This **Online Discussion section** is intended to give people a chance to engage the workshop topics in advance of the meeting, and will also provide an opportunity for those unable to attend in person to join in anyway. The discussion will be hosted on a **Slack channel** called #MathematicalHome, whose contents will be posted daily below, in this Online Discussion section of the workshop website. To request an invitation to the Slack channel, send an email to mathematicalhome(at)gmail.com . If you want to contribute to the Online Discussion without joining Slack, send your contribution to the same email, mathematicalhome(at)gmail.com and we will put it into the discussion stream manually if we consider it sufficiently relevant.

-Charles H. Bennett and Andreas Albrecht, co-chairs.

Some initial contributions:

Andreas Albrecht: Some Reflections on Boltzmann Brains, Tuning, and Cosmology

Leonid Levin: Assumptions of Randomness in Cosmological Models

Some questions:

Leonid Levin: "Suppose a max mass neutron star absorbs a little more gas and collapses into a black hole. Its mass does not change much, radius shrinks just a little (say, twice), but entropy grows by 20 order of magnitudes, approaching the combined entropy of all stars in the universe. Ordinary matter systems of radius R (in Planck units) cannot have entropies much over R^{1.5}, but black holes get R^2. (A bit of numerology: If 1/t is proton Planck mass, then the radius of neutron stars is ~ t^2 and of the universe about t^3. The universe entropy, ignoring black holes, would then be t^{4.5}, close to a single stellar black hole t^4. Is not this strange?) As I understand, Bekenstein–Hawking entropy R^2 was inspired by the theorem that the combined R^2 areas of black holes never shrink. So my question is: would a stronger theorem still hold that the sum of R^{1.5} of black holes never shrinks; any counterexamples?"