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.

视觉和动觉空间的几何形状是通过小巷实验来估计的。对于视觉通道，24 位观察者设置了深度延伸的杆，使它们看起来 1) 既不发散也不收敛，2) 以相同的横向距离分开，或 3) 垂直于额平面。杆的间距和观察者眼睛的高度是不同的。在每条指令下，另一组 20 名观察者在视觉上或动觉上将杆设置在视线水平上，而没有看到杆。我们获得了这些发现。首先，从斜上方看到的杆比在眼睛水平处看到的杆设置得更准确。其次，视觉设置在小间距时彼此平行，而在大间距时会聚到观察者，而动觉设置对于小间距的观察者来说是发散的，而对于大间距的观察者则是收敛的。感觉模式之间的这些差异可以通过自我中心的位置和对方向的敏感性来解释。第三，视觉或动觉设置与指令没有区别，这表明视觉和动觉空间是欧几里得的。第四，如果视角被夸大，则杆的近端的视角相对于远端的视角是由欧几里得几何描述的。最后，即使我们假设动觉角度被夸大了，杆近端的动觉角与远端的动觉角也没有用任何简单的几何学描述。感觉模式之间的这些差异可以通过自我中心的位置和对方向的敏感性来解释。第三，视觉或动觉设置与指令没有区别，这表明视觉和动觉空间是欧几里得的。第四，如果视角被夸大，则杆的近端的视角相对于远端的视角是由欧几里得几何描述的。最后，即使我们假设动觉角度被夸大了，杆近端的动觉角与远端的动觉角也没有用任何简单的几何学描述。感觉模式之间的这些差异可以通过自我中心的位置和对方向的敏感性来解释。第三，视觉或动觉设置与指令没有区别，这表明视觉和动觉空间是欧几里得的。第四，如果视角被夸大，则杆的近端的视角相对于远端的视角是由欧几里得几何描述的。最后，即使我们假设动觉角度被夸大了，杆近端的动觉角与远端的动觉角也没有用任何简单的几何学描述。表明视觉和动觉空间是欧几里得的。第四，如果视角被夸大，则杆的近端的视角相对于远端的视角是由欧几里得几何描述的。最后，即使我们假设动觉角度被夸大了，杆近端的动觉角与远端的动觉角也没有用任何简单的几何学描述。表明视觉和动觉空间是欧几里得的。第四，如果视角被夸大，则杆的近端的视角相对于远端的视角是由欧几里得几何描述的。最后，即使我们假设动觉角度被夸大了，杆近端的动觉角与远端的动觉角也没有用任何简单的几何学描述。