Thread by @Epidiah

When the goblins of the salt wastes realized they stood in the path of a fellowship's quest, they sent sent two of their own out into the world to find 13 orcs to either save their community from the impending disaster, or to avenge it.

But why 13?

Let's find out.

https://twitter.com/Epidiah/status/1124040574712143872

You start with nothing, because that's what you're born with.

Zero is a sacred number to these gobs, and it's important to note that they consider it a number. It is the beginning and the end. But it's nothing between, and so we must move on.

So we start with zero and one, because one is something. It's the first something. As far as the goblins of the salt wastes are concerned, we're not counting yet. We're just acknowledging that there's nothing and there's something. 0 & 1.

1 and one is 2.

This is where counting begins. This is the very first time that 1 isn't everything—that's the terrifying implication of 2 and the awful power of "and one."

0 is nothing.
1 is something.
2 is counting.
2 and one is the first big number.

This has a different feel altogether from the other numbers. It is both the number prophesied by 2 and the method 2 was made from 1.

It is clear to the gobs that things can go on from here, just by and-one-ing each number. Something clever happens right after 2 and one, but before we get to that, it's important to understand the place this "and one" process has in the culture of the goblins of the salt wastes.

The goblin "and one" is not so alien to us. We ourselves often use it to make any large number feel more distinct and real.

This is why 1,001 Nights is always read aloud as "A Thousand AND ONE Nights" and never the perhaps more grammatically correct "A Thousand One Nights."

But I don't have to tell you this. We've all read Borges' This Craft of Verse and can recognize this "fanciful precision" for the poetry that it is.

However, it's possible that this has become old hat to us. We may have lost a bit of that magic.

We say a baker's dozen or a cloth yard rather than 12 and one or 36 and one. We hide our and-ones, tucked in closets only to be brought out when they're needed.

Not so for the goblins of the salt waste. They proudly display their and-ones.

And-one is both poetry and process for them. It is a sure fire way to always get you that bigger number, should you need it; but more than that, it's the very promise of that bigger number!

After 2 and one, which we can call 3, there of course comes 2 and one and one, or 3 and one, or 4. But this is not how they would count it. 2 and one is the first big number. After that, you start building to your next big number.

Maybe think of it this way:

0+1=1

1+1=2

2+1=3

3+(1)=4

3+(2)=5

3+(2+1)=6

3+3+(1)=7

And so forth.

This, again, is not so alien to us. We might count to ten and then start over, adding ten to each number as we go. We would do this ten times and then start over, this time adding a hundred to each number. And so forth.

And so you might expect these goblins to do the same, but you would be forgetting the poetry of "and one" and it's power to make even bigger numbers.

First they count to 3:
1
2
2&1

Then they count to 3+3=6:
2&1+1
2&1+2
2&1+2&1

Then they count to 3+3+3=9:
2&1+2&1+1
2&1+2&1+2
2&1+2&1+2&1

AND ONE more time, they count to 12.
2&1+2&1+2&1+1
2&1+2&1+2&1+2
2&1+2&1+2&1+2&1

This is the next big number: 12.

And this is the pattern. Count to 12 twelve and one times to get the next big number: 156. Count to 156, one hundred fifty-six and one times to get to 24,492. Then count…

…well, you get the picture.

So why 13?

Because and-one is both a precise and integral part of their arithmetic and it is a part of the poetry of their language.

12 is a big number. The second big number, actually. But you know what's bigger than 12?

Twelve and one.

Anyway, look for my game 13 Orcs coming to a theater near you.

It is Eppy's secret wish that some day a significance of general interest for the big numbers of the goblins of the salt wastes will be discovered so that it is worthy of inclusion in the Online Encyclopedia of Integer Sequences.

oeis.org/search?q=3%2C+…

Oh shit, this might be a thing.

Just recruited @emilycare to co-write this game with me.

It…

…it might be epic.

The sequence of goblin big numbers gets out of hand FAST!

3
12
156
24,492
599,882,556
359,859,081,592,975,692
1.2950 × 10^35
1.6770 × 10^70
2.8123 × 10^140
7.9090 × 10^280
6.2552 × 10^561
3.9127 × 10^1,123
1.5309 × 10^2,247
2.3438 × 10^4,494
And so on…

The goblin very big numbers advance just as fast, but are one ahead at all times.

The sequence of goblin big numbers gets out of hand FAST!

3 & 1
12 & 1
156 & 1
24,492 & 1
599,882,556 & 1
359,859,081,592,975,692 & 1
1.2950 × 10^35 & 1
1.6770 × 10^70 & 1
And so on…

Playing around on my 50g, I found that a series that sums up the reciprocals of the goblin big numbers converges to roughly 0.423117754402…

BUT a series that sums up the goblin VERY big numbers converges ON ONE-FUCKING-THIRD!!!!!!!!!!!

Alright, folks, I'm no mathematician, but I think I figured out why the sum of the reciprocals of the very big numbers converges on ⅓ and it's such a goblin reason!

Are you ready?

Each VERY big number is equal to a big number and one. In the vernacular:

V = B+1

Each big number is equal to the previous big number, counted out as many times as itself, and one more time. So Bₙ₊₁=Bₙ × (Bₙ + 1) or Bₙ₊₁=Bₙ²+Bₙ

I'm getting fancy with the subscripts and superscripts here.

