Non Base10 Number Systems in Languages
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 cybermutiny
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Non Base10 Number Systems in Languages
Hey everyone, I just had a random thought the other day: it seems like every language I've ever dabbled in has used a base 10 number system.
Is anyone aware of a language or culture (from past or present) that did not use one?
Is anyone aware of a language or culture (from past or present) that did not use one?
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Re: Non Base10 Number Systems in Languages
I'm pretty sure French uses a base20 system. I don't know French though, so I don't know much more.
Re: Non Base10 Number Systems in Languages
French and scots Gaelic do some counting in twenties: soixantedix (70), quatrevingt (80). I don't know if that counts.
Scots Gaelic numbers: http://www.sf.airnet.ne.jp/~ts/language ... aelic.html
Scots Gaelic numbers: http://www.sf.airnet.ne.jp/~ts/language ... aelic.html
Last edited by goofy on Sun Jan 30, 2011 11:49 pm UTC, edited 1 time in total.
 Iulus Cofield
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Re: Non Base10 Number Systems in Languages
My Latin professor was recently talking about this. He said some scholars think English used to have a base 12 and that French and Latin used to have a base 20 system, which would explain the irregularities of numerals.
 gaurwraith
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Re: Non Base10 Number Systems in Languages
Let's go to the other thread, quick!
.The traditional Chinese units of weight were base16. For example, one jīn (斤) (approximately 256 grams) in the old system equals sixteen liǎng (兩) (16g). The suanpan (Chinese abacus) could be used to perform hexadecimal calculations
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Re: Non Base10 Number Systems in Languages
English also has a Frenchlike system for counting in base20, compare French "quatre vingt sept" (lit. four twenty seven) with "4 score and 7 years ago".
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Re: Non Base10 Number Systems in Languages
No it wouldn't. The words for 11 and 12 come from roots meaning, essentially, "one left over" and "two left over", which very clearly suggest a baseten system. And if Latin was ever base20, how come Roman Numerals so very clearly aren't?Iulus Cofield wrote:He said some scholars think English used to have a base 12...which would explain the irregularities of numerals.
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Re: Non Base10 Number Systems in Languages
No need to be hostile, sir.
As I said, that is what my Latin professor said. He's not an expert on historical English, so I'm not surprised neither he nor I knew that "eleven" means "one left over". Nor did he say it was a widely accepted theory. He was more saying, "This is a neat idea some people have had."
As for Latin, the Roman Numeral system clearly doesn't represent the linguistic origins of Roman numbers. IV is quattuor not undequinque, IX is novem, not undedecim. L is quinaquaginta, which is as regular as any multiple of 10 after 20 and before 100. I mean, what IS the base of Roman Numerals? I? V? X? L? C? A variable base depending on how large the number?
His evidence for a potential base 20 was that 18 and 19 are duodeviginti (20 minus 2) and undeviginti (20 minus 1), and that after 20 numbers go along the pattern viginti unus (twenty one), vinginti duo (twenty two) or unus et viginti (one and twenty), duo et viginti (two and twenty). Whereas before have individual names up to ten, then go undecim (one ten), duodecim (two ten), up to 17 then the aforementioned pair. He also mentioned French's use of base twenty as possibly connected. Again, he said "Some people think", not "This is definite fact." There's certainly other reasons to think Latin was always base ten.
As I said, that is what my Latin professor said. He's not an expert on historical English, so I'm not surprised neither he nor I knew that "eleven" means "one left over". Nor did he say it was a widely accepted theory. He was more saying, "This is a neat idea some people have had."
As for Latin, the Roman Numeral system clearly doesn't represent the linguistic origins of Roman numbers. IV is quattuor not undequinque, IX is novem, not undedecim. L is quinaquaginta, which is as regular as any multiple of 10 after 20 and before 100. I mean, what IS the base of Roman Numerals? I? V? X? L? C? A variable base depending on how large the number?
