Here is one answer from the electrical engineering(or, image processing) point of view. However this answer much non-mathematical and more for practical illustration. Since this is a non-mathematical answer, I have made it community wiki so that I don't get reputation.

In digital signal processing, you sample an analog signal into digital encoding, and let your microprocessor work with it. When you do sampling, you clearly lose some information and there is no way you can recover it. When you become too greedy and actually try to get more, the problem of "aliasing" will happen.

Here is the wikipedia link for aliasing.

For image processing, situation is even better for an illustration, since you can actually see wavy patterns. These are called Moiré patterns, and you must have seen it sometime in the real world. Here is a wikipedia link.