Shu sent me this excellent YouTube link about how the linguistics of numbers vary so much around the world. Bob might be especially interested with his mathematical background, and there are a lot of references to China.

Enjoyed this video, Kalleh. Fascinating!

Wasn't it? Usually I don't like to just post a link without analyzing the content, but this was hard to summarize since it was chock full of examples of how numbers vary in different languages. Definitely a good video though.

It's a good video, but it led me to expect something I didn't get. When he is talking about aliens he is saying, I think, that humans use numbers is such different ways that if we try to open communications with another group of humans by starting with 1+1=2, it might not work. But he gives no evidence of this.

Most of the video is about the etymology of words for numbers in some languages. So Danish words for numbers have some unusual etymologies. What does that have to do with how Danes use numbers?

He says "Dozen" and "score" are base 12 and base 20 counting systems, but I don't think they are. A base 12 system would have "dozen and 1" for 13, "dozen and 2" for 12, "dozen and A" for 22, "dozen and B" for 23, and so on.

He could have mentioned Scots Gaelic, which has more base 20ish features than English:

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")

This message has been edited. Last edited by: goofy,

Goofy, I always like you comprehensive analyses. I learned from this how very different the number system is across the world, though of course the language system, itself, is different, too, so I don't know why he was so surprised.

I can't remember an example, but do recall the Scots Gaelic "four and twenty" and such used in English literature.

Fom the nursery rhyme "..four and twenty blackbirds baked in a pie."

"four and twenty" is just a fancy way of saying "twenty-four".

The French system of using 20 was probably borrowed from Celtic: soixante-dix "sixty-ten" for 70 and quartre-vingt "four twenty" for 80.

The north England counting system yan tan tethera was perhaps borrowed from Celtic.
https://en.m.wikipedia.org/wiki/Yan_tan_tethera

A.E. Houseman's poem, "When I Was One and Twenty" uses it.

quote:

Originally posted by Geoff:
A.E. Houseman's poem, "When I Was One and Twenty" uses it.

Uses what? "One and twenty" and "four and twenty" aren't Celtic or base 20, they're just alterations of "twenty-one" and "twenty-four".

No system that uses ten symbols (0,1,2,3,4,5,6,7,8,9) can be anything other than base 10. Hexadecimal, base 16, has sixteen
symbols (0,1,2,3,4,5,6,7,8,9,A.B.C.D.E,F) and a base 20 system would need twenty symbols (0,1,2,3,4,5,6,7,8,9,0,A,B,C,D,E,F,G,H,I,J).
Things like "a dozen", "four and twenty", a "score" and so on are just different words being used to express base 10 numbers.

This message has been edited. Last edited by: BobHale,

Bob, what about a language with no writing system? Is it impossible to tell what base it uses, or does it make no sense to ask?

By "no writing system" are you including ways of writing down numbers?
For example, inventing one on the spot, would you count this as a writing system?
. : .: :: .:: ::: .::: :::: .:::: :::::

yes.
I'm asking because your definition of base seems to have everything to do with how it is written. That make sense to me. But it follows from that that if the language is not written, then it doesn't make sense to talk about what base it is.

Let's imagine for a moment that English had no written form.
There would still be sounds that corresponded to the numbers 0,1,2,3,4,5,6,7,8,9.

Although some are irregular there are sounds that correspond to ten times each of those. We make the intermediate numbers by saying the ten times number followed by the one times number. There are sounds that correspond to one hundred times the single number and we make intermediates there by saying the hundred times number followed by the ten times number followed by the one times number.

That structure is base ten, whether it's written down or not.
If we had twelve fingers it would most likely be single sounds for 0 to 11, another set of sounds meaning 12 times the single sounds and another set meaning 144 times the single sounds.

OK our "teens" are sounded (and written) differently to the "-ties" (twenty etc) and eleven and twelve are completely irregular but apart from that we have a regular sound-based base ten system.

Hope that makes my thinking clearer.

OK... so Hindi numbers from 1 to 100 are irregular. If Hindi had no writing system, would it be base 100?

Does it have any structure that can be used to determine those numbers or are they all separate sounds (and/or written symbols.)

How does it create the numbers between 100 and 10000 when speaking?

I don't have enough information to formulate an answer.

The wikipedia article notes that the numbers for twenty, thirty etc are unique but though the numbers in between aren't - they are produced in a predictable way. This doesn't seem to differ from our system to me. It also notes that there mathematics is base ten. The names of the numbers don't matter.

The difficulty in expressing what I mean here seems to stem from conflating three things - the number, the symbol for the number and the name of the symbol.

Ignoring all symbols and names of symbols the question of their base would be solved by giving them a pile of stones and seeing how they divided them up. If they have 76 stones and they make seven piles of ten and one pile of six they are using a base ten system. If they make six piles of twelve and one pile of four they are using base twelve and so on. Regardless of how they name them.

quote:

Originally posted by BobHale:
The wikipedia article notes that the numbers for twenty, thirty etc are unique but though the numbers in between aren't - they are produced in a predictable way.

I can't find that article but I disagree, they're not predictable, but you can see the remnants of a pattern:
http://www.omniglot.com/language/numbers/hindi.htm

Latin numbers are base 10 but Roman numerals are not, so what base did Romans use? Does it matter?

This message has been edited. Last edited by: goofy,

It's tme for my bed now but I'll find both that article (which was, I think, from wikibooks rather than wikipedia) and a good article I read yesterday about why the Roman system can be considered either as a base ten system or as a combination of base two and base 5. I wasn't entirely convinced by it but it was interesting.