RTAC #13: Strange Loops · 11:12am Apr 14th, 2017
There’s a common, though not dominant, fan theory floating around, that ponies use octal, rather than decimal.
It’s clever. It would make sense. That’s why it’s probably wrong. :)
So let me dig into canon sources and try to weasel out if they say anything about what ponies use for calculations and how do they measure their time when they aren’t using the deliberately ambiguous moons.
Numbers and Measurements
Let’s start with numbers themselves, because we can’t talk about calendar before we settle on what number base we’re talking about. Numbers come up extremely rarely on screen, following the general policy of avoiding written language, but they do appear, and I think I’ll just quote this shot from The Crystal Empire verbatim:
The square root of…
This statement is only correct, as the pony in the shot exclaims, in decimal: the square root of 546 is ~23.366642891095847, an irrational number. Were ponies to use base 8, “546” would be an octal number, and its decimal representation would be 348. The correct answer would be ~22.727375175375 octal, which is something like ~18.920887928424502 decimal.
1. Which is better than anything I can pull – my best feat of this kind is computing 232 in my head.
Twilight’s answer is 23.36664289109, which is close enough as to make no practical difference, and also shows she can calculate an approximation of a square root of a non-square number in her head to eleven digits,1 since there’s no practical reason I can think of she would remember this result. Notably, the digits ponies use are the same as ours in this case, even though usually, writing appears different enough to not be clearly readable.
To top it off, ponies do use the word “nine” a lot:
- In Newbie Dash, Soarin tells Dash “Check your nine” – which is, incidentally, a phrase that only makes sense if they use a 12-hour clock, because while he is saying that, he is approaching her from the left.
- In Suited for Success Rarity sings that “a stitch in time saves nine”
- In Scare Master Rainbow Dash utters “Ninety percent.”
- In Sleepless in Ponyville Sweetie Belle sings about “ninety-nine buckets of oats.”
- In Putting your Hoof Down Fluttershy offers “nine bits.”
- In It’s About Time Twilight asks Pinkie to recalibrate “the apertures on the nine-and-quarter catadioptric telescopes.”
- In Spike at your Service Spike counts aloud: “Six, seven, eight, nine, ten, eleven, twelve.”
This happens rather often, I could go on. In an octal number base, there’s no number nine. Moreover, in an octal number base, the decimal one hundred would not be round or otherwise special, so you have to assume some really significant translation shenanigans to cover for it. If you’re doing that, you might as well ignore everything else and try to produce an internally consistent Equestria that ignores canon entirely, you’ll get better results.
With that, we can be pretty sure ponies use decimal just like us, though it remains a Sandwich Problem why they do it.
While the focus of this post is on time, rather than space, it’s called a space-time continuum for a reason, so I should mention the measurement systems:
- Feet are mentioned as a measure of distance in Hearth’s Warming Eve, and May the Best Pet Win.
- Inches turn up in Griffon the Brush Off, Hearth’s Warming Eve, Fall Weather Friends, Family Appreciation Day, Inspiration Manifestation, Look Before You Sleep. It’s About Time contains a “nine-and-quarter” telescope, which is probably inches too.
- Miles are mentioned in Apple Family Reunion, The Gift of the Maud Pie, Hearth’s Warming Eve, Power Ponies, Spike at Your Service, A Friend in Deed…
I might have missed some, but I think I made my point. While the words denoting Imperial measurements turn up often, metric is apparently not unknown. Notably, in Griffon the Brush Off, Pinkie uses both metric and Imperial in the same sentence, and adds her own “smidgenmeters” for flavor. Metric occasionally comes up in comics.
In short, it’s exactly as silly as the current situation in the US. One notable case is Top Bolt, with its rather questionable statement of “He set the record for the fastest vertical acceleration rate! Five hundred feet in two seconds!” which I further discussed in the Points of Canon series post for that episode.
Sorry, there’s no sign of a “hoof” being used as a measure of distance.
Calendar
This has a lot of bearing on the series chronology theory, so take a look at that toy too. I also dealt with the moons exhaustively before. Now…
Ponies in primary canon mention and apparently use the following measures of time: Second, minute, hour, day, week, month, year, moon. While I could produce an exhaustive list, I believe it would be pointless, since this would take me all day and trivial searches through episode transcripts will turn up examples of all of them. We also have a “celestial era” mentioned in Testing, Testing 1-2-3 which we have no reasonable way to gauge at all because it is never mentioned anywhere else. Secondary materials further mention centuries. In the end, we know ponies have all those subdivisions in their calendar. Now we need to put them into a relation to each other and to any of our own temporal measurements, which is considerably more difficult. But we do have evidence:
- Spike timing Applejack and Rainbow Dash in Fall Weather Friends suggests a minute contains at least “22 seconds.”
