  We show that Lang's conjecture on error terms in Diophantine approximation
implies Honda's conjecture on ranks of elliptic curves over number fields. We
also show that even a very weak version of Lang's error term conjecture would
be enough to deduce boundedness of ranks for quadratic twists of elliptic
curves over number fields. This can be seen as evidence for boundedness of
ranks not relying on probabilistic heuristics on elliptic curves.
