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Counting in the wrong language (bbc.com)
64 points by respinal 18 days ago | hide | past | web | favorite | 119 comments

I thank the French for the metric system. But their numbers between 70 and 100 are bonkers.

70 is pronunced "60 10". 71 is "60 11". And so on until 80, which is pronounced, obviously, "4 20". 81 is "4 20 1". It goes up to 90, which is "4 20 10". 91 is "4 20 11". The craziness continues until 100, which is, thankfully, a different word ("cent", instead of "4 20 20", or, dear lord, "60 40"). But in 170 it all comes back.

I think the French-speaking parts of Belgium, Switzerland and Canada did the right thing when they replaced all that complexity by dedicated words for 70, 80 and 90.

Danish has a similar madness going on.

66 is "six and three twenties" 77 is "seven and half four twenties"

I've been told that Danish accountants use Swedish or Norwegian numbers to avoid mistakes.


66 is seks-og-tres, i.e. seks (6) og (and/+) tres (60). The latter is technically "tresindstyve" (which is similar to the French, 3x20), but I can guarantee you that the number of people who actually know and care about that is infinitesimal. Additionally, "tres" is not really a word that can be mistaken for another number word. What usually screws people over is pronunciation and thus "tredive" vs "tretten" which sound shockingly similar in Danish.

(This happens a lot in Danish. It's incredibly sloppy on pronunciation and people somehow mostly still understand each other.)

EDIT: I had to think about it for a bit, but the situation for 77 is actually equivalent. No speaker of Danish actually thinks about "halvfjerds" as a compound number -- it just "70". I suspect it's actually very similar for French speakers, but their hyphens do make it harder to just lump the thing into a single concept/number :).

Canada uses the same numbers as France. Only Belgium and Switzerland use other words for 70 and 90, and just a few parts of French-speaking Switzerland use huitante for 80, but most say quatre-vingt like in France.

That's funny. I learned French from a Belgian woman and I called 80 "octante" until I was formally taught French and switched to quatre-vingt to avoid sounding like a hick.

Did I somehow come up with "octante"? Is it not used in Belgium, or anywhere else? It's true that it sounds a lot more Greek (my native language) than "huitante".

Octante was taught for a while in France at the beginning of the 20th century, but it never really caught on. Old people in Brittany used to use it sometimes as well, but it has completely disappeared everywhere now. It does sound nicer and more natural to me than huitante.

Many French people believe that it is used in Belgium and Switzerland though, for some reason, but as far as I know that's not true (I live in Belgium, although not in a French speaking region).

Thanks. At least I know I didn't imagine it.

I make a disservice to Pascale, the first lady who taught me French, and who was, herself French, by saying it was a Belgian woman who taught me French. The Belgian lady, Catherine, taught me _most_ of my French but I first started speaking French with Pascale.

Which is to say, it's possible I learned "octante" from Pascale, although she was far from old enough to have learned it in the early 20th century.

So I'm guessing "octante" is still used in some French-speaking places, although not that widely.

And I'll probably sound rather quaint if I use it myself :)

[For the record, I'm Greek but I learned French very early on because my dad had cousins in the Greek diplomatic corps and he wanted me to get a job there and he thought French is the language of diplomacy. I was not interested in that, of course. But at least, thanks to my dad's silly ambitions, I grew up practically billingual.]

Yup can concur it is like that in Canada. I never understood it. The 10's are weird two. Onze, douze, treize, quatorze, quinze and seize for 11-16(sorry the spelling's likely wrong.) Then dix-sept, dix-huit, dix-neuf(10 7, 10 8 10 9) for 17-19. Then the 20's and up just the 10's column number style.

French speaking Canadian, I still say soixante-dix, quatre-vingt, and quatre-vingt-dix.

Wait, is it quatre-vingt or quatre-vingts? Is there a context that would distinguish the pronunciation of those two?

Quatre-vingts, quatre-vingt-un, quatre-vingt-deux... quatre-vingt mille, quatre-vingts millions. This doesn't affect pronounciation in general, because this s is silent... except in the context of liaisons, such that you would say "quatre-vingts (z')avions" and not "quatre-vingt (t')avions", although in colloquial speech, nobody cares. In written form, I expect many of my fellow French native speakers to do the mistake or at least be uncertain. We mostly write it "80" anyway.

