For many years, astronomers have promised that the study of pulsating white
dwarfs would ultimately lead to useful information about the physics of ma
tter under extreme conditions of temperature and pressure. In this paper, w
e finally make good on that promise. Using observational data from the Whol
e Earth Telescope and a new analysis method employing a genetic algorithm,
we empirically determine that the central oxygen abundance in the helium-at
mosphere variable white dwarf GD 358 is 84% +/- 3%. We use this value to pl
ace preliminary constraints on the C-12(alpha, gamma)O-16 nuclear reaction
cross section. More precise constraints will be possible with additional de
tailed simulations. We also show that the pulsation modes of our best-fit m
odel probe down to the inner few percent of the stellar mass. We demonstrat
e the feasibility of reconstructing the internal chemical profiles of white
dwarfs from asteroseismological data and find an oxygen profile for GD 358
that is qualitatively similar to recent theoretical calculations.