  We show that when observing the range of a chordal SLE$_\kappa$ curve for
$\kappa \in (4,8)$, it is not possible to recover the order in which the points
have been visited. We also derive related results about conformal loop
ensembles (CLE): (i) The loops in a CLE$_\kappa$ for $\kappa \in (4,8)$ are not
determined by the CLE$_\kappa$ gasket. (ii) The continuum percolation
interfaces defined in the fractal carpets of conformal loop ensembles
CLE$_{\kappa}$ for $\kappa \in (8/3, 4)$ (we defined these percolation
interfaces in previous work, and showed there that they are SLE$_{16/\kappa}$
curves) are not determined by the CLE$_{\kappa}$ carpet that they are defined
in.
