Friday, September 3, 2010

The very basic topology of the visual field

This topic may best be approached by examining the basic visual field that we experience in the complete dark, or in the Ganzfeld situation (i.e. with one half of a ping-pong ball placed over each eye). The former delivers a flat featureless black expanse: the latter a “cloudy” featureless white expanse. If we examine these with the eyes directed forward, we note that the field has a center straight ahead and a boundless periphery. Then we can turn our eyes from one side to the other. With the eyes directed to the side we notice that the center of the visual field remains where it was, now to one side of our new fixation point, which is near the rim. Note that these ‘eyes’ that we feel (experience) moving from side to side are not the eyes of the physical body but are the eyes of the body-image).

Next we can introduce structure by opening our eyes, gazing at a lit lamp bulb, and closing our eyes again. An after-image (AI) appears. This possesses some intrinsic properties—i.e. extension, shape, and colour—and extrinsic properties i.e. location at a particular position in the visual field, as well as topological and geometrical relations with other after-images in the same field. For example, one AI can be spatially BETWEEN two other AIs. Three AIs can form a triangle: four AIs can form a square, etc.. The edge of an AI can form a Jordan curve. Moreover, when we move our eyes we notice that the AIs move too to stay in the focus of attention.

These simple observations establish the important point that visual (phenomenal) space is a genuine space. A genuine space may be defined as that in which an entitiy can move about in. Tennis balls move in physical space A. After-images, as well as the eyes of the body-image, move about in phenomenal space B.

Two different genuine spaces in a cosmos can be related in three ways;—

i. A and B are different cross-sections in a higher-dimensional space C (Broad’s 1923 theory: since elaborated by others).

ii. B is a subset of A (as in the Identity Theory).

iii. A and B have no spatial relations and only causal ones (Price’s 1953 theory)

iv. Nevertheless, in all three cases, we are dealing with real spaces, and not imaginary, mathematical, phase spaces, etc.


  1. To all: if anyone knows how to delete Bob's figures from the non-French blogs which they are invading by some mysterious process please do so (via ) !!

  2. I did not know about the impression that there is a center to visual space in Ganzfeld perception irrespective of eye position. That is the first evidence advanced here of such a center, so that VS not only has a left and right side, a top and a bottom, but has a center as well: ergo, something comparable to a geometrical origin, and evidently independent of the fovea. Only the handedness is truly a topological property, because in topology inverting a space does nothing to it topologically, and the center could conceivably be displaced by stretching.

    What the simple observations of after images do not tell us is the relation between them and the rest of the typical contents of VS (i.e., the visual world). My impression is that after images exist on a plane of their own that seems almost on the outside of VS (the outside portion of it closest to the observer). I don't quite get the tennis ball comparison, because tennis balls are, after all, seen, just as the after image is a residual impression of the *seen* light bulb. Both tennis ball and after image refer to the *appearance* of things in VS, not their physical nature.

    To find an empirical means for ascertaining the topological relationship between VS and physical space would obviously partly solve the mind-brain problem. But perceptual space does not tell us how it is related to physical space, nor vice versa (nor to any other space, even the space of mental images). So I don't know how either Broad's nor Price's idea could be confirmed, any more than the identity theory can (nor the double aspect theory).

  3. Upon further reflection, the fact that no such center is apparent in the dark, but only in the Ganzfeld condition, suggests that there is an imhomogeneity apparent in the latter, but not in the former. It occurs to me that one thing that is not eliminated in the Ganzfeld condition is the bridge of the nose, which may furnish a perceptible stationery center for the observer that would not be evident in the dark. Ping pong balls anyone?

  4. Good points, Bill! Yes, "Center" is not the right word. "Central region" is better. It is what is directly ahead of "you" when you gaze into the dark. It has no exact size or shape. It is just what is in front as opposed to the equally vague "periphery". Normally when the eyes are central in their orbits and you are attending to what is in front of you, the VF looks circular and you are looking at its central area. But when you shift your eyes to the right, the center of attention now seems to be up against the periphery of the VF. The VF now seems (to me at any rate) more like an oval, and what was its "central area" now lies to the left of where I am looking now. If you mark the foveal region with a bright after-image and then shift your eyes to the right the image follows and now looks to be up against the rim of the VF, and where it was before you moved your eyes now is just black.
    I am not sure if these same things happen with a Ganzfeld which is usually as described as "cloudy": this need to be tested. Also I was really describing phenomenology and not topology: but the latter has to be derived from the former. (to be continued).

