The Problem with Numbers in Fantasy

Ishana wrote an excellent post on her blog about how etymology has no place in a fantasy novel, and I tend to agree with her. Sure, it is possible to create new languages if you really put your mind to it – Tolkien pulled it off in his creation of Middle-Earth, and it does make Middle-Earth seem more real and alive than it would have been otherwise. For mere mortals like us however, the time and effort could be much better spent on character and plot development. It is also easy to screw it up; if handled wrongly, your efforts will only confuse the reader and the quality of your novel will suffer as a result.

Now, most people are probably aware of language differences, since it is not an uncommon phenomenon in our own world. Most people however, do not possess the same awareness when it comes to numbers, or at least, I rarely if ever heard anyone discuss this topic. This is due to the fact that the way we handle numbers seem to be near-universal (apart from the linguistic aspects obviously). When I write 10 or 1111 on a piece of paper for example, almost everyone on Earth will know what I mean despite any cultural or language differences we may have.

But what about in fantasy or sci-fi, when we first come into contact with new races of beings who are intelligent enough to come up with their own number systems? I’m not even talking about the complicated stuff, like how the symbols are different or how they might handle math differently. Let’s assume for the purposes of this article that these elements are fairly similar to what we are used to, although having a different math system would create all sorts of problems. I would like to stick to something more basic and concentrate on the concept of base numbers. We are so used to thinking in groups of 10 that we hardly even think about it anymore. Computer programmers will probably be more aware about this, since they also tend to think in binary instead of decimal numbers. If you are familiar with binary numbers, you probably have an idea how counting in a different base number works. So now, the numbers 10 and 1111 actually mean something else. The binary number 10 is equal to the decimal number 2 and the binary number 1111 is equal to the decimal number 15.

The reason we use 10 as the base number is most probably because we have 10 fingers (or digit in Latin), which is why it is so universal. Think about it: Latin, Indian-Arabic and Chinese all developed numbers based on 10 independently. You could argue that Latin actually uses a base of 5 in their numerical symbols, since they have a different symbol for 5, 10, 50, 100, 500 etc., but in their speech, they certainly also use 10 as their base number. Interestingly, I found that the Mayan uses 20 as their base number when I did some research on Google, presumably because humans have 20 fingers and toes combined. Watch this YouTube video to learn how it works, which also provides a nice introduction of how counting in a different base number actually works.

So back to the topic at hand: what does all this have to do with a fantasy or sci-fi novel? Now remember that we use the number 10 as the base number because we have 10 fingers. Now, we often come across other races that have a different number of fingers than we do (For that matter, take the Simpsons. They would have their own number system with 8 as their base number!). So let’s imagine we have this hypothetical story.

We have a hero – let’s just call him Brandon for now – who is fighting against the evil legions of the Order of the Bloody Axe (OotBA) in the kingdom of Tarana. He has been able to amass 20000 warriors, but the OotBA possess a 50000 strong army. To have a fighting chance, Brandon goes in search of new allies. On his journey, he comes across this previously unknown underground race called the Morg’Hai with 3 fingers on each hand. It turns out that they have their own reasons to oppose the OotBA, so they decide to join forces. Brandon informs the Morg’Hai of the number of troops on each side (20000 for him, and 50000 for the enemy). The Morg’Hai informs Brandon in turn that they have 50000 soldiers. Upon hearing this, both Brandon and the Morg’Hai are ecstatic. With the advantage in sheer numbers, they should be able to defeat the OotBA quite handily.

Alas! Both Brandon and the Morg’Hai failed to acknowledge the fact that they are using different base numbers when they are discussing the number of warriors. The Morg’Hai actually use 6 as their base number which again corresponds with the number of fingers they have. Brandon mistakenly believes that the Morg’Hai have 50000 warriors! In reality, their army is much smaller than that. How much smaller? Let’s calculate:

Step 1) The number 10000 using a base-6 system is equal to: 6 x 6 x 6 x 6 = 1296

Step 2) 50000 is then equal  to: 1296 x 5 = 6480

Use this handy website to recalculate numbers based on different base numbers.

So instead of the 70000 warriors Brandon has in mind, they only have 26480 soldiers combined, far short from the number of soldiers the OotBA possesses. He goes into battle against the OotBA thinking he will liberate Tarana from their evil, but instead his army will be massacred, and the land will be overrun by the evil order. A thousand years of misery and suffering descend upon Tarana, all because of a stupid but crucial misunderstanding.

To summarize, this is what Brandon and the Morg’Hai are thinking of during their discussions:

I was going to mention what a bad idea it is to strive for 100% realism, but come to think of it, this might actually make for a very amusing short story. I already have the outline as it is. 🙂 But all joking aside, I think you can imagine what kind of problems you can encounter, and we haven’t even touched upon the subject of having different math systems yet! So unless you are willing to spend hours and hours researching and fine-tuning stuff like languages and number systems, I say it is better spend your time working on your writing skills.


Filed under Musings, Stories

2 responses to “The Problem with Numbers in Fantasy

  1. Ishana

    Hahaha, brilliant! I always wondered about the math aspect, never so much the base number aspect. Which is funny, since I work in a computer-related field and have taken several courses on programming.

    That sounds like a fascinating short story, too!

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