Oddities of Math and Language

[plaidviking]

While knitting, I come upon the realization that English has the remnants of Base 12 counting in our words for the numbers. For those of you unfamiliar w/ Base counting, it is essentially the number you count up to before your digit moves over. Now modern mathematics is based on Base 10, often given for the fact that we have 10 digits. Though this

Comments

[singingdragon]

Ainu - Base 5, at least the way you seem to be defining it here. Originated in Japan, no known roots in any other languages.

Italian - Base 16, arguably. Latin roots.

[plaidviking]

Yeah, not certain if these languages actually had roots in these Base counting, or perhaps there's another explanation. Thanks for adding more, can't believe I forgot Italian though.

[singingdragon]

Well, no, most of them are actually plain old Base 10 counting. The etymology of the unique number words (at least in the Romance and Germanic languages that I'm most familiar with) between 10 and 20 still reflect Base 10 counting; for example the English "eleven" comes from the Old English "one left" (as in, still one left over after ten), and "twelve" is "two left". "Dozen" for 12 is derived from the Latin "duo" and "decem". Similarly, you can see the Base 10 system in Italian in all the numbers 11-20, even if the construction switches around halfway through from putting the "dici" second ("undici, dodici") to putting it first ("diciassette, diciotto"). The words for numbers in the teens are still made from combinations of the words for 1 through 10 in every European language I've looked at

[plaidviking]

You seem to know quite a bit more than I do on this subject, but yes, I'm sure there have been a fair amount of research done into this. I might do some more thorough research into it to see if there are any other actual mathematical assocications.

It was just a thing I noticed and decided to do some prilimary examination of the occurance in other languages. But good to know about the mutation of words.

Also, how've you been. Seems like a long time since we've chatted.

[3rdragon]

Tonga/Chitonga (South-Central Africa, Bantu language) seems to have five. I can only find up to five in my two books, and at one point my teacher mentioned that Tonga only has words for up to five. (Mind you, I've also been told that you can count to anything you want in Tonga, it's just awkward, which would make sense if it really *is* base five. I'm curious how it's constructed, though.) Upshot of which is that everyone uses English for numbers, even if they only barely speak English otherwise.

And I clearly need to start using the light green Tonga lesson book, which not only has practice sentences like "My goat has aborted" and "My thing is defunct," but also gives both idiomatic and literal translations (Goat of-me it-throw-away and Thing-of-me it-die), which caters to my Yes, but what does it MEAN tendencies. And I'm just as likely to need to say, "My goat has aborted" as "Teacher, my fingers are on my hands" or "We are all farmers," which is what the other book is offering in terms of practice sentences. Although I

[singingdragon]

I couldn't find anything on Tonga specifically. I wonder if it's similar to the Luganda system? Same language family, but I don't know how closely they're related.

Amongst other wacky things, in Luganda 1-5 are adjectives, while higher numbers are nouns. I read through that wikipedia entry trying to work out how, let alone why, the class prefixes shift around in different number ranges, but I gave up. I would definitely say that "you can count to anything you want, it's just awkward" applies here.

[3rdragon]

Just looking at the words, not very, since I only recognize cognates in a few articles and the word for mine (wenge, compared to Tonga wangu. Well, actually -angu, plus a noun-agreement prefix). Uganda is most of two large countries away from here, which is a pretty big distance when it comes to African languages. I'm told that bantu languages are like romance languages, as far as similarities between languages: ranging anywhere from 'you can understand but not speak it' to 'you get a few cognates and a leg up on the grammar.' So perhaps the format of numbers is the same, if not the actual numbers.

I don't know if Tonga 1-5 are adjectives or nouns, since we don't use fancy grammar terms like that around here, but they do need to agree with the thing you're counting, which would suggest adjectives, but mostly I avoid thinking about nouns and classes and such.

[3rdragon]

While looking for something else, I found a Chitonga-English dictionary that does list numbers greater than five:

kamwi one eins
tubili two zwei
tutatu three drei
tune four vier
musanu five fünf
musanu akamwi six sechs
ikumi ten zehn
ikumi amusanu akamwi sixteen sechszehn
makumi obile twenty zwanzig
makumi atatu thirty dreissig
mwanda one hundred einhundet
cuulu one thousand eintausend

The a- prefix means with, so sixteen is literally "ten with five with one."
And ma- is one of the indicators of noun class, I think. You'll note that the -bile root is the same in two and twenty, and the -tatu root in three and thirty. No wonder everybody counts in English, especially considering how terrible most people's arithmetic skills are here.

[singingdragon]

And because I'm just that dorky, I went and looked up Klingon counting. Ancient Klingon was apparently actually base 3, but they started using base 10 after being in contact with other species. Amusingly, they ended up using words for musical notes (the Klingon equivalent of do re mi fa so la ti) for most of the new numbers.

There are a bunch of real languages that don't use Base 10. I found a fun list of number systems here.Huli - Base 15. From Papua New Guinea

[singingdragon]

Correction: Celtic languages do actually have systems for counting to more than 20. Wikipedia is just stupid.

[plaidviking]

Ah yes, Wikipedia. A good springboard for research, but in this age of instant gratification, we tend to latch onto it as law.

[singingdragon]

Yeah. It's just good enough most of the time that it can be hard to spot the failure points. If I'm ever more than casually interested in something, I'll tend to go looking for actual scholarly articles. You can find peer-reviewed articles on ANYTHING.

Well, almost anything. Once a couple of us were trying to figure out how quickly caffeine got into your bloodstream, since someone was wondering if that almost-instant buzz from coffee was biological or a psychosomatic anticipation of an actual caffeine buzz. Yeah, nobody has done that study. As far as we could find, nobody has ever bothered to test serum caffeine levels less than 15 minutes after drinking coffee, which is around when caffeine levels peak. That's more knowledge than I had, but it didn't actually answer the question. A biochemist friend looked into how easy it would be for us to just do the experiment ourselves, but apparently caffeine assays are difficult and annoying.

[helsha]

Old Norse is def base 12.
But of course, so is time.
I have a theory that base 12 systems come from polydactyly.
Base five also makes sense if you're just counting on one hand.
I've got nothing for base 32 or 15 though.