Inconsistent Images

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Rene Magritte

Rene Magritte was a famous 20th century surrealist painter. Surrealism aimed to transcend realist depiction of scenes available to ordinary perception. Under the influence of the new discipline of psychoanalysis, surrealists made use of such techniques as dream analysis to uncover the unconscious workings of the mind and the symbols that the unconscious works with. Not much of Magritte's oeuvre consists of literally inconsistent images, but at least one famous image does, Le Blanc Seing.

This painting utilises a technique like that of the Schuster fork, and illustrates how the mind constructs the impossibility. The mind puts together the separate elements into a "coherent" whole of these parts. The horse is thus bisected by a patch of background grass. Also, one of the tree trunks is in front of the horse but its base is behind the horse. It certainly seems that these elements are inconsistent with our conception of a rider in a forest. For example, it qualifies as an occlusion illusion, since reversal of occlusions is sufficient to produce a consistent image.

In homage to Magritte, we offer an Australian perspective on Le Blanc Seing. Everyone knows that Australia is full of tractors. So first, we have below Green Tractor, where the fragmented tractor appears in a setting of green trees from Magritte's European woodland.

 

But we move away from Europe and find ourselves among Australian gums.
The image below is called Green Tractor in Gums.

 

For a fair dinkum Australian image, we have below Massey Ferguson in the Bush.

 

And, to bring things full circle back to where we began, we have below an amalgam of the wheel and rider, called Wheel, Horse and Rider.

 

We noted above that Magritte liked strange sights, but not many of them are inconsistent. Is the image below (Elective Affinities 1933) consistent?

If the above is inconsistent , it is subtly so. The cage with the egg is suspended from a flat rectangular construction, and the egg looks like it is coplanar with the front surface of the suspensor, which would be incompatible with its being an oval egg. Yes? No?

 

Magritte had a truly interesting imagination. Another of his pictures, while not inconsistent, illustrates a mathematical principle relevant to our explanations. George Francis (A Topological Picturebook, Springer 1987) asked the sensible question: what sort of consistent space could the Penrose triangle exist in? The answer is clear: R2xS1.
This is difficult for we Euclidean creatures to visualise, but we can visualise one dimension down, R1xS1 , this is the cylinder. In R2XS1, two dimensions are infinite in both directions, while the third is rolled into a circle. That is, if light were to travel around the S1 direction, it would arrive back where it started (in some cosmological models this is exactly what would happen, albeit on a much larger scale). At any rate, we now look at Magritte's Portrait of Edward James.

This is what one would see if the third dimension were rolled up like a cylinder: light from the back of his head would proceed toward us, past us, go around the circle, and wind up appearing to us like the back of the head in the mirror.

Of course, if he turned around to look at you, he could look like this:

Title: Wittgenstein = -(Edward James)

 

Text: Chris Mortensen and Peter Quigley
Images: Steve Leishman and Peter Quigley
August 2008

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