  We compare the flow-like correlations in high multiplicity proton-nucleus
($p+A$) and nucleus-nucleus ($A+A$) collisions. At fixed multiplicity, the
correlations in these two colliding systems are strikingly similar, although
the system size is smaller in $p+A$. Based on an independent cluster model and
a simple conformal scaling argument, where the ratio of the mean free path to
the system size stays constant at fixed multiplicity, we argue that flow in
$p+A$ emerges as a collective response to the fluctuations in the position of
clusters, just like in $A+A$ collisions. With several physically motivated and
parameter free rescalings of the recent LHC data, we show that this simple
model captures the essential physics of elliptic and triangular flow in $p+A$
collisions. We also explore the implications of the model for jet energy loss
in $p+A$, and predict slightly larger transverse momentum broadening in $p+A$
than in $A+A$ at the same multiplicity.
