Let there be a Rubik's cube that in its "solved" state is painted with six colors, let us say red_1, orange_1, yellow_1, green_1, blue_1 and violet_1 . Now let us suppose that the cube is twiddled at random for a significant number of operations, and then painted anew, on the then-existing macrofaces, using six different paints each of which is transparent in visible light but reflects a specific band of infrared radiation, which I shall denote by red_2, orange_2, yellow_2, green_2, blue_2, and violet_2. Now let us suppose that the cube is handed to another person, called Observer 1, who will proceed to solve the cube by returning it to its original configuration. To Observer 1, the process will be like solving any other Rubik's cube; it is a matter of restoring each of the six macrofaces into their respective uniform original visible colors. Observer 1 cannot see the infrared-reflective paint. But now let us suppose that there is another Observer, #2, who is wearing infrared goggles. Observer 2 will see only the infrared paint and not the original paint. So, to Observer 1, the cube appears to be disarranged and he is about to solve it. To observer 2, the cube looks already solved. Observer 2 will now watch Observer 1 unscramble (to #1's eyes) the cube, and to Observer 2, it will appear like Observer 1 is disarranging it, because Observer 2 will see what to him looks like the orderly state of the cube in infrared "colors" disarranged as Observer 1 puts the visible-light colors back to normal. As a result, what appears to be the creation of greater order to one observer will appear to be creating greater disorder to the other. So this is a situation in which entropy seems to be moving in opposite directions simultaneously. which is not what one normally expects in connection with entropy.

An important question in analyzing this situation is to inquire whether Observer 2, who sees the cube start out in what looks like perfect order and become less organized, can detect, by observing Observer 1 solve (in visible light) the cube, that Observer 1 is in fact solving the cube. (Here, it is assumed that Observer 2 bases his conclusions solely upon the sequence of moves by Observer 1, without considering extraneous clues such as Observer 1's facial expressions, length of time spent on each move, etc.) In this situation, can observer 2 distinguish between Observer 1 pursuing a solution that will be, to Observer 2, invisible when completed ; and simply random moves by Observer 1?