How does the size of a collection of line segments change if we extend each segment to the corresponding full line? By the point-to-set principle of Lutz and Lutz, this classical problem is closely connected to understanding the information content of individual points on a line. We start by introducing this connection and some of the relevant tools, including Kolmogorov complexity. We then apply these tools to show that the packing dimension of any set in the plane does not increase under line segment extension. This allows us to prove the generalized Kakeya conjecture for packing dimension in the plane. Finally, we discuss versions of this problem in higher dimensions. This talk is based on joint work with Ryan Bushling.