Twenty-three stories deal with mathematical space, the fourth dimension, a cubic earth, two dimensional worlds, catastrophe theory, paradox, topology, and mathematical modeling
Rudolf von Bitter Rucker is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk genre. He is best known for his Ware Tetralogy, the first two of which won Philip K. Dick awards. Presently, Rudy Rucker edits the science fiction webzine Flurb.
"And so, gentlemen," concluded the man with dark glasses who insisted on calling himself Smith, "we have a problem. We know the formula is hidden under one of the squares of the chessboard. But we don't know which."
The twelve experts, assembled at short notice in the underground bunker, shifted uncomfortably and tried not to look at each other. Suddenly Griswold spoke up.
"Let me see if I have understood correctly," he said. "The late Professor claimed to have found a safe method for voyaging to other dimensions. He wrote it down just before his unfortunate demise, and we urgently need to find it."
Everyone nodded. The matter was evidently of vital importance; trillions of dollars had now been spent on extra-dimensional travel, but the results so far were, to say the least, unimpressive. Most of the luckless dimesionauts never returned. The few that did were inverted, reversed, shrunken, topologically deformed... not one had lived longer than a few minutes. But the country that first solved the puzzle would reap an unbelievable reward.
And now, the eccentric Professor Malakhov claimed to have found an answer. Unfortunately, he had suffered a fatal heart attack a few minutes later. He had just had time to communicate a few words to a colleague, and then it had all been over.
"So tell me again," continued Griswold, "exactly what it was he said."
"Well," replied Smith, "he didn't exactly say it. He was on a Skype connection."
A four-star general waved his hand impatiently.
"Makes no difference. Give us the message."
Smith looked down at the sheet of paper in front of him. "It's short. 'Chessboard. The biggest lie.' That's it."
"He hid it in his chessboard?" asked the general incredulously.
"Yes," said Smith. "There is a system of miniature secret drawers, one on each square."
"Well," said the general, "I suggest we search all the drawers. That will hardly take long."
"Ah," said Smith. "Unfortunately, the chessboard is rigged so that any attempt to open the wrong drawer will destroy the message. As will X-rays, neutron activation, and all other methods of trying to analyze the object's structure. We need to guess which square is correct, and right now we have one chance in 64 of doing that."
"What could he have meant by 'the biggest lie'?" asked a famous psychologist.
"We have of course thought about that a great deal," said Smith. "We think it may be a reference to a chess opening, perhaps one which involves an element of bluff. Our current best guess, based on information from a number of chess Grandmasters, is that the right square is b3."
"Wait," said Griswold. "Let me see the message myself."
Smith passed over the sheet of paper.
"If I am not mistaken," said Griswold, after studying it carefully, "Professor Malakhov was an algebraist?"
"That is correct," said Smith.
"Well," said Griswold, "in that case it is obvious. The message is under the black king."
Before anyone could stop him, he had reached over, picked it up, and pressed the concealed switch underneath. A little door opened, revealing a black micromemory card.
With a cry of relief, Smith picked it up and inserted it into the reader. It was immediately obvious that they had found the answer.
"But how did you know?" he asked Griswold incredulously.
Griswold looked smug.
"Malakhov was one of those people who never uses capital letters when typing," he said. "The message didn't say 'the biggest lie'. It said 'The biggest Lie' - evidently E₈, the largest exceptional Lie algebra. So the correct square was e8, the one the black king starts on."
Smith sighed. "Are all the stories in the book like this?" he asked faintly.
"No," said Griswold. "But some of them are nearly as bad."
I read this book years ago, and it has stayed with me. I was lucky enough to find a copy for 50p in a bookshop close to the University of Glasgow, and it's stayed with me for about twenty years. It's been part of my life. Although it has topics like Goedel's Theorem, fourth dimension, the liar paradox ("This sentence is false.") and even fun wordplays, you don't have to be a maths genius to read, understand and enjoy this book. You'll read accessible and intriguing fiction stories which will ignite your imagination, and your interest in maths. You'll absorb these topics better. Since the book has a series of short stories, you'll find, naturally, that some speak to you more than others. Isaac Asimov's story has stayed with me, in particular - I won't spoil it for you.
I was quite disappointed in this book. Being a graduate student in math, I was at first excited to find an anthology of mathematical stories. I had only read a few beforehand, including the classic 'Flatland', so finding 23 more stories collected together seemed right up my alley. Sadly, it seems the editor, Rudy Rucker, forsook quality and simply included any and all stories that had any semblance of mathematics. I only enjoyed about half the stories here, and appreciated the mathematical content in just about as many. I rated each story individually out of 5 stars and produced my average of 3/5. (Mild spoilers for some stories.)
‘1 to 999’ by Isaac Asimov A weak start to this anthology of math stories. This story is more about a mathematical play on words disguised as a clever riddle, which in reality was quite dull. I give it 2 stars.
