The Largest Library of All Times

Among Borges' fiction stories there is another one also related to books and infinity titled: La Biblioteca de Babel (The Library of Babel), an incredibly complex and labyrinthic library that has all the books of the universe. This story has been the subject of deep study among many writers especially by the English mathematician William Goldbloom Bloch, professor of mathematics at Wheaton College, in his book: The Unimaginable Mathematics of Borges' Library of Babel published by Oxford University Press.

In The Library of Babel Borges writes:

…each book contains four hundred ten pages, each page forty lines, each line approximately eighty black letters. There are also letters on the front cover of each book; these letters neither indicate nor prefigure what the pages inside will say.

Image credit: Rice+Lipka Architects.

Based in these numbers, Bloch computed that “each book consists of 410×40×80 = 1,312,000 ortho-graphic symbols; that is; we may consider a book as consisting of 1,312,000 slots to be filled with ortho-graphic symbols.”

Borges continues the description of the orthographic symbols used for all the books of this enormous library: “… all books, however different from one another they might be, consist of identical elements: the space, the period, the comma, and the twenty-two letters of the alphabet.” Hence, each book can at most use 25 different characters. Later, he adds: “In the Library, there are no two identical books.” 

So, ultimately, there are, says Bloch: about

10^1,834,097

books in the library.

William Bloch made this interesting computation for us when he asked himself: Could our universe possibly contain the Library? “… if the universe consisted of nothing but sand, it would hold at most 10⁹⁰ grains of sand”.

Borges' short story The Library of Babel is a good example of how extremely big numbers can fall beyond our comprehension, but nevertheless, they are not close to infinity. Well, no number, no matter how big it is, is ever near to reach infinity.

And then adds, “… suppose that each book is shrunk to the size of a proton, that is, shrunk to about 10^-15 meters across … then a cubic meter of the universe could hold

10¹⁵ × 10¹⁵ × 10¹⁵ = 10⁴⁵ 

books.”

How does this compare to the size of the universe? This is Bloch's answer to this question:

"It would take

10^1,834,013 

universes the size of ours to hold just the books of the Library.”

In other words,

The Library of Babel will extend far beyond millions and millions, and ... millions of parallel universes.

Image credit: Gerd Altmann via Pixabay.

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