Visual and kinesthetic alleys formed with rods

•Geometries of visual and kinesthetic spaces were revealed by alley experiments.•In each space, uncrossed, equidistant, and perpendicular alley settings were similar.•Alley settings were affected by lateral size of stimulus layout.•Visual settings were explained by Euclidean geometry.•Kinesthetic settings were not explained by Euclidean, hyperbolic, or elliptic geometry. Geometries of visual and kinesthetic spaces were estimated by alley experiments. For the visual alley, 24 observers set rods that extended in depth so that they appeared 1) to neither diverge nor converge, 2) to be separated by the same lateral distance, or 3) to be perpendicular to the frontal plane. The separation of rods and the height of the observer’s eyes were varied. Under each instruction, another group of 20 observers set the rods visually at eye level or kinesthetically without seeing the rods. We obtained these findings. First, the rods seen obliquely from above were set more accurately than the rods seen at eye level. Second, the visual settings were parallel to one another for small separation and were convergent to the observer for large separation, whereas the kinesthetic settings were divergent to the observer for the small separation and were convergent to the observer for the large separation. These differences between sense modalities were explained by the location of the egocenter(s) and the sensitivity to direction. Third, the visual or kinesthetic settings did not differ with instructions, suggesting that visual and kinesthetic spaces were Euclidean. Fourth, the visual angle of the near ends of the rods, plotted against that of the far ends, was described by Euclidean geometry, provided that the visual angle is exaggerated. Last, the kinesthetic angle of the near ends of the rods, plotted against that of the far ends, was not described by any simple geometry even when we assumed that the kinesthetic angle is exaggerated.