Numerals

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HoskhMatriarch
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Numerals

Post by HoskhMatriarch »

OK, I keep getting pestered by Gornec (even when I haven't made a new language) and I'd like to give him numbers, but none of my languages have numeral systems, except I think Spraka might have a few numbers (although Spraka is a fauxlang with most of the words copied from English and German and occasionally words from other Germanic languages so who cares). But, I really want to make some interesting systems. The first idea I had for a numeral system was basically Danish but with 11 and 12 as oneteen and twoteen and numbers greater than 10 that are 8 or 9 after being 1 or 2 before (so, twenty eight would be two from thirty) like Latin. That's not particularly creative. My second idea is almost completely normal except that 5-9 are one-five, two-five, three-five, four-five in "backwards" order even though twenty-one would be twenty-one in that order, and I don't like that idea much either, even if it's more creative and natural than Latin meets Danish. So, what are some of the most interesting numbers you all have seen or made?
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Sumelic
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Re: Numerals

Post by Sumelic »

Well, there's Piraha (there's always Piraha...) Actually, I've been thinking about this as well; do you mind if I add one more question? Does anyone know of a natlang where the default position for compound numbers is around the modified noun, in the following way:
one dog = one dog.sing
two dogs = two dog.plur
twenty dogs = twenty dog.gen
twenty-one dogs = one dog and twenty

I guess it could work around classifiers as well, something like the following:
one dog = dog one [animal-CLASS]
two dogs = one dog = dog two [animal-CLASS]
twenty dogs = dog [animal-CLASS] twenty
twenty-one dogs = dog one [animal-CLASS] twenty
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druneragarsh
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Re: Numerals

Post by druneragarsh »

Finnish has base numbers 1-7, forms 8 and 9 as "2 away from 10" and "1 away from 10" (though using the PIE dek- root), and has 10 be derived from "palm, hand".

For Proto-Ṭelö, I formed the numbers like this:
1 = finger, ḷirä
2 = pair, tẹsa (ordinal ḳora)
3 = 4 without 1 (4 1-PRIV), kärä ḷiräti
4 = palm, hand, kärä
5 = other hand, ḳora kärä
6 = hand and pair (hand pair-COM), kärä tẹsaka
7 = 8 without 1, ṭelö ḷiräti
8 = person, ṭelö
9 = 8 1-ASSOC, ṭelö ḷiräŋy
10 =8 2-ASSOC, ṭelö tẹsaŋu
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HoskhMatriarch
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Re: Numerals

Post by HoskhMatriarch »

Wow, these are some long numerals... https://en.wikipedia.org/wiki/Alyutor_language#Numerals
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Re: Numerals

Post by Micamo »

Tazaric numerals:

bún̪ wááŋ gá
little eye one.F
one little eye

bùn̪ wáàŋ d̪ó̤ó̤
PL\little PL\eye two.F
two little eyes
My pronouns are <xe> [ziː] / <xym> [zɪm] / <xys> [zɪz]

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Keenir
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Re: Numerals

Post by Keenir »

HoskhMatriarch wrote:OK, I keep getting pestered by Gornec (even when I haven't made a new language)
that's unlike him.

could he have gotten the wrong impression, that you were making more conlangs?
and I'd like to give him numbers, but none of my languages have numeral systems,
just say, in your post or in a reply to him, either
"Haven't gotten around to the numbers yet, sorry."
or
"Speakers of this conlang, just use the numbers of their neighbors."
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sangi39
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Re: Numerals

Post by sangi39 »

HoskhMatriarch wrote:Wow, these are some long numerals... https://en.wikipedia.org/wiki/Alyutor_language#Numerals
Meh, one through to five are basic, being two or three syllables long, which isn't too unusual and you can find these number with similar lengths in a number of languages (although it looks like three and four might be derived in Alyutor, but it's not mentioned, and some of the endings seem to drop in combined forms), and then ten and twenty are base numbers too. After that it's a case of multiplying and adding numbers together, which is pretty universal when it comes to forming higher and higher numbers (although oddly enough, twenty isn't used in forming higher numbers at all).

So 99 is basically ((4+5)x10)+(4+5) as opposed to the English (9x10)+9 or the French (4x20)+9 or the German 9+(9x10).