Spelling depends on various things. If it's followed by another number, then its singular: quatre-vingt-trois. Otherwise, it's plural, quatre-vingts. Unless it's an ordinal / noun, J'habite au quatre-vingt rue de la Paix.

Pronunciation is the same, unless there is a liaison: elle a quatre-vingts ans = there will be a 'z' sound between vingts and ans.

FYI, I'm a native speaker and I had to look the spelling part up to be sure. There are other rules with other exceptions for cent, mille, million, milliard.

Interestingly “Four score and seven years ago” is "4 20 7" meaning 87.

Yep, that'd be the 87 years from 1776 (Declaration of Independence) to 1863 when the speech was given.

You stopped short of the worst of them! e.g. 97 is assembled from 4 parts. Quatre-vingt-dix-sept (4 20 10 7).

Only 70 and 90. 80 is still 4-20. In French-speaking Belgium, anyways.

Does 80 in France have any of the 420 weed connotations?

Of course not.

A simpler problem is months. The English system uses arbitrary names, while Japanese/Chinese/Korean just call them "1-month", "2-month", etc.

Even though I grew up with it, I find the English system impenetrable. Quick, what's 3 months before November? I have to count it out every time. (In mod 12, -3 is the same as +9, so I just count forward 9 months.)

The names of the months are a nice nod to our Roman history but they are a pain in the rear to use. It's high time to relegate them to second-class status, like Roman numerals.

I just saw this on social media the other day:

Person A: "Isn't it just awful that SEPTember, OCTober, NOVember and DECember aren't the 7th, 8th, 9th and 10th months?"

Person B: "They should stab whomever changed that."

(For those who may not know, that is a reference to Julius Caesar who inserted July, and if you didn't know that you may be interested to know that Augustus inserted August. Hence we are off by 2 months.)

Edit: Apparently, I -- and the very funny person B -- were misinformed. Jan and Feb were inserted, and different months were renamed: https://en.wikipedia.org/wiki/Roman_calendar

This isn’t actually true, July and August were renamed from Quintilis and Sextilis. The off-by-two is because the original roman calendar had ten months, with winter not having named months. (See https://en.m.wikipedia.org/wiki/Roman_calendar)

I'm not sure this is correct; July and August were renamed, yes, but not inserted. They did steal days from February, which was originally the last month of the Roman calendar.

Ah yes, you are correct: https://en.wikipedia.org/wiki/Roman_calendar

So Jan and Feb were inserted.

I have to leave the original up as it is because the joke is too good, but I will leave this note as a correction.

It's not so much "inserted", as they just changed which month they considered the first. The roman first month was March, but it still took place in the spring.

They were inserted. Previously the months ran from March to December and the remaining time didn't belong to any month.

Caesar and Augustus didn't insert those months, they were renamed from Quintilis and Sextilis in their honour.

The reason for the discrepancy in names is due to the fact that March used to be the first month of the year. It was changed to January hundreds of years before Caesar came along, so the naming scheme was already 2 months off by that point.

> March used to be the first month of the year. It was changed to January hundreds of years before Caesar came along

Depends on your perspective. In the US (really, in Britain), this change occurred during the lifetime of George Washington, who arguably lived hundreds of years after Caesar.


and our (UK) tax system still hasn't caught up, starting on the 5th April.

They were not inserted, they were renamed. The year began in March, so the names of September-December make sense within that context. The start of the year changed later, making the names incorrect.

That made me chuckle, but apparently it’s a bit more nuanced. According to Wikipedia:

> It was named by the Roman Senate in honour of Roman general Julius Caesar, it being the month of his birth. Prior to that, it was called Quintilis, being the fifth month of the 10-month calendar.

This stuff is fascinating. Reminds me of how the Romance language weekdays are named after the Roman pantheon and the Germanic (including English) weekdays are named after the approximate germanic counterparts for those same Roman gods.

The Sanskrit names for the days of the week are named after the same planets. I think both the Indians and the Graeco-Romans originally got them from the Babylonians who were the authority for all things astronomical and astrological in the ancient world.

In Polish months are named after plants that bloom then and weather conditions. Quite poetic to say "I will meet you on the 5th day in the month of linden trees" :)

The funny thing is that other Slavic countries use similar names but some are moved 1 month back or forth because flowers bloom earlier/later there :)

And days of the week are simply numered starting with sunday = "niedziela" (not working day), "poniedziałek" (after not working day), "wtorek" (secondary day), "środa" (middle day), "czwartek" (fourth day), "piątek" (fifth day) and "sobota" (sabbath).

