Giulio Pepe edited Writing_goes_arm_in_arm__.tex  over 8 years ago

Commit id: 5ac30270162e4f1d63cfe56d3a9be9ba8da88971

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Now imagine a library which does not just contain all books, but all books that will be written and all books that could have been written. It could be a library containing books with every combination of characters. How big would this library be? What would a page at random look like? How hard would be to extract knowledge from such place? Jorge Luis Borges explored this idea in his short story: \textit{The Library of Babel}. An extract from the book reads:  \begin{quote}  The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable. Twenty shelves, five long shelves per side, cover all the sides except two; their height, which is the distance from floor to ceiling, scarcely exceeds that of a normal bookcase. One of the free sides leads to a narrow hallway which opens onto another gallery, identical to the first and to all the rest. [...] There are five shelves for each of the hexagon's walls; each shelf contains thirty-five books of uniform format; each book is of four hundred and ten pages; each page, of forty lines, each line, of some eighty letters which are black in color. [...] The Library is total and its shelves register all the possible combinations of the twenty-odd orthographical symbols (a number which, though extremely vast, is not infinite): Everything: the minutely detailed history of the future, the archangels' autobiographies, the faithful catalogues of the Library, thousands and thousands of false catalogues, the demonstration of the fallacy of those catalogues, the demonstration of the fallacy of the true catalogue, the Gnostic gospel of Basilides, the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books.  \end{quote} In such a universe, the people living in the library - called librarians - would live their lives exploring it and knowing nothing about it. With time, they would have realized that the library was made of all possible permutation of letters, by bumping into a book explaining combinatorial analysis. They would wonder about its finiteness, possible periodicity, presence of fundamental truths or of a person having read such book, which would be worshipped like a god. Cults formed and books containing gibberish destroyed in the vane hope of reducing the size of the library and find the hexagon containing such truths.  The size of this library would be roughly of 10^1,834,097 books, a number with almost two million zeroes. Humans are bad at dimensions, but a number that big is something that anyone can barely visualize or imagine, in this universe's standards. To put things to perspective, the universe has roughly 10^80 atoms in it. The Planck length is a fundamental physical constant of the universe and quantum mechanics hypothesizes that it is the shortest theoretically measurable length. The order of magnitude of this length is 10^-35 meters. In comparisons, there are around 10^185 (a number with almost two hundred zeroes) cubic Planck lengths in the observable universe.