Act II, scene ii of David Hume in the Library of Babel

In my previous post, I surveyed the abstract axioms of Borges’ imaginary library. The next paragraph of the story (Para. 8) contains a paradox: the Universal Library contains all possible books, but the probability of finding any particular book is close to zero:

When it was announced that the Library contained all books, the first reaction was unbounded joy. All men felt themselves the possessors of an intact and secret treasure. There was no personal problem, no world problem, whose eloquent solution did not exist—somewhere in some hexagon. The universe was justified; the universe suddenly became congruent with the unlimited width and breadth of humankind’s hope. At that period there was much talk of The Vindications—books of apologiæ and prophecies that would vindicate for all time the actions of every person in the universe and that held wondrous arcana for men’s futures. Thousands of greedy individuals abandoned their sweet native hexagons and rushed downstairs, upstairs, spurred by the vain desire to find their Vindication. These pilgrims squabbled in the narrow corridors, muttered dark imprecations, strangled one another on the divine staircases, threw deceiving volumes down ventilation shafts, were themselves hurled to their deaths by men of distant regions. Others went insane. . . . The Vindications do exist (I have seen two of them, which refer to persons in the future, persons perhaps not imaginary), but those who went in quest of them failed to recall that the chance of a man’s finding his own Vindication, or some perfidious version of his own, can be calculated to be zero. [ellipsis and emphasis in the original]

On the one hand, the Universal Library must contain so-called books of “Vindication” — i.e. “books of apologiæ and prophecies that would vindicate for all time the actions of every person in the universe and that held wondrous arcana for men’s futures” — but at the same time, given the unimaginable astronomical scale of the library, the probability of finding any of these magical books is zero for all practical purposes.

In other words, even though individualized Vindication books must exist in theory — after all, Borges’ Universal Library is a “total” library, since it contains all possible books (past, present, and future) that could be written — in the absence of a catalog or index of all the books in the Library of Babel, the probability of any given person finding his own specific Vindication book during his own lifetime is virtually nil.

Moreover, this demoralizing paradox will give rise to several different factions and a wide range of responses. In short, the search for truth will be transformed into empty inquiries and formalistic rituals; hope and optimism will mutate into blasphemous pursuits and destructive pogroms. I will survey these responses in my next post. To be continued …