Once upon a time, ponies did not know how to count very far. Clover the Clever tells her two young fillies the story of how her mentor, Starswirl the Bearded, learned the secret of counting from the dragons.
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The joke is that Starswirl cant count... right?
7000827 Well, it's certainly a joke to Hroghaan.
Really something. :D
This was a funny story, and I love that it subverts the expectation that there is going to be some grand revelation of how number systems are supposed to work. But I was confused by " Eventually, he could count to numbers as high as 16,777,215" because it is expressed how we think numbers are supposed to work. It made me think I missed something. It would have been funnier if it was something silly and only slightly less absurd like that number expressed in eights.
SUCH MAGNIFICENT THIGHS!
7350294 Couldn't tell if you figured it out from the comment, but I thought I'd explain why I used such an apparently arbitrary number.
By using base 8 as my counting scheme, I had left myself with a bit of a dilemma. On the one hand, I could have presented Starswirl's highest number as simply, 99,999,999, which is 16,777,215, or 8^8 - 1, represented in base eight. But that would be misleading, as most readers would interpret it in base ten. On the other hand, the hand I chose, I could have represented the number in base ten.
There's also a hidden theme in this story of Equestria having a different cultural history from our own, including not just material culture and oral history, but language as well. There are moments in the story where I intentionally write ambiguously, because I wanted some things to be "lost in translation." This instance is one of those moments.
Not only is there confusion about the base being used, but at least for this universe, the ponies of Equestria group digits in myriads (10,000), so in their counting system, they would represent the number you see as 9999,9999 (Nine thousand nine hundred ninety nine myriad, etc.). Just as we begin repeating digit names after the first thousand, they repeat digit names after the first myriad. Thus, you can see that Starswirl only came up with a number for myriad, and stopped there, allowing him to count to just under a hundred million. Perhaps he named the next order later, or someone else did. I haven't written a story for that. I doubt it would be very interesting.
Very nice.
Fun With Numbers!
I really love stories about Starswirl's time, as well as the Hearth's Warming Eve pageant's time, and this story does both wonderfully!
I could talk about the worldbuilding or the character work here, but rather than gush about how this is "follow you instantly" good, I want to indulge in a weird digression for a moment. Because halfway through the first scene I saw the following:
… and went, "Huh." Then "Huh!" again. What a wealth of detail about historical social attitudes this manages to pack into a mere two words.
It's tiny details like that that make this great. It's how many beautiful tiny details there are that make this great. (Plus Filly Luna and Hroghaan are total scene-stealers.) There's clearly so much effort behind the scenes to get all the little things right, and it shows. Well done.
7450356 This is another one of those moments I was telling ponygrad about. I got the idea from German culture, actually, where the words for husband and wife are simply, "Mann" and "Frau," which just mean man and woman. I like the idea of the way language and culture interact, in a weak-Sapir-Whorf kind of way, around small differences like that.
I'm really happy that my little things I put in for my own enjoyment are being caught and enjoyed by others.
This is rather deliciously reminiscent of Kiplings' Just-So stories mixed with a generous sprinkle of Goldings' faux-fairytale, The Princess Bride. I'm a real fan of tales told in the oral tradition like this, especially with all the very slightly off-kilter little bits that forcibly remind the reader: this is not our culture.
Great worldbuilding, great little story, and the dragon is especially wonderful!
Adorable.
Wonderful. I love the way you took this to Ten and One.
This is criminally underrated. Have another upvote
Criminally, indeed.
Fantastic.
Wouldn't unicorns have managed 5 and 10 using their horns and Pegasus 6 and 12 using their wings?
Plus I've always though counting with your teeth might be a possibility as well you could even run your tongue over them to keep track as you were going.
I've been meaning to read this one for a while. Very glad that I finally did. A wonderful blend of mathematics, world-building, and cultural calcification. After all, if you can't count past eight, the impulse of most will be to adapt to that limitation and reason around it, not to overcome it. It takes a genius to look at the way things have always been and ask "Why?"
Of course, do that too often and you get brick-eating mortar. Bit of a double-edged sword there.
In any case, thank you for this.
A truly intriguing Wastonian explanation for the use of the decimal base in Equestrian numerals. Adding to Favorites.
I'm sure there's some explanation around it, but I would have approached the Princess asking about how the treasury is used rather than how it is stored. General wages for guards and staff could be below 8 each (per day), but contractor fees would surely be higher? How much did it cost to build the castle, for example? The only answer I can think of is something like "we paid the (>8, so innumerable) builders 4 bits/gold each, each day, until the job was done", but that system would be ripe for abuse.
I like pony-mathematics. When authors seek my advice about which base to use, which does not apply to this charming story, I recommend Sexagesimal (Base60). I even wrote a BlogPost about why ponies might use the best base Balanced Ternary. I also like Myriads and feel that Scores should get as much respect as Dozens. I also like Fortnights. I wrote a BlogPost in response to an Economist explaining how we can use Radix-Economy for making our denominations more efficient. I am also a TauIst.
