Early physical cosmologies were based on interpretations of the cosmic redshift for which there was insufficient evidence and on theories of gravitation that appear to be falsified by galactic dynamics. Eventually, the big bang paradigm came to be guarded against refutation by ad hoc hypotheses (dark matter, cosmic inflation, dark energy) and free parameters. Presently available data allow a more satisfactory phenomenological approach. Using data on magnitude and redshift from 892 type Ia supernovae, it is first shown that these suggest that the redshift factor (1+z) is simply an exponential function of distance and that, for standard candles, magnitude m=5log[(1+z)ln(1+z)]+const. While these functions are incompatible with a big bang, they characterize certain tired light models as well as exponential expansion models. However, the former are falsified by the stretched light curves of distant supernovae and the latter by the absence of a predicted 1+z increase in the angular sizes of galaxies. Instead, the observations suggest that physical processes speed up and objects contract uniformly as an exponential function of time, standards of measurement not excluded, and only free waves being excepted. Distant events proceed, then, more slowly, while angular sizes remain unaffected, approximately as observed. Since all objects contract in proportion, the Universe retains a static appearance. A corresponding physical theory, which should also explain galactic dynamics, remains yet to be derived from first principles. A way to do this, satisfying also Mach's principle, is vaguely suggested.