98 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



on the right retina the image is at some point P R in the temporal 

 direction from P R . If an object is located at P', and if P' is not too 

 far removed from P , there may be fusion even of the images on P L 

 and P' R , though because of the more temporal location of P' R with 

 respect to P R , P' is judged nearer the observer than P . The situation 

 when P' lies beyond P is similar except that P' R is then medial to P R . 

 But if P' is moved much farther or much closer, fusion is no longer 

 possible, and two images result. We shall say that P L and P R are 

 corresponding points on the two retinas, whereas P h and any other 

 point P' R different from P R are disparate. 



While holding the fixation at P , any other point Q within the 

 binocular visual field will form an image on a point Q L of the left 

 retina, Q R on the right, and the images may fuse, but only if Q is not 

 too near or too far away. We suppose that associated with each point 

 Q L of the left retina there is a unique point Q R of the right retina 

 which corresponds to it, while Q L and any other point Q' R are dis- 

 parate. If Q has as its images the point Q L and a disparate point Q' R 

 not too far removed from Q R fusion may still occur, but fusion is in 

 some sense optimal when the images fall on corresponding points. 

 The extent of the disparity, or the absence of it, then provides a cue 

 for the localization of the point Q in the subject's visual space. It is 

 suggested that the degree of convergence, and possibly also the degree 

 of accommodation serve as cues for the localization of the general 

 region about P with respect to the observer, while the binocular dis- 

 parity gives depth to this region and makes possible the localization 

 with respect to P of the objects in its immediate neighborhood. Thus 

 pictures seen in a stereoscope are seen as vaguely somewhere far off, 

 although the positions of the various details with respect to one an- 

 other are very definite. 



The simplest neurological picture to correspond to this seems to 

 be the following. Suppose there is a binocular representation in the 

 visual cortex which is three-dimensional in character. Simultaneous 

 stimulation of corresponding points Q L and Q R on the two retinas 

 leads to maximal excitation a at an associated point of the binocular 

 cortex. Simultaneous stimulation of slightly disparate points Q L and 

 Q' R leads to excitation <r of somewhat lesser amount and at a some- 

 what different location. Simultaneous stimulation of widely disparate 

 points gives only subthreshold excitation, if any, in the binocular 

 cortex, though it may lead to excitation in the two cortical regions 

 where the retinas are separately represented (cf. Bichowsky, 1941; 

 Verhoff, 1925). This would involve at least three visual areas in the 

 cortex, two monocular regions, which might be only two-dimensional, 

 and one binocular region which corresponds, point for point, to a cer- 