Quite an enjoyable story you've written. Cultural history, reasoning for the mathematical system used, adventure and cuteness all in one. As Ianthe noted it is reminiscent of Rudyard Kipling's "Just So Stories."
7552519 Value is relative. Western culture has attempted to create unitary ways of standardizing value for so long, we've kind of forgotten the system that lies at the very root of it. A pony who works on the construction of a castle has a certain value in mind that could be met by object x, or object y. The pony who owns the land on which the castle is built also has a value in mind which could be object y, or object z. Obviously, object y is what they will settle on. For the owner pony, it needn't even matter how many of object y they have, as long as they have enough to cover the value of their castle, in this case, one, which they do have the ability to comprehend. Anypony who wants more simply wants too much.
7556102 I did consider briefly an alternating radix system for the way ponies count, but all told, most advanced counting systems don't crop up in native counting systems. Orally, counting systems are almost always decimal, if they offer specific numbers past three at all, and numeral systems are always either quinary, or some factor of decimal. Duodecimal crops up in measurement, because of how convenient it is for forming fractions, but the underlying system is very consistently decimal. The correlation to the number of fingers on our hands needn't be belabored, although is practically impossible to prove. I surmised ponies would likely have begun with counting their hooves in much the same way we theoretically began with counting our fingers, and added the device of a second pony being necessary to count higher to inject humor.
7560233
Western culture... and eastern culture, and middle eastern culture, and to a lesser extent most of the non-isolated pre-colonial American cultures. Discrete objects created for the sole purpose of trade (ie money) were created and used by most larger nations and cultures around the world for the last several thousand years. The only large nation I can find that was an exception is the Inca, but they don't appear to have had the concept of wealth at all.
So, one thing I don't get.
I realize that they don't doubt higher than 8 because they don't have names for those numbers, but why would the second pony need to be physically present to have access to 5-8? They know the numbers -- He demonstrated as much when counting with Rowan -- so what's stopping them from using them?
7560406 Fair enough, but even those are all human examples. Who's to say the inclination to conflate possession and quantity is universally innate? I can see in my minds eye a society that barters in perceived value, and not numerical value.
Who knows? Maybe they pay out Hearts and Arrows's weight in gold.
7564330 Star swirl was counting Hroghaan's fingers, just as if he were counting his and another pony's hooves. He never tried counting a third pony's hooves mostly because not enough ponies like him enough to hang around that long.
7567736
That works. You don't need to know the specific numbers to say one thing is as heavy as another, and being paid your weight in gold is something I've seen before.
7567736
Ok, but i still don't understand why there needed to physically be there.
Great story, and i liked it a lot, but it seems there is a lack of a certain part about the concept of zero.
Or am i missing something? do they count 1 to 10 or 0 to 9?
7576784 I don't really know whether I like the idea of Hroghaan teaching Starswirl about zero. He did only ask to be taught how to count past eight, and counting arbitrarily high doesn't actually require a concept of zero. The Romans and Hebrews got pretty darn far without it, as did the Babylonians. Plus, if I started to think too hard about counting concepts that a fully realized counting system needs, I'd need to represent negative numbers, fractions, decimals, imaginary numbers. I personally have no doubt dragons knew of these concepts when Starswirl encountered Hroghaan, but he never asked about them, and I'm sure the thought of him realizing he hadn't done so later on brought her a great deal amusement.
7578552
Fair enough. Though it would be an interesting read - "Star Swirl the bearded and the dreaded negative numbers".
Numbers and counting systems are weird...
Fortunately, the old English of the dialogue wasn't very much of a distraction, and the flow of the story certainly reads rather well as a mythological tale (even though it isn't in-verse). Of course, this being Star Swirl, he probably didn't do much of the teaching work himself. Clover probably learned the counting system from him, and its her efforts that really popularised counting above 8, as well as pioneering multiple mathematical fields to go with it. It was certainly an enjoyable story, in any event.
It's not too often I see Clover as being Celestia and Luna's mom. Every time someone does write it, I always have to ask myself if Twilight wanted to play Clover because she genuinely liked Clover as a historical figure, or if it was yet another form of her sucking up to Princess Celestia by playing her mother on-stage (that is, if it's general knowledge who Celestia and Luna's mother was). We've got bratty Celestia in this story too, which I always saw her as being when she was a filly.
I reviewed this story as part of Read It Later #61.
My review can be found here.
Loved this story, though that bit about 16,777,215 tripped me up; I tried to convert it to decimal, not realizing it was already in that base
7771706 Oh dear, that was the opposite of the intended effect! D:
7773259 It was the triple 7s that threw me off. I also forgot Starswirl was using bijective numeration, so it looked like a standard octal number
Full review here, but in brief: I found the world-building really interesting, and despite the fable's "'twas my ken" language being a bit much for me it was still a good read. Faved.