  This essay is based on a talk at Advances in Atomic, Molecular, and Optical
Sciences 2020 (AAMOS20) in a symposium honoring Prof. S. T. Manson's
decades-long contribution to photoabsorption studies. Quantum physics
introduced into physics pairs of conjugate quantities bearing a specific
complementary relationship, energy and time being one such pair. This gives
rise to two alternative representations, a time-dependent and a
time-independent one, seemingly very different but both capable of embracing
the same physics. They give complementary descriptions and insight, with
technical questions, theoretical and experimental, determining which may be the
more convenient and practicable at any juncture. Two recent topics, Cooper
minima in photoabsorption in Cl$^-$ and Ar, and angular-momentum barrier
tunneling of $f$ photoelectrons from Se in WSe$_2$, provide illustrative
examples, also of the role that technological developments over the past five
decades played in our approach to and understanding of phenomena.
