One of the most famous stories by Jorge Luis Borges is

**(**

*The Library of Babel***). This library contains all possible books. For this statement to make sense, we must specify the definition of a book. For Borges, each book is made of one million three hundred and twelve thousand characters, chosen among all the possible permutations of that length and built with a set of 25 basic characters (the space, 22 letters, and two punctuation marks).**

*La Biblioteca de Babel***, for the number of permutations of a certain number of symbols grows according to the factorial of their length. The factorial of a number N is obtained by multiplying together all the natural numbers from 1 to N:**

*The number of books in the Library is huge*
N!=1×2×3×...×N

The result of this operation grows disproportionately. Thus, 5! = 120;
10! = 3,628,800; 100!>9×10

^{157}. The number of books in the Library of Babel does not grow so quickly, because each book contains many repetitions of the symbols, which decreases the number of possibilities, but consider what will be the factorial of 1,312,000, if the factorial of 100 is a number with 157 digits.**. That set of books contains all the possible chains of that length, whether or not they make sense. But that means that it contains all the books that have ever been written; all that could ever be written; all translations of each book to all the existing or possible languages...**

*The number of books in the Library of Babel is huge, but it is not infinite*Jorge Luis Borges |

**. Their distribution in the Library is random, or at least the librarians think it is. It is true that one of the possible books (which we also don’t know where it is) must be**

*The problem is, we don’t know where each book is***; but it is also true that the Library must contain**

*the accurate catalog of the Library***. How can we know which one is accurate and which is false, if at any given time we have access to quite a small number of books?**

*a huge number of false catalogs***. But if you destroy one book, it is not a problem, for the Library contains millions of copies that differ from that book only in one character; several billion copies that just differ in two characters; and so on. All those copies can be considered copies of the starting book with one, two... errata.**

*Each book in the Library is a unique copy*
Borges didn't dream up what I’m going to say next, but

**; it contains your genome, kind reader; the genome of all human beings that have ever existed or could come into existence; and the genome of all living beings that have ever existed or could come into existence. How is this possible? Let’s think a little:***the Library of Babel also contains my genome*Poster of GATTACA,a film whose title is a DNA chain |

What is the relation of the number π, mentioned in the title, with all this? In another
post I mentioned that

*the digits of**π***. Actually, this has not been proven, but until now all the tests of randomness applied to the digits of π we know (currently 31 billion) have been met. Therefore a reasonable conjecture has been proposed, which states that the digits of π, in fact, probably meet all those conditions.***seem to fulfill all the conditions established by statistics to define what a random number is*
But then, it must happen that any sequence of the digits 0 to 9 that
comes to mind must be somewhere among the digits of π. For instance, the sequence 123 appears for the first time in position
1924 of the decimal digits of π (counted from the right
of the decimal point); 1234 appears at position 13,807; 12345 appears at
position 49,702; and so on.

Let us now consider that any finite sequence of letters (such as those
used to write the books in the Library of Babel) can be encoded using just the
ten digits. For instance, we could represent the space by 00; A by 01; B by 02;
and so on, including the two punctuation marks. A book in the Library could be
coded with 2,624,000 digits (two digits for each letter). And

*that number, however huge it is, will appear somewhere among the figures of***, if the conjecture mentioned is true. We probably won’t know where it is, but we also didn’t know how to find a specific book in the Library.***π*
The conclusion is
clear:

*the figures of***. And therefore, among the figures of π, we could find my coded genome; your genome, kind reader; the genome of all human beings that have ever existed or may come into being; and the genome of all living beings that have ever existed or may come into being. And since π has infinite digits, each of those genomes will appear repeatedly among the digits of π, not just once, but infinitely many times.***π contain the entire Library of Babel***The same post in Spanish**

**Thematic Thread on Mathematics: Previous Next**

**Manuel Alfonseca**

## No comments:

## Post a Comment