I love this stuff—it illustrates, simply and clearly, how our senses are not simply passive intakes of data from the world, but instead are the yield of complex computational processes carried out by assemblies of specialized neural tissue.
A familar example is the nearly half-century old random dot stereogram. If you present each eye separately with a set of data points, in the form of black and white pixels, which are off-shifted in just the way they would be if the two eyes were presented with a particular three-dimensional object, then, with a bit of training, it is possible to train your eyes to focus separately in a way which leads you to actually
see that three dimensional object, even though there is no such animal physically present—just the two off-shifted dot matrices! There is a simple example, with explanation of how it's done,
here. There has been a lot of work on the nature of the computation, and the local algorithms that implement this computation, in visual psychophysics, and the actual stereograms themselves have gotten pretty bloody intricate and fancy; see
http://www.ied.edu.hk/has/vrdemo/rds/ for some intriguing examples.
Both the stereogram model of 3-D perception and the stuff that the OP article is talking about are based on the by now overwhelmingly successful model of vision as the
construction of a mental scene based on synthesizing visual input data of several different kinds, and 'squeezing' these data using sophisticated mathematical tricks—tricks that are simulated by particular cell arrays at various places in the visual system. These optical illusions and weird effects are actually evidence for the existence of detailed computational procedures wired into our brain neuroanatomy; the explanation the chap cited in the article gives is in perfect accord with this model of how visual perception, and our senses generally, work.
It took me about a week to learn how recover the three-dimensional image visual by looking at stereograms with the right blurring of focus that allows the left eye to see only the left sterogram, the right eye only the right stereogram, and then allow higher-order processes to compute out the three-dimensional situation that, according to the brain's take on things,
must have given rise to those two separate inputs. Definitely worth it—being able to see 3-D images, without any special equipment, when all you have are two dimensional inputs, is a real kick... eerie, but fun as hell!