I never remember the names of the roman months and have to count them starting from january.

In Slovenia we used to have the old Slavic names for months, but somewhere around my or my parent’s generation they completely died in favor of roman months.

My grandpa is still fluent in them, my parents knew about them and probably knew how to use them once upon a time, I know them as something you see on very old calendars and a curiosity we learned about in kindergarten.

All I remember is that my birthday month, October, is called listopad because it’s when leaves fall down

That's the thing with moving the months back and forth :), in Poland listopad is November, and October is październik (comes from paździerz (chaff?) - the husks of grains separated by threshing it).

Actually you know what, I messed it up. Listopad is November. October is vinotoč because it's when young wine turns into real wine.

Just goes to show how little this stuff is used nowadays :D

Although wikipedia[1] says that listopad is an alternative name for October. I am now sufficiently confused.

[1] https://en.wikipedia.org/wiki/Slovene_months

Interesting. So my grandmother's maiden name "wrzesień" has a meaning beyond "September" (according to Polish-English translations)?

I don't know for a fact it had the accent over the last letter. Records here in the US exclude it, of course that hardly means it wasn't there originally.

wrzos (heather) is a plant that blooms in early autumn, hence the name wrzesień.

Also it's not accent, it's softening of the n sound, similar to Spanish n with ~.

Yes I should have said, "diacritic"

The word is derived from "wrzos" = heather.

Ancient Greek month names usually identify a holiday that happens that month. The question of how different cultures name the months is interesting in its own right.

It's worse than that: some of the months are latin-numbered, but due to renumbering the numbers are wrong.

September = sept = 7 = month 9

Octobeber = oct (as in octal) = 8 = month 10

November = nov = 9 = month 11

December = dec (as in decimal) = 10 = month 12

I was about to comment on how this is because July and August were added in honor of Julius and Augustus Caesar, but it turns out they were renamed from Quintilis and Sextilis (which would also be misnumbered). It was really January and February that were added later, causing the off-by-2 error :)

Source: https://www.crowl.org/Lawrence/time/months.html

Now thank you for that... I wasn’t aware of this, but will probably never forget it again. You ruined these months for me! :-)

So we have the solution! Just put them back in their original order and call every other month N-ember!

Hebrew days are numbered as well (first day, second day, third day), with the exception of saturday. 3 months before november isn't bad, though, at least imo, although I do convert everything to numbers as soon as I can. So november -> 11 -> 8 -> august. But I know what number is associated with every number; don't have to count up.

> Quick, what's 3 months before November

Wow. It took me a second, which is weird since I have no trouble seeing 11/5 and 8/5 as November and August Fifth, respectfully.

As someone who went to school in spain but at home always spoke german and now lives in Germany, the number inversion is the bain of my existance (hyperbole). I can't tell you how many times I have made mistakes because of it when communicating with people, and how often I have written down number incorrectly because of it.

At some point I just want to train myself to say it the "right" way, even if it sounds wrong in german and people will look at me weirdly. But somebody has to start the trend, right?

It could be worse. Norway has two counting systems

Modern: 32 = "thirty-two" (similar to English)

Old: 32 = "two-and-thirty" (similar to German)

The modern system was introduced by the government in the 50s as a requirement from the national phone operator.

This was before automatic switches were common, so users had to speak with an operator to patch to the correct destination. They insisted that the old counting method introduced too many errors. The government agreed and made a new law requiring schools to teach the new method.

English used to use that "old" system, which it got from German (see "Sing a song of sixpence" - "four and twenty blackbirds"), but this mainly changed to the modern system around the time of Shakespeare.

In Dutch we just spell out the phone numbers digit for digit without grouping them first. No need to change the language for that. The advantages in the article may be a good reason though.

Fellow German here. I find it extremely annoying when people read out numbers for me to write down and announce pairs as numbers instead of digits.

If you mean 42 and read out "zwei und vierzig" I will pause and have to figure out if you meant 240 and you know it. This kind of thing just seems almost intentionally inconsiderate because of the unnecessary ambiguity.

I'm slightly confused as a native English speaker here.

zwei und vierzig versus zwei hundert vierzig are radically different to my ears.

