Previously, Evolution-In-Materio (EIM), an unconventional computing paradigm, was addressed as a computing system which exhibits dynamical hierarchies. For different conceptual domains identified within an EIM system, a corresponding hierarchical level was defined and the state space description provided. Entropic relations established between such system descriptions show that one hyperdescribes another in an information theoretical sense. Hereby we report on those findings and revisit entropic relations between the level of material physics and the level of measurements via simulations of the addressed physical phenomenon. Evolution-In-Materio (EIM) (Miller et al., 2014), an unconventional computing approach, exploits physical properties of materials for computations. Materials are considered as bulks, unorganised matter, and manipulated under the guidance of an Evolutionary Algorithm (EA) towards achieving solution to a given computational problem. EA is run on a digital computer. Interaction with material physics (analogue) is realised via an interface board. For such a computing scenario different conceptual domains have been identified as shown in Figure 1. For each domain, a system description is provided in a form of a discrete state space description, i.e., a set of system states and a transfer function, as summarised in Table 1. The description is parameterised in the sense given by the system theory (Ashby, 1960). Since each state has a pertaining probability, the system is entropic. Also, description functions are defined which map states from a lower to a higher level in a sense described in (McGregor and Fernando, 2005).
EIM Systems and Hierarchies Within ThemGiven such state space descriptions, the following equations were shown to hold (Laketić and Tufte, 2016):where indices a and b refer to a lower and higher level respectively. Such entropic relations are equivalent to distinctness and state-dependence as defined in (McGregor and Fernando, 2005) being less than 1 thereby providing a proof that recognised hierarchical levels exhibit novelty and loss of information which are prominent characteristics of dynamical hierarchies. For the level of material physics, we use carbon nanotubes (CNTs) since the physical phenomenon manipulated for achieving computations in most of our experiments within NASCENCE project (Broersma et al., 2012) was the change of CNT conductivity due to the changes in the electric field.