Alright if Vₙ=Bₙ+1 then Bₙ=Vₙ-1, that's fairly straightforward.

Now substitute Bₙ=Vₙ-1 into Bₙ₊₁=Bₙ²+Bₙ to get Vₙ to Vₙ₊₁ without Bₙ. It'll start off looking a bit like this:

Vₙ₊₁=(Vₙ-1)²+Vₙ-1+1

(I'm so nervous I'm going to make a mistake here.)

Those 1s on the end bash each other into oblivion and we can multiply out the square at the beginning. So we end up with something like

Vₙ₊₁=Vₙ²-Vₙ+1

So we can start writing our infinite sum like this:

S = 1/V + 1/(V²-V+1) + 1/((V²-V+1)²+(V²-V+1)+1)+…

This is going to get unwieldy fast, and I don't have the goblin brain to handle it, but fortunately with just these first 3 elements we can see the pattern, after a little manipulation.

First, inspired by all the playing around on my HP 50g, I'm going to assume that:

S = 1/B

Or, in other words:

S = 1/(V-1)

Because our first Big number is 3 and our first Very big number is 3 and 1, or 4.

If S = 1/(V-1), then we can multiply S by V-1 to get 1.

When we do that to both sides of the S equation, we get something like this:

1 = (V-1)/V + (V-1)/(V²-V+1) + (V-1)/((V²-V+1)²+(V²-V+1)+1)+…

I know it looks ugly, but if we're clever, we can clamber beneath the salt wastes & lure our foes into tunnels only one adventurer wide.

Our first foe is 1 = (V-1)/V, which is a filthy lie, but a lie in which the truth is hiding. If we look at it in terms of big numbers instead of very big numbers, the lie looks like this:

1 = B/(B+1)

Which is a bit like four gobs trying to share three teeth.

If we let the next foe through the tunnel, we get:

1 = (V-1)/V + (V-1)/(V²-V+1)

To add (V-1)/V to (V-1)/(V²-V+1), we need a common denominator. The "easiest" way to get one, I think, is to multiply (V-1)/V by (V²-V+1)/(V²-V+1) and multiply (V-1)/(V²-V+1) by V/V.

That way both sides have V(V²-V+1) as a denominator and we have:

(V-1)(V²-V+1)+(V-1)V
------------------------
V(V²-V+1)

I fear my formatting is going to get real ugly here, but let's multiply those out. Time to get a scratch pad!

This is what our first two foes sum to:

(V³-3V²+V-1)/(V³-V²+V)

We're still pretending this equals 1 & it's still a lie, but V still equals B+1 so:

(V³-3V²+V-1)/(V³-V²+V)

can be rewritten as:

(B+1)³-3(B+1)²+B+1-1
-------------------------
(B+1)³-(B+1)²+B+1

I'm just going to let my calc do the next part, because, again, not a goblin.

We get:

B³+2B²+2B
----------------------
B³+2B²+2B+1

Now we've got 51 and 1 gobs trying to share 51 teeth.

This pattern continues on down the line. Every foe we let into the tunnel—I'm really mixing my metaphors here—increases the the numerator and the denominator by the same amount, which means the denominator is always 1 ahead.

No matter how many teeth we collect, we'll always have to share them among an equal amount of goblins AND ONE more!

Whatever integer we choose for our 1st big number, the fact that the very big numbers are always one more means summing up the reciprocals of the very big numbers approaches 1 over the initial big number.

I cannot tell you what this means for goblins, but delights me to no end.

Folks, it just occurred to me that 157 is both the third Very Big Goblin numer and 50 times π rounded to the nearest whole number, which is probably very good news for goblin engineering courses.

Setting the delightful mathematics aside, this game is shaping up to be pretty damn interesting to design. We're thinking about explicitly making it a two-parter.

Taking clear inspiration from Seven Samurai—and it's descendants, the original Magnificent Seven, Battle Beyond the Stars, Seven Samuroid, Three Amigos, etc.—the first part is a character creation game that's all about recruiting the 13 orcs & training montages for goblins.

The second part is all about the fellowship's assault on the goblins' home, where you find out if you recruited the right orcs and trained the goblins correctly.

Both parts will play very differently and you'll be able to play them independent of each other; but if you do play them together, the results of Part 1 will have a definite effect on how Part 2 (or Part 1 & 1) plays out.

I'm also personally rather excited because I'm going to finally hack some stuff from Minion Hunter, which I've been wanting to do FOR DECADES.

We played that game (and its expansion) obsessively back in the early 90s. Like, back-to-back games throughout the night, trying to see how far we could push it.

My copies are lost to the ages...

Oh good, it's almost 2 in the AM and I'm still thinking about orcs.

This has turned into the kind of morning where I almost made myself coffee just to get the energy to go out and have coffee.

I have accidentally made this thread as labyrinthine as the ruins of the ancient undersea kingdom now buried beneath the salt wastes where the goblins who inspired the thread make their home.

Apropos.

The Warm Tongue—so named because it tastes of citrus & chiles when spoken—is from a pact once forged with a sorcerer who no longer honors every oath he made, but there are some among the orcs & goblins with strength & patience enough to bend his will.

They speak it freely.

Good morning! More goblin math! Weren't you born under fortunate stars?

So for us non-gobs, 25 and 50 are useful and often significant numbers. They are, for example, typically anniversaries celebrated in a bigger fashion than the ones just before or just after.