Reasoning
- Apply the toy model at Q = 0: eta = (1 - P + PQ)/Q diverges - the posterior credence licensed by “we (and our planet’s habitability) are still here” is zero information about P, since every possible observer, in every world with any value of P, makes the same observation. Survival evidence discriminates between rival risk levels only through histories in which observers survive, and for Q = 0 classes all such histories look identical.
- Hence the Hut-Rees inference (natural cosmic-ray collisions on Earth/Moon exceed accelerator collisions by orders of magnitude, and we survived 4.5 Gyr of them, so accelerators are safe for the foreseeable future) is partially misleading: the Earth-survival leg supplies no anthropically clean information for observer-extinguishing outcomes. The paper notes the divergent Hut-Rees sub-argument that remains valid - the count of collisions in any conceivable accelerator is minuscule beside nature’s - while the survival-frequency leg fails uncorrected, and the LSAG report repeats the uncorrected form via the solar-system-duration argument.
- The unreliability applies equally to naturally occurring and human-induced members of the class; anthropogenic hazards generally leave no deep-history record at all, physics disasters being the rare exception where past-frequency reasoning is even attempted.
- Repair route acknowledged by the paper: conditioning on external evidence instead - e.g. Tegmark & Bostrom’s use of planetary-age distributions and Earth’s late formation date bounds the vacuum-decay rate below ~1e-9 per year - shows the shadow can be circumvented, not that the uncorrected survival argument stands.