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Technical Error (1946)
Arthur C. Clarke
(click on names to see more mathematical fiction by the same author)

Contributed by Sarah-Marie Belcastro

During the last phases of construction, a huge supercooled superconducting generator is accidentally given a surge of current. At that moment, an engineer is at the center of its field and is somehow flipped about his central left-right plane. The bulk of the story is about the ramifications of this event. Includes discussion of handedness of molecules and a Flatland analogy.

Published in The Magazine of Science Fiction and Fantasy, Dec 1946.

The idea that a person who had been "flipped" left to right might have trouble surviving because of the chirality ("handedness") of organic molecules is clever, and I don't recall seeing it in any of the other similar stories that are out there. It should also be said that this story is very well crafted. However, from a mathematical point of view there is not much there. Mathematics is mentioned in several isolated instances, but the primary mathematical content arises in this passage where the physicist is trying to explain to the board of directors what went wrong in the generator and what needs to be done to fix it:

(quoted from Technical Error)

"Well, here is Dr. Hughes, gentlemen. He will -- ahem -- explain everything to you. I have asked him not to be too technical. You are at liberty to interrupt him if he ascends into the more rarefied statosphere of higher mathematics. Dr Hughes..."

Slowly, at first, and then more quickly as he gainted the confidence of his audience, the physicist began to tell his story. Nelson's diary drew a gasp of amazement from the Board, and the inverted coins proved fascinating curiosities. Hughes was glad to see that he had aroused the interest of his listeners. He took a deep breath and made the plunge he had been fearing.

"You have heard what has happened to Nelson, gentlement, but what I am going to tell you now is even more startling. I must ask you for your very clsoe attention."

He picked up a rectangular sheet of notepaper from the conference table, folded it along a diagonal and tore it along the fold.

"Here we have two right-angled triangles with equal sides. I lay them on the table -- so." He placed the paper triangles side by side on the table, with their hyptenuses touching, so that they formed a kite-shaped figure. "Now, as I have arranged them, each triangle is the mirror image of the other. You can imagine that the plane of the mirror is along the hypotneuse. This is the point I want you to notice. As long as I keep the triangles in the plane of the table, I can slide them around as much as I like, but I can never place one so that it exactly ocvers the other. Like a pair of gloves, they are not interchangeable although their dimensions are identical."

He paused to let that sink in. There were no comments, so he continued.

"Now, if I pick up one of the triangles, turn it over in the air, and put it down again, the two are no longer mirror images, but have become completely identical -- so." He suited the action ot the words. "This may seem very elementary; in fact it is so. But it teaches us one very important lesson. The triangles on the table were flat objects restricted to two dimensions. To turn one into its mirror image I had to lift it up and rotate it in the third dimension. Do you see what I'm driving at?"

He glanced around the table. One or two of the directors nodded slowly in dawning comprehension.

"Similarly, to change a solid, three-dimensional body, such as a man, into its analogue or mirror image, it must be rotated in a fourth dimension. I repeat -- a fourth dimension."

There was a strained silence. Someone coughted, but it was a nervous, not a skeptical cough.

"Four-dimensional geometry, as you know" -- he'd be surprised if they did -- "has been one of the major tools of mathematics since before the time of Einstein. But until now it has always been a mathematical fiction, having no real existence in the physical world. It now appears that the unheard-of currents, amounting to millions of amperes, which flowed momentarily in the windings of our generator must have produces a certain extention into four dimensions, for a fraction of a second and in a volume large enough to contain a man. I have been making some calculations and have been able to satisfy myself that a hyperspace about ten feet on a side was, in fact, generated: a matter of some ten thousand quartic -- not cubic! -- feet."

Contributed by Vijay Fafat

The story was later published under “Reversed Man”. There are two stories I know of that also discuss the problem of mirror-reversed people having trouble with digesting left-handed amino acids:

a. “The Other Side of Heart” by George Gamow, which is about a man who takes a trip to South America and undergoes a Mobius inversion while returning.

b. “Ujvya Sondecha Ganapati” (Story in Indian language, Marathi, by the famous Indian astrophysicist, Jayant Narlikar. The title translates as, “The [Hindu Elephant-God] Ganapati with a right-handed trunk”). Lord Ganapati / Ganesha is an Indian god with the body of a man and the head of an elephant. The story, as I recall it from long ago, involves the appearance of idols of the Indian god, Ganesha / Ganapati, with left-handed trunks and is about a mirror-reversed man who starts starving because of his inability to digest “regular” food.

