  In the paper we prove two inequalities in the setting of ${\sf
RCD}(K,\infty)$ spaces using similar techniques. The first one is an
indeterminacy estimate involving the $p$-Wasserstein distance between the
positive part and the negative part of an $L^{\infty}$ function and the measure
of the interface between the positive part and the negative part. The second
one is a conjectured lower bound on the $p$-Wasserstein distance between the
positive and negative parts of a Laplace eigenfunction.
