You know what would happen if you made a real Death Star? And how many humans do you need to grow in tubes to power a robot society like in the Matrix? Stories can function perfectly well without proper math. However, making the correct calculations can enrich stories a lot.
A story of bodies
Let’s start with an example from my own writing.
In my short story Hostages, and my (unpublished) novel Aperture in the same universe, a race of alien parasites breeds humans to use as hosts.
Initially, my idea was that the parasites would have roughly 3,000 worlds, and two breeding worlds where they bred humans. Humans would be processed and shipped out to be used as hosts when their brain matured, at twenty-five. Sounds reasonable, right? Well, numerically speaking, anyway.
Enter math. Let’s do some back-of-a-napkin calculations. The aliens don’t want an advanced society, to prevent uprisings. They don’t want to overstress the environment either. However, on an Earth-sized planet, even supported by advanced alien technology, that means you can’t have more than three billion people or so. With a processing age of twenty-five, that means you’d be able to ship around 100 million bodies per year, tops. And that’s assuming you could even get the logistics for that to work – you’d have to ship out over two-hundred thousand bodies a day.
Okay, interesting math, but so what? Well, aliens will want to switch to new hosts when they start to show wear and tear. For a human body that’s around fifty – let’s assume good gene tweaking and a clean environment. That’s twenty-five years of use, meaning you can support roughly as many alien parasites per year as you have humans. Oops, 3,000 alien worlds supported by 2 human breeding worlds isn’t going to work, then, at all.
It turns out, I needed many worlds to support the host-hunger of my alien population. So, that had to change, and it gave me the idea of introducing various different host species provided by large corporations that the aliens could choose from like we would choose our cars.
Death stars and Matrix robots
So, what if we start to apply math to some of our favorite movies?
First up, the Death Star. Well, just about everything about the Death Star is a mess. How is it powered? What material is it made from that makes it not collapse in on itself? Where does gravity come from? How much food has to be shipped in each day, and where does the waste heat go? Well, people have discussed all this, but have come to no satisfying conclusion.
If you look at the planet Coruscant — you know, the planet-sized city where the Emperor lives — that has some problems of its own, mostly with waste heat. This would apply to any city-worlds, in fact, like for example Ravnica from Magic: The Gathering.
Next up, the Matrix. The idea behind the movie is that AI robots have taken over Earth. During the AI-human war, the humans blocked out all sunlight to prevent the robots from getting enough solar power, and so the robots started using humans in tubes to power themselves. The idea is cool, but how many humans would you need?
Well, the answer is actually quite simple: the laws of entropy and thermodynamics means growing a human body and keeping it alive requires more energy than you’re going to ever harvest from it. Feeding humans the remains of other dead humans won’t help to balance out the equation. It’s a planet-sized perpetuum mobile, and it can’t work. Oops.
Does this matter?
The short of it: no, not really. The Matrix and Star Wars did pretty well despite the flawed science and math. You can pave over a lot with good writing and believable characters.
However, there are risks. You can pave over the math, as long as your story doesn’t hinge on it. Star Wars established very clearly that the Death Star was a very dangerous weapon and that it could be destroyed with a missile through a ventilation duct. So, the science was bad, but the rules were clear enough and not too obviously nonsensical.
Also, making obvious math errors can be really glaring for those who know what they’re talking about. The more glaring the error, the more readers you’re going to lose. Imagine writing a story where the protagonist from current day Earth is whisked away to a 15 billion year old star… while the universe is only 14 billion years old.
Contrast that to the Matrix 2. In the second Matrix movie — minor spoiler — it turns out that Neo has special powers outside of the Matrix. It is never really explained why this is. The third Matrix movie sort of pushes Neo onto the pedestal of being the new Christ and that’s it. Which is why it didn’t work. You can fudge, but not on rules that the plot hinges on. That will make it feel like a deus ex machina.
Mess up your math at your own peril. If your plot hinges on a certain thing, make sure the math and science are right, or make sure you explain the rules clearly.
And, you can use math and science when world-building to make your world both more believable, and far more interesting. Creative solutions make things better than a hand-wave, because the hand-wave is the lazy way out.