Re: Types of numerals

--- In conlang@yahoogroups.com, R A Brown <ray@C...> wrote:
> Tom Chappell wrote:
>> --- In conlang@yahoogroups.com, John Vertical
> [snip]
>>>That there are no primitive non-cardinals
>>>relating to numbers other than 1 or 2.
>> But I think there are, though they may be rare.
>> What about English "quarter"?
> English "half" is surely a better example.
John was asking for words related to numbers other than 1 or 2.

> English "quarter" is derived through Old French from
> Latin 'quartarius' = "a fourth part", which in turn is derived from
> the ordinal 'quartus'. So I don't think "quarter" is a 'primitive'.
Clearly, diachronically speaking, "quarter" is derived, as you
detailed.
But, synchronically speaking, "quarter" is not derived from any
modern English word; (in particular, not from "four" or "fourth");
and that is what I meant.

> Most languages seem to have a word for 1/2 which is not related to
> their word for 2.
I think we suspected as much.

> But 1/4 seems generally (always?) to be derived from a word for 4,
Interesting.  I didn't know that.

> either in the language itself
(English is not an example)

> or, as in English, from another language.
Yes, English is an example of this.  I imagine many of us suspected
it, but I (for one) didn't know the details until you wrote them in.
Thank you.

>> What about the Ancient Egyptian words for "2/3" and "1/3",
>> whatever they were? (Does someone know?
> AFAIK there were not separate root words for these.
> You may be thinking of the fact that
You are, clearly, correct about the source of my mistake.

> in writing fractions were expressed as sums of "unit fractions"
> (reciprocals) (1/n).
I knew that; I think this was in "the Giant Golden Book of
Mathematics" I got when I was eight or so.

> My understanding is that the unit fractions were expressed by the
> symbol _r_ (which, inter alia, was the word for "part" - (the
> Egyptians only expressed consonants, never vowels) - followed by
> the numeral. So 1/3 would be: rIII.
I didn't know that.  Thanks for telling me.

> To do more complicated fractions you just added unit fractions, so
> for example, 2/5 would be expressed by; rIII rXIIIII (1/3 + 1/15).
I knew about the (1/3 + 1/15), but didn't know about the "rIII rXV".

> (I've used the familiar Roman symbols for 10 & 1 instead of the
> Egyptian symbols).
Can we even type in hieroglyphs and/or hieratic and/or demotic script?

> There was, however, a symbol for 2/3 -
Yes, I knew that; and that was the source of my error.

> - but it wasn't a 'primitive'.
I didn't know that.  Thanks for telling me.

> It was the symbol for _r_ (which was a stylized mouth, as the word
> for mouth was also _r_), with two small vertical lines beneath
> signifying the _dual ending_. In other words, it was the dual of
> the word for "part", i.e. 'two parts'. But it came to have the
> specialized meaning of "two parts (of three)", i.e. 2/3. It is read
> as _rwjj_ (IPA values) or _rwy_, depending upon the transliteration
> system used.
I didn't know _any_ of that.  Thanks for telling me;
I'm glad I know now.

>>>> "Two-thirds" was indeed "lexicalized" in Ancient
>>>> Egyptian, so I've read;
> No - a specialized meaning given to the dual of the lexical word for
> "part" - see above.
Yes, I see now.

> On the other hand, Classical Latin did have a lexeme meaning 2/3 -
> it was the masculine noun _bes_ (genitive: _bessis_ )
Yes, a previous poster gave a URL which tells the Latin lexemes for
each of 1/12, 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, 2/3, 3/4, 5/6, 11/12;
as well as, IIRC, 1/144, 1/72, 1/48, 1/36, 1/24.

>>>> and I wager "three-fourths" is lexicalized in
>>>> some natlangs, as well.
> You mean, like the Latin _dodrans_ (gen. _dodrantis_)
Yes, indeed.  Thanks.

>> Does anyone know for sure?
> I know that one for sure   :-)
Thanks, Ray.

Tom H.C. in MI