The Orwellian tone of the heading is justified. You can get people to believe almost anything about their own perception with a little sleight of hand.
The grey colour of square A is identical to the colour of square B.
The illusion is so compelling that it makes a great bar bet. To collect, make sure you have some Post-it Notes. Carefully block off the surrounding checkerboard squares with Post-it Notes, leaving just the squares containing A and B visible. (You'll need about six small notes.) Not until you place the last note does it seem even conceivable that the two colours could be the same. Then suddenly, they "snap" to the same medium grey.
(You can also prove it by copying the image into an art program and sampling the colour of A and then of B, which will show that they are in fact the same colour.)
How does the illusion work? The cylinder casts a shadow, darkening "white" square B (which is really grey). In terms of ink dots on paper, B is the same grey value as "black" square A. But the eye and brain have more important things to do than gauging absolute greyscale values. They are trying to make sense of the world, or in this case, a picture. That means attending to contrasts. We see a checkerboard on which all the "white" squares are the same colour, and a uniform shadow with blurred edges. The contrast between light and shadow doesn't interfere with the contrast of the checkerboard squares, or vice versa.
After this, how can you ever be sure of anything again? The catchword is psychophysics. Read up about it and be amazed!
(Of course, women have always known about psychophysics: if they wanted to look slim, they made friends with fat people. [As for me, I have lots of dumb friends.])
