Re: Types of numerals
| From: | Tom Chappell <tomhchappell@...> |
|---|
| Date: | Friday, January 13, 2006, 22:45 |
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--- In conlang@yahoogroups.com, John Vertical
> <johnvertical@H...> wrote:
>> From: tomhchappell <tomhchappell@Y...>
>>> ... Also, whenever I'm talking about "series",
>>> I mean an ordered infinite series where each
>>> member is related in meaning to the respective
>>> natural number. By my definition, all numerals
>>> must belong in some series (won't be much of a
>>> numeral otherwise).
>> Including fraction-words and/or
>> mixed-fraction-words?
> Well, fairly "random-looking" numbers might be
> hard to put into any one "natural" series, but
> then again, they're almost always expressed with
> two or more numerals - that is, "9/16" will be
> derived from "9" and "16" rather than "4" plus
> "1-1/x" and "x^2" morphemes (and that was still
> easy to reduce to one natural number!)
> Mathematical constants I guess will have to be an
> exception, especially since e and pi are both
> transcendental...
>
>>> .:BASIC SERIES:.
>>> Every language probably has the two basic
>>> series - the natural cardinals (one, two,
>>> three...) and the natural ordinals (first,
>>> second, third...) But is it always the former
>>> which is the open lexical category?
>> Both of them technically have to be "open" in
> order to accommodate numbers that have never
> before been used;
> I may be misusing the term "lexically open"...
> Nevertheless you seemed to figure out what I
> meant.
>> but in some languages one or the other is not,
>> in fact, an "open" (sub-category. In these
>> languages there is a highest number one can
>> count to.
> O_o
> Are you ruling compounds out too?
No, I can't rule out compounds, nor phrases ("phrasal
numerals"?), nor neologisms.
The examples are: English "vigintillion" (=10^120
"long count" (formerly "British system"), =10^63
"short count" (formerly "American system");
and English "centillion" (=10^600 "long count"
(formerly "British system"), =10^303 "short count"
(formerly "American system")).
To get higher numbers in English you would have to
multiplly "centillion" by some smaller number and then
add in whatever is left over; or else, create a new
word.
> Because even the most number-limited languages
> I've heard of (with only 1 and 2) allow "linear"
> number systems, where eg 8 = 2222.
Yes; that would be a purely "additive" system.
English, and many other languages (including all of
those that use a "base" in the same sense that English
is "base ten" and Danish is "base twenty"), have a
"multiplicative & additive" system.
If those languages could say "two twos of twos", that
would be a base-two multiplicative/additive system.
> (Also interpretable as a two-level base system
> with base 1&1.)
I don't get it. Explain? Thanks.
>>> Does any language have ordinals as the unmarked
>>> series instead?
>> I don't know of any language which has _all_
>> ordinals "marked" (especially in contrast to
>> cardinals); but as I understand it some
>> languages do have some ordinals that are just
>> as "primitive" as their corresponding cardinals.
> Yes, this is true - but all languages I know have
> a higher number of primitive cardinals than
> ordinals.
AFAIK this is correct; I, also, know of no language
that has more "primitive ordinals" than "primitive
cardinals".
>>> I presume that another universal feature is
>>> that while numerals are an open class
>>> (theoretically more open than any other word
>>> class - but lets not go there now), after a
>>> certain threshold, all words relating to a
>>> certain number will be derived similarily.
>> This is covered in some book either written by
>> or edited by Greenberg.
>> What you say is true for those languages
>> which "can handle" (i.e. have words for) the
>> biggest numbers.
>> In other words; up to a point, the statistical
>> implicational universal is, the higher numbers a
>> language "can handle", the more regular its
>> lexicogeny (rhematopoeisis) for numerals will be.
> Yep, I can see that.
Good. Thanks.
Do you know of any professional-linguist writings that
might corroborate or disprove that hypothesis?
>>> However... isn't it theoretically possible to
>>> have more than one "root series"?
>> _I_ don't see why not.
>>> This would probably need a base of 5 or less,
>>> given that languages usually have only very few
>>> non-cardinal numerals which are unrelated to
>>> the corresponding cardinal words.
>> I do not understand why you think your
>> conclusion follows from your premise.
> It does if for "need" you read "require in order
> to be remotely naturalistic" rather
> than "logically imply".
I understand your more-restricted, clarified,
implication; and I agree it's likely (more likely than
the less-restricted mis-reading of your original
remark); but I still don't see "why", just because
"languages usually have only very few non-cardinal
numerals which are unrelated to the corresponding
cardinal words", it follows that "in order to be
remotely naturalistic, having more than one 'root
series' would probably require a base of 5 or less".
>>> In fact, all languages I know of have 2 per
>>> series tops,
>>What does that mean, exactly? I don't understand.
> 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"? What about the Ancient
Egyptian words for "2/3" and "1/3", whatever they
were? (Does someone know? If I'm wrong about this, I
don't want to keep "talking through my hat" about it.)
>>> but I imagine languages with trial as a lexical
>>> number
>> Do you mean, "trial as a grammatical number",
>> i.e., on a par with singular and dual and plural
>> (and, possibly, paucal)?
[In essence, John says (among other things) "Yes, I
meant 'trial as a grammatical number'".]
>>> might have 3?
>> Why would the two phenomena have anything to do
>> with each other?
> Oops, yes, I meant trial as a grammatical number.
> Now, if the trial marker is unrelated to the word
> for "three", then we have our first example of a
> primitive number morpheme relating to 3.
I believe it is the case that many languages with a
trial number have the "trial marker" not obviously
related to the word for "three"; whereas many other
languages with a trial number have the "trial marker"
rather obviously related to the word for "three".
BTW Languages which have both a trial and a paucal,
frequently have the "paucal marker" obviously related
to the word for "four", even though there is no
language that has a "grammatical quadral number", and
no evidence that there ever was one.
BTW Languages which have no trial, but have both a
dual and a paucal, frequently have the "paucal marker"
obviously related to the word for "three"; and also,
frequently don't.
BTW Languages which have no dual, but have a paucal,
frequently have the "paucal marker" obviously related
to the word for "two"; and also, frequently don't.
BTW There is only one language I have heard of that
has "lesser paucal" and "greater paucal". It has no
dual nor trial. The marker for "lesser paucal" is
apparently related to the word for "three", and the
marker for "greater paucal" is apparently related to
the word for "four".
http://emeld.org/workshop/2005/papers/kibort-paper.html
and
http://www.e-meld.org/workshop/2005/papers/kibort-paper.doc
talk about it.
> And going on a more Sapir-Whorfy line of thought,
> a language with a trial would likely have more
> words, primitive or not, relating to 3, than one
> without. I argue that this would also increase
> the likelihood of having more than one primitive
> one.
This seems, to me, to be a valid point; and, keeping
in mind you said "likely" and "likelihood", I would
bet it is true (but not because I "like" the
Sapir-Whorf Hypothesis in general, though -- I don't
"like" it, as it happens).
>>> One could then split the class of numerals
>>> into "cardinal-derived" vs. "ordinal-derived" -
>>> maybe even contrasting other series purely by
>>> their roots.
>>> This is almost trivial to extend into
>>> mathematical series (half vs. halfth),
>>1) What does "halfth" mean?
> "Every halfth year" = "twice a year"
I think it likelier that _this_ idea would be
expressed as in English, "every half-year", rather
than "every half_th_ year".
> "The six-and-a-halfth"
> = "the one between the 6th and the 7th"
That sounds good. In fact I think that is probably
used in English -- although perhaps it isn't
considered "Standard English" when it is so used.
BTW In cities like Galveston Texas and Washington
D.C., where there are streets named "A Street", "B
Street", "C Street", and so on, there are even
"D-and-a-half Street" and "E-and-a-half Street", also.
> So this applies when a sequence has "whole"
> members and "half" members.
> Eg. some areas of the world (mostly plains of
> some sort) have a climate with two rainfall
> seasons per year; so something that's gone thru
> an odd number of them definitely in its
> X-and-a-halfth year.
I think I get it.
In English, in such a place, if somebody has lived
their for, say, nine rainy seasons, we would say "she
is now in the second half of her fifth year here" or
"she's now halfway through her fifth year here" (if we
didn't want to just say "she's been here for nine
rainy seasons").
> Might be also used idiomatically to something
> that's not exactly a half of the whole, eg. a
> band releasing an extended single could also be
> said to release their X-and-a-halfth album.
Because it's too "extended" to refer to as
merely-a-single, but too "single" to refer to as an
entire album? So we "pretend" it's "half an album"?
