Do You Mostly See Double? (revisited)

Wednesday, my senior seminar surprised me. We were talking about depth perception and how your eyes converge slightly when you focus on something nearby, when one student casually remarked that when he focused on a nearby object a more distant object in front of him (a student sitting on the opposite side of the seminar table, as it happened) appeared double.

I find it easy to get a double image by holding one finger about four inches before my nose and focusing in the distance, but I've always found it more difficult to get doubling by the converse operation of focusing on something close and attending to an object in the distance -- though many early introspective psychologists claimed that the phenomenon of doubling in the distance is common or even pervasive (e.g., Reid, Purkinje, J. Mueller, Helmholtz, Stout, Sanford, Titchener). Helmholtz, for example, writes:

When a person's attention is directed for the first time to the double images in binocular vision, he is usually greatly astonished to think that he had never noticed them before, especially when he reflects that the only objects he has ever seen single were those few that happened at the moment to be about as far from his eyes as the point of fixation. The great majority of objects, comprising all those that were farther or nearer than this point, were all seen double (1910/1962, III.7; see also this post).

This has always seemed to me introspective psychology gone awry. In a 2006 essay (Do Things Look Flat?), I conjectured that the attribution of pervasive doubling in visual experience had something to do with the popularity of stereoscopes in the late 19th century and the analogy between binocular vision and stereoscopy; but recently, especially in light of the view's relatively early roots, I've been more inclined to think it has to do with overemphasis of the theory of the horopter in binocular vision.

With this in mind, I asked the eight students in my seminar to converge their eyes upon their fingers before the nose and report on whether the student across the table seemed to them to double. I went to the board to write down poll numbers, yes or no. No need to write the numbers down, though -- all the students immediately said yes! (Well, one was quiet, but when I specifically asked him, he agreed with the others.) Evidently, I was the only one who didn't find the effect.

One student then said that he has always been very aware of the persistent doubling of things in vision. He or another student then recommended that we look at the Julesz random dot stereogram on p. 112 of Dennett's (1991) Consciousness Explained (which we were reading). Several students claimed that they could "fuse" it and see the square pop out by allowing their vision to double (though I should say not all the alleged pop-outers initially agreed on the shape that popped out). Here's the stereogram:

Now to me the prospect of trying to merge those two images in my mind to get a three-dimensional pop-out effect seems utterly hopeless!

I'm sitting in my office trying to get that doubling in the distance. I put my finger before my nose and compare its position to that of a V8 bottle six feet away. I close one eye, then the other, and notice how my finger seems to change position relative to the bottle. This gives me a sense of how far apart, maybe, to expect to see the doubled bottles when I converge my eyes upon my finger. Then I do converge my eyes. Maybe that bottle doubles -- but I'm not sure. I try again, and now it seems clear that there is no doubling.

But I've always had an unusually dominant left eye (I had "lazy eye" as a kid), so maybe I'm the one who's unusual? Do most of us always see most things double (per Helmholtz et al.)? Or does it take an unusual effort? My confidence that the Helmholtz quote is a bit of madness with which few ordinary observers would agree has been shaken.