In the Chumashan languages, apparently, 99 would have been something like ((2+4)x16)+3 since they used base-4 and base-16, while Komnzo, using base-6 would have it as (2x36)+(4x6)+3 while 72 would simply be (2x36) as opposed to the French (6x10)+12 or the English (7x10)+2.

I've used base-8, base-10 and base-5 so far in my conlangs, trying to shift the base-8 one into base-10 and base-12 and found that number length is pretty relative to the language, the base system they use and what number you're actually trying to use. Base numbers tend to be shorter than derived/combined forms and then the system kind of just starts over with a few extra syllables thrown in. In counting, they might find short cuts, such as only counting in units until they hit the next base and then only saying the full number at regular intervals (I tend to do this at work, e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, ...., 8, 9, 20, 1, 2, ... and so on) so that large numbers don't become a problem during counting. Specific numbers will likely turn up in set circumstances, while the majority of the time the bases will do, in a similar manner to English users saying "hundreds of people" or "thousands of flies" except Komnzo speakers will say "216s of people" or "1296s of flies".
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eldin raigmore
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Re: Numerals

Post by eldin raigmore »

How do speakers of your conlangs — and/or natlangs if you like — say and/or write the following eighteen numerals?
  1. 16
  2. 81
  3. 256
  4. 512
  5. 625
  6. 6,561
  7. 19,683
  8. 65,536
  9. 262,144
  10. 390,625
  11. 1, 953,125
  12. 33, 554,432
  13. 43, 046,721
  14. 134, 217,728
  15. 4,294, 967,296
  16. 152,587, 890,625
  17. 847,288, 609,443
  18. 7, 625,597, 484,987
In English these are
  1. sixteen
  2. eighty-one
  3. two hundred fifty-six
  4. five hundred twelve
  5. six hundred twenty-five
  6. six thousand five hundred sixty-one
  7. nineteen thousand six hundred eighty-three
  8. sixty-five thousand five hundred thirty-six
  9. two hundred sixty-two thousand one hundred forty-four
  10. three hundred ninety thousand six hundred twenty-five
  11. one million nine hundred fifty-three thousand one hundred twenty-five
  12. thirty-three million five hundred fifty-four thousand four hundred thirty-two
  13. forty-three million forty-six thousand seven hundred twenty-one
  14. one hundred thirty-four million two hundred seventeen thousand seven hundred twenty-eight
  15. four billion two hundred ninety-four million nine hundred sixty-seven thousand two hundred ninety-six
  16. one hundred fifty-two billion five hundred eighty-seven million eight hundred ninety thousand six hundred twenty-five
  17. eight hundred forty-seven billion two hundred eighty-eight million six hundred nine thousand four hundred forty-three
  18. seven trillion six hundred twenty-five billion five hundred ninety-seven million four hundred eighty-four thousand nine hundred eighty-seven
In case you’re wondering (you probably are), these numbers aren’t random.
They’re the values of A^(B^C) where each of A and B and C varies through the whole numbers from 2 to 5, except I didn’t include values greater than 3^(3^3). I also left out duplicates such as 2^(2^5) = 4^(2^4) = 4^(4^2).

I’m interested how languages, especially your languages, handle very large numbers.
Or which ones they don’t handle; I think European languages didn’t handle numbers as great as one million before the First Crusade.

If your language’s numeral system has a base other than ten, of course that will be interesting.
But even with base ten, your language might use the equivalents of myriads or crores or lakhs instead of millions and billions and trillions.
And if they use billions and trillions, maybe a billion is a million million and a trillion is a million billion, and a thousand million is a milliard.
And so on.
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Reyzadren
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Re: Numerals

Post by Reyzadren »

^My conlang would just say the digits out individually, amongst several methods. Easy.

Base 10, but it doesn't use thousand/million, it uses tenthousand instead.
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eldin raigmore
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Re: Numerals

Post by eldin raigmore »

Reyzadren wrote: 27 Sep 2020 23:56 ^My conlang would just say the digits out individually, amongst several methods. Easy.

Base 10, but it doesn't use thousand/million, it uses tenthousand instead.
If your base B is ten or fewer, it might be sensible to use the sequence
B^(2^n)
for a base-sequence, rather than
B^n.

OTOH if your base B is ten or greater, it might be more sensible to use the
B^n sequence, than the B^(2^n) sequence.

