Failing to See the Illusion

1. Call the actually odd one out ‘odd’ and the actually identical ones  ‘even’.

Then I think

2. When I look at the odd one in between the evens, it is supposed to seem to me that the odd and one of the evens look alike while the other even looks like the exception. But it doesn’t look like that to me.

3. Here is a possible explanation of why it would look the way it is supposed to in ‘2’. It is based on a hypothesis about (at least, visual) perception. This is notably promoted by Richard Gregory in his writings — in particular in his classic Eye and Brain. It also has roots in earlier work by Gestalt psychology.

(i) Visual experience of the world before us is (at least partially) a guess at how things are arranged before us in three dimensional space.

(ii) There are rules of interpretation in such experience (why? Evolution — they make running away from deadly things and running toward lively things easier).

(iii) These rules either

— Determine the visual experience, e.g., they determine what it is like to see something.

— Determine the judgements about visual experience, e.g., they determine how we interpret, or what we infer from, what it is like to see something (but not experience itself)

— Or both: depending on how you think about judgement and experience, e.g., experience is itself a judgement constrained by such rules. Or the rules constrain both experience and thinking about experience (but experience is not a judgement).

(iv) One such rule is that one interpret things as lying before one in three-dimensional space. There are principles that are followed which are very different from seeing something lying in a two-dimensional space, e.g., a pair of converging lines which, in two-dimensional space, make a triangle might be parallel lines receding away in three-dimensional space. Look at any picture of a road heading towards the horizon — or just look at a road heading towards the horizon. This is what gives perspective in art.

(v) So, with the ‘Turn in the Road’, our perception interprets what we see in three-dimensional terms. And what we see are three pairs of converging lines. In two dimensions, they meet at an angle, e.g., such as the vertex of a triangle. In three dimensions, though, they need not meet at an angle, but may just be receding parallel lines.

(vi) Part of the recession is about lines meeting at infinity, receding toward the same point at the far horizon. Multiple lines can recede to the same point. Also, one can have multiple points to which different lines recede:

E.g., look at any picture of a skyscraper presented as being from a storey in the middle of its height. The lines running down the building’s frame will recede toward two points — a point below you (toward the depicted ground) and a point above you (toward the depicted sky).

(vii) This hypothesis (which looks like a good one, explaining a wide range of phenomena), is why you might get this alteration in apparent exceptions/twinning in the ‘Turn in the Road’:

— When the odd lies between the evens, its lines recede to the same point as one of the evens. This twins them — they are similar because they are receding to the same place in three-dimensional space. The other even does not recede to that point, and so is the exception.

— Rearrange the odd and evens and this disappears. At best, all the images seem to recede to the same point (somewhere to the right); in that case, in the absence of this discriminating point of infinity, the different shape of the odd distinguishes it from the others.

But I don’t see the illusion. So, why not?

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