# Differences that are too small to see

Consider two identical pieces of paper.

Scenario 1: On both something is drawn in black ink. If the difference between the areas covered in black ink is sufficiently small, I cannot see the difference between the two drawings.

Scenario 2: Now imagine that the same parts are covered with ink, but their color differs. Again, if the difference is sufficiently small, I cannot see the difference.

Firstly: what causes this? I am aware of the terminology of just-noticeable differences/limina, but do not understand precisely what causes them. Is there some discretization of continuous signals going on that causes nearby signals' to be treated the same way?

Secondly: one person may have better vision than another, but are there physical constraints that are the same for any two persons and that imply that if the difference in scenario 1 or 2 is sufficiently small, no two persons will be able to see a difference?

Addenda: I phrased the question informally by not defining what a small difference' is, trusting/hoping that this does not lead to confusion. If desired, such statements can be made precise by adopting appropriate distance functions. In scenario 1, one way to measure distance between two areas covered in ink could be to use the Hausdorff distance; likewise, one way to measure the distance between colors in the second scenario could depend on the difference in responsivity of the three types of cone cells.

• I am having problems understanding your question. Would it be possible to add an image for your example? Also note that you may increase your chances of getting an answer over at cogsci.stackexchange.com. – vkehayas Sep 15 '17 at 19:03
• Thanks, I will give the cogsci site a try as well. Two concrete examples: load a digital image into your computer, change just the colour of a single pixel. This is typically not a difference you can see. Likewise, it is not clear at first sight whether the strings 0000000000 and 00000000000 are identical. Why exactly can we not see small differences? – Mark Sep 15 '17 at 19:48