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The slime mould Physarum polycephalum has been used in developing unconventional computing devices for in which the slime mould played a role of a sensing, actuating, and computing device. These devices treated the slime mould as an active living substrate, yet it is a self-consistent living creature which evolved over millions of years and occupied most parts of the world, but in any case, that living entity did not own true cognition, just automated biochemical mechanisms. To "rehabilitate" slime mould from the rank of a purely living electronics element to a "creature of thoughts" we are analyzing the cognitive potential of P. polycephalum. We base our theory of minimal cognition of the slime mould on a bottom-up approach, from the biological and biophysical nature of the slime mould and its regulatory systems using frameworks such as Lyon's biogenic cognition, Muller, di Primio-Lengelerś modifiable pathways, Bateson's "patterns that connect" framework, Maturana's autopoietic network, or proto-consciousness and Morgan's Canon., (Copyright © 2018 Elsevier B.V. All rights reserved.)

We studied animal's learning of spatial discrimination in an experimental environment. Turtles, Chinemys reevesii, were employed for the study. We focused on two independent aspects: (1) turtle's success rate in the task, which is the most common criterion to estimate the ability of the animals, and (2) the statistical properties of the time interval of the task, which is independent on the spatial criterion. For a statistical analysis, we employed the scheme of power law distributions which was recently used to estimate animal behaviors in relation to the idea of the fractal. We addressed the basic problem of whether these two criteria, or any other criteria for this matter, could or could not exclude an observer who studies the animal behavior. To demonstrate inseparability of an observer and the object, we conducted three different learning experiments: (1) complete spatial discrimination, (2) incomplete spatial discrimination, (3) another, different, complete discrimination, in this order. The incomplete one was taken to mean incomplete only for an observer. Our experiments reveal that the same result (success rate) was perceived differently by the animal if the attitude of the observer to the experiments differed. This observation comes to suggest that the notion of autonomous choice on the part of an animal is contingent upon the inseparability between an observer and the object.

The issue we address is whether an animal knows or understands the significance of learning. We constructed an animal's own conceptualization via resolving a paradox underlying the process of learning. We found a kind of self-similar pattern in the behavior of goldfish resolving a paradoxical experimental problem. The pattern can be considered as a solution to the paradox in the experiment. An animal's own learning should be revised through solving paradoxes. The dualism of mechanistic thinking and vitalism can thus be avoided.

We propose a weak definition for the usage of a tool for an ethological study of ants. In particular, we illustrate the usage of a cart in experiments on the transportation of foods by ants as employing a logical structure including a contradiction. The contradiction originates in ruling out the very term 'tool' from the description of the behavior of the animals. Focusing on a self-similar structure underlying the description of a contradiction, we observe a particular time-series sequence of ants' behaviors following a 1/f or Zipf's law. The behaviors following the 1/f or Zipf's law manifest an appropriateness of the notion of a cart as a logical jump.

Fish schools are frequently observed without a leader and an explicit condition forming school. Several models of schooling have been proposed focusing on the influence of neighbors, and introducing probability distributions, while these models are based on the separation of schooling and territorial behavior. We frequently consider the duality of aggregation of animals, in which behavioral patterns involve both attraction and repulsion, antagonistic with each other. The idea of probability does not explain this duality that can provide both schooling and territorial behavior. From these biological facts, we have constructed a behavior model in which the influence of neighbors is formulated by the interface between the states of neighbors and a map of changes in these states. This interface uses a self-similar nowhere differentiable transition map which is temporally constructed, encompassing a crucial duality of repulsive and attractive forces hidden in the interaction among fishes. We tested it with computer simulations against the biological reality of schooling and territorial behavior. Due to the influence neighbors can have on duality, the same model can show both schooling behavior with a high degree of polarization and territorial behavior.

Endophysics ultimately deduces an indefinite interface between an object and an observer. Objects, given such an interface, cannot be distinguished from the measurement process used to identify them. Evolutionary processes comprising of emergent properties and adaptability are seen in a new light. The concept of indefiniteness and/or paradox appears on the surface to be based on the epistemological framework of the Cartesian cut. However, perpetual processes consisting of generation and resolution of paradoxes are beyond the epistemological framework of measurement. They lead to the notion of progression, which one can refer to as ontological (or inherent) measurement.

Complex systems in which internal agents (observers) interact with each other with finite velocity of information propagation cannot be described with a single consistent logic. We have proposed the bootstrapping system of cellular automata for describing such complex systems using two types of complementary logic: Boolean and non-Boolean. We extend this in this paper to a system of time-discrete continuous maps using fuzzy logic in place of non-Boolean logic. Fuzziness implies the intrinsic ambiguity of internal measurement. The bootstrapping system evolves, changing the dynamics perpetually, so that the discrepancy between the two types of complementary logic may be minimized. The equilibration force defined from the strength of discrepancy forms a landscape for self-organization which is similar to the fitness landscape for evolution. Though they appear similar, the former is derived from the internal dynamics. The goal of evolution, when applied to the map of the Belousov-Zabochinsky reaction, is demonstrated to be near the border between periodicity and chaos. The behavior depends on the degree of fuzziness and the extent of noise. When fuzziness increases too much, the system becomes unstable. Near the boundary, it exhibits intermittent chaos with a background of 1/f noise.

