That's very cool. I read the proof and the explanation, and while I believe it, I still can't see it in the original image.

Apart from the reasons given in the proof (which make sense) I guess it's also because we "know" what a checkerboard should look like, and so the column and row positions of the two squares reinforce that they should be different colours. I wonder would the illusion be as strong if it was on a board with an unfamiliar pattern?

Malcolm: I can't see it either. I'm placing pieces of paper on the screen to block stuff off, etc, etc, but it remains maddeningly obvious that A is darker than B...

Interesting thought about a different pattern: I'd have to say that the problem would be in making a convincing fake shadow.

Cheers, Julian

In addition to Addison's two explanations, I think I see a third. Using the eyedropper tool on the 'A' & 'B' characters themselves, the 'B' character is somewhat darker than the 'A', increasing the contrast with it's surrounding square. But I still can't 'see' the trick either!

I placed a pen to cover all of the squares between square a and b and the colours appeared the same. Mind I had to block every part of the shadow. Leave any part of it there and the illusion remains.

Damn - tried it again and they look different