8 Given that $A B C D-A_{1} B_{1} C_{1} D_{1}$ is a unit cube, a black ant and a white ant start from point $A$ and crawl forward along the edges. Each time they finish crawling along one edge, it is called “finishing one segment”. The white ant's crawling route is $A A_{1} \rightarrow A_{1} D_{1} \rightarrow \cdots$, and the black ant's crawling route is $A B \rightarrow B B_{1} \rightarrow \cdots$. They both follow the rule that the line of the $(n+2)$-th segment must be a skew line to the line of the $n$-th segment. Suppose both the black and white ants stop at some vertex of the cube after crawling 2008 segments, the distance between the black and white ants at this time is $\qquad$
8 It is known that the paths taken by the two ants have a cycle of 6. After the black and white ants have walked 2008 segments, they stop at vertices $D_{1}$ and $C$ of the cube, respectively, with a distance of $D_{1} C=\sqrt{2}$.