  Understanding international trade is a fundamental problem in economics --
one standard approach is via what is commonly called the "gravity equation",
which predicts the total amount of trade $F_ij$ between two countries $i$ and
$j$ as $$ F_{ij} = G \frac{M_i M_j}{D_{ij}},$$ where $G$ is a constant, $M_i,
M_j$ denote the "economic mass" (often simply the gross domestic product) and
$D_{ij}$ the "distance" between countries $i$ and $j$, where "distance" is a
complex notion that includes geographical, historical, linguistic and
sociological components. We take the \textit{inverse} route and ask ourselves
to which extent it is possible to reconstruct meaningful information about
countries simply from knowing the bilateral trade volumes $F_{ij}$: indeed, we
show that a remarkable amount of geopolitical information can be extracted. The
main tool is a spectral decomposition of the Graph Laplacian as a tool to
perform nonlinear dimensionality reduction. This may have further applications
in economic analysis and provides a data-based approach to "trade distance".