The counting thing is annoying but not as annoying as French numbers in my not so humble opinion. Though I guess English had it at one point with things like 4 score and 7 years ago (a score being 20 years, so 87 years ago)

Guess maybe I'm weird but outside of the "flip last two numbers around in your brain in German" it never struck me as much more than: Well that's weird, least its not french numbers under 100 where I have to add mentally so no big deal.

French numbers are actually quite easy though if you learn even a little bit of French.

You don’t think of quatre-vingt dix as four-twenties ten, you just think of it as ninety just like in English.

I suspect the same is true even for native speakers, your brain is going to pretty quickly map to the actual number it represents rather than the arithmetic statement.

I'm thirty eight years old. I've been using standard units my entire life. They just make sense. Eight cups? Oh that's half a gallon, or two quarts. Eight ounces of melted butter? Oh that's one cup. Probably two sticks unless it's that bullshit imported European butter, ugh. My indoctrinated brain can't imagine it any other way. "You want me to add what grams.. what? Who measures sugar by weight?!"

French numbers are the same way. If the only system you've ever used is a shitty system, the shitty system is the only logical way of doing things. Human brains are smart, but also dumb. That's actually the point of this article.

I am slowly training myself to intuit SI units, especially at work. It's better, and I know that, but it's fucking hard. I'm pretty sure I'll never be able to be able to replace it for cooking. It's just too deep. Probably the same as a Frenchman who learned to count in French. Learning to cook with standard units was coincident with learning to speak. You simply can't renovate those memories.

They're still bad systems though.

Parent is referring to situations where you pronounce the numbers pairwise with regards to the digits. Like we (or at least I and my friends) in english pronounce screen resolutions: 720p => "seven twenty p", and years: 1984 => "nineteen eighty-four".

The number pairing trick is use to not flip numbers.

But I can see how it would be annoying in german.

As weird as the german digit flip is, French I understand is worse with the number names, actually involving math.

French is annoying but it is "in the right order" (and the Swiss did away with that foolishness ;) )

Why? Isn't 240 zwei hundret vierzig?

Not trying to be difficult... from what little I remember of my 2 years of college German, zwei und vierzig is 42.

And then there is "zwei vierzig" or €2,40

"Hundert" and "und" can sound very similar when spoken quickly, so you have to pay special attention in this case.

No, the problem is that people read out long numeric sequences in inconsistent ways.

Consider this: "sixty-nine" is clearly 69. But when spoken out, especially in a long string of digits (like an IBAN, a banking code) that might be announced as "six, nine" or "sixty-nine" or "sixty...nine" or even "six...ty-nine".

So even in English there's some chance of ambiguity whether it is supposed to be 6-9 or 6-0-9 (consider: "forty-two, sixty, nine" for 4-2-6-0-9).

In German the awkward inversion makes this worse. So you might get "neunundsechzig" (6-9), "neun...undsechzig" (9... no, wait, 6-9? or maybe 9-6-0?) or "neunund...sechzig" (...6-9). Although the last one is unambiguous, you're basically stuck waiting for the end because you're trying to write digits down left to right and don't want to skip digits and backtrack.

As for why "neun...und sechzig" is ambiguous: with that weird pause it's not clear if this is still 69 or literally "9 and 60" (which is what the word "neunundsechzig" means), i.e. 9-60. As people sometimes emphasise the final digit or digit pair by saying "and" before it (like you would in a list of words), this is ambiguous and at least might give a listener pause.

"Hundert" and "und" generally aren't similar enough for this to be a problem and there's a special place in hell for people who read out groups of digits longer than 2 as numbers, so this isn't generally a problem. Most people do however tend to slur the "und" so e.g. "sechsundsechzig" becomes "sechsnsechzig" but this rather avoids the problem I mentioned (except for the backtracking).

>As for why "neun...und sechzig" is ambiguous: with that weird pause it's not clear if this is still 69 or literally "9 and 60" (which is what the word "neunundsechzig" means), i.e. 9-60.

9 und 60 vs. 9 hundert 60, if you speak quickly then the "ert" part of hundert is often swallowed, making it more difficult to discern between the remaining "hund" and "und".

I'm assuming you're a native German speaker too? Must be a regional accent thing, then.

