Real Life has been happening fast and furious around here, so I’m reposting from my blog, with a few relevant thoughts about writing added.
Don’t worry: there will be no math.
People will keep mis-defining axioms. To boil the definitions I’ve been seeing down to the simplest possible statement: “An axiom is a statement which is self-evidently true.”
Axioms are more like rules of the game. For example, let’s look at some poker rules, because nobody confuses the rules for any type of poker with self-evident truths, right? And poker is an easy example for me, because I learned it sitting under the kitchen table and sneaking beers while the nominal adults in the family bet and bluffed.
(Caveat: this is not intended as a complete set of instructions for any given type of poker; I’m trying to keep it down to the minimum necessary to prove my point.)
Probably the simplest form of poker. Some of the rules are:
-Each player gets five cards
-Players may look at their cards
-There is a round of betting
-After the first betting round, each player may discard one to three cards face down and gets an equal number of cards, also face down, from the dealer.
-After all players have had a chance to draw, there is a second round of betting.
These are (some of) the axioms of Five-Card Draw. Note that none of them are self-evidently true; they’re just the rules of the game, and they can be changed to make variations on the game.
For instance, suppose you add a new axiom to those above:
-The four deuces (twos) are wild cards, which can be used as any card the holder needs to complete a hand (with one exception, which we don’t need to go into here).
This axiom isn’t “true” either, right? It’s just a new rule which makes for a slightly different game.
You can always add to the number of wild cards by changing that first axiom of Deuces Wild. My relatives, after a sufficient numbers of beers have been consumed, have been known to play Deuces, Fives, and Jacks Wild, which makes, as you might say, a wild game.
But suppose you change that first rule to “All cards are wild cards.”
Presto, the game collapses. Now you are free to declare that all your cards are aces and show a hand of Five of a Kind, Aces, which would be a winning hand – except that everybody ese has the exact same hand.
Not surprisingly, this is an axiom which is never used.
Making it interesting
Mathematicians (okay, I lied a little bit), just like poker players, like to work with sets of axioms that define an interesting set of possibilities. Sometimes these axioms appear to be obvious truths, like the rules of Euclidean geometry, which seem to be true statements about the world you can see. But pull back a bit, look at the whole world. It’s a sphere. And suddenly Euclid’s axioms don’t quite work. Parallel lines intersect. Your obvious truths… aren’t true any more.
And that’s why axioms are rules of the game, not self-evident truths.
Finally: relevance to writing
For writers of science fiction and fantasy: every time you build a world, you’re implicitly creating a set of axioms.
Science fiction writers: if you posit a world with no seasonal changes – where “season” is directly correlated with latitude – you’re implying the axiom “This world’s axis of rotation is perpendicular to its plane of rotation.”
Fantasy writers: A world where some people inherit the ability to do magic implies the axioms:
“The ability to do magic is passed down genetically.”
But if you throw in the axiom “A mage can do anything if he tries really, really hard” then what happens to your conflict? A tortured protagonist with serious inner conflicts may save the story, but probably won’t: the protagonist needs to face some problem that cannot be solved simply by the writer declaring it solved. I have a particular dislike for stories in which the final battle is resolved by pulling a mage’s unlimited power out of the writer’s hat. It’s a sure way to get the book walled and the author put on a no-read list.