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The Cube Root of Conquest (1948)
Rog Phillips

An evil dictator's plan to destroy and conquer the world is based on the work of one of his scientists, which allows travel into complex components of time. In order to do this, one is required to solve a cubic equation, which leads to the title of the story.

Here are some quotes from the story so you can get the flavor of its mathematical jargon:

(quoted from The Cube Root of Conquest)

Since there are only three dimensions of space, all things must be in our space. It is the time coordinates that determine whether we are aware of something or not....Mathematically, these other universes are expressed in co-oridnates that have the square root of a minus one as a coefficient. Also mathematically, these universes are imaginary, but not in the non-mathematical mythical sense. They are just as real as ours, but relatively imaginary or relatively non-existent.

All this has been known by others. They have also known that to make an imaginary value real it is only necessary to multiply it by the square root of a minus one. Then it becomes real. This fact became the entering wedge into the principal that enabled me to succeed in briding the abyss of right angle time travel.

We knew beforehand that it had to be a cubic equation. Each cubic equation has three roots for every value of the independent variable, which is in space. It also has three roots for every value of the time. Basically, that means that if any primal unit exists in our space, it exists in three fors, the positive, the negative and the neutral. These units are the positron, the negatron and the neutron...

I found this interesting since I do generally consider time to be a complex parameter in my mathematical physics research (it makes things much nicer from a purely mathematical, formal point of view!). However, I don't think there is really any way to make sense of what he says in the story about all of this...and it's besides the point anyway. All of this was just a way of convincing the reader that such travel between "the three universes" is possible so that you can follow with interest what happens to the evil dictator...and since it is not at all mathematical I won't give away the ending by telling you here what does happen to him.

Contributed by JG Day

I'm probably the 97th person to send this information to you, but the story Cube Root of Conquest by Rog Phillips (Roger P. Graham) was published in the October, 1948 issue of Amazing Stories.

No! Actually, Mr. Day, you were the first person to write to me about it. Since then, I have actually gotten hold of (a very poor) copy of the story, but I would be grateful for a cleaner copy if anyone is able to get me one!

Note that in its original printing, the title of the story had a mathematical misprint. As you probably know, x1/3 is the same as "the cube root of x" (because x1/3*x1/3*x1/3=x1/3+1/3+1/3=x). Another way to write "the cube root of x" is to put a little "3" in the crook of a radical (square root sign). In the title of this story, apparently confusing the two, they put a 1/3 in the crook of the radical! Also, I'd like to point out that the solution to a cubic equation is not necessarily called a "cube root", so the title is not actually well justified by the description of the cubic equation. Moreover, let me point out that here, once again, we see scientists dealing with what is apparently a polynomial equation in one variable. This is, I believe, much more common in fiction than in reality. More likely, whatever equation describes these situations is a partial differential equation. But then the author would not be able to refer to "the three roots" that every cubic equation has.

(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 The Cube Root of Conquest
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Imaginary by Isaac Asimov
  2. Aleph Sub One by Margaret St. Clair
  3. Lines of Longitude by Stephen Baxter
  4. Primary Inversion by Catherine Asaro
  5. Technical Error by Arthur C. Clarke
  6. An Episode of Flatland by Charles H. Hinton
  7. Left or Right by Martin Gardner
  8. The Fourth-Dimensional Demonstrator by Murray Leinster
  9. The Appendix and the Spectacles by Miles J. Breuer (M.D.)
  10. The Image in the Mirror by Dorothy Leigh Sayers
Ratings for The Cube Root of Conquest:
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:
3.5/5 (2 votes)

GenreScience Fiction,
MotifHigher/Lower Dimensions,
TopicGeometry/Topology/Trigonometry, Algebra/Arithmetic/Number Theory,
MediumShort Stories,

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(Maintained by Alex Kasman, College of Charleston)