Is perception isomorphic with neural activity?

The theory of visual stability proposed by Bridgeman et al. requires die existence of retinotopic maps in which neurons represent the spatiotopic position of objects through their activity. The authors reason that if the code for position is fully specified by the neural activity, it becomes independent of the position of neurons within the map (sect. 4.1, para. 3). These two aspects of Bridgeman et al.'s theory, namely, the retinotopy of the maps and the encoding of position through the activity regardless of retinotopic position, appear difficult to reconcile. Neurons within retinotopic maps in early visual cortex are known to have small receptive fields. Accordingly, a single cell cannot encode all possible retinal positions through its firing rate. If the head and trunk are fixed, the position of a11 object in space is the vector sum of its retinal position and eye position. Ifacell cannot encode all possible retinalpositions, it is difficult to imagine how it could do so for spatiotopic positions. This in turn entails that a neuronal population at a given location on the map cannot possibly encode an arbitrary head-centered position through its activity. The problem stems from the fact that in computing spatiotopic position in retinotopic maps, there is an intimate relation between what Bridgeman et al. call the inode ofrepresenting and the position of representing (sect. 4, para. 1). One relevant variable, retinal position, is itself represented by the map. As emphasized in the target article, this is not a problem for other visual attributes such as color or motion (sect. 4, para. 5-6). Extremely large receptive fields would certainly solve the problem (Zipser & Andersen 1988), but neurons in V1 or V2 do not have such large receptive fields. Nevertheless, it is still possible that the early visual cortical areas may support, partly or fully, a representation of the visual field that is suitable for determining visual stability during eye movements. We have presented a model for one way this could be done in a recent paper (Pouget e t al. 1993), inspired by the reports from several laboratories that eye position modulates visually driven activity in the lateral geniculate nucleus (Lal & Friedlander 1989; Lehmkuhle & Bar,o 1991) and area V1 and V3a of visual cortex (Galleti & Battaglini 1989; Trotter e t al. 1992; Weyand & Malpeli 1993). We have shown that such neurons could support a distributed representation of objects, including their head-centered spatial locations; the location is encoded by the modulationofthe visual responses ofneurons by eye position. We called this representation a retinospatiotopic map. The code for spatiotopic position in a retinospatiotopic map depends on both the pattern of activity and the s or, equivalently, if and only if positions in space are in a one-toone relationship with patterns of neuronal activity. Whether the patterns move to different locations in the brain as a result of eye movements is irrelevant for them, as long as the pattern stays the same. A retinospatiotopic map fails because it docs not encode head-centered position solely through an activity pattern but through a coinhination of activity and topography. The isomorphism criterion may be too strict, since even brain regions such as parietal area 7a and the lateral intraparietal area (LIP), which are believed to represent the position of objects in spatiotopic coordinates, would not qualify according to this strict requirement. Nonetheless, area 7a appears to contain a distributed representation of objects in body-centered coordinates (Andersen & Zipser 1988; Goodman & Andersen 1990; Zipser & Andersen 1988). It is possible that there is no invariant representation of spatial location anywhere in the brain. Would this make any computational problem that the brain must solve insoluble as a consequence? On the contrary, any invariant function, such as grasp of an object in space, could be computed from a distributed representation. Objects are grasped, brain activity comes and goes, and no invariant representation is to be found, anywhere, except perhaps at the level of the motoneurons. The strong isomorphism hypothesis is a conceptually simple one that would be convenient if true, but by no means necessary. We must begin to imagine how it could be that more than one pattern of activity can represent the same percept. Models provide a way to embody this otherwise difficult to accept possibility. This leaves open the question of what it is that constitutes the feeling that the world is stable, which may have quite a different answer from the question of how the stable world is represented. Note that stability has a much lower dimensionality than the world itself in the simplest case we need only a single scalar neuron that monitors stability. Such a stability monitor would need to receive converging inputs from many part of the brain and would act as a comparator for successive brain states. The brainstem would be a more likely place to find such neurons than the cortex. Such a system could be useful for balance and might even contribute to the control of posture. It could not, however, be used to coordinate transformations between sensory modalities, nor would it help in guiding actions. There is no reason different representations of the stable world might not be found in different parts of the brain for different purposes.