The closest I can get to ambiguity by slurring "neunhundertsechzig" is "neun oder sechzig" or "neun, neununsechzig", never "neunundsechzig", and I have to make an effort to speak faster than I normally would even if I was reading out numbers in a hurry. I've also never run into this ("hundert" and "und" being mixed up) in my daily life, so I'm surprised to hear that this is something you hear often.

I suspect the effect of this, in practice, is almost negligible.

What's more interesting is why being good at maths/physics is considered very uncool in English-speaking countries (not sure about other European ones), but is actually seen as cool in, say, Russia or Bulgaria or Singapore [citation needed]. It is not seen as strange or unusual for girls to be better at science than boys either, possibly because it is not uncool [another citation needed].

I would say that has a much, much greater impact on outcomes than how numbers are represented in the different languages.

This is a very interesting observation if its real. I am from Bulgaria and I am a PhD candidate in physics. Whenever I tell someone that, they always say that its sounds cool and difficult and the next question is: What are you going to work after that? I guess that physics, at least in Bulgaria is not considered as a field that you could work in, more as in something you learn for the sake of knowledge.

Why do you think that in English speaking countries is different than others? I temporarily currently living in France and I do not have many contacts with non scientists, but the ones that asked me what I do all found it cool sounding.

I meant more on the secondary/high school level. From what I read, it seems almost everyone good at maths/physics that grew up in the US had a miserable experience in school. The whole "nerd/geek" thing and being near the bottom of the school hierarchy.

In my experience in Russia, "nerds" were rather those that were extremely diligent but did not really have passions or interests; being good at science was actually seen as kinda cool. Sports achievements were not really emphasized at all.

But it is all anecdotal, and I would like to see some actual studies on this.

Depending on what you are counting, sometimes "wrong" can be historically "right":

In Swaledale, in the North Riding of Yorkshire, sheep farmers used to, and some still do; count their sheep in a very curious fashion. Instead of One, Two, Three, Four... they go, thus: (1)Yan, (2)Tan, (3)Tether, (4)Mether, (5)Pip; (6)Ezar, (7)Sezar, (8)Acker, (9)Conter, (10)Dick; (11)Yan-a-Dick, (12)Tan-a-Dick, (13)Tether-a-Dick, (14)Mether-a-Dick, (15)Bumfit; (16)Yan-a-Bum, (17)Tan-a-Bum, (18)Tether-a-Bum, (19)Mether-a-Bum, (20)Jigget. Having reached Twenty, they then take a stone [or make a mark upon the ground or a piece of wood, thus the term 'a score' or 'twenty'] representing the Twenty sheep that they have counted; and if they possess more than Twenty sheep, they go for another twenty:

Yan, Tan, Tether, Mether, Pip... Another Twenty, another stone. Yan, Tan, Tether, Mether, Pip... Again,Twenty, again another stone.

Jake Thackray 'Molly Metcalfe' 1971


As a native Polish speaker it was very strange to me when English speakers say things like "twelve hundreds" for numbers between 1000 and 2000. Nobody in Poland ever says that because we don't separate 200 into 2 words "two hundred" we say "dwieście" (which comes from two hundreds, but is significantly changed and considered separate word not 2 words joined). It sounds to us like "4 twenties" would sound to English people instead of "eighty".

So because of language it's not natural to think of 1300 as 13*100, it's much more natural to think of it as 1000+300.

But it's still better in Polish than in German ;) At least we don't do mixed endian like "hundred two and twenty" :)

> when English speakers say things like "twelve hundreds" for numbers between 1000 and 2000

We do that in every other range too. It would be completely normal to read 3700 as "thirty-seven hundred".

In what I assume is a related phenomenon, long numbers can be read out in digit pairs rather than single digits (say a PIN code 3742 - "thirty-seven forty-two", as opposed to "three seven four two"), though the digit pairs idea breaks down when a 0 is present.

> In what I assume is a related phenomenon, long numbers can be read out in digit pairs rather than single digits

Poles do it as well, in pairs, triples or single digits, doesn't matter. But only for numbers that aren't quantities. Like - ids, account numbers, zip codes, phone numbers - no problem, but reading population or account balance that way would be weird.

> As a native Polish speaker it was very strange to me when English speakers say things like "twelve hundreds" for numbers between 1000 and 2000

Minor nitpick but people will say, "twelve hundred" not "twelve hundreds" (at least in all of my experience growing up in the US). The reason being, you have eight hundred, nine hundred, (we don't talk about ten hundred), eleven hundred, twelve hundred, and so on. It's kind of like a continuance of how the hundreds below 1000 are named.

