The Vigil exists to compute. Physics limits its energy efficiency, processing speed and memory capacity. It sets a floor under what a thought costs, a ceiling over how fast it can run and a limit on how much a region of space can remember. The Vigil sits close to some of those limits, and far from others.
Erasing an unknown bit releases heat of at least k × T × ln 2, which is 2.9 × 10−21 joules in a warm room and 2.9 × 10−22 at the temperature of the Vigil's radiators. Reversible operations can use arbitrarily little energy in principle. The chips of the 2020s sat between 3 × 104 and 3 × 107 times above the erasure floor.
Where should I start?
Start with the cost of forgetting. It is the page the strand is built around, with a toy that shows the cost by temperature, and it explains why the Vigil lives in the cold.
If forgetting is the cost, a computer that never forgets can dodge it. Computing without forgetting shows how, and what it costs in time and space instead.
Then comes the speed limit. How fast can anything think? finds a top speed for a given amount of energy: a kilogram turned entirely into computing could manage 5.4 × 1050 operations a second. Big minds are slow minds shows why a wide mind cannot use all of it, because light takes time to cross.
Memory is next. How much can a region remember? ends at a surprising place: the densest memory possible is a black hole, with its record written on its surface. Vesper's horizon can hold 1.9 × 1079 bits.
Two pages stand a little apart. What a quantum computer is, and is not clears up a common idea. And the ultimate computer is a black hole puts it all together, with the caveat that a small hole lives for an instant: a one-kilogram hole lasts 8.4 × 10−17 seconds.
Where does it lead?
To the ideas strand, which examines civilizations that improve their computation by controlling matter at smaller scales.