MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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The Lost Books of the Odyssey (2008)
Zachary Mason
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The introduction to this novel is a work of pseudo-scholarship, explaining how the chapters to follow were decoded by an NSA cryptographer with the help of the author. The intro contains references to a few real mathematicians, but also a beautiful piece of "fictional mathematics" in its description of the apparent impossibility of the initial encryption and the possible interpretations. (Contrary to what it says in the liner notes, Mason is not really a professor of paleomathematics...at least not yet. However, he is the winner of a Starcherone Prize for having written this clever work of fiction.)

Note added Dec 2010: It turns out that the Introduction and Appendix which contain the mathematical fiction components appeared in the first edition of the book, printed by Starcherone Books, but not in the second edition, printed by Farrar Straus Giroux. So, depending on which version of the book you obtain, you may or may not be able to see any fictional mathematics in it (although the author claims the entire story itself has mathematical structure). If you are not able to get the right version in print, note that these wonderful pieces of pseudo-scholarship can still be found online at http://replay.waybackmachine.org/20080704030502/http://the-lost-books.com/chapters.htm.

We're told in the appendix that the Lost Books are quite old:

(quoted from The Lost Books of the Odyssey)

The first recorded accession of the Lost Books was into the Emperor Marcus Aurelius's library. Like many educated Romans he had an exaggerated respect for Greek learning, and, with the all the resources of Empire at his disposal, was able to compile the most complete collection of classical Greek texts then in existence. The library's catalog gives an abstract of each book--the Lost Books is described as, ``A code of great complexity, purported to be the Odyssey turned in on itself. A lock with many keys or many locks with a single key.'' Though the catalog survives, the library itself eroded rapidly in the years following Aurelius's death and was completely dispersed by the time the Western Empire fell--the fate of his copy of the Lost Books is unknown.

Thereafter the book turned up every few centuries in libraries and private collections. In 631 A.D. a Bavarian abbot wrote to a friend in Rome about the acquisition of the Lost Books, though he complained that it was locked within a cipher and that after many, many evenings of dedicated study he got no more for his pains than a headache...

Nevertheless, Mason's NSA connection was able to determine by applying his modern techniques that the book appeared to have been encoded using fractal compression techniques. Using a clue from Raymond Lully, they are then able to "break the code" and most of the book consists of the decoded chapters themselves. The chapters of the "Lost Books" themselves are beautifully written and full of intentional confusion and anachronism. Most mathematical among them is the final chapter whose narrative line has the structure of a Möbius strip. (See also here and here.) But, since the main mathematical content is contained in the introduction, I will focus the rest of this review there.

The most mathematically fascinating part of the introduction is the suggestion that the compression algorithm used to encode the book appears to be impossibly powerful by today's standards, let alone what one might have known in 800BC:

(quoted from The Lost Books of the Odyssey)

The Lost Books is legible for the first time in centuries but some mysteries remain. Even though the technique for decrypting the Lost Books is understood, no-one has yet discovered how to do the corresponding encryption. (This is counter-intuitive but I am told that the techniques for encryption and decryption are not always the mirror-images one might expect.) Also, James tells me that the book's information density is absurdly high, almost impossibly so. More precisely, the encoded text of the Lost Books is not big enough (in information theoretic terms) to hold the chapters we have extracted from it. This anomaly has excited considerable debate and given rise to three interpretations...

The first "interpretation" is that the story had to have been composed itself in a way that allowed for greater compression, by repeated use of elements, words, plot devices or whatever. This would have put restrictions on how the story could have been composed, but would have produced a greater compression in the end than would initially seem possible for a book of that length. This is an interesting idea, though not a mind blowing one. (For instance, I already know from experience that I can affect the size of the pictures taken by my digital camera by composing it carefully and avoiding the fine details or frequently changing patterns that would not compress well.)

The second "interpretation" is a bit more interesting: that they have not decrypted the books at all, but rather have merely imposed structure on the noise. This would be a bit like the facilitated communication controversy (where the facilitators appear to have been actually creating the messages from the people they were supposed to be interpreting) or like an algorithm that appears to produce an interesting signal that turns out to have actually just been a consequence of numerical approximation.

But, my favorite is the last "interpretation". It is suggested that the book may be able to have been compressed so compactly because it actually arises naturally as a mathematical structure. For instance, although the decimal expansion of the number π is infinitely long and contains no recognizable patterns, we can compactly write down an algorithm which would produce those digits. The introduction even names a movement of philosophers (including Kurt Gödel) who believe in such "hidden messages":

(quoted from The Lost Books of the Odyssey)

The third interpretation, which it would be ungenerous to call fanciful, is from outside the academy. It is espoused by the Theosophists, a sort of New Age religious society. The basis for their view is in the writing of the minor nineteenth century classicist Cyrus Maurer, who published what was first a famous and then a famously fraudulent translation of the Lost Books. He wrote that Homer was neither a bard nor a bardic society but, rather, a mathematician. Maurer contended that Homer's works are a priori literature, in the sense that they can be generated by the repeated application of a few simple mathematical operators. According to this theory, The Lost Books of the Odyssey can be derived from mathematical first principles in the same way as, say, Fermat's Last Theorem.

The Theosophists have been trying to discover these literature-producing operators for most of the twentieth century, so far without any success, despite the fact that some of the participants in this seemingly marginal enterprise have been truly eminent--most notably, Kurt Gödel, of the famous Gödel's Incompleteness Theorem, worked with them for some three and a half years. They argue (in a monograph entitled ``Maurer and the Inevitable Literature--the Hieratic Theorems of the Homerid Sages,'' available through the Theosophical Society's press) that the high information density of the Lost Books proves that it is a product of pure analysis rather than mere human artifice.

This immediately reminds me of Carl Sagan's Contact in which a hidden message is found in the number π.

In addition to Gödel, the introduction briefly mentions Alan Turing as the subject of another coded message that Mason dealt with in preparation for the lost books.

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(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to The Lost Books of the Odyssey
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. PopCo by Scarlett Thomas
  2. The Rule of Four by Ian Caldwell / Dustin Thomason
  3. Mulligan Stew by Gilbert Sorrentino
  4. Rosencrantz & Guildenstern are Dead by Tom Stoppard
  5. Lord Byron's Novel: The Evening Land by John Crowley
  6. The Kingdom of Ohio by Matthew Flaming
  7. A Suitable Boy by Vikram Seth
  8. 36 Arguments for the Existence of God by Rebecca Goldstein
  9. Against the Day by Thomas Pynchon
  10. Cryptonomicon by Neal Stephenson
Ratings for The Lost Books of the Odyssey:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
2/5 (1 votes)
..
Literary Quality:
5/5 (1 votes)
.

Categories:
GenreHistorical Fiction, Adventure/Espionage,
MotifAcademia,
TopicComputers/Cryptography, Fictional Mathematics,
MediumNovels, Available Free Online,

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(Maintained by Alex Kasman, College of Charleston)