15 July 1999 : Ralf
Hi Catherine, I found your page asking altavista for "impossible window".

I'm a psychologist who is interested in spatial perception. For my experiments I used the impossible window, which regrettably is different from the one in your collection of Oscar Reutersvärd. (By the way, the pictures are beautiful.)

You seem to be an expert on that impossible figures. That's why I dare to ask whether you know the author of the impossible window of which I have a very poor variant on my homepage. The only reference I have is that it was published anonymously in "Aviation Week and Space Technology" on the 23rd of March, 1964 (haven't seen that myself).

It would be nice to here from you.
Ralf Goertz - Institute for Psychology

18 July 1999 : Catherine
Hi Ralf, thanks for dropping by. I'm glad you liked the images.

I'd hardly call myself an expert, though as you can probably guess I am fascinated by optical illusions, and creating real 3D models of impossible objects makes a nice break from my other designing. When I say 'real', I actually mean 'virtual models' as they do of course only exist within my modelling program, but every one of them can also be made as a solid figure (out of wood, for example), though they only work when viewed from a specific angle.

The figure you have is not so much a window but rather a very distorted version of the standard four-sided multi-bar (or four-bar). There is no specific author, as it was discovered by many people and used in many different ways, including Breughel in the 16'th century, and lest you think I'm some kind of authority on the subject, I have two slim but excellent books by Bruno Ernst (who most certainly is an authority), entitled "Adventures With Impossible Figures" [Tarquin 1986] and "The Eye Beguiled" [Taschen 1986] (which has been republished at least once under a different name and may still be available), as well as few standard works on Escher including one by Ernst himself.

The chances are you already know how to create the 'square' version of the impossible four-bar, and I know it's bad netiquette to include attachments without permission, but in case you don't, I've taken the liberty of including a small (8k) image showing the process. It is sometimes referred to as square, to differentiate it from the trapezoid variation which results from an elongated tri-bar.

Lastly, I have added your email to my feedback section. Should you wish any or all of your contact details amended or removed, I shall of course do so.

19 July 1999 : Ralf
Hi Catherine, thanks for your answer. The howto for the four-bar is very interesting. Actually, the picture on my homepage is made differently (less clever). As I told you I am interested in spatial perception, and in our experiments subjects have to decide on the structural possibility of simple line drawings. We assume that this task is more easily performed by the right hemisphere of the brain.

But for these experiments we need a reference condition, that's why more complex stimuli are excluded. In our case the reference condition is the question: "Is the figure triangular or quadrangular?" So we use 4 different kinds of stimuli. I have attached them (hope you don't mind). The impossible quadrangle we used first (as seen in the attachment) seemed to be the natural extension of the Penrose triangle. But this stimulus was very different from the others so that is was too easily distinguishable. That's why we tried the four-bar. By the way, the stimuli are deliberately distorted. Each time the subject is presented with a stimulus it is a different representative of one of the four classes (the regularly shaped prototype is rotated, sometimes mirrored, and stretched).

Thanks also for the references, I try to find the books here.

24 July 1999 : Catherine
Ralf, thanks for the reply, and the illustration.

I see what you mean regarding the use of stimuli for determining the 'truth' of an object, for whilst it's fairly clear those on the left are possible (even if somewhat distorted) and those on the right are impossible, it's precisely the fact they aren't square that makes it harder to discover whether they are real or not.

There are also higher orders of multi-bars, pentagons and hexagons, and an impossible infini-n-gon which results in a curious sort of disk that looks rather like a tyre twisted into a Möbius strip. I've included it here as it's not too large. As you can see, the more sides there are, the less effective the illusion.

Here are some URLs you might find useful:- Illusionworks | Mark Newbold's Pages | Sandlot Science.