Gibson, Exploding Boxes, Invariants, and Higher-Order Invariants

So, Gennady believes that a solution to the exploding box type cases can be found in the following.  The skeptic, which would be me, puts the view on the table in the first half of this first paragraph.  Gibson's reply follows.

Gibson, 1979, p.140-141
"The central question for the theory of affordances is not whether thy exist and are real but whether information is available in ambient light for perceiving them. The skeptic may now be convinced that there is information in light for some properties of a surface but not for such a property as being good to eat. The taste of a thing, he will say, is not specified by light; you can see its form and color and texture but not its palatability; you have to taste it for that. The skeptic understands the stimulus variables that specify the dimensions of visual sensation; he knows from psychophysics that brightness corresponds to the intensity and color to wavelength of light, He may concede the invariants of structured stimulation that specify surfaces and how they are laid out and what they are made of. But he may boggle at invariant combinations of invariants that specify the affordances of the environment for the observer. The skeptic familiar with the experimental control of stimulus variables has enough trouble understanding invariant variables I have been proposing without being asked to accept invariants of invariants.

Nevertheless, a unique combination of invariants, a compound invariant, is just another invariant. It is a unit, and the components do not have to be combined or associated. Only if percepts were combinations of sensations would they have to be associated. Even in the classical terminology, it could be argued that when a number of stimuli are completely covariant, when they always go together, they constitute a single "stimulus." If the visual system is capable of extracting invariants from a changing optic array, there is no reason why it should not extract invariants that seem to us highly complex.

The trouble with the assumption that high-order optical invariants specify high-order affordances is that experiments, accustomed to working in the laboratory with low-order stimulus variables, cannot think of a way to measure them. How can they hope to isolate and control an invariant of optical structure so as to apply it to an observer if they cannot quantify it? The answer comes in two parts, I think. First, they should not hope to apply an invariant to an observer, only to make it available, for it is not a stimulus. And, second, they do not have to quantify the invariant, to apply numbers to it, but only to give it an exact mathematical description so that other experimenters can make it available to their observers. The virtue of psychophysical experiment is simply that it is disciplined, not that it related the psychical to the physical by a metric formula."

Ok.  So, Gennady thinks the invariants and higher-order invariants story is going to solve problem with the exploding box type cases.  But, grant Gennady and Gibson their invariants and higher-order invariants in light.  The problem remains: the physical surfaces on the outside of the boxes are what structure the light into invariants and higher-order invariants, but the inside of the boxes are what constitute or anchor affordances, such as for pick-up-ability, stand-on-ability, climb-on-ability.  So, both boxes are going to have the same invariants in the light and the same higher-order invariants in the light, so the visual perceivers will have the same visual perceptions.  The visual perceiver does not visually perceive the pick-up-ability of the exploding box, and since this visual perception is the same as visual perception of the normal box, the visual perceiver does not visually perceive the pick-up-ability of the normal box either.

The basic problem remains.  Simplifying: What structures light is typically on the outside of objects; what constitutes affordances are typically on the inside of objects.