- Timing Rainbow’s “ten seconds flat” in Friendship is Magic results in a time that’s pretty much exactly ten of our seconds, depending on where you start and finish. Pony seconds do not, therefore, deviate from ours by more than about 10%
- Applejack’s line in The Best Night Ever “First minute, first sale. Second… Fourth… Sixth… Sixtieth minute… no sales.” suggests an hour contains 60 minutes.
- In The Mane Attraction, Svengallop says “I want those things in twenty-four hours!” which makes precious little sense unless a day is 24 hours.
In short, there is little reason to think a day in Equestria is anything other than 24 hours, each of which contains 60 minutes, each of which contains 60 seconds.
It gets considerably more complicated further on up, though:
2. Notably, at different points in history, some human cultures used weeks of lengths other than 7, so it wouldn’t be too unusual for it to be shorter.
Ponies mention Monday, Tuesday, Wednesday, Thursday, Saturday and Sunday in primary canon, each of these names comes up at least once. Friday is mysteriously missing, but in Family Appreciation Day, Apple Bloom lets slip that Sunday immediately precedes a Monday. So a week is at least six days long, and its similarity to ours is clearly apparent.2
- In It’s About Time, Twilight presents us with a day planner that contains exactly 15 squares, arranged in a 5x3 grid. But since a week contains at least six days, it’s best to assume that we’re dealing with a seven-day week with two weekends, and weekends are so important that the planner includes a separate sheet for planning for those, for easier work/play separation. It still leaves an option that a month contains only three weeks. Either that, or we’re dealing with the effects of low cartoon resolution, the same thing that hides saddlebags from us in one shot and clearly shows them in the next, and then it doesn’t give us any information.
- In What about Discord Twilight and Spike refer to a three days her booksortcation takes as a “long weekend,” suggesting a normal weekend is two days long.
- In Friends Forever #32 we can see a radically normal looking (for us) calendar with 7-day weeks that start on Sundays, and the month is named June.
3. Post-publication addendum, a tidbit caught and contributed by Meta Four.
In Sisterhooves Social, Rarity cites the length of the week at seven days exactly, with six nights between them.3
So we can be satisfied that a week is seven days long and contains two weekend days. How long is a month? Are they equal or different?
- In Ticket Master, Spike reads aloud the invitation to the Grand Galloping Gala, which is to occur on the 21st of an unnamed month.
- In Daring Don’t, Rainbow counts the days to the next Daring Do book as “Three months and twenty six days” which sounds way too much like every month – or at least an average month – being 30 days long.
- In Equestria Games, Applejack says “Made me sit up proud like a cornstalk in August!” Apple family likewise mentions junebugs on multiple occasions, but we don’t know if this is a term related to the name of a month or not.
But that’s about it. The foundation of the notion of a 30 days long month is much shakier, but I think it’s still reasonable. We can, however, say nothing canonical about relative lengths of multiple months. How many months in a year?
- The song in Winter Wrap-up famously talks about “Three months of winter coolness.”
- This is further supported by Tanks for the Memories where Applejack says that “Tank’ll come back in a few months.” Winter is therefore invariably at least two months long.
That, unfortunately, is all the good evidence I have on hand. Enough references, time to theorize.
Theory
The above evidence is clear on those points:
- Equestrian day is measured in units very similar, if not outright identical to ours, in relative scale as well as base magnitude.
- Equestrian week is likewise very similar to the modern week in the US, though wiggle room exists regarding weekends and their positioning.
- The similarity continues on month and year scales, but the degree of the similarity remains uncertain.
4. This was seriously put forward to explain the ordering discrepancies in season 1 and 2 without anachronic episode ordering.
There is wiggle room if you need it, a lot of it, but the ideas that a season is one month long and a year is four seasons,4 and similar twisted calendars, are outside the reasonable with what we already have here.