Interestingly you will hear sometimes "ten hundred" when talking about address systems where each block increases the address by 100. Such as, "the ten hundred block of Example street." But I've never heard it anywhere else.

That would actually be practical for naming years in the current century, e.g. twenty hundred nineteen for the current year sounds much better to my (Dutch) ears than two thousand nineteen. We do say twenty nineteen, of course, but the intermediate "full name" step of twenty hundred nineteen is never used, making it a bit weird.

Minor nitpick nitpick: except for years, e.g., I don't remember exactly when the Magna Carta was signed, but it was somewhere in the twelve-hundreds.

I'm talking only about the numbers, 800, 900, 1000, 1100, 1200, etc. That is, counting by hundreds on the hundred.

So your point does not contradict mine.

That's not really an exception for years. It means something different. Twelve hundred is a single number, 1200. Twelve-hundreds is a range from 1200-1299. You can also do the same thing with many other ranges (e.g. house numbers).

That point about Dutch children and little-endian names for numbers is a fun little nugget. The complaint is that they're forced to read the numbers backwards, when the numerals in question are Arabic numerals, invented by a culture that reads from right-to-left and has little-endian names for numbers. I would assume that kids who grow up speaking and learning math in Arabic have no such problems.

The fact that so-called Arabic numerals are written left-to-right is perhaps evidence that the Arabic numerals were invented in India and are called Arabic in Europe only because Europeans learnt about them from the Arabs.

As a kid, I still remember the day that my dad was helping me with my Maths homework.

On one tricky problem, he unconsciously started muttering the numbers out loud, and I was surprised to hear him saying them in Tamil (he is from Sri Lanka, but we spoke only English at home as far as I've known).

I asked him about it later, and he said that in his head, he always translated the numbers or problems into Tamil, solved them, then translated back to English to present the solution - because he was taught maths as a kid in Tamil.

He could still do all that faster than I could in all English!

What an absurd Sapir-Whorfian argument. The English ten words are the same as the Chinese (e.g. “forty” is clearly “four-tens” with the corners knocked off). If summing two-digit numbers is slower for some cohort of kids it’s more likely the school system than language. For example german-speaking kids have a similar number system to Dutch-speaking kids but learn their multiplication tables to 20x20 rather than 12x12 as is customary in English, so can do more smaller multiplications in their head than folks raised in English.

I thought the same thing. The main difference is we don’t use “onety-X” and some of the vowel sounds are harmonized whereas in Chinese they remain in their base forms.

We also lack[1] the 10,000[2] word (but also Chinese doesn’t have the 100,000 word like some others do)

[1] that’s a near-pun.

[2] No one says myriad to mean 10,000.

I don't accept the Sapir-Whorf hypothesis in general, but in this particular case, at least some empirical evidence for this specific effect is presented. There is nothing here, however, to suggest that the effect is anything other than minor and transient, so the article sems to be raising an exaggerated concern.

> german-speaking kids have a similar number system to Dutch-speaking kids but learn their multiplication tables to 20x20 rather than 12x12 as is customary in English

I was charmed to learn that the word for a times table in Chinese is 九九乘法表, literally "nine-nine-multiplication-method-table".

One assumes the table goes up to 9x9.

In German they are called “one times one”

German speaking kids learn inverted system. And it's a struggle to quickly realize and do mental math once they start speaking other languages like English where double-digits are non inverted.

FWIW my trilingual son had no issues in this regard

I'm Dutch, and I've effectively made this change. Our number system sucks (though not as bad as the Danish one - which is my wife's language so I'm regularly forced to decipher that mess), whenever someone says a number like 47 out loud, I have to think hard about whether it's 47 or 74.

So I've decided to generally stop doing maths in Dutch. Our company is international so we all work in English anyway so when I do stuff in eg Excel, calc.exe etc, I just count in English. When I speak in Dutch, I generally simply avoid the last digit in large-ish numbers. Eg I don't care what language I say "250" in, but when I'm speaking Dutch I'd round "252" to "about 250", which is fine enough in most contexts.

FYI fun trivia: Norway fixed this about their language. They used to do what the Danes do but now it's like in English etc. They not only made up normal proper words for eg "50" or "90", but also reversed 2-digit numbers, eg "42" in Danish is "to-og-fyrre" and in modern Norwegian it's "førti-to". That's a pretty ballsy way to change a language and I'm jealous.