  5. Re Bill's second point about the relation of after-images and the rest of the contents of VF (VS). Since after-images can be observed to cover other sensations in the VF (usually falsely described as being "projected" on to e.g. a wall) presumably they are formed in the same space as ordinary visual sensations (in the form of Bill's "residual impressions"). I go into this point, as well as detailing the topological relations between them, at some length in "Analysis of Perception".
    However, there is evidence that AIs are located in the same space in which mescaline images are located. During a mescaline experiment in 1951 I looked at the gas fire in the room where the experiment was taking place (my Mews flat in London). This was of the old-fashioned kind with a ceramic 3D grid that glowed in the gas flame. I shut my eyes and the bright grid (an array of lines of small bright squares in rows) that was the after-image, slowly turned into shining globes that arranged themselves into a glorious psychedelic pyramid. And, of course, the world seen in the course of psychedelic visions can be vast. One of Weir Mitchells's subjects described the scene at which she was looking as representing "Time as well as immensity of Space. Here were miles of rippled purples, half transparent, and of ineffable beauty." As Blll says "After images [may] exist on a plane of their own". But this plane seems curiously elastic. It almost suggests that, when we take mescaline, it starts behaving like the glass egg in H.G. Wells's short story of that name, and starts giving us a glimpse into the Collective Unconscious itself (as Jung wrote to me in a letter in 1952). So, perhaps as Bill suggested earlier, the VS is literally surrounded by the Collective Unconscious?

  6. Huxley made this latter suggestion in "The Doors of Perception". He linked it to Bergson's theory that the function of some brain mechanisms is to inhibit the spontaneous activity of the psyche: and mescaline (by stimulating serotonin 2A receptors) merely removes this inhibition. I have frequently commentated that it seems odd that a brain of a person, who lacks any artistic talent, can nevertheless produce visions that many very reliable, sober and honest people have said are far more beautiful than any natural scene or the product of any artist.
    Actually H.G. Wells' Glass Egg enabled the user to see the surface of Mars: I have merely adapted his story for another theme.

  7. Upon viewing any visual scene, and fixating on it for a long moment, if one then closes one's eyes, the scene does not literally go to total blackness, but there is still a lingering impression of the scene, of much lower intensity, that does not just fade, but seems to disintegrate, and in a certain way. For example, parts of contours disappear first around what was foveal, while the periphery more quickly disappears, or seems to do something like melting--the ridigity of visual form seems no longer present, rather like what John says of the after image of the light fixture as experienced on mescaline, except less elaborately. In other words, whatever contraints are holding the visual objects together are no longer operative--except perhaps in the case of eidetikers. There is also a reduction of the sense of externality, as if the residual impression contracts towards the observer in some way--as if to the depth plane of the visual field nearest the observer, if considered binocularly.

  8. The centricity of VS as a function of direction of gaze: Perhaps there is indeed a sense that the overall shape of VS changes from appearing spherical when looking straight ahead to oblate when looking towards the periphery. It would be nice to find a means of quantifying this change of shape empirically.

    I would ask, where does one localize phosphenes or floaters in VS? In binocular VS, they do not appear to be "inside" it, but more on the "outside" of it--but we do not seem to have a sense of them being something "inside" our eye. When due to injury there is blood inside the optic media, I wonder where it is "seen" to be? Do patients report it being "inside" their eyes?

  9. It may be that the apparent position of after images in VS is contingent of the point of fixation: Just now staring at a lamp long enough to get a good negative after image of it, I found that it appeared not where the lamp was when I looked at the wall to the right and back of it, but was localized to the right and back of it!

  10. Further to the dissolution of visual objects/visual world immediately after we close our eyes, and thinking about John's description of psychedelically-enhanced after images, I am reminded of the "perceptual-release theory" first put forward by neurologist Hughlings Jackson, and later elaborated by psychiatrist Louis Jolyon West, which proposed that what keeps us from dreaming or hallucinating while we are awake is the incoming stream of perceptual stimulation from the periphery. The absense of that incoming stream of stimulation "releases" endogenous factors that take over (in general terms, and obviously this would explain the effects of sensory deprivation and some of the bizarre experiences had in Ganzfeld conditions).

    In ordinary seeing with eyes open, perhaps it is the same: that peripheral stimulation is structuring what we see, yet as soon as the incoming stream is shut off, the visual structure is "released" and decomposes (but apparently not instantly, given the existence of after images, for one).

  11. Yes, the visual field is never completely black even in the complete dark, as Francis Galton discovered. There is always some faint activity going on, such as blue clouds drifting about and faint mazes. These arise from spontaneous activity in the retina and visual cortex.

  12. I thought that I would interject a few comments on the subject of the interrelationships between the two spaces. I don't think that much can be done a priori here, but at least implications can be explored of various somewhat plausible assumptions. For example consider the hypothesis that causes and their immediately-temporal effects are spatially continguous - i. e., that there is no action at a distance. Assuming that the visual system works in parallel and not serially (as in a television signal), and I think there is a lot of empirical evidence for parallel processing in the brain, then corresponding events in the two spaces would also have to be spatially contiguous. At least I think that the implications of this hypothesis are worth exploring.


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