Fractions, Currency, other math stuff (Re: Basic Math)
Danny Wier
Clinton Moreland-Stringham wrote:
> Aelya numbers are one thing I have pretty complete. They go as
>follows:
>
> 0 (zero) : nath 1 : en
> 2 : ya 3 : si (-re)
> 4 : car 5 : len
> 6 : sar 7 : sath
> 8 : ooth 9 : ayen / een
> 10 : de / del / des
[sorry for the snip]
For my conlangs:
P forms numbers very much like Japanese. There are numbers from one
through ten, the teens are formed as 10-1, 10-2, etc., and twenty and up
by ten are as 2-10, 3-10, 4-10, etc. There are then words for hundred,
thousand, million, billion, trillion, etc. Fractions will be formed
simply as cardinal number for numerator, ordinal for denominator (six
and one third, etc.).
For Tech, I'll be using a base-20 number system with a word for hundred,
then large numbers being based on powers of ten-thousand (for example:
152,639,842 is translated "one hundred million twoscore twelve hundred
and three and threescore ten-thousand eight and fourscore hundred and
four and twoscore"). Negatives will be expressed as "one less", "two
less", etc., and of course there is _c'iphr_ /ts)'ifr/ "zero". (All I
got made up is the number zero right now; sorry.)
Fractions will come about a different way: the basic common fractional
unit is the twelfth, and the word is the ordinal of "twelve"; it's based
on the word for "part, division". There is also a word for half. So in
classical terminology, a sixth is called "two parts" (actually "part" in
the dual number) and a fourth is called "three parts" (actually "part"
in the small plural). The fraction "one twenty-fourth" was called "half
part". This has to do with an older method of measurements of time --
"part" of a day corresponded to two hours. (However, other fractions
use ordinal numbers: 2/5 is "two fifth parts", etc.
The Techian monetary unit, the Tech pound (=A3Tk), is likewise divided, a=
s
the British pound was before declimatizaion (in 1971, right?), except
the denarius replaces the shilling. One pound equals twenty denarii;
one denarius equals twelve pence, and the smallest monetary unit is the
half-penny. (All currency is in coins, all the way up to the one
hundred pound gold coin; unless one takes into account the paper notes,
which are gold certificates used mostly by banks that can go up to ten
thousand pounds.)
Danny
Padraic Brown
On Sun, 18 Jan 1998, Danny Wier wrote:
[snippage of interesting number stuff]
>=20
> The Techian monetary unit, the Tech pound (=A3Tk), is likewise divided, a=
s
> the British pound was before declimatizaion (in 1971, right?), except
1971 is correct, though the first (regular issue) decimal coins were in
1968.
> the denarius replaces the shilling. One pound equals twenty denarii;
> one denarius equals twelve pence, and the smallest monetary unit is the
> half-penny. (All currency is in coins, all the way up to the one
> hundred pound gold coin; unless one takes into account the paper notes,
> which are gold certificates used mostly by banks that can go up to ten
> thousand pounds.)
Are you sure you've got that straight? The denarius _is_ what became the
English penny, while the solidus became the shilling. The relative
proportions are correct, though (12d.=3D1s.; 20/- =3D L1). Do the Techians
have any peculiar laws concerning the use of these high value notes?
(e.g., it is illegal to own a US$ 100000). Also, do the Techians have all
the "odd" denomination coins (with their associated nomenclature)?
>=20
> Danny
>=20
Padraic.
Mark E. Shoulson
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FWIW, Yf Rgalin has a pretty simple number system, with a small twist or
two which are probably Good Things.
The numbers 1-9 are simple roots, with 10 being made a "number-forming
element" like Klingon's "-maH". So to say "10" you need to say "one-ten".
This regularizes things like Esperanto, which has dek, dudek, tridek for
10, 20, 30. Instead of ten, two-ten, three-ten, Yf Rgalin has one-ten,
two-ten, three-ten, etc. The "ten" element can't stand on its own.
Numbers up to 99 form in the usual way, one-ten-one, one-ten-two, etc etc.
