The meeting of railway lines at infinity and the apparent convergence of rays within a view are phenomena that can be modelled geometrically by lines meeting at a point (see The Limits of Empiricism).
The most important and obvious feature of this point is that nothing flows into the observation point. There is no flow into the observation point in my experience, it is a point relative to which events have an angular displacement but the events are always in their positions in space and time.
The geometrical model of my vision would be due to light if I were "seeing" from the centre of the pupil of my eye. Clearly this cannot be the case. The way that only one photon can be at a point yet vision is simultaneous, coupled with the way the objects in a view are separate from the viewing point and not carried into it, shows that the geometrical model does not model the path of light rays or the path of any material object. It is purely a geometrical model. If the model applies to my vision then it applies to space and time itself rather than to a material flow.
There is also a temporal viewing point, an instant in the present at the position of the spatial viewing point.
Experiments and observations
If I look through one eye at a pin the pin has a fairly crisp outline until it is brought to within about 20 cm of the eye. Closer than 20 cm and the pin acquires a fuzzy outline with an opaque centre, at about 14cm the pin becomes a grey blur that is wholly transparent. Distant objects that are seen through the fuzzy outline or blur appear slightly distorted and fine upright lines in the distance can appear to be double.
If I trace the light from parts of an object 155mm wide and set 60cm away from my eye using a line of pins (ray tracing) then, provided the nearest pin is >15 cm distant so not blurred excessively, I obtain straight lines of pins that converge to a point that is almost exactly in the middle of my pupil. The pins deviate from the lines by no more than 1.5mm anywhere over the 60cm. The lines converge to a point at the centre of my pupil and maybe plus or minus 1mm from the surface of the eye.
Performing this experiment with two eyes is fraught with difficulty. The pins become double images if I focus on the distant object and the distant object becomes double if I focus on the pins. I imagined for a while that there might be a protocol that would deal with these problems (see note) but they were too complex.
In everyday life I do not notice double images and scarcely ever notice the way I can see right through small objects when focussing on distant scenes. What usually happens when I focus on a small object then look at a distant object is that the small object is transparent if it overlies a distant object of interest and opaque if it is to one side. If I investigate this closely I find the small object forms a double image, both of which are semi transparent. However, unless I am paying attention the double image is not obvious and only one image seems to be present.
If I look at railway lines or straight roads they converge to a point in the far distance. This occurs whether I use one or two eyes. This effect is typical of viewing from a point, the angular displacement of the separation between the tracks decreasing with distance.
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| Tracks subtending angles at a point. |
If I look at a painting then look at a view the principle difference is that I can move into the view. The difference between a flat wall and a window is that there is the possibility of movement through the window. If I wave an arm out into the room around me there is a feeling of motion that spans the second or so of the motion. My body is at the centre of a volume of action space that increases with separation from my body.
If I observe a branch swaying in the wind the movement occurs at the branch, the movement is an angular displacement at my viewing point. Distant branches sway through less of an angle at my viewing point that nearby branches. If I listen to someone talking the speech occurs at their lips and I hear whole words extended in time at that position.
The sounds from an orchestra occupy definite positions in perceptual space and are extended through time at those positions. The spatial viewing point is also a "listening point" in that the positions of sounds subtend angles through space at that point.
If I listen to music on a stereophonic music system with my eyes closed I can imagine the sounds of different instruments coming from the positions of the musicians in the orchestra. I hear whole notes extended through time at the positions of the musicians in imaginary perceptual space.
The end of any bar of a tune or word occurs now, at the instant of its ending.
A particular sound, such as a spoken word has the same time extension whether it is heard at a speaker 100m away or 3m away. Although distant sounds subtend an angle through time at my listening point they subtend the same angle no matter how far away is the source. This suggests that either the relationship between time extension and spatial extension is different from the relationship between lateral and radial spatial extensions or that temporal events are placed at a fixed distance from the viewing point or there is some unsuspected model that will describe events. The geometry is further complicated by the probability that what appears to be radial distance from the viewing point is actually a temporal distance or a mixed spacetime displacement.
Note: - a description of an aborted binocular ray tracing experiment.
If I look at a distant object through two eyes with a pin 10cm in front of my nose then shut my left eye there is a slight movement of the distant object to the left. If I shut my right eye the pin jumps to the right. (ie: Right eye dominance).
If I use two eyes to perform the ray tracing experiment it requires a protocol because if I focus on the object for more than about 10 seconds I get a blurry image of two pins (my right eye becomes less dominant). If I shut the left eye then look again the secondary image becomes faint for 2-5 secs. The protocol is therefore to shut the left eye then open both eyes then place the pin within 5 secs.
Focussing on the object and placing the pins in line according to the protocol I obtain fairly straight lines until about 18cm distance from my two eyes. When the pins are closer than 30cm I must guess the central position of the pins, there being a possibility of placing them in a zone defined at its limits by whether the two eyes jointly or right eye is most important. The positions of the pins could be joined by a straight line with, surprisingly, again only 1.5mm max deviation from the line. I was averaging the position of the pins between the positions given by the two eyes jointly and the right eye and the resultant lines through these average positions converged on to a point about 8cms behind and and 0.5cm to the left of my right eye (ie: a point in my head).
If I continue the ray tracing experiment closer than 18cm from my eyes with both eyes open I get two highly discrepant sets of curving converging lines that converge on each eye separately.
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