5. Wherever those came from, cause they sure as hell didn’t evolve with that sun above them, with all that we know.
It would still be reasonable to assume that pony calendar is fundamentally saner than ours, if only for the reason that while our calendar was created to account for natural cycles, and has to handle irregularities resulting from that, pony calendar does not: Celestia moves the sun. While biological processes in plants5 would necessitate the existence of seasons, and dictate their lengths, they can adapt to slightly different lengths of seasons or years just as easily as they adapt to a change in climate. Celestia has wiggle room to make the calendar make sense, so it’s logical to assume she does.
And this kind of calendar is exactly what I have been assuming:
- 360 days a year, exactly, because Celestia said so.
- 12, even, 30-day long months, because the Civil Service likes things to be orderly when they can’t all be decimal.
- 24-hour day, because whatever the natural pony circadian cycle is, it’s close to that much.
- 60 minutes an hour, 60 seconds a minute.
- A 1000-hour long, stable moon that sets the basic rhythm.
That puts the Sandwich Problem front and center: there is no reason whatsoever for ponies to adopt these measurements that we can see.
But I have things to say about the Sandwich Problem, or Aporia wouldn’t exist. :)
As far as I can tell, the octal base system in fanon is entirely based on a friendship joke, enhanced slightly by some dodgy 'low cartoon resolution' shots of clocks here and there early on.
Units discussion still begs the question, 'what's a foot?' At least for ponies.
4495905
Strange, I don’t think I have heard the joke.
Good question! Two possible answers I can think of right now:
The perpendicular-linguistics answer: The word “foot” used for the length measurement has different etymology from the word “foot” used for the feet of dragons and occasionally animals with paws. Being homophones is an accident.
The historical-origin answer: A non-pony culture introduced the imperial measurements and they survived through custom. They had feet. Possible candidates would be jackals.
4495907
The version I've seen is in Numberography, but the short version is that "the highest number ponies could count up to with their hooves was four, eight if they had the help of a friend".
4495921
Pfft. You can count to 16 with just four hooves, and if you have eight to play with, you can go straight up to 256! :)
I'm still not entirely sure why octal is a fan theory. I personally went for a dozenal base system for my AU story, but in my numerous rewrites, I wrote it out by accident, so there's no mention of the ponies using a different number system at all.
My explanation for dozenal? I went on herd size. When I do the research, I keep seeing the factoid: "herd size varies between 7 and 30". So, I just decided the modal number was 12; herds were more likely to have twelve individuals, although other herd sizes existed.
4495929
That could be a neat explanation for the 24/60/60 day, if we can support that herds actually existed and define what they actually were. Which, at the current state of canon, would be somewhat problematic, there’s no sign of any kind of herds or their existence in the past.
Maybe soon, though.
4495926 By that theory, we ought to be operating on a base-35 or 36 system based on how many ways people can count using knuckle-position systems. It seems... excessive. But, like I said, the four-or-eight theory is a cheap joke, similar to the clover leaf metaphor for Trinitarian theology.
I kind of already assumed that ponies used real life systems of time and space measurement by default, but thank you for doing the leg work of actually proving most of it, and finding the hard limits of how far this can be pushed.
They'd use base 12 in all likelihood (given the number of moons in a year is more useful mathematically than the number of days between lunar phases: 7). We would too if it weren't for the fingers.
I believe 'Celestial Peace' (Testing, Testing) actually refers to just after Nightmare Moon, probably after they put some political spin on the event. So I consider it a similar concept to B.C./A.D. / B.C.E./C.E. . It also makes for an easier time putting down years on dates that sound nice. I believe the new season will be 1003 or 1004 using this logic.
Some theories just say that the 'show' is translating their numeric system to one that's familiar to us.
Make of that what you will.
My personal headcanon to stick 'em into base-10 is to say that they based it off of some pegaus mathematician's feathers or something. Or the sections from a unicorn's horn from a specific side. Or to really grasp at straws, using the number of limbs and their head, times two. With pegasi not counting their wings, because. Unless they do, and just omit a leg they're standing on while they're counting.
And I still have a story planned that is literally about the metric and imperial systems clashing, so that'll be fun. (I decided pegasi traditionally use imperial, while everyone else has moved to metric. It'll be great.)
4495954
Look at your left hand. Open the palm and look at the folds on each finger as one phalanx transitions into the next. By numbering them left to right, top to bottom, and using the tip of your thumb to mark them off, it becomes easy and natural to count in base 12 – having two hands, you can easily express a 2-digit base-12 number, and count to BB, i.e. you’d top out at 144 decimal.
