a list compiled by Alex Kasman (College of Charleston)

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Self-Reference ENGINE (2007)
Toh EnJoe

As of 2015, the work of fiction which made physicist Toh EnJoe a famous author in Japan is finally available in English translation. The separate pieces are not quite short stories, and the whole is not quite a novel, but together they are definitely a work of mathematical fiction, even if it is a very bizarre one, since math runs as a theme through much of the book. The relation between finite and infinite, in particular, seems to come up frequently, and the concept of Laplace's Demon is also discussed.

Certainly, the most mathematical portion is A to Z Theory, which nearly does stand alone as a short story. [In fact, it was published separately in Strange Horizons March 2013, where it can be read for free.) In this part of the book, twenty-six famous mathematicians (whose last names just happen to each begin with a different one of the twenty-six letters of the alphabet) at the same moment have a realization about a brilliant but previously unnoticed result involving the binomial theorem. They separately write their discoveries up in research papers that they all submit to the same journal. Believe me, the author knows how unlikely that sounds, as does the journal editor he creates. An even less believable explanation (involving Sherlock Holmes) is offered, but I do not think we are expected to think about its likelihood very seriously. In fact, I found it difficult to take any of the ideas being discussed seriously.

The entire premise of the book is that spacetime has been thoroughly (and either intentionally or unintentionally) disrupted by the actions of sentient computers (a.k.a corpora of knowledge). In the new universe that results, it is difficult for the inhabitants to understand anything, and the reader is in much the same boat. The cover of the book compares this work to those of Lem and Borges. However, it seemed to me that it is more like Richard Brautigan's novels in which alternate worlds are described poetically, but without the focus and clarity necessary to muster the big ideas that Lem and Borges are able to address. And, although some might describe the writings of those authors as "weird", Self-Reference ENGINE get far weirder. For example, consider the talking sock named Bobby who is a relatively important character.

In another very mathematical part of the book, Rita attempts to answer her grandfather's challenging question of whether there is another girl "almost surely like" herself. The answer she develops is like a proof. We are asked to imagine a space whose dimensions are equal to the number of molecules in the universe. This somehow led to a discussion of a line segment where a each person was represented as a point, and since there are (apparently, in Rita's universe) infinitely many people, the conclusion was that they had to be grouped together in such a way that everyone almost certainly had a doppelgänger. Certainly, the feeling of this discussion was reminiscent of a mathematical proof. However, I didn't understand what this had to do with a space of the specified dimensions, I didn't understand why we were talking about a finite line segment (if it was an infinite line, then the infinitely many people could have been spread out equally spaced along the line without any of the "bunching up"), and I don't see how the conclusion reached was reasonable in any case. (All I can see one concluding is that there is at least one limit point, but this hardly suggests that nearly everyone has a double.) So, even though this story did remind me of The Library of Babel, it was nowhere near as meaningful.

I am always open to being corrected. The author has a Ph.D. in physics and presumably knows quite a bit about real math. Perhaps I missed a very deep and interesting idea or two here. Perhaps the depth was lost in translation. If so, please let me know. However, in the end I was left with the impression that this surrealistic work of fiction plays with ideas, but doesn't have much to say about them.

Frequent site contributor Vijay Fafat had these remarks to make about the "A to Z Theory" portion of the book:

Contributed by Vijay Fafat

This beautifully philosophical fabulist story reminded me of Asimov’s fictional piece, “The Jokester”, where a grandmaster asks Multivac about the origins of jokes and from where they come, and in the end, reaches a surpising conclusion. The present story has echoes of the same type of questions: “Where do mathematical theorems originate? What is their relation to Reality?

The author starts off with a very hilarious proposition: 300 years ago, a group of 26 of the world’s foremost mathematicians almost simultaneously sent in manuscripts about a hitherto unknown theorem related to the Binomial Theorem. Thought to be a practical joke at first, or a hoax, the world was quickly convinced about the veracity of the “A to Z Theorem”, named after the initial letters of the 26 authors. Much discussion about its nature followed, till “The Event” occurred, where the fabric of the universe changed, rendering the theorem meaningless.

(quoted from Self-Reference ENGINE)

One night, all of a sudden, the theorem simply shattered into so many meaningless strings of characters. It was as if the fluctuations of numberless particles formed themselves by chance into letters and were scattered in the air.

From there, the discussion and the description unfold both philosophically and comically, including a bizzarely funny theory that the entire episode was the handiwork of one Professor Moriarty...

Is there a universe-spanning Intelligence which is seeding these theorems into the weave of our spacetime? Are time and history forking every time such theorems are updated or rendered meaningless? Is there a finite progression to mathematical discovery? You have to read the story to savor this - there is no point in summarizing and spoiling it.

Absolutely enjoyed this work!

More information about this work can be found at
(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 Self-Reference ENGINE
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. How to Live Safely in a Science Fictional Universe by Charles Yu
  2. The Girl with the Celestial Limb by Pauline Melville
  3. Spacetime Donuts by Rudy Rucker
  4. The Library of Babel by Jorge Luis Borges
  5. Red Zen by Jason Earls
  6. Borzag and the Numerical Apocalypse by Jason Earls
  7. Incomplete Proofs by John Chu
  8. Machines Like Me by Ian McEwan
  9. A Catastrophe Machine by Carter Scholz
  10. Gödel geht [Gödel's Exit] by Andreas Findig
Ratings for Self-Reference ENGINE:
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:
3/5 (1 votes)
Literary Quality:
3/5 (1 votes)

GenreScience Fiction,
MotifProving Theorems, Sherlock Holmes,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)