  We consider the classic online problem of scheduling on a single machine to
minimize total flow time. In STOC 2021, the concept of robustness to distortion
in processing times was introduced: for every distortion factor $\mu$, an
$O(\mu^2)$-competitive algorithm $\operatorname{ALG}_{\mu}$ which handles
distortions up to $\mu$ was presented. However, using that result requires one
to know the distortion of the input in advance, which is impractical.
  We present the first \emph{distortion-oblivious} algorithms: algorithms which
are competitive for \emph{every} input of \emph{every} distortion, and thus do
not require knowledge of the distortion in advance. Moreover, the competitive
ratios of our algorithms are $\tilde{O}(\mu)$, which is a quadratic improvement
over the algorithm from STOC 2021, and is nearly optimal (we show a randomized
lower bound of $\Omega(\mu)$ on competitiveness).
