Re: Types of numerals

tomhchappell wrote:

> > Descendants of Latin numbers occur so often in English
> > that they can be considered separate roots.
>
>Yes; so, the simplest English word) derived from each Latin number
>(other than 1 or 2) that is not obviously related to an English
>number, should be considered "a primitive non-cardinal relating to a
>number other than 1 or 2".  Right?
Right, unless one wants to call the root forms cardinals (compare
"tripartite" ~ "three-parter")


> > Also, this in turn is then an example of two largish sets of
> > unrelated (or opaquely distantly related) number roots in one
> > language!
>
>I think Greek and Latin versions of "one, two, three, six, seven,
>nine" may appear to be related to the corresponding English versions,
>but Greek and Latin versions of "four, five, eight, ten" do _not_
>appear to be related to the corresponding English versions IMO.
I agree with tri-, sexe- and non-, but uni-, septe- and duo- are already a
little hazy, and the others you suggest are even less recognizeable.


> > I think mass-noun-numerals are still cardinals;
> > like count-noun-numerals, they describe an _amount_
> > rather than a rank or order.
>
>To me, that means they aren't ordinals;
>it _doesn't_ make them cardinals, IMO.
Technically, you're right, but my (linguistic) intuition still claims that
they're cardinals; I guess primarily because ordinals are marked with
respect to cardinals, and numbers like "pi" are unmarked.
If cardinals' "adjectival" and"prominal" and perhaps other usages were split
into different words, they could be made universally marked, too.
Especially, if measures of mass nouns behaved differently from measures of
count nouns, real numbers *would* end up as their own, non-cardinal
category.


> >> The "eth" value of some function (say "f") would be
> >> f(e), that is, f(2.718281828459045...).
> >> The "-4th" value of "f" would be f(-4).
> >
> > Yes, they can certainly be interpreted in *some* contexts as
> > meaningful, but I doubt you're going to think of any *useful* ones.
>
>Since I consider mathematics, even pure mathematics, "useful", I'll
>have to ask you to change "any" to "many".
...I've often used those sorts of constructions too, so I plead changing
"useful" into "useful outside of mathematics" instead.


> > And "pair" isn't particularily mathematical anyway.
>
>Oh yes it is! [Details withheld in the interests of space.]
A set with two members? Eh, OK then.


> >> In particular, you don't object to,
> >> "For each n>2, many languages which have their own
> >> "words for 1+(1/2) and 2/3, and which have a
> >> "special word for 1/n, will also have special words
> >> "for 1-(1/n) and 1+(1/n)."
> > Correct, assuming that regularly derived words aren't "special".
>
>I _think_ that might have been part of what I meant by "special",
>or "own".
I'm not agreeing then - lots of languages have a way of regularily deriving
reciprocals, but I haven't seen ways of regularily deriving 1±1/n for
arbitrary natural n.


> >> In this particular case, the "'" in "se'ennight"
> >> represents that the "v" is left out, but the two "e"s
> >> are both pronounced.  So the "se'en" part of the word
> >> is pronounced as, in length, stress, and tone, two
> >> syllables.  The second "e", because it is unstressed,
> >> should technically be pronounced as a schwa, but since
> >> it directly follows a stressed short "e" (IPA symbel
> >> [e]), it sounds very much like an unstressed and
> >> lower-toned [e].
> > So _all_ apostrophes are pronounced as hiatus (or schwa?)
> > No risk of running into dialectal glottal stops?
>
>Well, in Standard English, both Standard American English and British
>Received Pronunciation, an apostrophe always represents "sounds left
>out".  It won't usually be pronounced "schwa", and in fact usually
>won't be pronounced at all.
I ask because this seems to put some checked vowel sounds into open
syllabes. I've never heard of /E/ occuring before other vowels; does it
become /eI)/ or (non-rhotic 'lects only) /E@)/?


>there is no glottal stop in "chaos", nor in "vacuum".
"Vacuum" has a third syllabe? I just say "vacume".


> >> BTW I understand English once had a labio-dental
> >> semivowel (approximant);
> > /v\/ in English? Really?
>
>So I've read somewhere -- I don't know where.
>
> > So where did it come from and whence it went?
>
>(You mean, "whence did it come and whither did it go?" ;-) )
Um, probably. :]

Still, I've browsed thru
http://en.wikipedia.org/wiki/Phonological_history_of_the_English_language
a few times and there's nothing on the topic there.