‘Four Brands of Impossible’ by Norman Kagan A ridiculously sexist, racist, and all around terrible story. Any mention of women is to describe them in a sexual way, or to rant about them dating the wrong people. Norman peddles the same old falsehood about how only young mathematicians ever make meaningful work, all through an obnoxious character who paints pure mathematicians in an arrogant and pretentious light. There’s nothing much in the way of plot or story development, either. I give this 1 star.
‘Tangents’ by Greg Bear The first of many stories in this collection about slipping into a higher dimensional space. A gifted young boy finds a way to truly visualize and understand four dimensional space, and uses music to study it. A nice homage to Flatland. I give it 3.5 stars.
‘A New Golden Age’ by Rudy Rucker I didn’t enjoy this story, mostly due to my personal bias. This story revolves around turning mathematical theorems and proofs into sensory experiences to be enjoyed by anyone, and to, at least temporarily, produce complete understanding of the results. It ends with lay people not appreciating the experience of what mathematicians would call beautiful results, and instead enjoying the flawed works of a crackpot. This is where I disagree, I do not think this would happen in real life (or at least I just hope this). I like to think that clear understanding is the only thing coming in the way of realizing and appreciating the beauty of a mathematical result, and so this device would not fail to elicit a positive reaction from anyone if it can guarantee understanding. For this I can only give this story 2.5 stars.
‘The Professor and Colonel’ by Ruth Berman I was confused by this story, or rather the intentions of the writer in writing it. It seems to me like a slice of life take on a conversation between Professor Moriarity, renowned criminal and mathematician in the Sherlock Holmes universe, and his brother, a Colonel. Reading this story gave me the impression that Ruth was trying to explain Moriarty’s involvement in the criminal world, to support his brother and his own research. This paints him in a much gentler light, quite a contrast from what is found in Conan Doyle’s work, which threw me off. But it was still an enjoyable read. I give this story 3.5 stars.
‘The Maxwell Equations’ by Anatoly Dnieprov This story, which is about a conspiracy by mathematical Nazis, was a good use of mathematics in fiction. It didn’t raise the field on a romantic pedestal, but simply showed us the life of a professor working on hard math problems, until it takes a dramatic turn. It was quite enjoyable. I give it 4.5 stars.
‘Left or Right?’ by Martin Gardner Another fun and very story about slipping into a higher dimensional space, and returning possibly mirrored. I’ve seen this concept explored in a couple other stories, notably by Arthur C. Clarke in his story ‘Technical Error’. I give it 4 stars.
‘Immune Dreams’ by Ian Watson A story about a man, his irrational belief that his dreams are telling him he will get cancer, and a bunch of paragliding. The math mentioned is catastrophe theory, which the main character uses to convince himself of his imminent sickness. A pretty fun read. I give it 3.5 stars.
‘Forbidden Knowledge’ by Kathryn Cramer The worst piece of work in this anthology. I won’t even give it the benefit of the doubt by calling it a story. The only element of math used in the story is a throwaway quote from an abstract algebra textbook, with no real use to the plot, although I’m not sure if there even is one. It begins with a painfully terrible and sexist description of the female main character: “...but the Reformist Executive Committee had decreed that because of her superior IQ, 167 plus or minus three points for experimental error, and because of her good looks—although her hair was mousy brown and cut too short, she had a lovely, rounded bottom—the job was hers.” (p. 125) The rest of the story revolves around… palindromes? And then murder? Nothing makes sense or goes anywhere, and the writing is all around horrendous. Everyone in this room is now dumber for having read this. I give it 0 stars, and may God have mercy on our souls.
‘Gödel’s Doom’ by George Zebrowski Another take on Gödel’s results about consistency, ending in a surreal interpretation of what would happen to free will if a work-around is found. A fun read. I give the story 3.5 stars.
‘The Tale of Happiton’ by Douglas Hofstadter An interesting and witty satirical story about how we just don’t care about preventing our inevitable doom, even in the face of clearly explained probabilities. I give it 4 stars.
‘The Finagle Fiasco’ by Don Sakers An odd but weak story about mathematicians and philosophers weaponizing Murphy’s laws. I give it 2.5 stars.
‘Convergent Series’ by Larry Niven This was a pretty fun read, with the main character using math to trick a demon in a very clever way. I give it 4 stars.
‘The No-Sided Professor’ by Martin Gardner This is yet another fun story about the idea of slipping into a higher dimensional space, all while subtly introducing many more abstract concepts in geometry. I give it 4 stars.
‘Euclid Alone’ by William F. Orr Absolutely the best piece in this anthology, and arguably the only one that reads like the work of an actual professional author. Its quality of writing blew me away, the emotions it conveyed felt so real, and the character interactions made this story come to life. And it has actual proper mathematical content that is both pleasing to a mathematician and, I would think, would be understandable to a layperson. It discusses the ramifications of a proof about the inconsistency of Euclidean geometry, from a formal logical perspective, but interweaves it with a beautiful story about his relationship with an artist friend, all while touching on grief. This story alone justifies obtaining this book, even if only just to read this one. I give it 5 stars.
