Tutorial on Embodiment

4.2.2. Quantifying information structure*

Thus far, we have been referring to the information theoretic implications of embodiment in a mostly informal sense. However, the information content or structure present in the sensory and motor modalities can be quantified. Lungarella & Sporns (2006) presented several methods for measuring the (undirected) information present in sensory modalities (Shannon entropy, mutual information, integration, and complexity). To extract directed, or causal, relationships, such as from sensors to motors or vice versa, they employed transfer entropy; however, other measures are also available, as analyzed in Lungarella et al. (2007). Polani and colleagues have devised a different measure, empowerment, which measures how much influence an agent has on its environment, but only that influence that can be sensed by the agent's own sensors (see online lecture or Jung et al., 2011). Yet another embodiment quantification method was presented recently by Thornton (2010), testifying the recent attention given to this subject. One of his case studies features a passive dynamic walker that we have (less formally) analyzed in the section on locomotion. Although such analysis tools are equally suited for animals and robots engaged in behavior, robots, as we have already discussed, are significantly easier to monitor and manipulate.

Online lecture:

Daniel Polani
University of Hertfordshire, UK
On Informational Principles of Embodied Cognition


* adapted from Hoffmann and Pfeifer, 2011


Jung, T.; Polani, D. & Stone, P. (2011), 'Empowerment for Continuous Agent-Environment Systems', Adaptive Behavior.
Lungarella, M. & Sporns, O. (2006), 'Mapping information flow in sensorimotor networks', PLoS Comput Biol 2, 1301-12.
Lungarella, M.; Ishiguro, K.; Kuniyoshi, Y. & Otsu, N. (2007), 'Methods for quantifying the causal structure of bivariate time series', Int. J. of Bifurcation and Chaos 17, 903-921.
Thornton, C. (2010), 'Gauging the value of good data: Informational embodiment quantification', Adaptive Behavior 18(5), 389-399.
Hoffmann, M. & Pfeifer, R. (2011), The implications of embodiment for behavior and cognition: animal and robotic case studies, in W. Tschacher & C. Bergomi, ed., The Implications of Embodiment: Cognition and Communication, Exeter: Imprint Academic, pp. 31-58.