Plasticity and the Perception of Higher Dimensions

Sacks and Siegel in Nature report on the recovery of steroscopic vision in a patient suffering from stereo blindness for 50 years. If cortex is indeed that plastic, I can't help but ask, "why stop with only 3-dimensions?" Besides being cool, there might even be practical applications in training individuals to be able to see objects in spaces of four dimensions and higher. Data about a complex dynamical system might be handled more easily if its multidimensional state-space can be directly grasped by the human visual system. Things might "pop-out" of a data set that might otherwise be difficult to detect.

Questions arise as to how to train someone to pull this off. What does it even mean for vision to take place in higher dimensions? It might be useful to think about the geometry of photography for a bit here. The photography of a three-dimensional object involves a projection onto a two-dimensional surface. Stereoscopy is accomplished by integrating projections from a single 3-D object onto two different 2-D surfaces. By analogy, photography in the fourth dimension would involve the projection of a hypersolid onto points in a 3-D volume. 4-D steroscopy ("Hyperscopy"?) would then involve, I guess, the integration of projections of a single 4-D object onto points in different 3-D volumes.

One might question whether a person, being only 3-D, could possibly accompish hyperscopy, given that our irritable surfaces--our retina, etc.--are essentially only 2-D. The key to realize is that the dimensionality of our sensor arrays is potentially surmountable. The points in, e.g. our retina, can be mapped onto points in a volume--this is precisely what enables plain-old steroscopy in the first place. And our brains are capable of representing higher-dimensional state-spaces: gustory state-space is at least four-dimensional and olfactory state-space is six-.

Here then, in theory, is how to train someone to be hyperscopic. First, off, the 4-D objects are going to have to be computer generated. Second, computer simulated 3-D retina--3-D arrays of voxels--will be projected onto by the 4-D objects. Third, information from each of these voxels will be projected--via video goggles--to a dedicated portion of the person's visual field. That is, the visual field will be partitioned into the same number of subregions as there are voxels in the 3-D computer-simulated retina. Fourth, equip the person with some means of rotating the 4-D objects (since having control over inputs seems to be important in perceptual plasticity). Fifth, train the person to perform 4-D object recognition tasks. Objects in the training set should include objects that can only be distinguished by their 4-D charactersitics.

If such a training regime could be successful executed, would it be 4-D vision? Would the hyperscopist have 4-D qualia?