His evidence for a potential base 20 was that 18 and 19 are duodeviginti (20 minus 2) and undeviginti (20 minus 1), and that after 20 numbers go along the pattern viginti unus (twenty one), vinginti duo (twenty two) or unus et viginti (one and twenty), duo et viginti (two and twenty). Whereas before have individual names up to ten, then go undecim (one ten), duodecim (two ten), up to 17 then the aforementioned pair. He also mentioned French's use of base twenty as possibly connected. Again, he said "Some people think", not "This is definite fact." There's certainly other reasons to think Latin was always base ten.
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Re: Non Base10 Number Systems in Languages
gaurwraith wrote:Let's go to the other thread, quick!.The traditional Chinese units of weight were base16. For example, one jīn (斤) (approximately 256 grams) in the old system equals sixteen liǎng (兩) (16g). The suanpan (Chinese abacus) could be used to perform hexadecimal calculations
Perhaps, but the actual spoken number system in Chinese is a base10 system. I just find it interesting that so many cultures used a base10 system. It makes me think there is some innate tendency for humans to think in 10s.
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Re: Non Base10 Number Systems in Languages
cybermutiny wrote:It makes me think there is some innate tendency for humans to think in 10s.
A simpler explanation would be that humans have 10 fingers.
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Re: Non Base10 Number Systems in Languages
Danish uses a base 20 system, I think, to some extent. I believe I've also heard that that's true for Basque.
Danes still mostly use base 10, but base 20 for all the tens.
*Waits for Dane to enter thread and correct*
Danes still mostly use base 10, but base 20 for all the tens.
*Waits for Dane to enter thread and correct*
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Re: Non Base10 Number Systems in Languages
http://en.wikipedia.org/wiki/Number_names
However, some of the stuff there is also dubious. It's ridiculous to say that only because English and German have (by now) morphologically simple words for 11 and 12, they have duodecimal systems. But at least one would now know what languages to look at.
However, some of the stuff there is also dubious. It's ridiculous to say that only because English and German have (by now) morphologically simple words for 11 and 12, they have duodecimal systems. But at least one would now know what languages to look at.
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Re: Non Base10 Number Systems in Languages
Scots Gaelic
deich air fhichead (30 literally "ten and twenty")
dà fhichead (40 literally "two twenty")
dà fhichead is a deich (50 literally "two twenty and ten")
trì fhichead (60 literally "three twenty")
etc...
deich air fhichead (30 literally "ten and twenty")
dà fhichead (40 literally "two twenty")
dà fhichead is a deich (50 literally "two twenty and ten")
trì fhichead (60 literally "three twenty")
etc...
Re: Non Base10 Number Systems in Languages
Romans didn't have a base anything number system, in the sense that we would use it the word: their numerical symbols weren't digital. "Base" is a concept that we humans pinned down only relatively recently, sometime after the invention of zero. Since this is the case, older languages obviously will not fit the mold.
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Although you can count binary on your fingers, if you stretch.
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Although you can count binary on your fingers, if you stretch.
 Iulus Cofield
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Re: Non Base10 Number Systems in Languages
Whoa, I'd never thought of counting binary on my fingers instead of in my head. That's actually incredibly easy and strangely relaxing.
Anyway, it's certainly not possible to a a basex symbol system without zero, but linguistic number systems seem to pretty clearly exist. At some point the names for numbers have to become recursive or it necessitates as many words as you have usable numbers. Of course you can just throw out doing math and just have a few numbers in your language, but the benefits of counting and math are fairly plentiful.
Anyway, it's certainly not possible to a a basex symbol system without zero, but linguistic number systems seem to pretty clearly exist. At some point the names for numbers have to become recursive or it necessitates as many words as you have usable numbers. Of course you can just throw out doing math and just have a few numbers in your language, but the benefits of counting and math are fairly plentiful.
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Re: Non Base10 Number Systems in Languages
I remember that the Babylonians counted in base 60, which is how we ended up with things such as 60 second in a minute/60 minutes in an hour as well as 360^{o} to a circle.
