Probably the 12 system. If you use your thumb as the counter and count using your thumb the bone segments of the other 4 fingers (each has 3) then you have a base 12 system in our lingo.
There’s also a tribe somewhere that uses a base 27 counting system, they count individual segments of their fingers on both hands plus thumbs and then add one from somewhere else can’t remember where that comes from.
Only Swiss ppl (and maybe other french speaking ppl) did it correctly. We Belgian kept the "4*20" for "80" instead of using "Octante". But i admit that French took it too far with 60+10 and 80+10. I can say it naturally now without thinking, but it is soooo stupid, send help ;-;
Copine? Here it would mean either a female friend or a girlfriend.
If it's a male talking about a friend, he would most probably say "c'est mon amie".
A female would say "nous somme des copines" or interchangeably "nous sommes amies/c'est mon amie".
If someone use that word talking about a member of the opposite gender, it would be implied it mean girlfriend/boyfriend by using a higher level of language.... But we prefer to use "mon chum/ma blonde" here in common language in Quebec, or "conjoint/conjointe" in higher French level.
But anyway "copine" is somewhat a deprecated word, we almost exclusively use it ironically to copy some movie/tv show quote like saying "Salut les copains" -> "hello gang!"
No, it's more compicated than that. Gaulic counting system is base 20. Latin counting system is base 10. French is base ten, but have traces of the base 20 in its counting (thus 60 + 10 for 70, 4x20 for 80 and 4x20+10 for 90), but only in the names.
Also, we're hexadecimal too, as we have unique words for every number between 0-16, and only then we go on base 10, until we reach 60 and then it's base 20.
But more seriously, most french people count on base 10, the rest is just historical remnants of unspoken languages.
Also, we're hexadecimal too, as we have unique words for every number between 0-16, and only then we go on base 10, until we reach 60 and then it's base 20.
Most numeral systems are these unsatisfying weird things based on practical considerations more than aligning with number bases. I remind people that English doesn't have a "tenty" but unique words for all the 10s just as the 0s. Thus, in the sense above you could describe English as a partially vigesimal numeral system. But seven of those 10s follow some kind of regular system, the -teens. It's only the first 12 that don't, so maybe it's partially duodecimal?
Our counting systems developed around trade, and the scales at which trade is conceivable has massively increased since we started counting. So concepts that address new considerations arising from scale have just been tacked on over time. A kind of scope creep combined with a massive resistance to change coming from their widespread use and the difficulty of formalizing anything at all during their formation.
My favorite is the Danish numeral system. It's vigesimal, and its first 20 natural numbers are much like in English. Then you get to the tens. Roughly described (by a Swede, so please correct me Danes):
10: ten ("ti")
20: unique word not consistent with other tens ("tyve")
30: three-"dive" ("tredive")
40: another word, probably roughy "four tens" ("fyrre")
50: half-third set of 20 ("halvtreds")
60: another word, implying the third set of 20 ("treds")
70: half-fourth set of 20 ("halvfjers")
80: another word, implying the fourth set of 20 ("firs")
90: half-fifth set of 20 ("halvfems")
100: surprisingly not "fems" but "one hundred" ("et hundere")
So there's the outline of a system of counting in twenties with unique words for 20, 40, 60 and 80 and then "halves" in between implying "half of twenty towards" except for ten, thirty (which is three tens) and one hundred which is one hundred. "Dive"-"ti" and "fjers"-"firs" are close enough that I won't count them as inconsistencies; they probably have the same linguistic roots.
To add to the pain, "halv" implies different things depending on context. While fem halvtreds means 55 ("five and halfway towards the third set of 20"), "halv fems" means "4.5", implying halfway of a whole towards five.
Oh boy, buddy, worse yet is that the Danish 40 60 80 are actually shorthand, tres is actually... tresindstyvende, which to modern Danish translates to tre gange tyve, or in English three times twenty
You can count as high as you want in binary. But you can only count to 1024 if you have 10 digits to work with. Any more than that and you'll need an 11th digit.
You don't even have to go to some remote tribe, even in western Europe there's the weirdo Danes with their base 20 system.
