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Aleph Sub One (1948)
Margaret St. Clair

Contributed by Fred Galvin

This is a little known story by a well known author from the Golden Age of Science Fiction. The math content is high, and it's a good story, definitely belongs on your Mathematical Fiction page.

(quoted from Aleph Sub One)

From the Blurb: Seeking to improve her math via a robot calculator, future housewife Oona all but wipes out the world with a question!

For those who may not know, "Aleph" is the first letter of the Hebrew alphabet (a close relative of "a" and "alpha"). This was used as a mathematical symbol by Georg Cantor who needed a notation for the different "sizes" of infinity. Specifically, Aleph with a subscript of "zero" is the cardinality (or size) of the set of all whole numbers. As Cantor famously proved, other infinite sets may be "larger" than this in the sense that there is no one-to-one correspondence between the sets. For instance, the set of all fractions has the same size (again Aleph Sub Zero) as the whole numbers because they can be paired up in a surprising but sensible way. On the other hand, the set of all real numbers (decimal expansions) is larger because no matter how you may try to pair it up with the whole numbers, some of real numbers are left unpartnered. (This is the "diagonalization" argument.) So, we need other sizes of infinity, which Cantor denotes by increasing the subscript on the Aleph. Aleph sub one (for instance) is the next largest size of infinity (one size larger than Aleph sub zero). Now, if you're hearing this for the first time, you may be wondering about the relationship between Aleph Sub One and the previously mentioned "size of the set of real numbers". Good question...and it's not one I can adequately address in this location. By definition, Aleph Sub One cannot be larger than the cardinality of the reals. But, it could be smaller, or it could be equal. The assumption that the latter is true goes by the name "the continuum hypothesis", and I will summarize the status here only by saying that the question of which is true (if that question has any meaning) is not resolvable by standard set theory.

Anyway, in this short story by St. Clair, Oona experiments with Aleph Sub One using a machine that "visualizes" mathematics for the user, with disastrous consequences.

Originally published in Startling Stories, Vol. 16, No. 3, January, 1948. (Part of St. Clair's "Oona & Jick" series of humorous short stories about everyday life in the future.) Reprinted in the anthology "New Eves: Science Fiction About the Extraordinary Women of Today and Tomorrow", edited by Janrae Frank, Jean Stine, and Forrest J. Ackerman, Longmeadow Press, 1994.

Thanks to Fred Galvin for bringing this interesting story to my attention!

Contributed by Alex

I find it interesting that the author is described as being a feminist when the main character of this story is a dizzy woman whose inabilities with mathematics are just one symptom of her overall mental limitations. Did St. Clair feel that she had to write using the stereotypes of her day to get published? Or was she of the opinion that since there certainly are some women (as well as men or people of any category) who are less than impressive in their intellectual achievements, writing one more story about a woman like that was not in conflict with her political views about gender equality?

Anyway, mathematically, the story is interesting because the machine allows her to "see" things like why (a+b)2=a2+b2+2ab (this is easy to visualize in geometric terms) as well as other mathematical concepts that had eluded her before. This is perhaps enlightening from a mathematics education point of view. In terms of technology, however, the story is so dated as to be "quaint" at best and "laughable" more likely. (The supposed "first robot brain" of the story is so far removed from the computers of today that the idea -- also appearing in the story -- that we'd all be commuting to work by helicopter seems realistic in comparison.)

Definitely fun to read and says a lot about mathematics.

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Works Similar to Aleph Sub One
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Four Brands of Impossible by Norman Kagan
  2. The Cube Root of Conquest by Rog Phillips
  3. The Sinister Researches of C.P. Ransom by Homer C. Nearing Jr.
  4. Drunkard's Walk by Frederik Pohl
  5. Skylark of Valeron by E. E. Doc Smith
  6. The Living Equation by Nathan Schachner
  7. Scandal in the Fourth Dimension by Amelia Reynolds Long (as "A.R. Long")
  8. The Brink of Infinity by Stanley G. Weinbaum
  9. Flower Arrangement by Rosel George Brown
  10. The Higher Mathematics by Martin C. Wodehouse
Ratings for Aleph Sub One:
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:
4/5 (1 votes)
Literary Quality:
3/5 (1 votes)

GenreHumorous, Science Fiction,
TopicGeometry/Topology/Trigonometry, Infinity,
MediumShort Stories,

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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)