  We consider massless scattering from the point of view of the position,
momentum, and celestial bases. In these three languages different properties of
physical processes become manifest or obscured. Within the soft sector, they
highlight distinct aspects of the infrared triangle: quantum field theory soft
theorems arise in the limit of vanishing energy $\omega$, memory effects are
described via shifts of fields at the boundary along the null time coordinate
$u$, and celestial symmetry algebras are realized via currents that appear at
special values of the conformal dimension $\Delta$. We focus on the subleading
soft theorems at $\Delta=1-s$ for gauge theory $(s=1)$ and gravity $(s=2)$ and
explore how to translate the infrared triangle to the celestial basis. We
resolve an existing tension between proposed overleading gauge transformations
as examined in the position basis and the `Goldstone-like' modes where we
expect celestial symmetry generators to appear. In the process we elucidate
various order-of-limits issues implicit in the celestial formalism. We then
generalize our construction to the tower of $w_{1+\infty}$ generators in
celestial CFT, which probe further subleading-in-$\omega$ soft behavior and are
related to subleading-in-$r$ vacuum transitions that measure higher multipole
moments of scatterers. In the end we see that the celestial basis is `just
right' for identifying the symmetry structure.
