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The coordination dynamics of mobile conjugate reinforcement

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Abstract

What we know about infant learning and memory is founded largely on systematic studies by the late Carolyn Rovee-Collier (1942–2014) and her associates of a phenomenon called mobile conjugate reinforcement. Experiments show that when a ribbon is attached from a 3-month-old infant’s foot to a mobile suspended overhead the baby quickly realizes it can make the mobile move. The mobile, which offers interesting sights and sounds, responds conjugately to the baby’s vigorous kicks which increase in rate by a factor of 3–4. In this paper, using the concepts, methods and tools of coordination dynamics, we present a theoretical model which reproduces the experimental observations of Rovee-Collier and others and predicts a number of additional features that can be experimentally tested. The model is a dynamical system consisting of three equations, one for the baby’s leg movements, one for the jiggling motion of the mobile and one for the functional coupling between the two. A key mechanism in the model is positive feedback which is shown to depend sensitively on bifurcation parameters related to the infant’s level of attention and inertial properties of the mobile. The implications of our model for the dynamical (and developmental) origins of agency are discussed.

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Notes

  1. Various words are used to describe the baby’s leg movements, such as “foot thrusts,” “kicking” and so forth. In actual fact, the baby moves its legs (quasi-)rhythmically and the usual quantities of phase, amplitude and frequency are applicable.

  2. We are reminded of Newton’s words in a letter to Oldenburg in 1675: “self-motion,” Newton remarked, “is beyond our understanding” (cited in Gleick 2003, p. 105).

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Acknowledgments

We wish to express our gratitude to Maxine Sheets-Johnstone for her inspirational and insightful writings on animate movement and for her encouraging comments on this work. Thanks also to an anonymous reviewer and the Editor, Leo van Hemmen, for helpful comments that improved the MS. The research was supported by a grant from the US National Institute of Health (MH080838), the Chaire d’Excellence Pierre de Fermat and the FAU Foundation (Eminent Scholar in Science). Preliminary versions of the paper were presented by JASK at the 18th Herbstakademie on “The Circularity of Mind and Matter,” Heidelberg, Germany, March 26–27, 2015, and the 110th Meeting of The Society of Experimental Psychologists, Charlottesville, VA, April 17–18, 2015.

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Authors and Affiliations

  1. Center for Complex Systems and Brain Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    J. A. Scott Kelso & Armin Fuchs

  2. Intelligent Systems Research Centre, Ulster University, Derry ~ Londonderry, BT48 7JL, Northern lreland

    J. A. Scott Kelso

  3. Department of Physics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    Armin Fuchs

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  1. J. A. Scott Kelso
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Correspondence to J. A. Scott Kelso or Armin Fuchs.

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Kelso, J.A.S., Fuchs, A. The coordination dynamics of mobile conjugate reinforcement. Biol Cybern 110, 41–53 (2016). https://doi.org/10.1007/s00422-015-0676-0

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