  Random sampling in high dimensions has successfully been applied to phenomena
as diverse as nuclear resonances, neural networks and black hole evaporation.
Here we revisit an elegant argument by the British physicist Dennis Sciama,
which demonstrated that were our universe random, it would almost certainly
have a negligible chance for life. Under plausible assumptions, we show that a
random universe can masquerade as `intelligently designed,' with the
fundamental constants instead appearing to be fined tuned to be achieve the
highest probability for life to occur. For our universe, this mechanism may
only require there to be around a dozen currently unknown fundamental
constants. We speculate on broader applications for the mechanism we uncover.