"Hundred" is an element like "ten", because when you read "nine-ten-nine"
tro go any higher you need to say "one-ten-ten", and that means modifying
an element by itself, which is naughty. So there's "one-hundred." The
same goes on... one-hundred-one-ten-one for 111, etc. At 1000, all's well:
it's one-ten-hundred, with "hundred" modified by a *lower*-order element,
and that's just dandy. I don't need a new element until 10,000 (9999 being
nine-ten-nine-hundred-nine-ten-nine). And so on up the line: each new
element is the *square* of the one before it, and the math is fairly
unambiguous: each element multiplies the growing number by its value as you
read left to right. This doesn't rely on artificialities like 1,000 as a
unit of higher math.
~mark
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Terrence Donnelly
Vogu has a base-5 number system. The numbers from 1 to 4 are the
basic units:
azg 'one'
nazg 'two'
tazg 'three'
gozg 'four'
The first power of 5 (5^1) is represented by the element -pong (as
an aside, the word for 'hand' is bupong), to which the basic elements
are prefixed. Units within each multiple of 5 are expressed as
suffixes:
apong 'five'
apongihzg 'six [(5^1)+1]'
apong nazg 'seven'
napong '10 [2*(5^1)]
napong gozg '14'
The next power of 5 is represented by the element -pongpong:
apongpong '25 [1*(5^2)]
napongpong tapongihzg '66'
5^3 is represented by the element -tabj 'count'.
There are also a few special words, e.g.: avek 'person' is also used to
represent 'a score (20) items'.
The only downside is that numbers can get pretty long very quickly, but
the Kadane (who speak Vogu) don't normally use very large numbers in
conversation anyway. Anything over 100 is usually just referred to as
yumosht 'a lot'.
-- Terry
http://www.geocities.com/Area51/Corridor/2711
Danny Wier
taliesin the storyteller wrote:
>Furthermore: I'm thinking of scrapping the decimal system,
>replacing it with octals. This fits with the base24 system
>(8*3), but it rather crashes with the base5 system, which is
>what the decimals derived from in the first place... I don't
>think I can replace either the base5 or the base24 system,
>because of their important role in gvenen culture.
Well, an octal system isn't as unnatural as one might think. Imagine:
according to who you ask, some people (probably most people) would say
we have ten fingers. Some would say eight fingers, not counting the
thumbs. This would be easier to translate to computer binary or
hexadecimal, so there are advantages to an octal system. The
disadvantages is the lost of the regularity of five (ten is five times
two, eight is two times two times two), as well as it being a change of
thinking for we that have been raised on decimal. But there are
languages that use quintal (base five; I want to say some Papuan
langauges do this but I could be wrong), vigintesimal (base twenty;
Mayan is base 20 and 400), and even sexagesimal (base sixty) in the case
of Babylonian (well, it's really based on 10 and 60).
Another system I like is duodecimal (base twelve), which I use for Tech
fractions (I also previously posted that Tech whole numbers are base 20,
even with distinct names for the numbers from eleven through nineteen).
>'Nough complaining, here's the question: what do you
>generally *do* when you need to redesign major sections of
>your langs? Start a new one? Feed the dozens of pages you've
>already written to the trash-can? Despair and get drunk?
>(hmmm... good idea. nah...)
In the dozen some-odd years that I have been working on what would
become Tech I have started, stopped, restarted, tuned-up, overhauled,
started over, and chunked in the trash, catching it on fire and dancing
around it singing various bawdy tunes. Most of the time I'm obsessed
with it, complete with love-hate relationship. P, on the other hand, I
mostly keep on the shelf and make an occasional contribution to when I
feel like it.
>Perfectionism sure ain't good for you.
No, but it keeps you busy.
Danny
Dirk A Elzinga
On Tue, 20 Jan 1998, Danny Wier wrote:
> taliesin the storyteller wrote:
>
>
> >Furthermore: I'm thinking of scrapping the decimal system,
> >replacing it with octals. This fits with the base24 system
> >(8*3), but it rather crashes with the base5 system, which is
> >what the decimals derived from in the first place... I don't
> >think I can replace either the base5 or the base24 system,
> >because of their important role in gvenen culture.
>
> Well, an octal system isn't as unnatural as one might think. Imagine:
> according to who you ask, some people (probably most people) would say
> we have ten fingers. Some would say eight fingers, not counting the
> thumbs. This would be easier to translate to computer binary or
> hexadecimal, so there are advantages to an octal system.
