Re: Types of numerals

First, the New Stuff:

How about verbs?

English has "double" and "treble" (or "triple"), for making the object
bigger or more numerous by a factor of two or three, respectively.

English also has the set phrase "half again as ..." for increasing some
attribute (perhaps size or quantity) by a factor of 1.5.

English also has the verbs "to half (smthng)" and "to quarter (smthng)"
and "to decimate (smthng)".

"To half smthng" may mean either "to divide smthng into two equal pieces"
or "to reduce smthng to half as [attribute] as it was before".

Likewise, "to quarter smthng" may mean either "to divide smthng into four
equal pieces" or "to reduce smthng to a quarter as [attribute] as it was
before".

"To decimate smthng" means "to reduce smthng by removing one-tenth of it".

---

Wouldn't it make sense for a language having verbs equivalent to "half"
and "quarter", to have a verb for "to divide smthng into three equal
pieces"?

Wouldn't it make sense for a language having verbs equivalent to "half"
and "quarter", to have a verb for "to reduce something to one-third as
[attribute] as it was before"?

Wouldn't it make sense for a language having verbs equivalent to "half"
and "decimate", to have a verb for "to reduce something by removing one-Nth
of it" for N=3, 4, 5, 6, 7, 8, or 9?

---

In L. Neil Smith's science-fiction novel "Their Majesties' Buccaneers",
there is a species -- the lamviin -- who, along with every other species
native to their home planet, have trisexual reproduction, three sexes, and
a body plan relentlessly built on a plan-of-three (radially symmetrical).
Any thing that a body has more than one of, it has at least three of (for
instance, three limbs, three jaws, and, a three-lobed cerebrum); and if it
has more than three of them, it has a power-of-three of them, arranged in
three equal groups (for instance, nine feet/hands and twenty-seven digits;
three hand/feet per limb for three limbs, and three digits per hand/foot
for nine hands/feet.)

In that story, the lamviin have a word for "two-thirds of"; but they never
use a word for "half of". Similarly, I expect they have a word for "one-
third of"; and a word or words for one or both of "one-and-a-third of"
and "one-and-two-thirds of".

-----

Now, on to answering your post.

--- "Mark J. Reed" <markjreed@...> wrote:
> This is going to bounce from the list since I'm
> over quota, I just realized.  So I'll send it to
> you so you can cogitate on it before I re-send it
> to the list tomorrow. :)
Thanks.

> ---------- Forwarded message ----------
> From: Mark J. Reed <markjreed@...>
> Date: Jan 7, 2006 6:54 PM
> Subject: Re: [Theory] Types of numerals
> To: Constructed Languages List
> <CONLANG@...>
> On 1/7/06, tomhchappell <tomhchappell@...>
> wrote:
>
>> Yes, linguists writing in English use "numeral"
>> to mean "words for numbers", to distinguish
>> from "number" usually short for "grammatical
>> number" (singular, plural, etc.)
>
> Well, I didn't know about that usage.  Of course,
> I'm not an actual linguist.
> Dadgum linguists -  always messin up language.
> Say they're just being descriptive, but at the
> same time they're modifying whatever language
> they're doing their describing in.
> :)
Uh-huh.
What Heisenberg's Uncertainty Principle ("you can't observe something
without affecting it") is to Quantum Physics, the following is to
Linguistics; "you can't use a language without changing it".

>> "Both" is to "two" as "???" is to "three", and so
>> on. In some English writing from the 19th and
>> early 20th centuries, "both" is used to
>> mean "all three of", as well as "all two of".
>> Might a series meaning "all two of" (both), "all
>> three of", ..., "all n of", ... be useful?  How
>> much of this series is attested in natlangs?
>
> I don't know the answer.  It would seem to have
> limited utility; the exact value of n in "all n
> of" seems less important, in general, than the
> fact that it's "all" of the items under
> discussion.
Nevertheless, English (and other languages -- one of the classical
languages contributed the English prefix "ambi-" meaning "both") has a
special word for "all two of", and apparently English users have or had
a "felt need" for a word for "all three of".  I think for "smallish" N, the
concepts in this series might be individually lexicalized; with the
probable system being that, the higher N is, the likelier the word is to be
regular and transparent (if it exists at all).

> Also, you asked what "halfth" vs "half" would
> be.  I can easily imagine a formation analogous
> to "halfth" meaning something like "the halfway
> point".  After all, many children will proudly
> tell you that they are, for instance, four and a
> half years of age; that would imply that they
> have passed their four-and-a-halfth birthday.
> (I have passed my thirty-seven-and-a-halfth
> birthday this past November and will celebrate my
> thirty-seven-and-three-quartersth in February. :))
Interesting idea; that might make sense.

BTW When Lyndon Johnson was JFK's Vice-President, LBJ's press secretary
(Bill Moyers) and LBJ decided that there was probably some job more
exciting than being the Vice-President's press-secretary.  The Peace Corps
had just been created, so Johnson got Kennedy to nominate Moyers to head up
the Peace Corps.  During the Senate confirmation hearing on this
nomination, the question came up whether such an important Federal role
should go to someone so young.  One Senator asked Moyers his age, and
Moyers replied: "Twenty-eight _and_a_half_, Senator."

> Of course, such a construct would probably be a
> later, learned addition to the set of linguistic
> numerals.
> Speaking of which: why do you not consider "pi"
> to be a numeral in the linguistic sense?
But I do consider "pi" to be a "linguistic numeral".

I don't know what I said to give you the idea I don't, but maybe it was
when I said "a numeral is 'spelled with' digits".
1) I only meant that, "_Most_ numerals can be spelled _mostly_ with digits".
2) The use and sense of the word "numeral" in that sentence (and in the
whole story of me teaching Math for Elementary Ed Majors), is a different
sense, and a different sort of use, from that in the story about linguists
distinguish words-for-numbers from grammatical number.

OTOH, maybe it was because I said I don't expect to introduce words for
irrational numbers in my first conlang(s).
1) I haven't gotten around to much of the conlang at all -- even
the "counting numbers" (positive natural cardinals less than [in my
case] 'base-to-the-(base-to-the-base power)') is just a sketch, at this
point.
2) Words for famous irrationals such as the square-root of two, the golden
ratio, and pi, are mostly "learned" words, not usually primitive in known
natlangs.  If I design a conlang for an ancient (similar to the Mesopotamia
of Gilgamesh, or Imperial Rome) or medieval society, I expect any words
they have for irrationals to be, similarly, learned rather than primitive.
3) OTOH 'my other conlang' is supposed to be for an interstellar multi-
species spacegoing society containing Artificial Intelligences, which has
been spacegoing, interstellar, multi-species, and had AI citizens, for so
long that the language basically developed with all of these things as
givens.  In that language, perhaps these "famous irrationals" should have
their own, monomorphemic words; and so, perhaps, should the imaginary unit
("i", the square-root of "-1").

> It is thoroughly lexicalized and probably more
> associated with the numerical value than the
> letter of the Greek alphabet in the minds of most
> Anglophones . . .
Good reasons to consider it a "(linguistic) numeral", that is, "the name of
a number".

Tom H.C. in MI

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