Imagine that you have a picture of an apple and a picture of grapes. You need to decide what picture has the higher contrast. You know that there should be a significant enough difference between the pictures. But each picture has 2 states (one with low contrast and the other with high contrast). You don't know what states are "true". So the apple can have way more contrast than the grapes or vice versa. Moreover, you can't even measure the states good enough (get an exact number describing the contrast). It seems like there's no way to decide. Illustration

But then you get another picture, with a banana. And (somehow) you know that the banana has to have way more contrast than the grapes. Though the level of contrast of the banana is unknown (very vague), you only know that the banana is visible and recognizable. So it's impossible to compare the banana to the apple or the grapes.

But now you know what states of the apple and the grapes are true! Because if the banana had a much higher contrast than grapes in the high contrast state, the banana would just vanish. And that's obviously impossible, the banana can't have that much contrast (whatever its level of contrast is, it has to be visible).

In a more general case you can imagine more complex relationships between more objects (pictures) that have more possible states. But the idea is supposed to stay the same: you look for the relations that lead to "impossible" results and deduce what relations are possible. Illustration (another one)

Do you know an algorithm that compares objects in a similar way? Takes a bunch of uncertainties and figures out the right answer through the relationships between those uncertainties? Can this algorithm be related to some specific types of functions?



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