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Re: Non Base10 Number Systems in Languages
Iulus Cofield wrote:Whoa, I'd never thought of counting binary on my fingers instead of in my head. That's actually incredibly easy and strangely relaxing.
http://en.wikipedia.org/wiki/Finger_binary
 gmalivuk
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Re: Non Base10 Number Systems in Languages
Yeah, though they used base10 for each base60 "digit".Plasma Mongoose wrote:I remember that the Babylonians counted in base 60, which is how we ended up with things such as 60 second in a minute/60 minutes in an hour as well as 360^{o} to a circle.
Re: Non Base10 Number Systems in Languages
The only ones that come to mind are ancient civilizations.
Mayans used a base20 system, with places. Meaning that the first position was the 1s (019 by 1s), the second was the 20s (20380 by 20s), the third was the 400s (4007600 by 400s), etc.
And as mentioned the Babylonians used a hexagesimal system with alternating 60106010 places.
I'd imagine there are some groups that could use a basefive system, much the way that tallying works. Both Western European tally marks (i.e.,  plus a slash) and Chinese/Japanese tally marks (i.e., 正 or 玉) count up in fives. But there's no position significance; it's just counting in fives. KF
Mayans used a base20 system, with places. Meaning that the first position was the 1s (019 by 1s), the second was the 20s (20380 by 20s), the third was the 400s (4007600 by 400s), etc.
gmalivuk wrote:Yeah, though they used base10 for each base60 "digit".Plasma Mongoose wrote:I remember that the Babylonians counted in base 60, which is how we ended up with things such as 60 second in a minute/60 minutes in an hour as well as 360^{o} to a circle.
And as mentioned the Babylonians used a hexagesimal system with alternating 60106010 places.
I'd imagine there are some groups that could use a basefive system, much the way that tallying works. Both Western European tally marks (i.e.,  plus a slash) and Chinese/Japanese tally marks (i.e., 正 or 玉) count up in fives. But there's no position significance; it's just counting in fives. KF
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Re: Non Base10 Number Systems in Languages
goofy wrote:dà fhichead is a deich
Hey now, no need for crass language.
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Re: Non Base10 Number Systems in Languages
Actually, the second place had only 18 digits in the Mayan system.Kizyr wrote:Mayans used a base20 system, with places. Meaning that the first position was the 1s (019 by 1s), the second was the 20s (20380 by 20s), the third was the 400s (4007600 by 400s), etc.
I don't know that that's how I'd describe it. As I recall, it's more like the equivalent of writing a million as 4374640, and then understanding that it's meant to be read as 04374640, where each individual digit has its normal baseten meaning but the pairs indicate powers of sixty.And as mentioned the Babylonians used a hexagesimal system with alternating 60106010 places.
Re: Non Base10 Number Systems in Languages
gmalivuk wrote:I don't know that that's how I'd describe it. As I recall, it's more like the equivalent of writing a million as 4374640, and then understanding that it's meant to be read as 04374640, where each individual digit has its normal baseten meaning but the pairs indicate powers of sixty.Kizyr wrote:And as mentioned the Babylonians used a hexagesimal system with alternating 60106010 places.
Yeah, that's what I had in mind, just more clearly/accurately explained. Thanks for the clarification. (I suppose the better way to state it would be either as a base60 system if you consider the numbers in pairs, or an alternating 106106 system if you consider the numbers in isolation?)
gmalivuk wrote:Actually, the second place had only 18 digits in the Mayan system.Kizyr wrote:Mayans used a base20 system, with places. Meaning that the first position was the 1s (019 by 1s), the second was the 20s (20380 by 20s), the third was the 400s (4007600 by 400s), etc.
Wait what? Where'd the other two go? KF
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Re: Non Base10 Number Systems in Languages
I think there are a handful of quinary systems in some of the languages of Vanuatu but can't recall which ones they are.
