To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions.

A flexible body image is required by animals if they are to adapt to body changes and move effectively within a structurally complex environment. Here, we show that terrestrial hermit crabs, Coenobita rugosus , which frequently change shells, can modify walking behaviour, dependent on the shape of the shell. Hermit crabs walked along a corridor that had alternating left and right corners; if it was narrow at the corner, crabs rotated their bodies to avoid the wall, indicating an awareness of environmental obstacles. This rotation increased when a plastic plate was attached to the shell. We suggest that the shell, when extended by the plate, becomes assimilated to the hermit crab's own body. While there are cases of a tool being assimilated with the body, our result is the first example of the habitat where an animal lives and/or carries being part of a virtual body.

Animals making a group sometimes approach and sometimes avoid a dense area of group mates, and that reveals the ambiguity of density preference. Although the ambiguity is not expressed by a simple deterministic local rule, it seems to be implemented by probabilistic inference that is based on Bayesian and inverse Bayesian inference. In particular, the inverse Bayesian process refers to perpetual changing of hypotheses. We here analyse a time series of swarming soldier crabs and show that they are employed to Bayesian and inverse Bayesian inference. Comparing simulation results with data of the real swarm, we show that the interpretation of the movement of soldier crabs which can be based on the inference can lead to the identification of a drastic phase shift-like transition of gathering and dispersing. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.