  Some of the most worrisome potential singularity models for the mean
curvature flow of $3$-dimensional hypersurfaces in $\mathbb{R}^4$ are
noncollapsed wing-like flows, i.e. noncollapsed flows that are asymptotic to a
wedge. In this paper, we rule out this potential scenario, not just among
self-similarly translating singularity models, but in fact among all ancient
noncollapsed flows in $\mathbb{R}^4$. Specifically, we prove that for any
ancient noncollapsed mean curvature flow $M_t=\partial K_t$ in $\mathbb{R}^4$
the blowdown $\lim_{\lambda\to 0} \lambda\cdot {K_{t_0}}$ is always a point,
halfline, line, halfplane, plane or hyperplane, but never a wedge. In our proof
we introduce a fine bubble-sheet analysis, which generalizes the fine neck
analysis that has played a major role in many recent papers. Our result is also
a key first step towards the classification of ancient noncollapsed flows in
$\mathbb{R}^4$, which we will address in a series of subsequent papers.