The World Atlas of Language Structures gives a fair number of base20 and hybrid vigesimal/decimal languages at wals.info/feature/131
The World Atlas of Language Structures gives a fair number of base20 and hybrid vigesimal/decimal languages at wals.info/feature/131

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Re: Non Base10 Number Systems in Languages
Personally, I think it may have been a coincidence that a lot of languages used a base 10 counting system then became powerful, spreading their mathematical systems to other cultures. Who knows what the counting systems were like back in the days when no one knew there was anyone else in the world outside of their wittle, tiny villages. Language contact can have extreme impacts on both language and culture, so I wouldn't be surprised if the base 10 counting system spread through contact.
Also, as a slightly on topic note, East Asian languages have base 10 counting systems, as someone mentioned Mandarin earlier. However, it's not exactly the same as English, as we split our larger numbers up as such:
10
100
1,000
1,000,000
But Japanese and Mandarin, and I believe Korean, although I only just started recently on Korean, make a cutoff at 10,000. So, 20,000 instead of "twenty + thousand" is "two + ten thousand." I forgot what the word is in Mandarin, but in Japanese it's 万 (まん, man, [maɴ]). Pretty cool, but it makes counting in Japanese above 10,000 a PAIN.
Also, as a slightly on topic note, East Asian languages have base 10 counting systems, as someone mentioned Mandarin earlier. However, it's not exactly the same as English, as we split our larger numbers up as such:
10
100
1,000
1,000,000
But Japanese and Mandarin, and I believe Korean, although I only just started recently on Korean, make a cutoff at 10,000. So, 20,000 instead of "twenty + thousand" is "two + ten thousand." I forgot what the word is in Mandarin, but in Japanese it's 万 (まん, man, [maɴ]). Pretty cool, but it makes counting in Japanese above 10,000 a PAIN.
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Re: Non Base10 Number Systems in Languages
And it had nothing whatsoever to do with the number of fingers we have?fənɑlədʒɪst wrote:I think it may have been a coincidence that a lot of languages used a base 10 counting system then became powerful

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Re: Non Base10 Number Systems in Languages
gmalivuk wrote:And it had nothing whatsoever to do with the number of fingers we have?fənɑlədʒɪst wrote:I think it may have been a coincidence that a lot of languages used a base 10 counting system then became powerful
Ah well, I have a funny definition of coincidence. I'm sure they're correlated, but the number of languages that don't use base 10 is enough for me to say it's not universal, just statistically significant... which I don't care too much about statistics when it comes to languages anyway. That's why I'm a phonetician and not a phonologist, despite my username haha.
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Re: Non Base10 Number Systems in Languages
Universal or not, I think the simplest explanation for the prevalence of base10 in so many disparate otherwise quite different cultures is that we all have 10 fingers.fənɑlədʒɪst wrote:Ah well, I have a funny definition of coincidence. I'm sure they're correlated, but the number of languages that don't use base 10 is enough for me to say it's not universal, just statistically significant.
Re: Non Base10 Number Systems in Languages
Exactly which languages are you clinging to not having base 10? Some of the languages listed here have a vigesimal system true, but even they are deep down base 10. French for instance does organise things as "sixtyfour" and "sixtyseventeen" but the way they say 74 is soisant dixsept (60 10 7) because their numbers 17 18 and 19 are dix sept, dix huit, and dix neuf respectively, 107 108 109. Even though they have unique words for 11 12 13 14 15 16 they chose to form 17 18 19 with ten. En plus they have unique words for 20 30 40 50 60 and 80 is formed with 420. This really suggests a base 10 system to me, albeit one in which they don't have unique numbers for 70 and 90. I think the same pretty much applies to danish.
All of the other nonbase 10 systems listed are based on multiples of 10: 20 or 60, and I'd be curious to find out whether their spoken forms reflected this fact or whether they were base 10 systems written in more complex ways for whatever purpose.
All of the other nonbase 10 systems listed are based on multiples of 10: 20 or 60, and I'd be curious to find out whether their spoken forms reflected this fact or whether they were base 10 systems written in more complex ways for whatever purpose.
