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Battlefield Earth: A Saga of the Year 3000 (1982)
L. Ron Hubbard
(click on names to see more mathematical fiction by the same author)

In the year 3000, the human race has nearly been destroyed by the Psychlos, an evil alien species who dominate thousands of planets in many universes. Although they view the few remaining humans as little more than pests who continue to infest the planet that they have conquered, one human named “Jonnie” is educated by a corrupt Psychlo who intends to use him as part of an intricate smuggling scheme. Eventually, Jonnie is able to use the knowledge he gains to defeat the Psychlos and free humanity.

Of course, I had heard about this science fiction novel which is as famous for its controversial connections to the Church of Scientology which its author founded as for its literary content. (See, for example, this Wikipedia entry.) However, until I received an e-mail from Julie Willis at Galaxy Press, I was unaware that it was also an example of mathematical fiction. They kindly sent me a free copy of the book, which I have finally finished reading. So, let me run through some of the ways that math appears:

Near the beginning of the book, Jonnie is being educated by directly downloading information from disks into his brain. At first he is learning only how to read, but he picks a random disk just to see what is on it and learns that if all three sides of a triangle were equal then so were the angles. The funny thing is, because he had skipped ahead he knew this fact about triangles and angles even though he did not yet know what triangles and angles were or even what it meant for things to be equal.

There is quite a bit said about the fact that Psychlos (who have five claws on one paw and six on the other) use a base 11 numerical system. I'm not sure what would give Hubbard the idea that there's something particularly wonderful about base 10 or particularly bad about base 11, but it says things like:

(quoted from Battlefield Earth: A Saga of the Year 3000)

“For paper computation the best system is called the ‘decimal' system, based on ten…Psycholo mathematics are based on eleven; some people call the the ‘undenary' system. It's difficult so I won't try to teach you that….I can teach you the ‘decimal' system much more easily…Whenever they discover it on some planet they engrave the discoverer's name among the heroes…”

In my opinion, that's nonsense, but it also isn't terribly important to the plot.

Another mathematically interesting (but not terribly important) passage concerns the evolution of the Psychlo digits from pictographs, many related to mining:

(quoted from Battlefield Earth: A Saga of the Year 3000)

“Zero is an empty mouth; see the teeth? One is a claw; just one talon. Two is a being and a pick. Three is a being, a shovel and a rock. Four is a mine cart; see the four corners? Five is what we call the `off' paw, the one with five claws,…Ten is a lightning bolt; symbol of power, now just a slash. Eleven is two paws clasped; that represents contentment.”

But the important mathematical aspect of the book concerns the bizarre form of teleportation on which the whole Psychlo empire was based:

(quoted from Battlefield Earth: A Saga of the Year 3000)

Space was dependent only upon three coordinates. When one dictates a set of space coordinates one shifted space itself. Any entry or mass contained in that space thereupon shifted with that space shift.

It was precisely to protect this secret method that Psychlos carefully guarded all of their mathematical knowledge. Their mathematics had quite a reputation for being impossible to understand. As a non-Psychlo alien explains to Jonnie:

(quoted from Battlefield Earth: A Saga of the Year 3000)

“My dear fellow, every wizard brain in the universe for 302,000 years has tried to figure out Psychlo mathematics. It can't be done. Oh, it isn't their arithmetic. An eleven-numeral system is not too strange. There's a race that had twenty-three different numerals. It's their silly equations. Nothing ever balances. Texts? Anybody can pick up their texts. They're meaningless! Pure rubbish…”

On page 971 of this tome, Jonnie finally learns (from a Psychlo who had been exiled for the crime of believing in souls) that all Psychlo equations are encrypted. The encryption scheme is based on the association of an integer to each letter of the Psychlo alphabet and the names of the eleven gates at the Imperial Palace of Psychlo (“Betrayer's Gate”, “Devil's Gate,” “God's Gate”, “Infernal Gate”, etc.):

(quoted from Battlefield Earth: A Saga of the Year 3000)

He took a book, Force Equations off his shelf. “It doesn't matter which types of equations in Psychlo higher math. They're all the same. You mentioned ‘force equations' so we'll use those. No difference.”

With a dig of his claw, he opened the book to the point where all the equations were summarized and pointed to the top one. “Now you see this B? You might think it is a symbol for something in Psychlo mathematics. But there is no B that represents anything mathematical except `Betrayer's'.”

He pulled the first paper back. “So where that B occurs, we see that the letter B has number value of two. So we just have to add or subtract or whatever it says to do to B, the number two.

“When we get to the second stage of the equation, there is no letter but a Psychlo mathematician knows you must take the second letter of ‘Betrayer's' which is E and then look up the number value of E which is five and factor the second stage of the equation with five. Now you get the same equation to its third stage and a mathematician knows he has to factor it with the number value of T which is twenty. And so on.

“If the letter in the original equation were I, then we would use its number value and follow right on down with the number values of the letters for ‘Infernal'…

A few thoughts about this:

  • What a weird coincidence that the letters B, E, and T in the Psychlo alphabet are associated to the numbers 2, 5 and 20, their positions in the English alphabet (not to mention the fact that "Betrayer's" is an English word.)
  • If any intelligent alien ever found some Psychlo equations for things that they already knew (like the Pythagorean theorem or Schrödinger's equation), they would serve as a sort of Rosetta Stone and it probably would be pretty easy to figure out this code in less than 302,000 years.
  • As explained, the letter "B" can never be used in a Psychlo equation for anything other than "Betrayer's". Presumably, this is not true only for B but for all of their letters. Then, I wonder what they use for variables or named constants...

Keep in mind that there is a lot more to this book than math. (For example, there is some chemistry, lots of warfare, and Jonnie's clever plan to overthrow the Psychlos. And, if you read between the lines then it also expresses some of Hubbard's opinions about psychologists and governments.) As for the writing itself, it seems like very old-fashioned science fiction to me. Even though it was written in 1980, it reads like a cross between the pulp “sci-fi” of the early 20th century and the "space opera" SF from the 1950s and 1960s. If you are someone who loves that old stuff, that would be a great endorsement. But, not everyone does. So, based on your own tastes and the math-focused excerpts above, you can decide for yourself whether you'd like to read L. Ron Hubbard's “Battlefield Earth”.

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Works Similar to Battlefield Earth: A Saga of the Year 3000
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Dangerous Dimension by L. Ron Hubbard
  2. The Algebraist by Iain M. Banks
  3. The Mathematicians by Arthur Feldman
  4. Children of Time by Adrian Tchaikovsky
  5. Contact by Carl Sagan
  6. Old Faithful by Raymond Z. Gallun
  7. Diamond Dogs by Alastair Reynolds
  8. Q.E.D. by Bruce Stanley Burdick
  9. Dragon's Egg by Robert L. Forward
  10. Doctor Who: The Turing Test by Paul Leonard
Ratings for Battlefield Earth: A Saga of the Year 3000:
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 (1 votes)
Literary Quality:
3/5 (1 votes)

GenreScience Fiction,
MotifAliens, Religion,

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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)