Visual perception, receiving a two-dimensional (2D) visual input, often constructs the three-dimensional (3D) perceptual image. Although there are generally multiple structures in the external world that give an equivalent two-dimensional retinal image, the perceptual process naturally and easily infers only one 3D structure as the solution. However, the following problems are not obvious at all: what kind of structure can be obtained as a 3D perceptual image from certain 2D information, and why do we get a three-dimensional perceptual image instead of a two-dimensional one. In the present study, we investigate this problem by untangling the Necker Cube phenomenon, and propose a novel theory of three-dimensional visual perception from the viewpoint of the efficiency of information coding. Among the possible structures that can yield the 2D retinal image of the Necker Cube, the structure of the typical three-dimensional perceptual image of the Necker Cube maximizes the symmetry (in group theory). This maximization of symmetry is characterized by the pairs of adjoint functors (in category theory). Therefore, according to this proposed theory, “the Necker Cube” in the three-dimensional space is perceived as the most efficient encoding of the two-dimensional retinal image.

When conversational participants jointly attend to an object in the environment, how do they refer to it through their utterances and/or body movements to refer to it? Hindmarsh and Heath (2000) has proposed that participants employ the principle of recipient design of visual reference, wherein they design a visual reference as to provide recipients with clearer views of the relevant objects and scenes. In this study, focusing on a visual reference to an object occluded by a referrer/recipient's body or another object in the environment, we conducted detailed analyses of three segments collected from natural conversation data. The results show that some visual references were characterized as follows: (1) not providing a “clearer view”to the recipient, (2) not referring to the position or direction of the object directly, (3) specifying the spatial layout of the referrer, the recipient, an occluding object, and a referent. These results suggest that the recipient design of visual reference is sufficient, if an object is referred to visually, such that the recipient can recognize the spatial layout of the referrer, the recipient, and the object. Hence, even if clearer views are not available, a referent can be established visually if the recipient is provided with a guide to it.

Humans can utilize the other persons' knowledge as their own knowledge as a function of the mirror neuron. In this study, we examined whether knowledge of results (KR) is utilized for self-motor adjustment when a person is provided with others' adjustment motion, and what kind of motor information is transmitted between people. The participants performed a jumping height adjustment task involving a vertical jump. This task involved adjusting the target height (50% of the height of a maximum effort trial), with obtaining the KR for each trial. We conducted the task under the following two conditions: (i) individual condition (12 subjects), with one subject performing four trials; and (ii) group condition (12 groups), with four subjects performing one trial each, while they observed others' motions and shared their KR. We collected the data on ground reaction forces and coordinates of twenty body points. Under both conditions, participants gradually approached the target jumping height as the number of trials increased. When the transition of jumping height was approximated using a logistic curve, both waveforms were found to be similar. This finding demonstrates that the learning patterns of both conditions are similar, which means that others' KR is utilized in self-motor adjustment. Additionally, when examining the way of height adjustment, we found that the jumping height was adjusted by the “power”of the shoulder and hip joints under both conditions. Therefore, we considered that the KR, and the “power” of the joints corresponding to adjusted motion, were transmitted through observation, hence making the adjustment of jumping height possible. We concluded that motor adjustments are connected not only by the aspect of the behavior but also by the aspect of motor control. These outcomes can be applied to new motor learning methods for rehabilitation and can provide expert tips for human movement.

This article describes the reality of interaction among teachers and researchers in the process of lesson study. For this purpose, we used a project of learning sciences as a research field and selected teachers (the main teacher and surrounding teachers) and researchers as research participants. We first collected and analyzed process data of two cases of lesson study such as teachers' lesson plans, learning materials, reflection notes, participants' comments on them, and their observation of the lesson. We also conducted a retrospective interview of the main teacher and one of the participating researchers to yield narrative data. The analyses showed that the main teacher did not accept the opinions of the researchers directly nor instantly. However, he changed his view in the whole process of lesson study especially when he noticed the reality of students' learning as he wrote the teachers' reflection note which was designed by the researchers to foster teachers' learning. The researcher also learned from the process by proposing his own hypotheses of how students would learn in that lesson, responding to ideas of the main teacher, and verifying the hypotheses based on the evidence of students' learning.