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Re: Non Base10 Number Systems in Languages
cybermutiny wrote:Hey everyone, I just had a random thought the other day: it seems like every language I've ever dabbled in has used a base 10 number system.
Is anyone aware of a language or culture (from past or present) that did not use one?
one of Martin Gardner's books had a whole section on basebased (so to speak) puzzles, introduced with a history of number bases. there were apparently lots of indigenous tribes in various areas that used all sorts of small bases4, 5, 8, 12, etc.usually derived from some other counting habitcount on the spaces between the fingers, count fingers and feet, etc.
lojban supports hexadecimal directly (any number containing the words for digits AF is hex by default), and arbitrary bases through 16 by adding a "base" notation (e.g. if you want to express the decimal number 142 in base 12 you can say the equivalent of "BA base 12").
Re: Non Base10 Number Systems in Languages
ZLVT wrote:French for instance does organise things as "sixtyfour" and "sixtyseventeen"
also that's pretty much unique to French French (it seems to have originated as an injoke by Louis XIV's courtier's). swiss, belgians, and quebecois (and some francophone african countries) say "septante", "huitante" (or "octante"), and "nonante".
Re: Non Base10 Number Systems in Languages
As far as I know, septante and nonante are only used in Swiss and Belgium, and huitante in Swiss only.
A minority of African countries may do as in Belgium, but I doubt Canada is different from France in that regard.
Anyway, what ZLVT said. The French have probably counted by twenties and tens in the middle ages, but today it's just a matter of words for numbers.
A minority of African countries may do as in Belgium, but I doubt Canada is different from France in that regard.
Anyway, what ZLVT said. The French have probably counted by twenties and tens in the middle ages, but today it's just a matter of words for numbers.
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Re: Non Base10 Number Systems in Languages
About a month ago at a concert I saw a performance of a song called Pi, in which one verse was the recital of digits of pi in lojban, in base 16 of course (the first digits are 3,24 by the way). Such a beautiful celebration of geek culture.
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Re: Non Base10 Number Systems in Languages
I want to make a baseπ system. It would finally be rational! And math would be impossible.
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Re: Non Base10 Number Systems in Languages
Pi doesn't magically become the ratio of two integers just because you've got a terminating representation of it.
Re: Non Base10 Number Systems in Languages
in a pi based system would our concept of integer not now rely on pi?
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 Iulus Cofield
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Re: Non Base10 Number Systems in Languages
1) π/π=π
2) Therefore, π is a rational numer in a baseπ system
3) ?????
4) Math is now impossible.
2) Therefore, π is a rational numer in a baseπ system
3) ?????
4) Math is now impossible.
Re: Non Base10 Number Systems in Languages
π/π=1 no matter what base you use.
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Re: Non Base10 Number Systems in Languages
It wasn't a very funny joke anyway.
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Re: Non Base10 Number Systems in Languages
No. Integers are the numbers you can get if you start from zero and keep adding one, along with the numbers you can add to those to get zero (i.e. the negatives). Unless we change the meanings of zero and addition, the integers don't change.ZLVT wrote:in a pi based system would our concept of integer not now rely on pi?
Re: Non Base10 Number Systems in Languages
Danish uses a base 20 system, I think, to some extent. I believe I've also heard that that's true for Basque.
Danes still mostly use base 10, but base 20 for all the tens.
*Waits for Dane to enter thread and correct*
OK, here I am. Only the numbers 50, 60, 70, 80 and 90 are base 20, and even they are not at all obvious to a modern Dane. E.g. "halvtreds" is a contraction of "halvtredje sinde tyve", which is "halvtredje", litterally halfthird, an obsolete term for two and a half, "sinde", an obsolete word for times, and "tyve", twenty. And by obsolete I mean that they are never used and most people don't understand them.
BTW this why "halvtreds", fifty, has a silent d and "tres", sixty, does not. "Tredje" has a d, "tre" does not.
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