Maybe we are anthropically more likely to find ourselves in places with low komolgorov complexity descriptions. (“All possible bitstrings, in order” is not a good law of physics, just because it contains us somewhere).
Another way of thinking about this, which amounts to the same thing: Holding the laws of physics constant, the Solomonoff prior will assign much more probability to a universe that evolves from a minimal-entropy initial state, than to one that starts off in thermal equilibrium. In other words:
Description 1: The laws of physics + The Big Bang
Description 2: The laws of physics + some arbitrary configuration of particles
Description 1 is much shorter than Description 2, because the Big Bang is much simpler to describe than some arbitrary configuration of particles. Even after the heat-death of the universe, it’s still simpler to describe it as “the Big Bang, 10^zillion years on” rather than by exhaustive enumeration of all the particles.
This dispenses with the “paradox” of Boltzmann Brains, and Roger Penrose’s puzzle about why the Big Bang had such low entropy despite its overwhelming improbability.
Another way of thinking about this, which amounts to the same thing: Holding the laws of physics constant, the Solomonoff prior will assign much more probability to a universe that evolves from a minimal-entropy initial state, than to one that starts off in thermal equilibrium. In other words:
Description 1: The laws of physics + The Big Bang
Description 2: The laws of physics + some arbitrary configuration of particles
Description 1 is much shorter than Description 2, because the Big Bang is much simpler to describe than some arbitrary configuration of particles. Even after the heat-death of the universe, it’s still simpler to describe it as “the Big Bang, 10^zillion years on” rather than by exhaustive enumeration of all the particles.
This dispenses with the “paradox” of Boltzmann Brains, and Roger Penrose’s puzzle about why the Big Bang had such low entropy despite its overwhelming improbability.