The three murders that the unnamed detective must investigate occur in very different times and places. The first is the drowning death of an acolyte of Pythagoras in ancient Greece who has empirically worked out what we now know as Mersenne's laws for the frequency of a vibrating string. The second is the death of an unfortunate UVM student in 2008 who was participating in a demonstration with ropes of John Horton Conway's rational tangles. And the third is the death in 2075 involving an anti-gravity device utilized during a game of billiards that Isaac Asimov famously wrote about in his short story The Billiard Ball. Somehow, the investigator is able to travel to all of these times and places (even the one he acknowledges is fictional) and can interact with witnesses. In fact, Professor Priss from The Billiard Ball becomes a main character in the story and introduces the investigator to an important theorem that he proved (proves? will prove?) in 2031:

It mentions and utilizes serious works of scholarship by many people including Albert Einstein, Gerard t'Hooft, and (especially) Max Tegmark. However, it appears to me that the real star of the story is not any of the fictional characters or real researchers but instead a particular cellular automaton that it presents in a figure and in greater mathematical detail in the appendix. We are told that this one cellular automaton exhibits a combination of features (separately visible in the figure) that make it like the real universe and would explain why math is able to at least partly explain reality.

IMHO: If a framing story makes an abstract mathematical idea either more interesting or more understandable to a reader, then I consider that a good use of mathematical fiction. But, sometimes it simply makes a weak argument seem more compelling. As with many of the serious works that discuss the idea that the underlying reality of the universe is the iteration a deterministic, finite and discrete algorithm, I happily follow Bolognesi's argument when it shows that such objects can exhibit lots of interesting features reminiscent of things we see around us, but disagree when it seems to leap from this to the conclusion that reality is nothing but a cellular automaton. (I think these examples certainly open up the possibility that this is the case, and it is one we should consider.) When claims that we now have evidence that the universe is a discrete cellular automaton appear in a scholarly work of non-fiction, which does seem to happen relatively frequently, I consider it to be unreasonable and unacceptable by academic standards. Presumably, one can "get away" with more in a work of fiction like this, but I worry that the fictional aspects (such as the supposed theorem from the future which is stated as if it were a fact) will trick readers into being convinced by an argument that really is not entirely valid.

Some Notable Allusions/Connections: The title of this story is clearly a reference to an old joke about the unreasonable assumptions made by mathematicians. (Looking around, I see that sometimes the subject of the joke is a cow and the butt of the joke is a physicist. But, the basic idea is the same.) Also, presumably the drowning is a reference to the anecdote about Hippassus being drowned for discovering irrational numbers. Finally, although I have no reason to think the author had it in mind, since this work of fiction features a fictional character interacting with another character that he consider fictional, I will suggest that it might be interesting to utilize The Geometry of Narrative to analyze it.

This work of fiction appeared in the book Trick or Truth?: The Mysterious Connection Between Physics and Mathematics edited by Anthony Aguirre, Brendan Foster, and Zeeya Merali, published by Springer in 2016. Thanks to Vijay Fafat for suggesting that I add it to this database and to Allan Goldberg for pointing out that it is available as a free PDF from FQXi.org.