The mathematics of fantasy

As some of you may be aware, when I'm not reading or writing or talking about fantasy literature, or editing, or trying to convince Baby Smith that throwing things on the floor for me to pick up isn't the Best Game Ever — when I'm not doing any of that, I'm also a mathematician. And this was going to be a serious post about how maths and fantasy may seem poles apart, but in fact share a requirement for rigorous underlying logic and an understanding of how changing one variable affects another … or something like that. Because along the way, it turned into something altogether sillier.

It turned into this.

The Mathematical Rules that Govern All Fantasy Worlds: a Short Treatise by A.F.E. Smith

Theorem 1: Few > Many

In any conflict, the less numerous side will always defeat the more numerous. This is especially true if they are making a heroic last stand that's almost certain to end in death (see Theorem 2).

Corollary 1: If you're the leader of a well-trained, well-armed and fully manned army, beware. You'd be better off sending all your most experienced soldiers home and throwing half your equipment away.

Theorem 2: Pactual(event) = 1 – Ptheoretical(event)

The more improbable an event, the more likely it is to occur. This law was first discovered by Sir T. Pratchett (reference his invaluable paper on the subject, Guards! Guards!). Anything that's a vanishingly long shot but gives the hero a slim chance of survival will inevitably come through. In contrast, events that are almost certain to happen usually don't.

Corollary 2: If you're a protagonist faced with a really easy and foolproof way of achieving your goal, you need to make it harder for yourself in order to be sure of success.

Theorem 3: Duration of anything ∝ requirements of plot

Sometimes people may travel more quickly on foot than on horseback. Sometimes it may take a day to cover half a mile and sometimes dozens of miles may be walked in a day. And sometimes it may take a hero a week to recover from a wound that would have confined any normal person to bed for months. Basically, the value of any given unit of time is as malleable as plasticine in the sun.

Corollary 3: There's no point planning a journey based on sensible data, like how fast the average person walks/rides/airships. You'll reach your destination when it's convenient for the author and not before.

Theorem 4: Boy + girl ≡ ♥

If a male and a female are thrown together for long periods of time then they will inevitably fall in love. Particularly if they hate each other to start with.

Corollary 4: Be careful who you agree to go on a quest with. You WILL end up sleeping with them.

Theorem 5: {Good}∩{Evil} = ∅

People are either on the side of Good, or on the side of Evil. Regular mixed-up shades-of-grey humans don't come into it. In the Venn diagram of morality, there is no intersection between right and wrong.

Corollary 5: Entire non-human species can be similarly categorised. So if you're an orc with a keen sense of justice who prefers flower arranging to ripping people's heads off with your teeth, bad luck! No-one will ever know, because you'll be cut down as one of a faceless horde somewhere around Chapter 35.