Contributed by Chris Chiesa

I just wandered into [this page] and saw the remarks to the effect of there being only two other stories involving a character who had been "flipped" (in effect through a fourth physical dimension) so that his body could no longer digest Earthly foods due to chirality reversal.

I recall there being a third such story.

It was a Star Trek short story or novella -- alas, I can't remember whether it was Spock Must Die!, or something in one of the The New Voyages books, but it was definitely "original series" and appeared well before the "modern era" of hundreds or thousands of Star Trek books -- so, probably before the first Star Trek movie came out, so sometime between 1964 and 1980. As I recall the storyline, a duplicate of Spock is created, either through a Transporter accident or an experiment gone wrong -- but no one knows except Spock himself. The two Spocks conspire to keep the event a secret -- I don't remember why -- but someone pieces things together, such as the reversed Spock not appearing for meals and spending an unusual amount of time in his quarters where, it turns out, he has jury-rigged a synthesizer of reversed-chirality nutrients to keep himself alive. I don't know if you could find the identify of this story based on my skimpy rundown, but -- it's out there somewhere! If I ever had the book, I undoubtedly still do -- but to find it... :-(

Chris, it looks like you may be getting some assistance from a stranger who believes he can help:

Contributed by Stuart Herring

[note to editor: this is in response to Chris Chiesa's comment concerning the "Spock Must Die!" novel, rather than the "Technical Error" story by Clarke. I offer some extensions and corrections/clarifications.]

Spock Must Die! was the very first "Star Trek" novel; it was by James Blish, published in 1970. A (near-)duplicate of Spock is created, when a tachyon-based experimental Transporter beam is reflected instead of completing the transport. The duplicate's behavior is a bit off, and becomes more and more strange; eventually, it is deduced that he is a mirror-image version: laterally inverted, down to the atomic scale. (The crew notice the reversed Spock not appearing for meals and spending an unusual amount of time in his quarters where, it turns out, he has jury-rigged a synthesizer of reversed-chirality nutrients to keep himself alive.)

The discussion of reverse chirality biomolecules in fiction continues:

Contributed by Eric Weatherby


In your discussion of Arthur C. Clarke's short story "Technical Error" you said:

"The idea that a person who had been "flipped" left to right might have trouble surviving because of the chirality ("handedness") of organic molecules is clever, and I don't recall seeing it in any of the other similar stories that are out there."

While one example has already been suggested to you, I wish to point out another that may qualify. In Lewis Carroll's "Through the Looking Glass", the first chapter shows us Alice talking to a kitten about the world on the other side of the mirror, and she says, "How would you like to live in Looking-glass House, Kitty? I wonder if they'd give you milk in there? Perhaps Looking-glass milk isn't good to drink."

I have no way of knowing whether Mr. Carroll knew about molecular chirality and its biological implications, but the beginnings of such knowledge were available at the time.

Finally, in the process of checking my facts for this email, I have discovered that I am far "behind the curve" on investigating this subject: Wikipedia.

Eric Weatherby

As amazed as I am that there is a Wikipedia entry for this obscure topic, I'm afraid this discussion seems to be taking us far away from the main subject of this Website, which is mathematics in fiction. But, I am pleased to be able to point out that this earliest appearance of a fictional reference to the dangers of reverse chirality -- even if dubious IMHO -- is attributed to an author who was a professional mathematician.

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Works Similar to Technical Error
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Left or Right by Martin Gardner
  2. The Image in the Mirror by Dorothy Leigh Sayers
  3. The Plattner Story by Herbert George Wells
  4. Turnabout by Gordon R. Dickson
  5. An Episode of Flatland by Charles H. Hinton
  6. The Appendix and the Spectacles by Miles J. Breuer (M.D.)
  7. The Cube Root of Conquest by Rog Phillips
  8. The Next Dimension by Vladimir Karapetoff
  9. Message Found in a Copy of Flatland by Rudy Rucker
  10. And He Built a Crooked House by Robert A. Heinlein
Ratings for Technical Error:
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:
2.5/5 (4 votes)
Literary Quality:
4.2/5 (5 votes)

GenreScience Fiction,
MotifHigher/Lower Dimensions,
MediumShort Stories,

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