## Abstract

There are numerous examples that show how the exploitation of the body’s physical properties can lift the burden on the brain. Examples are grasping, swimming, locomotion, and motion detection. The term Morphological Computation was originally coined to describe processes in the body that would otherwise have to be conducted by the brain. In this paper, we argue for a synergistic perspective, and by that, we mean that Morphological Computation is a process which requires a close interaction of body and brain.

Based on a model of the sensorimotor loop, we study a new measure of synergistic information and show that it is more reliable in cases in which there is no synergistic information, compared to previous results. Furthermore, we discuss an algorithm that allows the calculation of the measure in non-trivial (non-binary) systems.

## In a nutshell

Synergistic information is the information that is contained in two or more random variables about another, that cannot be extracted if a subset of the random variables is known. The most commonly presented example is the logical XOR

X | Y | Z = X XOR Y |
---|---|---|

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

The output Z is unpredictable if only X or Y are known. If we know that X=1, then Z=0 or Z=1 with equal probability. This also holds for X=0, Y=0, and Y=1. To predict the output Z, both inputs X and Y have to be taken into account. This is referred to as synergistic information.

In the context of this paper, we investigated morphological computation as the synergistic contribution of the world state W and the action state A with respect to the next world state W’. The paper expands on this idea. The goal of this post is to summarise the approach and to present the results.

We use the complexity measure presented in [?].

The idea is summarised in the figure below. Both plots show a causal diagram for three random variables, X, Y, and Z, in which X is causally dependent on Y and Z.

The undirected edge refers to the input distribution p(y,z). The figure on the left-hand side shows the full model, which means that the conditional p(x|y,z).

To be continued …

The results are summarised in the following figure: