A relatively brief explanation of Boltzmann Brains

(Initially written for the LW Wiki, but then I realized it was looking more like a post instead.)In 1895, the physicist Ignaz Robert Schütz, who worked as an assistant to the more eminent physicist Ludwig Boltzmann, wondered if our observed universe had simply assembled by a random fluctuation of order from a universe otherwise in thermal equilibrium. The idea was published by Boltzmann in 1896, properly credited to Schütz, and has been associated with Boltzmann ever since.The obvious objection to this scenario is credited to Arthur Eddington in 1931: If all order is due to random fluctuations, comparatively small moments of order will exponentially-vastly outnumber even slightly larger fluctuations toward order, to say nothing of fluctuations the size of our entire observed universe! If this is where order comes from, we should find ourselves inside much smaller ordered systems.Feynman similarly later observed: Even if we fill a box of gas with white and black atoms bouncing randomly, and after an exponentially vast amount of time the white and black atoms on one side randomly sort themselves into two neat sides separated by color, the other half of the box will still be in expectation randomized. If the Solar System had arisen by a fluctuation of order, in expectation the rest of the universe would be a random smear; even taking our own Solar System for granted, the appearance of the rest of the universe would be vastly-exponentially improbable.The increased still-infinitesimal likelihood of "just one solar system fluctuates out of chaos", compared to "one Hubble-sized volume randomly fluctuates out of chaos", is vastly vastly greater than the ratio of a Hubble volume's size to a solar system's size. So if you pick a solar system that is part of a system that has randomly fluctuated out of chaos, the incredibly incredibly vast majority of solar systems like that find themselves alone in a larger bath of chaos.Indeed, if a fluctuation out of chaos gives rise to a s