>>2) Many languages derive all but finitely many
>> unit fractions from ordinals. Thus, a language
>> might have 1/2 (every language I know), 1/3
>> (Ancient Egyptian?), and 1/4 (English) may have
>> lexically-independent forms (in fact 1/2 usually
>> does, and not only 1/3 and 1/4, but often 2/3
>> (Ancient Egyptian?) and 3/4 (no example comes to
>> mind), do as well); but "1/n" for "n" > 4 might
>> denoted by a word which is a short form of the
>> phrase "the nth part of" (English, and every
>> other language I know how to express fractions
>> in). If that were the case for your language,
>> how would a speaker speak of "the qth member of
>> a series" when "q" is a fraction? You'd have to
>> be able to derive an ordinal from an
>> ordinal-derived numeral.
> The reciprocal is still not ordinal in *meaning*,
> so just toss another ordinal affix in.
> Eg 1/3th - "thirdth". Another example in
> Finnish: "kolmasosas" ("kolme" = 3,
> "-s" = ordinal, "osa" = part.) The final ordinal
> affix tags to the last part of the expression,
> the word for "part" in this case.
> (Finnish does have a "more lexicalized" version
> of "1/3" too, employing the explicit reciprocal
> affix "-nnes", but then the meaning somehow gets
> a little hazier.)
Interesting. I _think_ I see what you mean...?
>>> but it might be possible to carry it over to
>>> grammatical series too - eg. contrasting the
>>> (cardinal-derived) word "trio" with an
>>> (ordinal-derived) word meaning maybe something
>>> along the lines of "third member of a trio".
>> Interesting and useful idea!
>> You should know, however, (as I suspect you do),
>> that English, for example, has many words for
>> "a collection of two (somethings)"; the words
>> depend largely on what the "somethings" are, but
>> for many "somethings" there is more than one
>> word denoting "two (somethings)".
>> These words are often morphologically
>> independent both of the noun for the singular
>> and of any other form of the numerals "two"
>> or "second". In other words, they are totally
>> suppletive.
>> English also has many words for "a collection of
>> (many somethings)"; these are called "collective
>> nouns", and are likewise completely suppletive.
>> But the words for pairs, braces, yolks, etc.
>> are morphologically independent of the
>> collective nouns, as well.
>> I believe English has a few words meaning "a set
>> of three X" for just a few particular
>> nouns "X". I can't think of them at the moment.
> Might be, but they're then either so obscure that
> I've never come across them or the meaning
> of "trio" is archaic and not recognized any more.
I still haven't been able to think of any. I expect
they are either obscure or archaic, as you guessed.
>>> .:A MATHEMATICAL P.O.V.:.
>>> "Mathematical series"
Since we're talking mathematics now, I have to tell
you, as I didn't tell you earlier, that in
mathematician-speak "series", (unless modified, as in
"time series"; and even sometimes when modified),
ordinarily refers to an (infinite) _sum_; that is, to
the _sum_ of a sequence.
The things we've up-'til-this-point called "series",
are usually called "sequences".
>>> are technically still cardinal sequences,
>>> formed by filtering the natural numbers {0, 1,
>>> 2, 3...} thru some random function.
>> I think it may make more sense to think of them
>> as functions whose domain-of-variation for their
>> argument is the finite _ordinals_, rather than
>> the finite _cardinals_. "X sub n" represents
>> the nth member of the sequence X; it does not
>> represent n of anything.
> Well, yes, they're closer related to the natural
> ordinals than the natural cardinals in that
> sense;
Glad you see it -- that means I've communicated!
> but you still end up with cardinal real numbers.
What do you mean, "cardinal real numbers"?
Do you mean "real numbers are more cardinal than
ordinal"?
Because I think a real number applies to mass nouns,
not to count nouns; and I'm not sure a "real" number
is either cardinal _or_ ordinal, though I suppose both
a cardinal-like number and an ordinal-like number can
be made out of a "real" number.
> As covered above, "halfth" is already
> non-trivial; what would you think of "eth"
> or "negative fourth"?
See my previous paragraph.
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).
> (I do not know the precise set theoretical
> definition of "ordinal", but I suspect it might
> deviate from its linguistic definition a little
> here.)
Right. The "linguistic definition" of "ordinal number"
is pre-theoretical and informal. The set-theoretic
definition is formal, and not naively intuitively
obviously connected to the "linguistic definition";
though some would say that the connection is
intuitive, 'tho' perhaps not obvious, to a _non_-naive
intuition.
>>> AFAIK, only reciprocals (half, third,
>> quarter...) and exponents of the base number
>> (ten, hundred, thousand...) are lexical anywhere.
What about English pair, dozen, score, gross?
>> Not forgetting that bases of four, five, twelve,
>> and twenty, are also pretty common compared to
>> base-ten, according to Greenberg's book.
> Certainly. Hence "exponents of the base number"
> and not "exponents of 10".
>>> Unusually geeky loglangs might have more, but
>>> even then, I doubt whether expressing eg. -6 as
>>> something along the lines of "unsix" would be
>>> useful.
>>> ...And speaking of negative numbers, why
>>> doesn't -1 have a name on its own, but i does?
>> But it does; "-1" is its name.
> I mean a name unrelated to "1".
I see.
I did. Interesting.
>> Actually many languages have a way to express
>> missing-a-few or lacking-a-few. King James's
>> version of one of St. Paul's letters translates
>> his expression as "forty lashes save one", i.e.,
>> a certain number of times he was sentenced to
>> receive 39 strokes with a scourge.
> Yes, that indeed works!
Glad I brought it up, then.
> Let's suppose a language that has an affix
> meaning approx. "almost, but still missing a
> few". Add that to "none" and walla* [John
> misspelled "voila" on purpose here], there we
> have the name for -1.
Hmm. "Not quite enough to be nothing". Sounds like a
great insult-word.
>>> If yes, I could imagine lexicalizing other
>>> simple fractions too, like 2/3 and 3/4.
>> "Two-thirds" was indeed "lexicalized" in Ancient
>> Egyptian, so I've read;
If anyone can prove me right or wrong about the above,
I'd like to read or hear it.
>> and I wager "three-fourths" is lexicalized in
>> some natlangs, as well.
Does anyone know for sure?
>>In fact, I think the following to be
>> likely "statistical implicational 'universals'";
>> *** For each n, many languages which have a
>> special word for 1/n, will also have special
>> words for 1-(1/n) and 1+(1/n).
>> **** Languages which have their own words for
>> 1+(1/2) and 2/3 are probably much more
>> consistent about satisfying *** than other
>> languages.
>> ***** A language which satisfies *** for a
>> natural number n>2, probably also satisfies ***
>> for most or all natural numbers m where 1<m<n.
>> The above predict that:
>> :Most languages (such as English) which have a
>> special word ("half") for 1/2, should have a
>> special word for 1+(1/2).
>> ::Most languages which have special words for
>> 1+(1/2) and 1/3, should have a special word for
>> 1+(1/3).
>> :::Most languages which have special words for
>> 2/3 and 1/4, should have a special word for 3/4.
> *** looks dubious -
> I'd require n>2 there too.
So you'd say:
"For each n>2, many languages which have a
"special word for 1/n, will also have special
"words for 1-(1/n) and 1+(1/n)."
> "Half" is so much more basic a concept
> than "one and a half".
You're probably right.
> The other two I'm not going to object to.
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)."
>>> .:OTHER NUMERALS:.
>>> So what other numerals are there?
>>> English has at least the
>>> "group numerals" (single, duo, trio...), the
>>> "repeat numerals" (once, twice, thrice...)
>> Well-spotted. You're ahead of me.
>>> Polygons, time-period names ("biweekly") etc.
>>> are probably best considered compound words.
>> As in "fortnight" (fourteen nights)
>> and "twelvemonth"? Also I have
>> seen "se'ennight" to mean "week".
> Yes, clearly compounds.
> BTW, what does that apostrophe represent, elision
> or blurred speech or what? I've seen
> similar "one letter droppings" in other
> archaisms / ruralisms too.
In English orthographic spellling, "apostrophes" ("'")
are _usually_ meant to stand in for something left
out. So, yes, it _usually_ represents elision -- not
always of a single letter, but usually of letters
representing sounds that are not pronounced in the
compound word (or whatever) as used by the individual
being quoted. Thus, "bo's'un" for "boatswain", and
"fo'c's'le" for "forecastle"; and, I imagine,
"Chu'm'ley" (or maybe "Ch'um'ley"?) for
"Cholmondoley".
(An actual Brit could provide many more examples, I
bet; or, an actual nautical English-speaker.)
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].
BTW I understand English once had a labio-dental
semivowel (approximant); perhaps this sound took the
place of the apostrophe in "se'ennight" as it was once
pronounced.
Modern English L1-speakers have no problem telling
that Spanish-accented L2-English-speakers are
substituting a bilabial voiced fricative for the
labio-dental "v" in English words. Perhaps it wasn't
so difficult for Old English speakers to tell the
difference between a bilabial approximant ("w") and a
labiodental approximant.
BTW I understand also that English once had just one
phonemic labiodental fricative /f/; it usually was
pronounced as its voiceless allophone, but,
intervocallically (i.e. between two vowels), it was
pronounced as its voiced allophone. Thus "ofer" was
pronounced, roughly, [over].
>>> 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"? In English, those terms refer to
currency-notes or currency-bills.
The Shi'a, iiuc, are mostly divided into "Sevenners"
and "Twelvers"; the "Twelvers" recognize a sequence of
twelve Imams as all being legitimate, while the
"Sevenners" recognize only the first seven of them as
being legitimate.
>>> and we also have a sequence which are used as
>>> the names of the number symbols,
>> In my "Math for Elementary Education Majors"
>> courses, these were called "numerals". (They
>> were made up of "digits".)
>>> as well as sort of pronouns for things with ID
>>> numbers...
>> Interesting! The closest I've seen in any
>> natlang is the ordinals.
>> The idea of "ID numbers" is too recent to have
>> been incorporated into any natlang developed
>> before the 19th century, I thought; I'm
>> surprised Finnish has something (besides
>> ordinals) for this.
>> Does an "ID number" have to be a natural number
>> in Finnish?
> No, it doesn't. Even with a non-trivial complex
"complex", here, is used in the linguistic sense; you
are not talking about a "number with a non-zero
imaginary part".
> number like 0.466 ("zero dot four six six"), one
> can just add the suffix -onen to the last numeral
> of the expression and obtain an "ID numeral".
Wow.
> 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.
> The regular forms of 8 and 9 have been supplanted
> by forms that, for 2-7, mean "duo" thru "septet".
Very interesting. Not something I knew, nor even
suspected.
>>> What other sequences are you aware of? I might
>>> be overlooking some obvious one.
>> !I just thought of one!
>> "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".
> Nice!
Thanks. Glad it helped.
>> Might a sequence meaning "all two of"
>> (both), "all three of", ..., "all n of", ... be
>> useful? How much of this sequence is attested
>> in natlangs?
> That's the only one I know of.
You mean, "both" and its translations, is/are the only
one you know of?
Me too.
> But yes, it still suggests a new sequence.
I'm glad I could help.
> Particularily interesting is how these relate to
> the group names in some situations with regards
> to definiteness:
Yes, that is particularly interesting, (even though I
am not completely sure that I'm completely certain
what you mean). I will find out more, and read
carefully, and think about it.
> "____ pears were thrown away."
> "A pair of" implies two wholly indefinite pears.
> "The pair of" implies two wholly definite pears.
> "Both" implies an indefinite group of two
> definite pears (considered a pair for the first
> time!)
Interesting analysis; definitely at least _some_ uses
of these phrases, _do_ mean what you've proposed they
mean. You _may_ be _entirely_ correct.
> (The opposite, a definite group of two indefinite
> objects, is probably impossible, or at least very
> rare
Maybe so.
> - how can you perceive a physical set without
> perceiving any of its members?)
I'm not sure perceivability is related to definiteness
in the way you seem to be implying.
"Definiteness" is usually analyzed as a
grammaticalization of a, or some,
pragmatic-and/or-semantic statuses; usually (one or
both of) the following two: "identifiability" and
"inclusiveness". Since "both" involves inclusiveness
-- "all two of" (or possibly "all three of"?) -- it
could be said that "both" of anything is definite,
whether or not the "anythings" were identifiable.
In any case, if the set-of-two is both (oops!)
identifiable _and_ inclusive, it's definite.
It's possible to have an identifiable group of things,
yet speak of one of them unidentifiably -- I could say
"one of them" in circumstances where my addressee
knows exactly who "they" are without knowing which
_one_ of them I meant.
>>> There's also the possibility of
>>> adding "generic" numerals to each
>>> series. "Number" is essentially a generic
>>> cardinal, and "nth" might count for a generic
>>> ordinal... but it's a little iffy beyond those.
>> "Numeral" is a "generic name-of-number", as well
>> as meaning "name of number".
>> "Digit" is a "generic numeral-less-than-the-
>> base", as well as other meanings.
>> "Part" or "fraction" might be a "generic
>> reciprocal"; it might also be a "generic
>> positive-number-less-than-one". There is no
>> reason against polysemy, having it mean both.
> Also: "a few times" - for the "repeat" series.
> "To divide", "multiply", "lessen" fit for the
> verbal sequences you propose below,
You mean, as generic members?
> but they don't seem particularily random-
> quantitive rather than simply qualitative.
What do you mean, exactly?
> Same for "group" and "all" and their associated
> numerals.
Again, what, exactly, do you mean?
>> 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.
> You're right!
Glad I could help.
> I have been completely overlooking verbs.
(Well, I'd completely overlooked voicing, when we were
talking about vowels, until you brought it up.)
> Someone mentioned (in a message I can't find
> again just now) that the ordinals are essentially
> adjectival and the "repeat series" adverbial.
I don't know who said it either, but it seems right.
> Cardinals seem to act as adjectives ("four
> tangerines on the table and three in the bowl")
> and pronouns ("the four are to be eaten").
That looks right, too.
> Theoretically, these two meanings
The two meanings of cardinal numbers? -- the
adjectival meaning and the pronominal meaning?
> could be split apart - these new pronouns having
> an interesting relation to your "all x of" words.
I think I see what you mean. That could be
interesting.
> Compare "both children got a present" <> "the two
> children got a present". Some sort of part -
> whole distinction. What was it called again?
I don't know, sorry.
> I remember this was discussed at some point just
> last fall.
I don't remember that discussion.
> Well, the verbs you bring up are of the form "to
> make something into x" or "to become x" (no
> tr/itr disctinction). What other verbing affixes
> are relevant here? Any ideas?
I don't have any more at the moment.
>> English also has the set phrase "half again
>> as ..." for increasing some attribute (perhaps
>> size or quantity) by a factor of 1.5.
> Never came across it before,
Look at
http://vetmedicine.about.com/library/viewers/uc-halfagain-b.htm
http://thescooponsmoking.org/xhtml/quizzes/deathAndDiseaseData.php
http://www.istaria.com/page.php?pg=characters&mid=Half-Giants
http://www.shirky.com/writings/half_the_world.html
http://www.meyerweb.com/eric/css/tests/css2/sec10-08a.htm
http://www.helpfulgardener.com/lilacs/03/lilacs.html
http://horizons.crgaming.com/races/viewarticle.asp?Id=189
> but "make 1+1/x" seems just as useful (or
> unuseful) as the "make 1-1/x" series you're
> suggesting below.
Glad you like it.
>> English also has the verbs "to halve (smthng)"
>> and "to quarter (smthng)"
> Same sequence, interbred with reciprocals.
Not strictly; 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."
>> and "to decimate (smthng)".
>> "To decimate smthng" means "to reduce smthng by
>> removing one-tenth of it".
> Never heard this particular meaning either...
BTW apparently some on list have heard this used with
the meaning "to make one-tenth of ...".
My words for that concept -- destroying 90% of
something and leaving only 10% of it -- is "a one-log
kill".
Destroying 99% and leaving only 1% is "a two-log
kill"; destroying 99.9% and leaving only 0.1% is "a
three-log kill", etc.
Hitler's regime accomplished a one-log kill of the
European Jews of his time.
>> Wouldn't it make sense for a language having
>> verbs equivalent to "halve" and "quarter", to
>> have a verb for "to divide smthng into three
>> equal pieces"?
Note this is the _second_ meaning of "halve" and
"quarter" mentioned above. (*)
>> Wouldn't it make sense for a language having
>> verbs equivalent to "halve" 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 "halve" 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?
> The last two are easy - just add morphemes
> for "1/x", or "1-1/x" and "to make smTN into x".
> The first makes sense too, even if it's less
> trivially derivable.
> Of course derivation isn't absolutely necessary.
> The English words are exactly the same as the
> reciprocals -
So far, I agree.
> and I've heard "third" used in the
> first sense too: "We thirded the income of the
> show." "The pie was thirded." etc.
I have never heard either of these expressions in
English.
I have never heard any verb form that was a form of
the word "third", except as a joke for the second
second of a motion; viz.,
"I move thus-and-such"
"I second the motion"
"I third it".
Are you sure these aren't translationisms?
>>> ---------- Forwarded message ----------
>>> From: Mark J. Reed <markjreed@m...>
>>> 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".
> I might say that that's why I am here in the
> first place - making a personalang to minimalize
> the damage :)
Interesting.
--------------------
Thanks for writing.
Tom H.C. in MI
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