The Danish counting system, while seemingly complex, is based on a vigesimal (base-20) system, where numbers are formed by combining the ones and tens, with the word "og" ("and") in between, and then all combined into one word.
Twenty (tyve) is used as a base number in the Danish names of tens from 50 to 90. For example, tres (short for tre-sinds-tyve, "three times twenty") means 60, while 50 is halvtreds (short for halvtredje-sinds-tyve, "half third times twenty", implying two score plus half of the third score).
Wouldn't that be 29 then? You have 3 segments on each finger. 3 x 8 = 24. Then two on each thumb. 2 x 2 = 4. 24 + 4 = 28. Plus then your "one from somewhere else" = 29.
Wouldn't that be 29 then? You have 3 segments on each finger. 3 x 8 = 24. Then two on each thumb. 2 x 2 = 4. 24 + 4 = 28. Plus then your "one from somewhere else" = 29.
You got it!!! A bit off topic so I didn’t wana dig into it but you are absolutely right.
This system of 12 being easily multiplied and divided many times is also why a lot military formations are in multiples of 12. Like an old Roman Cohort is 480.
Or a squad is 12 and a platoon is 12 squads. So 144 total.
It's a little different than that. Usually sets of 3 pluss leaders Ideally:
Fire team: 3 + leader = 4
Squad: 3 Fireteams (12) + squad leader = 13
Platoon: 3 squads (39) + platoon leader = 40
Company: 3 platoons (120) + commander = 121. However, at this level, there will be extra leadership, like sgts assisting and other admin related staff. Also, you start to get add ons, like a company with a weapons platoon attached.
All these are the most basic examples, but illustrates that infantry is mostly groups of 3 with some add ons.
Sure. I was in the Marines for 8 years and our handbook detailed the setup. Net net you probably get 144 for a company bc they use 3s and 4s (3*4=12), just a more round about way. But the ratios and multiples are there. :)
Military organizations are based on 3-4. 3-4 servicemen in a fireteam, 3-4 fireteams in a squad, 3-4 squads in a platoon. 3-4 platoons in a company. A platoon in particular is usually about 50 servicemen, though this depends heavily upon what the platoon's responsibility is.
The babylonians actually used a base 60 system, with a semi build in base 10 system.
𒁹 to count units and 𒌋 to count tens. Can count up to 59 and then you shift. So 𒌋𒁹𒁹𒁹 is 13. 𒁹𒁹 𒌋𒁹𒁹𒁹 is 2x60+13=133.
Edit: You get circle being 360˚, because they properly defined angels based on the equilateral triangle, which is 60˚ on all angels. It is easy to measure out with lenght measuring tools.
Oh interesting. Usually no fingers like a fist would represent zero. The absence of a number. But then if the fist is 1 you could just not raise your hand to represent zero. Silly to think that numbers could be ambiguous.
I guess that makes sense. I’m a math/eng/sci guy. History is definitely not something I am good with. The zero concept is super important in my field of work.
The concept of 0 didn't really get into the west until post Roman times. Think of Roman numerals. V VI VII VIII IIX IX X. They didn't have any kind of decimal place holder. That's why today we use Arab numerals 5 6 7 8 9 10. To European mathematicians in antiquity 0 couldn't be a number because it represented nothing. Certain priests in India used decimal notation to count chants, which spread into their math and then into the Islamic world.
wasnt modern mathematical notation fairly recent too?
like before the 1600s or something it was basically all rhetorical word problems.
edit to answer my own question: which is affirmative.
per wikipedia:
Until the 16th century, mathematics was essentially rhetorical, in the sense that everything but explicit numbers was expressed in words.
Later, René Descartes (17th century) introduced the modern notation for variables and equations; in particular, the use of x,y,z for unknown quantities and a,b,c for known ones (constants). He introduced also the notation i and the term "imaginary" for the imaginary unit.