....

The sequence in which each is the square of the previous one, starting at ten, is
Ten 10
Hundred 100
Myriad 10000 (I think this is what you meant by “ten thousand”?)
Myriad-myriad or hundred-million 100,000,000
10^16 or ten quadrillion
10^32 or hundred nonillion
10^64 or ten vigintillion

I don’t see any point in going greater than 10^80.
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Reyzadren
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Re: Numerals

Post by Reyzadren »

eldin raigmore wrote: 28 Sep 2020 01:42
Reyzadren wrote: 27 Sep 2020 23:56 ^My conlang would just say the digits out individually, amongst several methods. Easy.

Base 10, but it doesn't use thousand/million, it uses tenthousand instead.
Myriad 10000 (I think this is what you meant by “ten thousand”?)
Yes, ten thousand = 10000
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Iyionaku
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Re: Numerals

Post by Iyionaku »

Reyzadren wrote: 27 Sep 2020 23:56 ^My conlang would just say the digits out individually, amongst several methods. Easy.

Base 10, but it doesn't use thousand/million, it uses tenthousand instead.
That's interesting. Are there any natlangs who express big numbers like this?
I'm not saying you cannot absolutely do this - it's your conlang, after all. But I lay awake last night for a while thinking about it, and I (as a linguistic amateur, mind you) can see many practical problems with it.

Mostly, you have no idea how big a number is until it's said completely. For instance, take the simple question "how big was the turnover of this company last year?" And now somebody answers "well, it was a total of two four five eight zero zero zero zero zero Dollars."... and you need to count how many digits were said in your head. So was it four zeros? Or five? What exactly was the first number again?
Also, you don't have any redundancy in case you couldn't the speaker properly. In English or Chinese (among all other natlangs I know) you can still get how big the number was at all, even though you didn't completely understand the number. "It's [inaudible] thous-[inaudible] forty-five" - you still know it's in the 4-digits, or maybe 5. In griuskant, someone might just hear "it's [inaudible] four [inaudible]", leaving the listeners completely clueless.

These are just my thoughts and I might be completely wrong here. Maybe some of the more adept or professional linguists in this board can share their thoughts on that.
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Reyzadren
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Re: Numerals

Post by Reyzadren »

^Eldin raigmore posted very specific large numbers, without trailing zeroes. In general conversation with approximation, like your example, they would also use place values. In griuskant, this can be expressed with the standard form as usual, which is coefficient x 10^magnitude.

:con: griuskant (without script here)

zhe pludsaenae degnastae sloukekson az voe? 2.458 x 10^8.
/'ʒə 'pludsene 'dəgnaste 'slɔukəksɔn az vɯ? 'tʃaus gəz 'hiɔdliugθuan 'kəru 'θuan/
this group-PL-POSS-PASS-POSS back-year-POSS trade-plus-EB-PASS is howmany? 2 decimal 458 10magnitude 8
How big was the turnover of this company last year? Well, it was a total of 245800000 dollars.

Of course, having 1 convenient place value at the end would still require one to wait, but the opposite also has problems: Every intermediate place value is repeated, and at the end, I might have forgotten the initial magnitude [:O]
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lsd
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Re: Numerals

Post by lsd »

I do the same in sajátnyelvföld...
and all languages do it in writing without the need to count the digits...
you just have to write/pronounce them in short, regular groups...
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eldin raigmore
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Re: Numerals

Post by eldin raigmore »

It seems to me that some natlangs group them in twos and fours and maybe eights (not sixteens unless the base is lower than ten.)
Some natlangs group them in threes and sixes; not aware of any that group them in twelves.
I will be surprised if that exhausts the possibilities.

The numbers I asked about are all powers of 2 or 3 or 4 or 5. That’s why none of them have trailing zeroes in decimal representation.

If you would like to express, for instance, all the B^(2^n) where B is your base and n runs from, say, zero to 9, go ahead!
That would be particularly interesting if B is one of 4 or 5 or ten or twelve or twenty. Ten and twenty seem to be the most common exponential bases in WALS.info. Twelve is popular among conlangers. And when Greenberg’s students studied them, those five bases — four, five, ten, twelve, and twenty — were found to be most common among the languages in their sample.

2^(2^9) is probably going to be bigger than your computer can express exactly.
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