(2), 135–175. http://doi.org/10.1086/286983

Hermer, L., Spelke, E. S. (1994). A geometric process for spatial orientation in young children. Nature, 370(3), 57–59. http://doi.org/10.1016/S0010-0277(96)00714-7

Hermer, L., Spelke, E. S. (1996). Modularity and development: the case of spatial reorientation. Cognition, 61(3), 195–232. http://doi.org/10.1016/S0010-0277(96)00714-7

Hohol, M. (2017). Wyjaśnić umysł: Struktura teorii neurokognitywnych (Wyd. 2). Kraków: Copernicus Center Press.

Hohol, M. (2018). Od przestrzeni do abstrakcyjnych pojęć: W stronę teorii poznania geometrycznego. W: R. Murawski, J. Woleński (red.), Problemy filozofii matematyki i informatyki (ss. 29–143). Poznań: Wydawnictwo Uniwersytetu Adama Mickiewicza.

Hohol, M., Wołoszyn, K. (2016). Ewolucja umysłu. W: M. Heller, J. Życiński, Dylematy ewolucji (ss. 293–310). Kraków: Copernicus Center Press.

Hohol, M., Baran, B., Krzyżowski, M., Francikowski, J. (2017a). Does spatial navigation have a blind-spot? Visiocentrism is not enough to explain the navigational behavior comprehensively. Frontiers in Behavioral Neuroscience, 11(154). http://doi.org/10.3389/fnbeh.2017.00154

Hohol, M., Cipora, K., Willmes, K., Nuerk, H.-C. (2017b). Bringing back the balance: domain-general processes are also important in numerical cognition. Frontiers in Psychology, 8(499), 17–5. http://doi.org/10.3389/fpsyg.2017.00499

Horst, S. (2016). Cognitive pluralism. Cambridge: MIT Press.

Izard, V., Spelke, E. S. (2009). Development of sensitivity to geometry in visual forms. Human Evolution, 23(3), 213–248.

Izard, V., Pica, P., Spelke, E. S., Dehaene, S. (2011). Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences, 108(24), 9782–9787. http://doi.org/10.1073/pnas.1016686108

Kant, I. (1993). Prelogomena do wszelkiej przyszłej metafizyki, która będzie mogła wystąpić jako nauka. Warszawa: PWN.

Kaplan, D. M. (2011). Explanation and description in computational neuroscience. Synthese, 183(3), 339–373. http://doi.org/10.1007/s11229-011-9970-0

Kelly, D. M., Spetch, M. L., Heth, C. D. (1998). Pigeons' (Columba livia) encoding of geometric and featural properties of a spatial environment. Journal of Comparative Psychology, 112(3), 259–269. http://doi.org/10.1037/0735-7036.112.3.259

Kinzler, K. D., Spelke, E. S. (2007). Core systems in human cognition. Progress in Brain Research, 164, 257–264. http://doi.org/10.1016/S0079-6123(07)64014-X

Kourtzi, Z., Kanwisher, N. (2001). Representation of perceived object shape by the human Lateral Occipital Complex. Science, 293(2001), 1506–1509. http://doi.org/10.1126/science.1061133

Lakoff, G., Núñez, R. E. (2000). Where mathematics comes from. New York: Basic Books.

Landau, B., Lakusta, L. (2009). Spatial representation across species: geometry, language, and maps. Current Opinion in Neurobiology (Vol. 19, ss. 12–19).

Lee, S. A., Vallortigara, G. (2015). Bumblebees spontaneously map location of conspecific using geometry and features. Learning and Motivation, 50, 32–38. http://doi.org/10.1016/j.lmot.2014.10.004

Maguire, E. A. (2001). The retrosplenial contribution to human navigation: A review of lesion and neuroimaging findings. Scandinavian Journal of Psychology, 42(3), 225–238.

Margules, J., Gallistel, C. (1988). Heading in the rat: Determination by environmental shape. Animal Learning & Behavior, 16(4), 404–410. http://doi.org/10.3758/bf03209379

Mayr, E. (1961). Cause and effect in biology. Science, 134(3489), 1501–1506. http://doi.org/10.1126/science.134.3489.1501

Menzel, R., Greggers, U., Smith, A., Berger, S., Brandt, R., Brunke, S., et al. (2005). Honey bees navigate according to a map-like spatial memory. Proceedings of the National Academy of Sciences, 102(8), 3040–3045. http://doi.org/10.1073/pnas.0408550102

Milford, M. J., Wyeth, G. F. (2008). Mapping a suburb with a single camera using a biologically inspired SLAM system. IEEE Transactions on Robotics, 24(5), 1038–1053. http://doi.org/10.1109/TRO.2008.2004520

Minini, L., Jeffery, K. J. (2006). Do rats use shape to solve "shape discriminations"? Learning & Memory, 13(3), 287–297. http://doi.org/10.1101/lm.84406

Miłkowski, M. (2013). Explaining the computational mind. Cambridge, MA: The MIT Press.

Miłkowski, M. (2014). Wyjaśnianie w kognitywistyce. Przegląd Filozoficzny - Nowa Seria, 2(86), 151–166. http://doi.org/10.2478/pfns-2013-0040

Miłkowski, M. (2016). Function and causal relevance of content. New Ideas in Psychology, 40(Part A), 94–102. http://doi.org/10.1016/j.newideapsych.2014.12.003

Moser, E. I., Moser, M.-B., McNaughton, B. L. (2017). Spatial representation in the hippocampal formation: a history. Nature Publishing Group, 20(11), 1448–1464. http://doi.org/10.1038/nn.4653

O'Keefe, J., Dostrovsky, J. (1971). The hippocampus as a spatial map: Preliminary evidence from unit activity in the freely-moving rat. Brain Research, 34(1), 171–175.