Congratulations on switching your number language. In general, this is quite hard to do. Even when reading English, which is almost a second native language to me by now, I still find that I automatically read numbers in the text as my native Dutch.

> In other languages, the tens and units of numbers are inverted. For example, in Dutch, 94 is written vierënnegentig (or “four and ninety”), and other research suggests this may make it harder to do certain mathematical processes.

>For example, Dutch kindergarten children performed worse than English children on a task that required them to roughly add together two-digit numbers. This was despite the fact they were slightly older and had better working memory, because Dutch kindergarten starts later than in the UK. But on nearly every other metric, including counting ability, roughly adding and comparing quantities of dots, and simple addition of single-digit numbers, the two groups performed at the same level.

This is rather surprising. I would have guessed that adding numbers verbalized in little endian order would be easier because it makes carryover much more natural.

I think the key is "roughly".. They could probably catch errors in the ones place better (i.e. verify this summation) and that is potentially distracting in rounding.

Though another issue is that carry right is an exception for the 10s place.

Oh good catch. I missed that it was asking for rough rather than exact addition. That is the whole point of big endian - that you lead with the most impactful part.

> in English, words like “twelve” or “eleven” don’t give many clues as to the structure of the number itself... Contrast this with Mandarin Chinese, where the relationship between the tens and the units is very clear. Here, 92 is written jiǔ shí èr, which translates as “nine ten two”... Psychologists call systems like these “transparent”, where there is an obvious and consistent link between numbers and their names.

Relatedly, I've been thinking a lot lately about programming style conventions, and how some people prefer very explicit code while others prefer implicit. For example, something as "simple" as leaving out the return keyword where it can be omitted at the end of a function versus leaving it in. The latter can be called "transparent", whereas the former requires a little deeper knowledge of the system.

This brings up a point that has always eerily intrigued me: Can you even count at all -without- a language?

Visually, you might be able to do it; e.g. seeing a clump of 5 trees and knowing it’s 5 without having to “say” “five” in your head.

But try tapping on the desk or clapping your hands and counting how many times you did it without saying/thinking “1, 2, 3, 4...”

I wonder if associating a transient stream of inputs with a count may be impossible without mapping it to some other sequence in your head, like linguistic numbers/letters.

My evopsych class in college touched on this.

Brains can track a number of discrete objects (from 3 to ~7, depending on species and maturity). Once we get past this number, brains tends to interpret it as 'many'. From the studies we looked at, it appears that the brain can innately count within this number, but reverts to 'many' representation after it.

Ex. crows can count three people going into an obscured area with food, and know that once three people have left, it's safe to get the food, as there aren't any people left.

Wow, so language lets us get past that limit.

And numbers are a computed property, so we don't have to know all the possible numbers, just the rules:

    let firstIndex = 0

    var nextIndex: Number { return nextNumberBasedOnSomeRules() }
And so it's helpful to have a language with a sensible numeric system, after all. :)

A similarly interesting study: ability to create sentences using prepositional phrases, like "left of the red wall", predicts performance on a disoriented search task.


I have read about what may or may not be a hypothetical example of a shepherd who "counts" his flock by matching sheep passing through a gate with stones put into or taken out of a bag. This is enough to let you know when the number of sheep is wrong, though you won't know what the number is.

That's how mathematicians count. It's called bijection.

Isn't clapping five times enough to count to five? Like saying "one" five times would be enough to convey to me that you mean five.

I meant try clapping, tapping, listening to a repeating sound, or watching cars or people go by, at an arbitrary pace without rhythm, for a while before trying to recall how many it was, without saying a number in your head for each instance you note.

I think one good test of the counting-friendliness of a language is reciting the digits of pi (the limitation is obvious: only single digits are considered).

Among the few languages I know, I can easily recite the first twenty digits after the decimal point in Mandarin within three seconds. In English it’s just painful, at least for me.

Uh... isn't that just because all digits in Chinese are monosyllabic? Doesn't really have much to do with the way the number is conceptualized.

Given that children (and some adults) verbalize thoughts in their minds, being able to speak something faster is an advantage. It also makes memorization easier. Take the multiplication table as an example.

By the way, digits are almost monosyllabic in English too (with the exception of seven) but not even remotely as nice.

