"William E. Emba"
Hal Draper took a break from his life's work of promoting Marxism,
and wrote one science fiction story. The information explosion, and
associated storage and retrieval problems, is humorously examined
in this short story. (This story is also of historical interest,
containing one of the earliest predictions of the Web.)
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
Gödelian self-reference is discovered in the indexing system, the
whole lbry, and with it all of human civilization, collapses overnight.