O'Keefe, J., Nadel, L. (1978). The hippocampus as a cognitive map. Oxford: Oxford University Press.

Poucet, B., Chapuis, N., Durup, M., Thinus-Blanc, C. (1986). A study of exploratory behavior as an index of spatial knowledge in hamsters. Animal Learning & Behavior, 14(1), 93–100. http://doi.org/10.3758/BF03200043

Prinz, J. J. (2006). Is the mind really modular? In R. J. Standton (Ed.), Contemporary debates in cognitive science. Malden.

Samuels, R. (1998). Evolutionary psychology and the massive modularity hypothesis. The British Journal for the Philosophy of Science, 49, 575–602.

Samuels, R. (2004). Innateness in cognitive science. Trends in Cognitive Sciences, 8(3), 136–141. http://doi.org/10.1016/j.tics.2004.01.010

Sheynikhovich, D., Chavarriaga, R., Strösslin, T., Arleo, A., Gerstner, W. (2009). Is there a geometric module for spatial orientation? Insights from a rodent navigation model. Psychological Review, 116(3), 540–566. http://doi.org/10.1037/a0016170

Sovrano, V. A., Bisazza, A., Vallortigara, G. (2002). Modularity and spatial reorientation in a simple mind: encoding of geometric and nongeometric properties of a spatial environment by fish. Cognition, 85(2), B51–B59. http://doi.org/10.1016/S0010-0277(02)00110-5

Spelke, E. S., Gilmore, C. K., McCarthy, S. (2011). Kindergarten children's sensitivity to geometry in maps. Developmental Science, 14(4), 809–821. http://doi.org/10.1111/j.1467-7687.2010.01029.x

Spelke, E. S., Lee, S. A., Izard, V. (2010). Beyond core knowledge: Natural geometry. Cognitive Science, 34(5), 863–884. http://doi.org/10.1111/j.1551-6709.2010.01110.x

Sutton, J. E., Newcombe, N. S. (2014). The hippocampus is not a geometric module: processing environment geometry during reorientation. Frontiers in Human Neuroscience, 8, 244. http://doi.org/10.3389/fnhum.2014.00596

Thinus-Blanc, C., Ingle, D. (1985). Spatial behavior in gerbils (Meriones unguiculatus). Journal of Comparative Psychology, 99(3), 311–315. http://doi.org/10.1037//0735-7036.99.3.311

Thinus-Blanc, C., Chabanne, V., Tomassi, L., Peruch, P., Vauclair, J. (2010). The encoding of geometry in various vertebrate species. In F. L. Dolins, R. W. Mitchell (Eds.), Spatial cognition, spatial perception (ss. 99–116). Cambridge: Cambridge University Press.

Thrun, S. (2002). Robotic mapping: a survey. In G. Lakemeyer, B. Nebel (Eds.), Animal navigation - a synthesis (ss. 1–36). San Francisco, CA.

Tinbergen, N. (1963). On aims and methods of ethology. Zeitschrift Für Tierpsychologie, 20(3), 410–433. http://doi.org/10.1111/eth.1963.20.issue-3

Tolman, E. C. (1932). Purposive behavior in animals and man. Berkeley, CA: University of California Press.

Tolman, E. C. (1948). Cognitive maps in rats and men. Psychological Review, 55(4), 189–208. http://doi.org/10.1037/h0061626

Tomassi, L., Vallortigara, G., Zanforlin, M. (1997). Young chickens learn to localize the centre of a spatial environment. Journal of Comparative Physiology a: Sensory, Neural, and Behavioral Physiology, 180(5), 567–572. http://doi.org/10.1007/s003590050073

Urbańczyk, P. (2014). Geneza intuicjonistycznego rachunku zdań i Twierdzenie Gliwienki. Zagadnienia Filozoficzne W Nauce, 56, 33–56.

Vallortigara, G. (2012). Core knowledge of object, number, and geometry: A comparative and neural approach. Cognitive Neuropsychology, 29(1-2), 213–236. http://doi.org/10.1080/02643294.2012.654772

Vargas, J. P., López, J. C., Salas, C., Thinus-Blanc, C. (2004). Encoding of geometric and featural spatial information by Goldfish (Carassius auratus). Journal of Comparative Psychology, 118(2), 206–216. http://doi.org/10.1037/0735-7036.118.2.206

Wang, R. F., Hermer, L., Spelke, E. S. (1999). Mechanisms of reorientation and object localization by children: A comparison with rats. Behavioral Neuroscience, 113(3), 475–485. http://doi.org/10.1037//0735-7044.113.3.475

Webb, B. (2012). Cognition in insects. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 367(1603), 2715–2722. http://doi.org/10.1098/rstb.2012.0218

Wehner, R., Räber, F. (1979). Visual spatial memory in desert ants, Cataglyphis bicolor (Hymenoptera: Formicidae). Experientia, 35(12), 1569–1571. http://doi.org/10.1007/BF01953197

Wystrach, A., Cheng, K., Sosa, S., Beugnon, G. (2011). Geometry, features, and panoramic views: Ants in rectangular arenas. Journal of Experimental Psychology: Animal Behavior Processes, 37(4), 420–435. http://doi.org/10.1037/a0023886

Zoccolan, D., Oertelta, N., DiCarlo, J. J., Cox, D. D. (2009). A rodent model for the study of invariant visual object recognition. Proceedings of the National Academy of Sciences, 106(21), 8748–8875. http://doi.org/10.1073 pnas.0811583106