‘Love Comes to the Middleman’ by Marc Laidlaw A rather cute story about people living in miniature houses inside other houses that are themselves inside larger houses. A neighborhood community of giants and tiny people, going all the way up and down, their interactions, and discussions of their art world. I give this story 3.5 stars.
‘Miss Mouse and the Fourth Dimension’ by Robert Sheckley A math (or rather a math-inspired) story portraying your classic supernatural-connoisseur-turned-author trying to make profit from attempting to see in four dimensions. Nothing of much interest happens, nor was the read interesting in itself, so I give it 2.5 stars.
‘The Feeling of Power’ by Isaac Asimov Asimov’s work seems to be very hit-or-miss with me. I either love his work or I’m very confused as to how anyone would find it interesting. This story is in an odd middle ground. It’s about a futuristic society “rediscovering” basic arithmetic after computers and calculators have replaced any and all need for it. At first seen as an unbelievable skill, it quickly turns to military use. Probably a satire? Either way I can only give it 3 stars.
‘Cubeworld’ by Henry H. Gross A very strange story about turning our planet into a literal cube to prevent a worldwide cataclysm, as if that itself weren’t one. It explores interesting ideas about how society could be divided among the six faces of the Cubeworld, though if I wasn’t convinced this story was some sort of weird satire I would have a few criticizing words to say about them. I give it 3 stars.
‘Schematic Man’ by Frederik Pohl. A simple yet plain story about creating a program via copying all the information about one’s mind, but with strangely placed sexual excerpts throughout. Probably not so surprising considering this was published in Playboy. I give it 2.5 stars.
‘Time’s Rub’ by Gregory Benford This story caught me by surprise at the end, in the sense that I hated the first couple pages and loved the last ones. Perhaps I just don’t enjoy Gregory’s writing style: his unusual descriptions and metaphors using out-of-place overly complex language threw me off. But as I read on, the details of the plot grabbed my interest, and the ideas presented, those of achieving immortality through once again uploading one’s consciousness and comparing the happiness resulting from either choice, captivated me. Plus using a bit of game theory as a plot device was satisfying to read. I give this story 4 stars.
‘Message Found in a Copy of Flatland’ by Rudy Rucker This is an interesting take on the history and lore of ‘Flatland’ by Edwin A. Abbott, the classic mathematics story that should be in any math major’s reading list. This short story was a fun read and pretty well written. I give it 3.5 stars.
‘The Mathenauts’ by Norman Kagan Norman once again disappoints. He crams every fancy-sounding mathematical jargon he can think of in this story for no other reason than to include them, it seems. If you haven’t studied mathematics, this will all be meaningless and the story will do nothing for you; if you have studied mathematics, you will cringe at the overuse and misuse of all the terminology. This makes Norman sound like a failed math major (which itself seems to be a common theme in his stories) who wants desperately to sound smart and interesting, which makes for an uncomfortable read. Overall, outside of some interesting descriptions and short-lived ideas, the plot is vague, it reads more like a long poem, but not a good one. I give this story 1.5 stars.
Mathematical Science Fiction is an unusual genre and this is the only example I own. It has probably been ten or more years since I first read this book and it all seemed fairly new (i.e., I didn't remember much). Mathenauts contains 23 short stories, 14 of which I really enjoyed.
The stories, of which many plots are topologically oriented, vary from vaguely mathematical ("Convergent Series" by Larry Niven - 5.5 pages of something short, simple, to the point and amusing) to meandering character studies ("Four Brands of Impossible" by Norman Kagan, a 28 page tale that is more about a mathematician's personal and professional issues than about math) to far-reaching statements on mankind ("The Feeling of Power" by Isaac Asimov - 10 pages of thought-provoking post-apocalyptic allegory). There is something in this book for everyone, even those not enamoured with math (though they may have to skip around a bit if that is the case).
A wonderful collection of mathematical based science fiction. A few examples: "1 to 999" by Isaac Asimov "Tangents" by Greg Bear "Gödel's Doom" by George Zebrowski "Convergent Series" by Larry Niven "The Feeling of Power" by Isaac Asimov
Every couple of years I check this out of the library, not only to enjoy rereading it, but to help ensure it doesn't get discarded (it is no longer in print and hard to find).
Rucker proves to be as good an SF anthologist as he is an SF writer and emeritus professor of all sorts of cool stuff. Looking through the table of contents after I completed this anthology, I realized that I liked 19 out of the 23 stories, and even loved a few of them! I couldn't have imagined that (A) there would be 23 stories out there with mathematics as a central theme and (B) I would enjoy 19 of them. I had to throw something mathematical into this review, so that fraction works out to be 83% of the stories. And can I also indulge my inner Discordian by pointing out, once again, that there are 23 stories in total? I suspect that wasn't entirely a coincidence, given Rucker's various interests and proclivities. If you want your mind stimulated in unusual ways, but don't want to receive a grade at the end of the semester, this collection of stories is a good place to start.