Author: Hal Draper
Original language: English
Publication date: 1961
Knowledge is expanding exponentially, as humanity fills the galaxy and then some. But advances in physics (which Draper describes in fictional mathematical terms) are able to keep up with the storage problem, until all of human knowledge, for all time to come, is packed into one drawer. Of course, there is one wee problem. Retrieval is ultimately macroscopic. And so the indexes grow. And when they get miniaturized, the indexes to the indexes grow. And so on, which then leads to a higher-order index of the iterated indexes, and then so on again. All this is spelled out in some detail.
The neverending recursion, while threatening to grow to Ackermann-like proportions, is still manageable. But when a spontaneously generated G?delian self-reference is discovered in the indexing system, the whole lbry, and with it all of human civilization, collapses overnight. . .