  The sky-averaged (global) 21-cm signal is a powerful probe of the
intergalactic medium (IGM) prior to the completion of reionization. However, it
has so far been unclear that even in the best case scenario, in which the
signal is accurately extracted from the foregrounds, that it will provide more
than crude estimates of when the Universe's first stars and black holes form.
In contrast to previous work, which has focused on predicting the 21-cm
signatures of the first luminous objects, we investigate an arbitrary
realization of the signal, and attempt to translate its features to the
physical properties of the IGM. Within a simplified global framework, the 21-cm
signal yields quantitative constraints on the Lyman-alpha background intensity,
net heat deposition, ionized fraction, and their time derivatives, without
invoking models for the astrophysical sources themselves. The 21-cm absorption
signal is most easily interpreted, setting strong limits on the heating rate
density of the Universe with a measurement of its redshift alone, independent
of the ionization history or details of the Lyman-alpha background evolution.
In a companion paper we extend these results, focusing on the confidence with
which one can infer source emissivities from IGM properties.
