What to do & see
If you have two roughly equivalent eyes you will see a "sausage" floating in front of you in mid air, by following these steps:
1. Hold your hands in front of you, at 20–30 cm distance from you, at eye level.
2. Point your index fingers against each other, leaving about 2 cm distance between them.
3. Now look “through” your fingers, into the distance behind them.
4. The sausage should appear now, and you can change its length by varying the distance between the finger tips.
5. For most observers, the sausage will look blurred, at least initially.
6. If you try to look at the sausage, it will disappear, it is only present if you look at something more distant than your fingers.
7. It helps if the background is rather homogenous and has a color very different from your fingers.
Basically, this "sausage" is caused by two mechanisms,
1. physiological double images, and
2. interocular rivalry and suppression.
When you look at your fingers, the gaze direction of your two eyes is angled towards each other, so that their lines of sight meet at the target. When you then look into the distance, your eyes shift slightly outward, making their lines of sight nearly parallel. For close objects the image in the two eyes is consequently no longer at the right position, the images are no longer merged and can appear double for your “inner eye”. This is quite normal and occurs all the time, usually these double images are suppressed. So, if the two images overlap, why then doesn't the compound image look like the neighbouring figure on the right?
At the end of the image of each finger, there is a rivalry between the image from the two eyes when the brain tries to combine them. In one eye the finger ends, in the other it continues. So what does your brain do in such rivalry situations? If the two images are rather similar, the percept can oscillate between the alternatives. Here, however, we have a high contrast step in one eye, namely the end of the finger, where it is replaced by the background. In rivalry the eye with the higher contrast wins, at least locally; this is here meant by the term "suppression". In the figure on the left this high contrast step is symbolised by the yellow halo.
Hermann Grid
The widely known Hermann-grid illusion (Hermann 1870).
Dark patches appear in the street crossings, except the ones which you are directly looking at.
Rather weak, but in every textbook…
See below for the classical explanation. HOWEVER: see the next page for a convincing rejection of this explanation.
The classical explanation
1. Why do we see the dark patches?
Look at the left part of the left diagram and assume an on-center retinal ganglion cell. Its receptive field is indicated by the reddish disk. When the ganglion cell is, by chance, looking at the grating so that its centre ('+') is positioned at a crossing (left-top), there are 4 bright patches in the inhibitory surround. A ganglion cell looking at a street (left-bottom) however only gets 2 inhibitory patches, so it will have a higher spike rate then the one at the crossings. This was measured by Baumgartner (1960) in Freiburg, see picture on the right.
2. Why don't we see the patches when we look right at them?
Because then we direct the fovea at the crossings, and in the fovea the receptive fields are much smaller (see the small reddish disks on the right of the left figure). With such small receptive fields it obviously does not matter whether they are at the crossings or not.
3. Why is this explanation, so plausible it sounds –and it is in every textbook– not the full story?
See the next page for a simple refutation.
Scintillating Grid
If you look around in the neighbouring figure you will notice the appearance and disappearance of black dots at the crossings.
Even though this figure looks similar to the Hermann-Grid, it is markedly more vivid. Furthermore, the effect is probably caused by different mechanisms than those causing the Hermann-Grid effect.
Question: Do the streets or the squares influence the colour of the apparent disks?
As you notice in the neighbouring figure, red streets leave the disks black. But if the squares are red (move mouse over figure), the disks acquire a reddish tint...
Impossible Objets
What to observe –
The neighbouring contraption consists of the so-called “devil’s fork” (top right, also known as “blivet”), the “Penrose Frame” (centre) and the “hexnut” (3 of them bottom left, an enlarged specimen bottom right). Boggle your mind when trying to envisage to build such an object.
Comment –
Our brain reconstructs an internal 3-dimensional world model from the flat retinal image.
The oldest –known to me– example of an impossible scene: “Madonna and Child ~ Adoration of the Magi” from the Pericope of Henry II around 1025. The impossible architecture in that painting, however, seems not done purposefully to me, in contrast to Hogarth’s ‘Frontispiece’. Often the first impossible object is attributed to Reutersvard (a design for a Swedish stamp), however Albers and Hogarth were clearly earlier. After the Penroses formally described the phenomenon, examples abound, beautifully drawn for instance by Escher.
A draw-it-yourself impossible object
On the left you see an animation where you can draw along.
Start with 6 vertical equidistant lines, give them hats. You get a rendition of “3 towers” or a “three-pronged fork”. Obviously, a sensible 3-dimensional interpretation.
Cover the top, and draw connecting circle segments at the bottom. You see the bottom of a square bar, bent into an U-shape. Again, a sensible 3-dimensional interpretation.
However, uncovering the top also reveals the fact that the two interpretations are not compatible with each other.
to be continued....
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