Why can I see my fingers connected when they haven't touched? If you take a close look at one of your fingers with one eye, it’s like your finger has an atmosphere with several layers(!):

Now get two of your fingers so close that their atmospheres touch, you see a bridge connecting them that gets wider the more the atmospheres pass through each other


 A: There are three effects that could be involved:


*

*Diffraction and interference of light coming from behind your
fingers when they arrive at the narrow space between your fingers
(single-slit diffraction):

(Source: http://labman.phys.utk.edu)

*Parallax: Your pupil has about 4mm in diameter and therefore each
part might see a slightly different picture than another one(much
like when you see two fingers when looking at one with two eyes
open, but much less noticeable).

(Created by Shanker Pur - license: Creative Commons Attribution-Share Alike 3.0 Unported)

*Diffraction of light reflected by each of your fingers (I had posted
this as a possible answer in the question details and now I moved it
here). When light from a point source passes a narrow slit, we have
single slit diffraction (shown in the picture at the top); now if
light passes through a circular aperture (such as a pupil) somewhat
the same thing happens, but the diffraction pattern will be circular
rings:

(Photograph from Cagnet, Francon, and Thrierr, Atlas of Optical
Phenomena, Springer-Verlag, Berlin, 1962.)
Now consider you have two point sources with their diffraction
patterns close to each other. If the two sources are very close to
each other, the diffraction rings are not distinguished and it
becomes impossible to resolve the two sources:

(Photograph from Cagnet, Francon, and Thrierr, Atlas of Optical
Phenomena, Springer-Verlag, Berlin, 1962.)
The smallest angle you can distinguish (resolve), known as the
Rayleigh criterion, (calculated from the arguments above) equals 1.22*wavelength/Diameter of the aperture
Exactly the same thing can happen with your fingers.

It's easy to determine that the first effect doesn't have a significant effect: just go to a dark room and point a flashlight at your fingers from their front, meaning that no light would come from behind them; you'll see that you can still see the atmosphere layers!
Now about the second and third effects:
Diffraction from the light of your fingers at your pupil can be calculated from: θ ∝ /D (explained above); while the angle difference because of parallax can be calculated from: θ ∝ D. I realized that the atmosphere effect(!) happens when your eyes aren't focused at your fingers. If you focus at your finger(s) (meaning that the diameter of your pupil decreases), both the atmosphere and bridge effects don't seem to happen. This is easily explained by parallax (as shown by its formula), but if it were because of diffraction, both the atmosphere and bridge effects should've become stronger (as again shown by its formula). Therefore we may conclude that atmosphere and bridge are caused by parallax although this wouldn't explain why we see several layers! 
So ultimately I don't exactly know what the cause is (maybe it's something entirely different that I haven't noticed), but I concluded that it's not the diffraction of light passing from between the fingers (or at least its effect is barely noticeable).
A: I tried the finger experiment right now. I can't relate the text you mentioned to this, so its better to wait for other answers. Having said that, I just realized something. If your finger's are actually not touching in the region you are observing through, then the darkness that 'appears' to join one finger to another will change in thickness as you move your head around a bit, while observing the same gap. My guess is that the light wave diffracts around your fingers in such a way as to cause destructive interference at the initial position of your eye, making it seem like a lot of dark bands placed side by side between your fingers. On moving your head a bit sideways, you will see some of these dark bands disappearing, as a result of which the region between the fingers will appear clearer. This seems like a normal case of diffraction to me. However, i may be very wrong. 