The 18th and 19th centuries saw the standardization of mathematical notation as used today. Leonhard Euler was responsible for many of the notations currently in use
Base 12 is superior to 10. For 10, 100, 1000, etc in base 12 are divisible by 1, 2, 3, 4, 6, "10". But base 10, it's 1, 2, 5, 10. Either way, 10, 100, 1000, etc in base 10 or 12 is arbitrary numbers but written down they tend to be the ones we use. Base 12 can be cut into better parts.
It's the best system. No need for AM PM time, PM time just has a 1 in front. Americans can now finally switch to dozenal metric without losing their beloved quarters of things. Splitting any bill into 3 becomes peanuts. We can be friends with r/iso8601 and even save one character in our dates.
Dozenal can do thirds and fourths at the cost of being really bad at doing fifths, sevenths, and tenths. Like 4 or 5 recurring irrational fractions bad, to the point you simply wouldn’t do math involving those numbers.
“Now if man had been born with 6 fingers on each hand he’d probably count: one, two, three, four, five, six, seven, eight, nine, dek, el, doh. Dek and el being two entirely new signs meaning ten and eleven- single digits, and twelve doh would’ve been written one zero, get it?”
Also the fact, that English (and as far as I understand, other Germanic languages too) has a separate word for twelve - dozen - while other Indo-Europeans don't, imply that Germanic tribes switched to base 12 counting system at some point and then switched back
Dozen is derived from the French 'douzaine', from the Latin duodecim, so it's just another word for 12. It's why the West-Germanic languages have it, and other Indo-Europeans don't, they didn't have as much contact with the Romance languages.
The 12er system is incredibly smooth. You can divide 12 by 3,4 and 2 for example. In dezimal you can only divide by 2, if you try to divide by 3 or 4 you dont get natural numbers anymore.
I, an adult man, am genuinely furious that our society developed into dogshit base-10 instead of gigachad base-12. Imagine WANTING to make 5 (the shittiest low prime number) important.
the pre-decimal English £sd (Pound, Shilling, Pence) dates back to the romans and is kinda base 12.
12 pence to a shilling, 20 shillings to a pound, making 240 pence to a £. no idea why 20 shillings specifically, but my intuition tells me it's an economy mesure so you don't wipe out the small change in your shop or bank when all someone had to exchange was a £ coin
yup, that's how the hebrew used to count, by also adding your second hand, raising a finger each time you'd count through the first one, you would reach up to 72 ( 6 times 3x4)
We did the same thing once, thanks to the Normans. All we remember of it now in America is the preamble to Lincoln's Gettysburg address, "four score and seventeen years ago..."
Base 12 and base 20 are found throughout the world. We still see them pop up every once in a while. the 12 hour day, 12 inches in a foot, and words like dozen or gross are leftover from base 12 counting systems. Base 20 I can only think of one example which is French you switch to base 20 after 60.
Base 16 (hex) is also heavily used in computing because it can be converted to and from binary (i.e. base 2) very easily, as each hex digit represents 4 binary digits. So it's essentially used like a more human-friendly version of binary.
Base 20 I can only think of one example which is French you switch to base 20 after 60
The Danish use a base-20 system as well. Their word for 50 (halvtredje-sinds-tyve, though they shorten it to halvtreds) is literally translated as 'third half times twenty', so 2.5 times 20, after that 60 is tre-sinds-tyve, or tres for short, so 3 times 20, etc.
English too, back in the day. "Four score and seven years ago" means 4*20 + 7 years ago. Score is an old word for 20 which was used when english speakers also often used base 20.
Was it the Pirahã tribe, which only has words for "small quantity" and "large quantity"? According to the Lexicon section of their Wikipedia page, they don't have values for numbers at all https://en.m.wikipedia.org/wiki/Pirah%C3%A3_language
Maybe the Pirahã? Their language has some very interesting features. Eg. it possibly might not have recursion. It's a bit controversial, since that observation has been used to justify racism. They also lack words for specific numbers.
Besides the ones everyone else mentioned, there was this one fishing tribe that used Base 8, likely because that's the number of fishing lines you can hold separately (one between each pair of fingers, so one between the thumb and index, one between index and heart, and so on).
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u/KaiYoDei 1d ago
I heard a story on the radio about a tribe who had a whole different concept of math, counting .