Four, there are 1990 points distributed on a straight line. We will mark the midpoints of all possible line segments with these points as endpoints. Try to find the minimum number of distinct midpoints that can be obtained.

 untranslated text:
直线上外布着1990个点, 我们来标出以这些点为端点的一切可能的线段的 中点. 试求至少可以得出多少个互不重合的中点.

 translated text:
There are 1990 points distributed on a straight line. We will mark the midpoints of all possible line segments with these points as endpoints. Try to find the minimum number of distinct midpoints that can be obtained.
Four, Solution: Let the two points that are farthest apart be denoted as $A, B$. Consider the 1988 line segments formed by $A$ and the other 1988 points excluding $B$. The midpoints of these 1988 line segments are all distinct, and their distances to point $A$ are less than $\frac{1}{2} A B$.

Similarly, for point $B$, we can obtain another 1988 distinct midpoints, which are all less than $\frac{1}{2} A B$ away from point $B$.

Including the midpoint of $A B$, we have a total of $1988 + 1988 + 1 = 3977$ distinct midpoints.

On the other hand, when the 1990 points are equally spaced, the number of distinct midpoints is exactly 3977.

In conclusion, the minimum number of distinct midpoints of all possible line segments is 3977.