It’s actually more convenient to count in base 12 than in base 10 using fingers. Using binary allows for an even better expression density, but is a bit more complicated…
4495958
I did mention that. :) I think the degree of translational non-transparency this would involve is so high that it’s cheaper to ignore everything and bin the rest of the canonical data.
There is some precedent for that. Aviation buffs like imperial because altimeters graded in feet provide a more convenient scale for practical atmospheric flight.
There's no digit 9, but "nine" can still be the word for the corresponding number. After all, English has a special word for 11. Even "ninety-nine" can be some special invention, like "eleventy-one" from The Hobbit. (But, as you said, that square root is correct only in the decimal system.)
4495965
I think you mean "leventy-leven".
4496045
Clever! But at the frequency we see 9 at, pretty horrifying.
4496053
That’s what I said? 123456789AB. If it’s base16, it’s 123456789ABCDEF…
4496070
I know, I'm just being silly.
Weeks are definitely 7 days long. See "Sisterhooves Social," Rarity's reaction to learning how long Sweetie Belle will be staying with her:
I read one interesting AU fic where the ponies have a base 12 number system. The logic there was that, pre-unification, the earth ponies and unicorns counted in base 4 (because four limbs) while the pegasi counted in base 6 (because six limbs), so the post-unification government went with the lowest common multiple.
More specifically, that specific winter was scheduled to be at least two months long, and probably no more than four. (Here let me put in another plug for my Variable-Length Equestrian Year theory...)
4495958 *Groan*. I've told myself for a while that of course Celestia would hate to reset the calendar from her sister's banishment, and the calendar would have to be counting from something else like the defeat of Discord, which would make a whole lot of sense as the start of the "Era of Peace"... but here it is right in the episode itself. The first "Celestial Year of Peace" starts with Nightmare Moon's banishment.
4496100
Nice catch!
4496103
My interpretation was that this was the first year since the founding of the United Kingdoms. A nice date to commemorate and not connected to Luna being banished at all…
4496123 Very good idea. Could also be any other event really close to Nightmare Moon's banishment.
4496070
Why? It's three squared, and both three and two are pretty important numbers. Three tribes, three months a season, two sisters, six elements of harmony (three times two) and probably many more occurrences.
It's also true that you can find numeric correspondence everywhere if you look hard enough, but I'm adamant that the nine is important for some mystical reason.
4496222
Because every mention of “ninety percent” would automatically turn into 112%, for example. Other similar consequences would require the reevaluation of every statement involving numbers.
Do you want to argue with Rainbow Dash about percent?!
4496227
Depends how you interpret ninety.
If we are talking about an octal system and we consider nine as the number following eight (so 11 in oct) then ninety may become 110, which corresponds to 72 in base 10.
If we consider ninety as 90 in the decimal base and hundred from the percent as 100 in the octal base then you are cheating.
Edit: Ignore my post, I had a brain fart there. It works only in case we use base 12
Devil's Advocate time.
Why? If you're counting on hooves, that'll give you hexadecimal or quartal. Wings complicate things (and suggest pterippi would use a different number system!); I'm pretty sure I've seen them "count" on feather-fingers…
Gryphons might use octal.
Didn't they mention someone being X apples tall, or is that only other gens?
4496053
http://www.bzarg.com/p/how-to-pronounce-hexadecimal/
http://evincarofautumn.blogspot.com/2011/09/how-to-pronounce-hexadecimal-numbers.html
There's a better proposal for pronouncing₁₆, involving the third digit being pages and the fourth being banks, but I perpetually have trouble finding it.
I'd actually missed the octal fan theory until after I'd already settled on octal for the Equestria in Friendship is Sufficiently Advanced - complete with counting system based on the joints of the forelegs - although I did remember the eight-hour clocks seen in some early episodes; the closest I'd come is reading Amras Felagund's fics with their duodecimal system, complete with douzaides, grossenturies, and meggrossia.
(And which choice I made mostly because my normal worldbuilding stomping ground is my "firm SF" setting, and as such, seeing worlds with no Watsonian connection to Earth-humans using Earth-human numerals, measurements, etc., tends to induce my best Sweetie-Belle-yells-OH-COME-ON! impersonation.)
