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.”
Uh, no.
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.)
Five-Card Draw
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.
Deuces Wild
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.
Everything’s Wild
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:
“Magic exists.”
“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.
Axioms matter.
Mad Genius Club 
Yeah, axioms can bite you in the butt if you aren’t careful. Had to explore one set and realized that I needed to modify a lot of stuff. Luckily I hadn’t written myself into a hole and I am able to fix the axioms by adding in new stuff. Means more writing, means better plot points, means better world building.
“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.”
Yes! Unlimited anything isn’t interesting – limitations are more interesting than powers, and the creativity and effort to work around them are what make me want to find out if they pull it off!
I tend to think of Axioms as “building blocks” often in terms of logic and reason.
IE If “this” (Axiom A) and “this” (Axiom B) , then the following is true.
The “fun” is that not only do people think of them as “self-evident truths”, but they don’t even “think” of them when arguing positions.
That is, the Axioms are so deeply rooting in their thinking that they can’t accept that others don’t also hold those Axioms so they don’t even factor in their arguments.
In terms of writing, the writer has to think about the Axioms behind the “natural laws” and behind the created cultures.
One culture that I was created didn’t include “rights” with its cultural axioms but had the axiom of “responsibility” toward other classes and toward others with a class.
IE Neither Masters or Slaves had Rights, but Masters had Responsibilities toward their Slaves and Slaves had Responsibilities toward their Masters.
Exactly! Most people aren’t even aware of the axioms they rely on.
Like certain political arguments.
Recent political movement A takes for granted that people are fully convinced that B is wrong. In that context of ‘B is wrong’, fundamental to the credibility of their having a platform at all, they make arguments X, Y, and Z. But if you, say, follow X and Z to their logical horrible end, it fundamentally undermines the notion that B is wrong. *head desk*
It is easier to build a political consensus around a set of axioms and following them to their logical end than it is around whatever is convenient for this one guy to say at the time. Okay, if you have an apparatus of state terror run by this one guy, that approach gives a pretty good excuse for purging whatever opposition dares raise its head. But the terror approach doesn’t build the level of dedication that supports a government deep in its heart even in circumstances that harm one’s interests.
IE Neither Masters or Slaves had Rights, but Masters had Responsibilities toward their Slaves and Slaves had Responsibilities toward their Masters.
They had this in Negima, where the slave collar was a magic device that was initially introduced with the ability to induce some kind of pain or electric shock, but turned out later to have other capabilities, including protecting the slaves from (certain?) mistreatment, sexual abuse, death etc – which could be nullified by the slave surrendering that right to protection.
Axiom merely makes me think of a package of CAD tools I was cursed with sometimes having to install, ages ago, when I was a young co-op. ‘Twas a persnickety and time-consuming install that IT had to do for reasons dealing with both licensing and the fact that getting the install wrong could hose the CAD software already installed.
and if the person using magic doesn’t simply wish there problems away, it is axiomatic that magic has some rules and doesn’t ‘just happen’
This is actually very useful for the current WIP. Especially the ‘combining apparently contradictory magic systems’ part. (Five series decided they were in the same universe. I’m sure THEY thought it was hilarious. I’m not so sure.)
Next up: Analyse the axioms for each culture and see what underlying ‘rules’ are implicit that would explain the axioms of usage.
Thanks!
Oooh. That sounds like an interesting fanfic.
Original work so working out cannon.
Where it really gets interesting is when the mathematical axioms are perfectly clear, consistent, and reasonable, but the results following from them are incredible.
I found this with my work on logic. I kept coming up with results that flatly contradicted accepted wisdom and common sense. Retraining my intuition so I could understand and accept what the math said had to be the case, and what kind of sense it made was mindtwisting. (Although I naturally prefer it think of it as enlightening and mindstraightening…)
Reminds me of quantum physics.
In Moose Poker, if you declare Moose, you have to go out the cabin’s door, and call in a moose. If it comes, you win. (From an old humor column from Outdoor Life, by Ed Zern, IIRC, which I may not,)
C.S. Friedman had one fantasy series where the axiom of magic was that each magical use literally used up lifespan of the user—with one major exception that is a plot point. You have to have limitations on magical use, preferably within certain cultural accepted methods. For instance, good magic gotten through non-harmful methods and bad magic through harmful ones, or trickster characters having immense power but screwing up what they’re trying to do as often as they are successful. Or something that isn’t immediately obvious, but there are limits that the characters acknowledge.
In David Eddings’s Belgariad/Malloreon universe, there were two limitations on magic mentioned.
First, the more magic you cast, the more “personal” energy you lost. IE Cast too much magic and you can kill yourself.
Second, if you make a major change in the “environment, there will be major secondary actions that could cause major problems. One young magician caused a thunderstorm for what seemed to be good reasons but there would have been major changes in climate/weather caused by that actions. Fortunately, the other magicians were able to prevent such changes. Didn’t stop them from “chewing him out”. 😉
Ah, Garion. “Why me?” *chuckle*
Yah. Nothing EVER stopped ANYONE from chewing Garion out.
Not even the voice of Purpose in his head, so to speak.
Who, I am amused to note, enjoyed tweaking Belgarath’s nose as well.
And the Prophecy was at least poiite about it. Most of the time. Which put it head and shoulders above everyone else.
*chuckles!!!* It was quite the amusing character too!
Third, if you try to magic something out of existence, the magic rebounds on you and you die. 🙂
In the WIRevision, mages can only work in one specialized area. They are sorted into guilds, and woe betide someone trying to master two or more specialties. But at the same time, everyone assumes that somewhere else, there are or were mages capable of much greater, more generalized magics. But that may have been “back when” or “the people over the sea,” and so no one bothers trying it.
In the second book, the exception appears.
A spectacularly bad anime implementation of this was used in Maburaho:
1. Everyone is born with the ability to cast spells N times.
2. The higher your N, the higher your social status and employment prospects.
3. Casting your Nth spell kills you instantly.
For students at the top-flight magical high school the story was set in, N might be around 30,000. Naturally, you’d expect them to be trained to use their spell-count wisely, to ensure long, productive lives that benefited themselves and others. Instead, I’d say the average student cast 20-30 spells per day, guaranteeing that most would be dead before graduation. Axiomatically speaking, it was utter bollocks.
(Our Hero had only 8, but because anime, his superior bloodlines meant every girl in school wanted to bear his children; hijinks ensued)
The gold standard for getting it right is likely still the Lord Darcy stories.
-j
See also Brandon Sanderson’s “Laws of Magic” which are really three rules for writing that he uses. Let’s see… ah, https://coppermind.net/wiki/Sanderson%27s_Laws_of_Magic has a summary.
1. An author’s ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic.
2. Limitations > Power. The limitations of a magic system are more interesting than its capabilities. What the magic can’t do is more interesting than what it can.
3. Expand on what you have already, before you add something new.
Of course, none of this really applies in the old OLD stuff. There the axiom was, “Magic is mysterious and inscrutable, and no POV character can work up the slightest understanding of it.”
Merlin can do pretty much anything. So he doesn’t show up much. And much of the story is everyone else dealing with the fallout after he’s come and gone.
If you avoid deus ex machina, it can work pretty well. Tolkein thought so, anyway…
because nobody confuses the rules for any type of poker with self-evident truths, right?
Little known fact… the original draft of the Declaration of Independence listed “three of a kind beats two pair” right after “all men are created equal”.
There will be no math because this is . . . the aftermath!
Thank you ladies and gentlemen, I’ll be here all week. And next week.
Who’s got the carp?
I believe the obligatory response is: Aaaarrggghhhh.
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.
Any particular examples you’re thinking of?