Yet another weird SF fan
 I'm a mathematician, a libertarian, and a science-fiction fan. Common sense? What's that?Go to first entry

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 Yet another weird SF fan

### A Seveneves Calculation

In the novel Seveneves by Neal Stephenson, the Moon explodes, causing the surface of the Earth to become uninhabitable for 5000 years. There is a colony or two of humans who survive in deep mines. Let's calculate how deep the human hole goes.

The thermal diffusivity of rocks appears to be around 1 mm2/s. 5000 years is around 1.6 × 1011 seconds. You can expect the heat from the “hard rain” to diffuse to a depth of $$\sqrt{1.6\times 10^{11}}$$ millimeters or 400 meters. Three times that distance should be safe, so the colony would only have to be $$\frac{3}{4}$$ miles down. It might be doable.