In Jorge Luis Borges’s 1939 essay The Total Library, we catch our first glimpse of the Library of Babel. Borges, like many writers and artists, kept revisiting favorite themes. The Total Library of 1939 is best considered a Library of Babel construction site. The foundation crews are busy excavating whatever esoteric material will support the library, and the future librarians are engaged in collecting and indexing the books that will fill the seemingly endless shelves of the Library of Babel.
In this same 1939 essay, Borges mentions that you will find valid proofs of Fermat’s Last Theorem in the vast combinatoric universe of the Total Library. In 1939, Fermat’s Last Theorem was a conjecture. Andrew Wiles found the first proof in 1995. Borges got lucky. Fermat’s Last Theorem turned out to be a theorem. And yes, Wiles’ 1995 proof and gazillions of alternate proofs are indeed somewhere in the Total Library. What would have happened if Fermat’s Last Theorem was invalid? For example, Thomas Hobbes and John Wallis engaged in a multi-decade 17th-century feud over squaring the circle. Squaring the circle is an ancient problem in Euclidean Geometry. The problem is simple to state. Construct a square with exactly the same area as a given circle using only the classic tools of an unmarked straightedge and compass. In perhaps the most erudite and steadfast display of cranky hubris in history, Hobbes put out one invalid circle squaring proof after another that Wallis gleefully eviscerated in that delightful 17th-century warring pamphlet style. Circle squaring is impossible. When Hobbes and Wallis were squabbling, the problem was still open; it wasn’t shown to be impossible until the 19th century, long after both men had died.
However, the question remains: Will Hobbesian-style circle quadrature proofs exist in the Total Library?
We will find many invalid Hobbesian quadrature proofs. We will also find all of Wallis’s commentaries that point out exactly where Hobbes screwed the geometric pooch in each one. We will also find every other crank-created circle quadrature and innumerable refutations thereof. Broadening our search, we will find this humble blog post. And you, dear reader, if you kindly comment, your comment will be in the Total Library, too. But, in the vast universe of Total Library gibberish, we won’t find a single valid circle-squaring proof. Mathematical impossibility is absolute. It even rules in imaginary realms. So, the Total Library is not quite total; it cannot contain what does not exist.
Analyze the Data not the Drivel 