Explaining the Poggendorf Illusion

According to Wiki's entry on The Poggendorf Illusion"To this day, it is not known why this illusion happens. There are many theories about why this simple geometrical illusion occurs, but none proposed gives a satisfactory account for all the conditions under which it diminishes or appears. It could be that the human visual system is extremely poor at interpreting the path of diagonal lines, although it is not understood why."

Nope. It's quite simple really - you have to remember that you have two eyes, so if there is an obstruction between you and whatever you are looking at (Wiki's entry uses a diagonal line, but it's easier to explain with a face) your left eye can see part of the face which your right eye can't, and vice versa. But the obstruction looks more or less the same to both eyes.

So, because it is the face you are concentrating on, your mind will try to stitch together as much of the face as possible, so what you [think you] see is (from left to right) the part of the face as seen through your left eye, the obstruction, and then the part of the face as seen through your right eye.

There are degrees of this - if the obstruction is much closer to the face, your mind will not attempt this trick and if the obstruction is considerably nearer to you than to the face you are looking at, you will actually see the face correctly and two semi-transparent images of the obstruction. Ultimately, the effect is most noticeable if the obstruction is exactly half way between you and the face you are observing.

As examples, imagine you are at a barbecue party at seat diagonally opposite Arnold Schwarzenegger, and there is an umbrella pole exactly half way between you. If you keep one eye shut, or if you took a picture with a camera, what you would see is the upper picture, but if you have both eyes open, what you [think you] would see is the lower picture.The difference between the two is that in the upper picture, I just laid a white strip over the picture, and for the bottom picture I tore the picture down the middle and separated the two halves by about half an inch. Despite the fact the lower picture is "wrong" it does not look any less natural than the upper picture.

If we substitute 'diagonal line' for 'face', your mind plays the same trick - it shifts the left hand half of the line to the left and the right hand half to the right, thus the dotted line which would join up the two parts of the diagonal line would be flatter than the diagonal line. So we are used to seeing things slightly "wrong" and this is why in the Wiki example, it looks as if the black line on the left lines up with the blue line on the right.