Let \({\mathcal F}\) be a family of mutually nonoverlapping unit balls in the \(n\)-dimensional Euclidean space \(\mathbb{R}^n\). The distance between the centers of \(A,B\in{\mathcal F}\) is denoted by \(d(A,B)\). It is proved, among others, that if \(d(A,B)< 4\) and \(n\geq 5\), then \(A\) and \(B\) are always visible from each other, that is a light ray emanating from the surface of \(A\) reaches \(B\) without being blocked by other unit balls. Furthermore, if \(d(A,B)<\sqrt{2}[n/2]\), then any small ``shake'' of \({\mathcal F}\) can make \(A\), \(B\) visible from each other.