TITLE: Unexpected applications of Dvoretzky's theorem
QUESTION [21 upvotes]: Dvoretzky's theorem is a classic of convex geometry. Recently at a conference in quantum information I learned (from Patrick Hayden's talk) about a nontrivial application of the theorem to a problem in quantum cryptography (which was solved previously, but using more complicated tools). What are the unexpected applications of Dvoretzky's theorem that you have heard of, if any?
(by "unexpected" I mean applying it to a problem which is not directly connected to convex geometry, functional analysis etc. or perhaps is connected, but requires phrasing the problem in a different language in a non-obvious way)

REPLY [7 votes]: An exotic application to cosmology was suggested by K. Villaverde, O. Kosheleva, and M. Ceberio, Why Ellipsoid Constraints, Ellipsoid Clusters, and Riemannian Space-Time: Dvoretzky's Theorem Revisited.

Modern cosmology asserts that space-time is high-dimensional with
  some complex metric. Still, we observe a locally Euclidean metric in
  our four-dimensional world.
  Dvoretzky’s theorem explains this phenomenon: we observe a section of a
  high-dimensional convex unit ball, and such a section is close to an
  ellipsoid, implying a locally Euclidean metric.