Biologically motivated computing presents us with a measurement process in science. It triggers an epistemological shift from state-oriented physics to measurement-oriented physics, in which we can find a parallelism with Wittgenstein's shift from rule following to a language game. We argue here that an approximation or computing process can be viewed as a language game and propose an idea of proto-computing which is metaphorically formalized through disequilibration between tree- and loop-program, as a model for measurement-oriented computing.

A learning experiment was designed using "Renju (Go-bang)". The matches could proceed with prior indefiniteness, distinct from probability, as under the finite VOP (velocity of observation propagation). The information of each situation in the first game SSG and one in the replay SRE were investigated with the basic strategy derived from the "Renju" rules. The behavior of the difference (SRE (i)-SSG (i)) suggested that prior indefiniteness turned into definiteness, suggesting that perpetual decision change occurred and that it perpetually allowed observers to construct higher levels of hierarchical learning logic.

Describing a system in which internal detection or observation proceeds at a finite velocity is always destined to end up with a form of self-contradiction. For any formal language, for such a description, we must assume that the velocity of observation propagation or VOP be infinity. In the present paper, we propose a self-referential scheme intended for formally describing a system exhibiting the process of disequilibration propagating at a finite VOP, and find that a global logic can emerge from local disequilibration. Conservative cellular automata of Margolus type, for instance, enable disequilibration to be replaced by such a process that the number of particles is not conserved globally while appearing to be conserved by local observers. One cannot determine local rules universally. Nevertheless, global logic emerges as a result of the dynamics of a one-to-many type mapping. This is a fundamental aspect of natural languages or communication relevant to natural life and intelligence.

Systems involving both intracellular and intercellular computation are destined to be described as non-computable. We propose a model for such systems by introducing the inconsistent relation of Boolean and non-Boolean logic. Cellular automata fashioned model exhibits an evolution like class 4 located at the edge of chaos, while there is no local rule for universality existing over the whole space in our model. A system featuring the inconsistent vertical scheme is approximately articulated into a hierarchical system, whose wholeness cannot be deduced by any approximated local rule. In other words, undecidability between a part and whole comprises a hierarchical structure.

A principle of self-organization toward a critical state is proposed as a metadynamics of evolutionary processes. When the propagation velocity of information is slow as in living systems, discrepancy occurs between the virtual process and the actual one. The degree of discrepancy is defined for discrete dynamical systems on the scheme of perpetual disequilibration (PD), proposed by Gunji and others. It is supposed that adaptable systems tend to evolve so that the discrepancy may be minimized. A principle of the minimum degree of PD is applied to cellular automata and Boolean networks. These complex systems have the minimum degree of PD at the border between order and chaos, and thus are expected to evolve to the critical state at the edge of chaos. This self-organized criticality is a generalized form of Bak's self-organized criticality.

Life seems to be at the border between order and chaos. The Game of Life, which is a cellular automation to mimic life, also lies at the transition between ordered and chaotic structures. Kauffman recently that the organizations at the edge of chaos may be the characteristic target of selection for systems able to coordinate complex tasks and adapt. In this paper, we present the idea of perpetual disequilibration proposed by Gunji and others as a general principle governing self-organization of complex systems towards the critical state lying at the border of order and chaos. The rule for the Game of Life has the minimum degree of perpetual disequilibrium among 2(18) rules of the class to which it belongs.

In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicitly. It is an extension of Spencer-Brown's idea of time, however. The definition of time is segregated into two parts, corresponding to the syntax and semantics of language, respectively. In this context, time reversibility is defined by the formalization of the relationship between time and self-consistency. This idea has also been discussed in the context of designation and/or naming. Here we will discuss it in the context of cellular automata and explain the structure of one-to-many type mappings. Our approach is the first attempt to extend autopoietic systems in terms of dynamics. It illustrates how to introduce an autopoietic time which looks irreversible, but without the concept of entropy.

We propose a perspective for living systems, emphasizing that living systems are organized through the recognition of themselves and their surroundings. Oscillator functions in Brownian Algebra are introduced, supposing that the oscillation can be regarded as metabolism of the living state. We illustrate the idea of the self-repairing model in non-articulated coralline algae. Since various cells of this plant are assumed to be identified with the periodic sequence of oscillations, the individual periodic sequence characterizing a cell is supposed to be determined by a local-interaction rule which can be regarded as the process of self-organization through the recognition of local shape. Owing to accidental injury the rule characterizing a cell's own state can be transformed, and it entails another periodic sequence. We express the oscillator as state flow diagrams, and analyze the relationship between the transformation of the period and the injury which is represented by the removal of transient in flow diagrams.

Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.