An important goal in both artificial life and biology is uncovering the most general principles underlying life, which might catalyze both our understanding of life and engineering lifelike machines. While many such general principles have been hypothesized, conclusively testing them is difficult because life on Earth provides only a singular example from which to infer. To circumvent this limitation, this article formalizes an approach called radical reimplementation. The idea is to investigate an abstract biological hypothesis by intentionally reimplementing its main principles to diverge maximally from existing natural examples. If the reimplementation successfully exhibits properties resembling biology, it may support the underlying hypothesis better than an alternative example inspired more directly by nature. The approach thereby provides a principled alternative to a common tradition of defending and minimizing deviations from nature in artificial life. This work reviews examples that can be interpreted through the lens of radical reimplementation to yield potential insights into biology despite having purposely unnatural experimental setups. In this way, radical reimplementation can help renew the relevance of computational systems for investigating biological theory and can act as a practical philosophical tool to help separate the fundamental features of terrestrial biology from the epiphenomenal.