> >> Perhaps it wasn't so difficult for Old English speakers
> >> to tell the difference between a bilabial approximant
> >> ("w") and a labiodental approximant.
> > Myself having /v\/ in my L1, I can confirm this.
> > The velarization of /w/ of course also eases things up.
>
>Yeah, I guess it would, if /v\/ is _not_ velarized.
I guess it might be allophonically, especially in situations where it stems
from earlier /G/ (some u_u and Vu_V environments) but it's certainly
stereotypically rather clear. Finnish has lost almost all traces of its old
palatalization system, which I guess also featured allophonic velarization.


> >>>>> In Finnish, the simplest polygon names are
> >>>>> derived instead (with the generic agentative
> >>>>> affix -iO),
> >>
> >> So a pentagon is a "fiver" and a decagon is a
> >> "tenner"?
> >
> > No, only "triangle" and "square" are derived this way.
>
>Ah.  A triangle is a "three-er" and a square is a "four-er"?
Yes. Actually, I realize, "-ee" might be a slightly better translation for
"-iO", since in those rare cases where it adds to a transitive verb root, it
has a resultative function instead.


> >>> This only works with decimal system tho, not with
> >>> fractions.
> >>
> >> That is, not with "common fractions" like one-third or
> >> two-sevenths or four-ninths?  Clearly it works OK with
> >> decimal fractions like 0.466.
> >
> > "Four-hundred-sixty-six thousandths" or "four tenths six hundreths
> > six thousandths" certainly is a fraction, but "zero dot four six six"
> > isn't.
>
>I think it is; I think "zero period four six six" is synonymous
>with "four tenths six hundredths six thousandths".
Still, it's not the same expression. The syntax for the affix demands a form
ending with a digit or power-of-10 numeral in basic form.


>"Percent" occurs frequently, but "parts per thousand",
>"parts per million", and "parts per billion" occur less frequently.
And "perdeca" "°/" seems to be nonexistant. :)


> > NAND and XOR would be easy additions to this
> > family, were they not tricky to generalize for
> > more than 2 arguments.
>
>XOR is commutative and associative -- it should present no problems
>generalizing to any finite positive number of arguments.
Technically, yes, but as you've discussed with Jim Henry, it's not obvious
if an exclusive-or applied to more than two objects means 1) exactly one, 2)
some but not all (ie. ((OR) AND (NAND))) or 3) something in-between.
If someone knows well a language which has an inclusive/exclusive "or"
distinction, it would be interesting to hear how's the case there.


>This was the part I was asking "What do you mean, exactly?" about.
>What (exactly) is "random-quantitative"?
>How (exactly) is it different from "simply qualitative"?
Mostly it's a question of scale. For instance, 10000±2000 is qualitative;
9408.177 is random-quantitative, even adding "±0.03" (at least if there's no
specific meaning to the number.)


> > draw attraction
>
>You mean, "draw attention"?
Aggh, sloppy writing. Yes.


> >> these two verbs have two meanings.
> >> One meaning is "to make half" or "to make 1/4";
> >> (*) but "halve" also means "two divide into two
> >> (nearly) equal pieces", and "quarter" also means "to
> >> divide into four (nearly) equal pieces."
> >
> > Hmm, true. I think this 2nd meaning is not even really directly
> > reciprocal; you did write "to divide into 2 parts" and not "to
> > divide into halves".
> > I mean, if we assume it IS reciprocal, what would be the natural
> > number equvalent? "To divide into 1/2 parts?" Would that be "to put
> > two similar things together" or what?
>
>Interesting question.  I suppose it could mean "join pairs of similar
>things together so that you end up with half as many separate pieces
>as you started out with, but without discarding any of them."
>
>I don't know; does "marry" or "mate" cover this idea?
Or just "pair". However, none of those convey conjoining (and yes I know
halving doesn't *have* to involve breaking), and "to halve" sounds like a
more basic concept anyway. Who knows, maybe it's the original root word and
"half" was derived from it, and not the other way.


>Tom H.C. in MI
Also, thanks for all the interesting information that got snipped from this
reply.

John Vertical

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