  The past decade began with the first light of ALMA and will end at the start
of the new era of hyperdimensional astrophysics. Our community-wide movement
toward highly multiwavelength and multidimensional datasets has enabled immense
progress in each science frontier identified by the 2010 Decadal Survey,
particularly with regard to black hole feedback and the cycle of baryons in
galaxies. Facilities like ALMA and the next generation of integral field unit
(IFU) spectrographs together enable mapping the physical conditions and
kinematics of warm ionized and cold molecular gas in galaxies in unprecedented
detail (Fig. 1). JWST's launch at the start of the coming decade will push this
capability to the rest-frame UV at redshifts z > 6, mapping the birth of stars
in the first galaxies at cosmic dawn. Understanding of their subsequent
evolution, however, now awaits an ability to map the processes that transform
galaxies directly, rather than the consequences of those processes in
isolation. In this paper, we argue that doing so requires an equivalent
revolution in spatially resolved spectroscopy for the hot plasma that pervades
galaxies, the atmospheres in which they reside, and the winds that are the
engines of their evolution.
