  Recent high redshift surveys for 21-cm absorption in damped Lyman-alpha
absorption systems (DLAs) take the number of published searches at z > 2 to 25,
the same number as at z < 2, although the detection rate at high redshift
remains significantly lower (20% cf. 60%). Using the known properties of the
DLAs to estimate the unknown profile widths of the 21-cm non-detections and
including the limits via a survival analysis, we show that the mean spin
temperature/covering factor degeneracy at high redshift is, on average, double
that of the low redshift sample. This value is significantly lower than the
previous factor of eight for the spin temperatures and is about the same factor
as in the angular diameter distance ratios between the low and high redshift
samples. That is, without the need for the several pivotal assumptions, which
lead to an evolution in the spin temperature, we show that the observed
distribution of 21-cm detections in DLAs can be accounted for by the geometry
effects of an expanding Universe. That is, as yet there is no evidence of the
spin temperature of gas rich galaxies evolving with redshift.
