The Unimaginable Mathematics Of Borges' Library Of Babel - Plot & Excerpts
—Herman Melville, The Piazza Tales and Other Prose Pieces In what follows, we briefly discuss two subtle points from above. First, we examine why the libits must be the same shape while comparing their respective Grand Patterns. If they are allowed to be dissimilar, we'll use, as an example, the two extreme examples from earlier in the chapter: we'll say a tower libit is a slender tower of stacked single hexagons, while a floor libit is completely contained in one floor. Imagine seven tower libits, six of them adjacent to a central one, that are exactly the same save that in their top hexagons, four books are permuted into slightly different positions. Then the towers are all identical except in the top hexagons, and even there, each top hexagon contains the same books as the others. (See figure 64.) We claim that no floor libit can accommodate this distribution, for any floor libit that contains any hexagon of the central tower libit necessarily also contains a hexagon of at least one of the adjacent tower libits.
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