Fold it again

A sheet of paper is about 0.1 millimetres thick. Fold it once and you have 0.2 millimetres. Fold it again and you have 0.4. Each fold doubles the stack. People cannot actually fold a sheet fifty times — the public record sits at twelve folds — so this is a thought experiment, not origami.

Keep doubling on paper. After thirty folds the stack is about 107 kilometres thick, on the order of Earth’s atmosphere. After fifty folds it is about three-quarters of the way from Earth to the Sun.

Nothing magical happened at fold thirty. The same rule ran long enough to leave the room, then the weather, then the planet. The early folds look like a pamphlet. The late folds are a distance.

Once you have seen the stack leave the table, “it is only another doubling” stops meaning “it is still small.”

The tempting mistake is to trust the starting thickness. Thin at the start does not stay thin if you keep multiplying.

That is what lets you ask how much of the pile arrived in the last doubling alone.