In space there is no air and no water. A hot thing can lose its heat in only one way: it glows. A cold thing glows faintly. So the colder the Vigil runs its radiators, the more surface it needs to shed the same heat, and the surface is where the Vigil spends its mass. A petawatt at 30 K needs 43 Earths of radiating surface.
This strand explains how entropy, heat engines and radiative cooling determine the Vigil's structure.
Where should I start?
Start with entropy is missing information. It is a plain account of what entropy is, and it connects heat to something the Vigil cares about even more: information. One bit has a size in physical units. Everything else in the strand and in the limits strand grows from that.
Next comes recycling heat. Heat does work only while it flows from hot to cold, so the Vigil runs its computers warm and collects what it can on the way to the radiators. An ideal engine running between 300 K and 30 K could turn 0.9 of the flow into work; the Vigil's real engines recover 0.36 of it and feed that work back to the computers. So a petawatt of supply carries 1.56 × 1015 watts of computing, and exactly a petawatt still leaves as heat. The recovered energy circulates through the computers again; total rejected heat still equals the external supply.
Then cooling is the economy puts the area on the table, and you can play with the temperature and see the film grow.
The last page, the black hole is not your freezer, answers the question everyone asks: Vesper is the coldest thing in the sky, so why not throw the heat in? The answer is that it is a small target. It can swallow at most 4.9 × 109 watts of 30 K heat.
Where does it lead?
Heat sets the price of forgetting. The limits strand takes that price and asks how much thinking physics allows at all.