In one of the less-reputable areas of Ricochet – you know, the areas your mother warns you about – a conversation went something like this… (Spoiler alert, this post gets nerdy so fast, all the other posts will threaten to take your lunch money just for reading the next sentence.)
Person 1: What races do you usually play in Dungeons & Dragons? (See? Told ya. Cough up that money.)
Me: Oh, half-elves, half-orcs, halflings.1
Person 2: Wait, that adds up to one-and-a-half.
Me: Well we can’t play third-elves, third-orcs, and thirdlings,2 as that would imply infinite ancestry.
Screech! That’s everyone hitting the brakes and asking, “say what?” So, for gits and figgles, let’s look deeper into that statement by going seriously mathematical. (Any lunch money left? Keep reading and you won’t.) Let’s go with elves, because going with orcs goes into weird, unpleasant places and not the Fifty Shades of Gandalf the Grey places.
Let’s take a human and an elf. Now they love each other very much, get married, and have a baby. Because humans are generally the baseline race of any fantasy world, we call their offspring a half-elf. This half-elf falls in love with a human, they get married, and have a child. Now, genetics doesn’t work with such precise ratios, but for the purposes of this exercise, we’ll say this child is one-quarter elf.
Our one-quarter elf then falls for an elf (and hopefully not the same family as his elf grandparent because awkward3), they have a child and this one is … okay since we’re sticking with precise ratios, we can calculate about five-eighths elf. Yes, we’re getting complicated. It’s going to get worse. Because this mixed breed falls for a human and their child is five-sixteenths elf. And this goes on, back and forth.
Since we’re following elf blood, the progression goes something like this:
1, 1/2, 1/4, 5/8, 5/16, 21/32, 21/64, 85/128, 85/256, etc., etc., and so forth.4
To demonstrate this in decimals, we can quantify it thusly …
1, 0.5, 0.25, 0.625, 0.3125, 0.65625, 0.328125, 0.666015625, 0.3330078135, etc., etc., and so forth.5
Note that we’re dancing around two decimal approximations here, that is 0.33333… and 0.6666… That is, 1/3 and 2/3, respectively. But because each ratio has a numerator that is an exponent of two, we never really get to those. Or, to go all Calculus on you guys, the limits of both as they approach infinity is 1/3 and 2/3. Thus, someone who is 1/3 elf requires infinite ancestry.
Great, CUD, you say, you just wasted all the time it took me to read this for a theoretical diatribe about your fantasy game bloodlines. I regret reading this, I regret thinking anything you write is worth it, and I regret joining Ricochet.6
“But wait!” I say. Don’t leave yet, as this goes beyond my narrow scope. We have to go back to the Epic of Gilgamesh, that ancient Babylonian work. Gilgamesh is described as being one-third god. What was an absurd little exercise for me was a major character description of Gilgamesh. By our calculations, this means the Babylonian writing this epic implies Gilgamesh had infinite ancestry.
“Whatever,” you might say. “Those rubes probably had no idea.” Actually, I would disagree. Given that Babylon had extensive architecture and were also avid astronomers, we can infer that they had rather extensive mathematical knowledge. Although decimals weren’t invented yet, they did have a strange, somewhat base-60 numbering system7 that sounds incredibly complicated, but in fact opens up a very large number of ratios for that mathematically inclined people. Many more ratios than our simple base-10 does.8 It would not be entirely unreasonable to assume that they knew very well what was being implied when describing Gilgamesh as one-third god.
It is believed by some that many of these ancient cultures believed in a world that repeated constant cycles. A base observation of the world would seem to back that up. The sun rises and sets. The seasons cycle through spring, summer, autumn, and winter. For archeologists studying ancient Babylon, this has proven a problem. They did keep documents, but they are never organized chronologically – there was perhaps no perceived need to assume the cycles did not change.
Such thinking may even have stultified invention and scientific thought some. If what you have now is what you had before and will have in the future, why seek what is new? If it is something we had before, we’ll have it again when the cycle comes. In fact, the first breakaway from this way of thinking is recorded in Genesis in the story of Abram.
We are introduced to Abram and Sarai by way of cycles. A predecessor marries, has children, lives a little longer and dies. This is repeated again and again until we are introduced to Abram and Sarai and we are told Sarai is barren.9 The cycle of this introduction is broken. The story begins. Abram is then commanded to go to the place G_d will show him. Uncertainty – something antithetical to the concept of cyclical existence – is not only introduced, but embraced as Abram goes forth. There is a definitive beginning and definitive end to this story. There is no cycle.
This idea spread through the embrace of Judeo-Christian ideas in the West and the world, which is why the idea of infinite ancestors sounds so foreign and unreal. There’s no way this could be as we know the universe has a beginning and an end.
And we got there discussing elves and orcs. You’re welcome.10
1Yes, halflings aren’t really a half-breed. The original D&D actually used Hobbits, which are a breed of Men in Middle-Earth Lore. However, the Tolkien family sent a little cease and desist action that way and thus “Halfling” was created as a separate race which looked suspiciously like Hobbits but didn’t have enough specifics to be sue-worthy.
2Still not a mixed-breed. It’s a joke. Work with me, people.
3Elves are commonly a fantasy race that’s long-lived. We’re talking centures, if not around a millenium or even immortal. There, that’s something you know.
4Writing fractions in text is not pretty.
5Writing lists of decimals in text is less pretty than that.
6Don’t regret joining Ricochet. It’s great here. If you’ve lasted this long you’ve only yourself to blame.
7It was actually more complicated than that. It had aspects of base-10 and base-60 together.
8Base-10 gives you 1/10, 2/10, and 5/10. You don’t even get a quarter out of this. Where’s your fancy metric system now, buddy?
9Genesis chapter 11.
10No refunds on your lunch money, by the way.