The physical processes that determine the properties of our everyday world, and of the wider cosmos, are determined by some key numbers: the constants of micro-physics and the parameters that describe the expanding universe in which we have emerged. We identify various steps in the emergence of stars, planets and life that are dependent on these fundamental numbers, and explore how these steps might have been changed, or completely prevented, if the numbers were different. We then outline some cosmological models where physical reality is vastly more extensive than the universe that astronomers observe (perhaps even involving many big bangs), which could perhaps encompass domains governed by different physics. Although the concept of a multiverse is still speculative, we argue that attempts to determine whether it exists constitute a genuinely scientific endeavor. If we indeed inhabit a multiverse, then we may have to accept that there can be no explanation other than anthropic reasoning for some features our world.
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