We hold this truth to be self-evident, that good principle and good practice go hand in hand. The principles of Bayesian analysis derive from elementary symmetries, and nothing more. In sympathy with those same symmetries, and noting that every invariance broken is generality forgone, we develop the practice of Bayesian computation. This approach leads to nested sampling and Galilean Monte Carlo. Nested sampling is the canonical prior-to-posterior compression algorithm, and Galilean Monte Carlo (GMC) is the canonical multidimensional exploration strategy. Though inspired by high dimension, these general methods apply to problems of all size.