# Answer to where is the white knight? - Optical Illusions

### Where is the white knight?

Our questions were:

• Puzzle: Which of the two knights is the white knight (i.e. which is the lighter of the two)?
Is it the one on the middle of the chessboard, or the one on the top left?
• Which square is lighter, the knight square in the middle or the knight square at the top?

The incredible answer is: both knights, and both squares on which they stand, are exactly the same shade of grey (RGB = 107, 107, 107) with identical light shading of the pieces.

 We know that this is difficult to believe. Even enlarging the image and examining it closely fails to convince you.For instance in the image on the left would you believe that the knight on the top is standing on a square that has exactly the same grey value as the square on which the lower knight is standing? Even if you stare at the picture for a long time and concentrate intensely your eyes and brain will tell you that the bottom one is clearly lighter. One way to convince yourself is to punch two small holes in a paper and hold it up to the screen, so that only the knight and the squares on which they stand are visible. You will see that the are exactly the same. We have done this electronically in the following image:

 Another way is to copy the image into a paint program and use the colour pipette to determine the colours. Even better: cut out a small section of knight and square and insert it as a floating element in the picture. Move the section to its original place and then to the over to the same location on the other knight. You will see that it blends in perfectly.

Here's a small animation that shows the knights changing places.

The original picture was created by Edward H. Adelson, Professor of Vision Science at MIT, and had no knights on it. They were added by Mig Greengard. If anything Adelson's version is even more incredible.

 Can you believe that the squares marked A and B in the above picture have exactly the same?If you use a pipette to examine the squares you will see that both are exactly the same shade of grey (RGB = 107, 107, 107) Once again closer scrutiny does not help. Or are you able to convince yourself that an identical shade of grey was used in the picture on the right?

We can try the experiment in the real world. Here's a picture of a chessboard with a shadow cast over the left side.

Which square is lighter, A or B? The answer is B! If you cut out a bit of the B-square and move it over A you will see that it is actually slightly lighter than A.

In greyscale the effect remains unchanged: the cut-out in the picture above was taken from B and inserted in A. It is clearly lighter than the surrounding.

A description of the illusion is given at Prof. Adelson's web site. Essentially it says that our visual system does not simply measure the light coming from a surface, but interprets the luminance in the context of its surroundings. The brain knows that a light surface in a shadow may reflect less light than a dark surface in full light. Adelson explains how the brain determines where the shadows are and how to compensate for them in order to determine the shade of gray that belongs to the surface.

"The first trick is based on local contrast. In shadow or not, a check that is lighter than its neighboring checks is probably lighter than average, and vice versa. In the figure, the light check in shadow is surrounded by darker checks. Thus, even though the check is physically dark, it is light when compared to its neighbors. The dark checks outside the shadow, conversely, are surrounded by lighter checks, so they look dark by comparison.

A second trick is based on the fact that shadows often have soft edges, while paint boundaries (like the checks) often have sharp edges. The visual system tends to ignore gradual changes in light level, so that it can determine the color of the surfaces without being misled by shadows."

It is important to note that none of the above is a defect in our visual system, but rather a very sophisticated system that process the data that it receives. "The visual system is not very good at being a physical light meter, but that is not its purpose. The important task is to break the image information down into meaningful components, and thereby perceive the nature of the objects in view."

#### The correct solution

So unfortunately we will have to modify the solution we gave above. Both knights might be exactly the same shade of gray, as are the squares on which they stand. But the human eye and brain process the image correctly and tell us that the one in the middle is a white knight on a white square and the one on the top a black knight on a black square.

Putting it another way: if you set up a real chess board with the objects positioned as above, using a white and black knight, then you will get exactly the same result as in the above picture. Just because on the photographic plate the two pieces and squares have the same shade of grey does not change the white knight into a black one, or the white square into a black one. We simply have to accept that our cognitive system understands shadows correctly and still recognises that the knight in the middle is white.