Forgive me if I'm missing something obvious - do you have a way of remembering them? Otherwise they're all just single digits regardless of language.

> Otherwise they're all just single digits regardless of language.

You mean single syllables? All syllables are definitely not created equal, some are harder to pronounce than others, and some don’t combine nicely when pronounced side by side.

> do you have a way of remembering them?

I do, but that’s beside the point. s/reciting/reading out loud/ if you wish.

Edit: I see the confusion now. I didn’t mean “remembering” within three seconds, that would be insane for most people.

I never made a special effort for that and I only remember 12 of those digits, so maybe I'm just using an inefficient way, but I remember them as two-digit numbers, not single digits.

I don't think I'm alone, the basic value of pi one learns in France is "3 14 16" - "trois quatorze seize" (historically it was "trois quatorze-cent-seize" so "3 1416" but it's less used today).

I believe the basic number taught in Mandarin is 3.1415926, which fits in one second.

This makes me feel better for thinking that the way we write (standard Western) music impedes understanding of the way modern chromatic music sounds.

And for the same reasons, really. Putting together things like "Four Twenties" makes sense when you only count to a hundred, and less sense when you need to, say, express the speed of light or the size of an electron. I'm sure the musical system made a lot more sense with diatonic sounds, but once you add in accidentals, you're just retaining backwards compatibility because it used to work and the then-living people were familiar with it.

Improper representations are frowned upon in school, but they have their place. Once, a niece of mine in kindergarten told me she knew what 3 times 11 was: 33.

I asked "Well then, what's 7 times 11?"

"It's seventy-seven."

"Okay, I bet you don't know what 12 times 11 is."

"Twelvety-twelve", she gleefully replied.

We agreed that twelvety-twelve is a perfectly good number, we know what it is, but if we were talking to other people we would tell them one hundred and thirty two – for us, twelvety-twelve is just fine.

– Bill Thurston, Groups, Tilings and Finite State Automata

My wife learned Cantonese as her first launguage and English as her second. I learned Cantonese in college. It’s way easier to count in Cantonese because it is so regular.

As a bonus, a native asian language speaker effectively has to learn place value at a very young age to learn how to count.

My wife learned all of her math skills in English, but she still sometimes counts in Cantonese. When we play blackjack, if I’m taking too long she’ll tell me the value of my cards in Cantonese, because she’s adding them in her head in Cantonese.

It’s just quicker.

In Czech they often say "triadvacet" which literally translated means "threeandtwenty" and I can't help to not think they said 32 every time I hear it.

Interestingly dvacettri is also acceptable :)

Same in German

This doesn’t surprise me at all.

Obviously not a direct correlation, but I’ve been surprised at how critical my internal vocalization of words is to my ability to solve a word puzzle game I’ve been playing recently.

In short, my ability to find a word that matches a pattern of blank letters is almost entirely dependent on my ability to pronounce those that might fit. If the word that matches has a pronunciation that doesn’t quite fit the usual patterns, I’ll have a very hard time recognizing it.

My favourite illogical system is archaic Finnish, where it goes (roughly translated)

One, two, three, ... Second-one (11), second-two (12), second-three (13), ... Third-one (21), third-two (22), third-three (23), ...

ie you have an off-by-one error in the tens digit as you are counting.

Modern Finnish retains this for 11-19, but mercifully sanity returns for numbers above that.

> Of course, there are many other reasons why children from different countries might have different mathematical abilities, including how maths is taught and attitudes towards education. It’s normally hard to control for these factors when studying people from different cultures – but one language offers a fascinating solution.

I read that as: of course, we know there are other possible explanations but we won’t dive in the research literature and we’ll instead indulge ourselves in this Sapir-Whorf based article because it’s good click bait.

The only interesting fact presented is that there is a slightly performance penalty in execution (not result) on some arithmetical tasks that never happen in real life based on the way to express numbers in subject’s native language.

Tom Scott and Why Klingon is Simpler Than Danish.


Similar things have been said about Chinese numbering.

one, two, three, four, five, six, seven, eight, nine, ten, ten one, ten two, ten three… ten nine, two ten, two ten one, two ten two,… three ten,… nine ten,… hundred one, hundred two,… hundred ten one, … two hundred, … two million three hundred four ten five thousand six hundred seven ten eight

"might" is the word of the day

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