  We connect recent conjectures and observations pertaining to geodesics,
attractor flows, Laplacian eigenvalues and the geometry of moduli spaces by
using that attractor flows are geodesics. For toroidal compactifications,
attractor points are related to (degenerate) masses of the Laplacian on the
target space, and also to the Laplacian on the moduli space. We also explore
compactifications of M-Theory to $5$D on a Calabi-Yau threefold and argue that
geodesics are unique in a special set of classes, providing further evidence
for a recent conjecture by Raman and Vafa. Finally, we describe the role of the
marked moduli space in $4$d $\mathcal{N} = 2$ compactifications. We study split
attractor flows in an explicit example of the one-parameter family of quintics
and discuss setups where flops to isomorphic Calabi-Yau manifolds exist.