As such, much like with squiggles that only become readable text when relevant and identical-looking books without spinal titles filling libraries, I stick with blaming Translation Convention, paraphrasing narrators, and other similar means of waving my hands real hard and inviting people to pay no attention to the alicorn behind the curtain.
4496618
In general, any non-decimal system would make sense, as long as a counting method appropriate for ponies can be devised in it, and see Cordial Nova right below your comment with that counting system based on joints.
The reason it would make sense is that as far as we know, we only use base-10 because of the ten fingers, and nobody came up with a better explanation as to why it was so widespread. Certain cultures had other systems, but in the end base-10 won in multiple cases.
And fingers are one of those things ponies conspicuously don’t have.
She would still need to compute it first. :)
Not as far as I remember. Apples were used by fans to estimate the pony distance scales, though…
4496619
The particular problem with the non-decimal numeric system and the extant corpus of canonical and quasi-canonical sources is that the translation convention becomes highly convoluted if you assume it also covers something so fundamental.
For example, Rainbow Dash’s iconic phrase “twenty percent cooler” makes no sense when octal is involved under translation convention: Users of octal would not use a cent equal to 100₁₀ – they would have 100₈ equal to 64₁₀. Producing one fifth of it results in the nonsensical 12.8₁₀, which is 14.631463146314₈… Dash would have to have used 25% or another fraction which wouldn’t require her to think in irrational numbers. In this particular case the specific fraction doesn’t matter. There will be cases where it does, and they are very likely to produce difficult to resolve contradictions.
By the time you’re waving your hands so hard, you might as well upgrade to wings and divorce the canon early. If the little things said don’t matter and the little things seen don’t matter, a policy that they don’t matter at all, and your Equestria just looks similar to whatever mess they made on screen this season will save you grief and hair. :)
4496880
You linked to me twice, rather than to the other comment.
Some say one cannot read in a dream…I've had adequate counterexamples, though.
Or in that massive library that is her erstwhile Canterlot home she has some pterippus-intended volumes of trigonometry-related calculations for navigation.
4496882
Ack! Fixed. 4496619 – sorry, I need to link this comment in a new comment again, otherwise you won’t get a notification…
Seeing as how even Wikipedia does not consider 546 a very interesting number, I find that rather doubtful. There might be a table for calculating square roots around that library. In fact, there probably is.
But memorizing it would be more work than learning to calculate it with a digit-by-digit method. :)
4496886
Are you accusing Twilight Sparkle of being practical?
4496887
In her own, Twilight-y way of being practical? Yes. Why, when you just need a single number, memorize a whole book of tables, when you can instead study a much more interesting equation that lets you derive the entire book in your head, and then prove that the tables contain numerous misprints? :)
4496880
My reasoning there does rather rely on the difference in translating exact and colloquial numbers.
(The example I had in mind at the time, from my own universe, was a district of bars, taverns, etc., in one city which, after coining the relevant duodecimal terminology, could be accurately translated the Street of Sur-Dodeciad Bars, but which beforehand I had always called the Street of Ten Thousand Bars despite a strictly literal translation being the Street of Twenty Thousand, Seven Hundred, and Thirty Six Bars. After all, it's not like the district in question has exactly 20,736 bars any more than it has exactly 10,000, but ten-thousand conveys approximately the same impression of great number to the English-speaking ear that sur-dodeciad does to the locals.
So on the same principle - and in the absence of a formal measurement system for coolness, never mind awesomeness and radicalness - I think it's fair to assume that "20 percent cooler" is a fair creates-proper-impression-on-the-English-speaking-ear translation of "12 peroctcen cooler", even if not a numerically exact gloss of the literal Equish.)
Where I'm really going to have to throw canon overboard in this area is going to be where the above-mentioned weekday names are concerned. Much as the image of Viking unicorns (who don't need to add additional horns to their helmets) amuses me mightily, I'm pretty sure I can't handwave or wingflap fast enough to justify Germanic-paganism-in-Equestria, however much I extrapolate from Mjölna...
The show staff clearly use units similar to our own in order to make the show easily accessible to their human, largely English-speaking audience (and because it's easier for them). It's true that MLP gets translated into lots of other languages, but the world is used to coping with English translations.
As an Englishman, I apologise for four hundred years of cultural export.
In my own fic, I used octal for precisely the opposite reason: I wanted to make the ponies more alien, to underline that they were a species living on their own planet in the same universe.
You skipped the [mis]use of "millennia", of course.