Five problems in chthonic physics
1. Consider a perfect sphere, of uniform density d and radius r, which has just been discovered in the deepest vault of a newly-found pyramid in Egypt. If it is exposed to a metaphysical potential V(x) of the type described in the Voynich Manuscript, derive the width of the ghastly chasm that is about to yawn open beneath the vault, and give the most likely half-life of the sanity of any observers.
2. What physical processes lead to the formation of lightning? Assume a day-old corpse is placed in a standard reanimation chamber. Using Cornelius’s animatory decay equation, estimate the size of thunderstorm that will be needed for a 50 percent chance of full revival.
3. Describe the chain of fusion reactions that provide the Sun’s primary energy source. When the planets align, calling the Old Ones from the void, that other set of reactions that Science dare not name will start up in the Sun’s heart. Estimate, from basic physical and mystical principles, the time that an observer located on the Earth would need to observe a change in the Sun’s output from the starting of the Other Reactions, and show that this far exceeds the time required for humanity to succumb to the ghastly malignities of the Old Ones.
4. If an ancient flooded city is submerged in a water-filled well of 50m diameter and 100m depth, show that water pressure will be sufficient to seal shut that city’s haunted temples, given that they demonstrate a typical level of cacodemonaical activity. Assume a team of investigators, heedless of the awful phantasms lurking below, descend to the city in a spherical submarine of radius 3m. If energy transport within the well is primarily by convection, how long after their intervention will it take for the surface of the well to be contaminated by the soul-annihilating stench of evil?
5. Consider a vast, crawling horror beyond the capacity of the healthy human mind to imagine. Is approximating the horror by a uniform cylinder of length x and length r a valid strategy for preserving the desperate shreds of your rational mind for long enough to scrawl a warning message in the tunnel to this accursed place? Assume moderate light levels and approximately one litre of blood for ink.