In a book by Leanne Hinton, _Flutes of Fire_, there is an interesting
essay on the number systems of a sample of California languages. In Yuki,
an octal system is used with the relevant "counters" being the _spaces_
between the fingers. Here's what Kroeber had to say about it in the
_Handbook of California Languages_:
The Yuki system of counting--and it alone among all the Yukian
languages--is not decimal or quinary, but octonary. Only the
Salinan and Chumash, far to the south, follow an analogous
quaternary method. It is remarkable that the Yuki counted on their
fingers as regularly as any other people in the State. The
explanation is that they did not count the fingers but the spaces
between them, in each of which, when the manipulation was
possible, two twigs were laid. Naturally enough their "hundred"
was 64.
(cited in _Flutes of Fire_, p 118)
Dirk
--
Dirk Elzinga
elz...@u.arizona.edu "All grammars leak."
http://www.u.arizona.edu/~elzinga - Edward Sapir
JOEL MATTHEW PEARSON
Awhile back I posted on the counting system in Tokana. Here's a summary
of that post:
The Tokana count using a base ten system, but (as in some natlangs) there
are underived words for "eleven" and "twelve", from which names for larger
multiples may be derived.
The numbers from 1 to 12 are:
es one kelu seven
hen two nioh eight
ehte three teiek nine
kin four tam ten
kian five elhu eleven
ihtah six huoi twelve
Adding the suffix "-ta" multiplies these by ten (except that 100 is a
separate word, "kunma").
henta twenty
ehteta thirty
kinta forty
kianta fifty
ihtata sixty
keluta seventy
niohta eighty
teiekta ninety
kunma one hundred
elhuta one hundred ten
huoita one hundred twenty
To form the numbers 13-19, 21-29, 31-39, etc., compounds are formed using
the linker "-pa(h)", which is related to the word "pama", meaning "on top
of":
ehtepatam three-on-ten thirteen
kimpatam four-on-ten fourteen
kianypatam five-on-ten fifteen
ihtapatam six-on-ten sixten
etc.
espahenta one-on-twenty twenty-one
hempahenta two-on-twenty twenty-two
(Note that "elhupatam" = "eleven-on-ten" and "huoipatam" = "twelve-on-ten"
are also acceptable for 21 and 22...)
espahehteta one-on-thirty thirty-one
hempahehteta two-on-thirty thirty-two
ehtepahehteta three-on-thirty thirty-three
etc.
teiekpateiekta nine-on-ninety ninety-nine
kunma hundred one hundred
espakunma one-on-hundred one hundred and one
hempakunma two-on-hundred one hundred and two
etc.
teiekpakunma nine-on-hundred one hundred and nine
elhuta eleventy one hundred and ten
espahelhuta one-on-eleventy one hundred and eleven
hempahelhuta two-on-eleventy one hundred and twelve
("Elhupakunma" = "eleven-on-hundred" and "huoipakunma" = "twelve-on-hundred"
are also acceptable here...)
huoita twelfty one hundred twenty
espahuoita one-on-twelfty one hundred twenty-one
etc.
niohpahuoita eight-on-twelfty one hundred twenty-eight
teiekpahuoita nine-on-twelfty one hundred twenty-nine
For numbers larger than 129, compounds must be used. Note that the
order of powers is the reverse of English:
ehteta ki kunma thirty and hundred 130
espahehteta ki kunma one-on-thirty and hundred 131
hempahehteta ki kunma two-on-thirty and hundred 132
etc.
hen kunma two hundreds 200
es ki hen kunma one and two hundreds 201
niohpakinta ki hen kunma eight-on-forty & 2 hundreds 248
Note that there is no word for "thousand" in Tokana. You count tens of
hundreds instead:
niohpakinta ki espateiekta kunma
eight-on-forty and one-on-ninety hundred
"ninety-one hundred and forty-eight"
= "nine thousand one hundred forty-eight"
kianypakeluta ki hempahuoita kunma
five-on-seventy and two-on-twelfty hundred
"twelfty-two hundred and seventy-five"
= "one hundred twenty-two hundred and seventy-five"
= "twelve thousand two hundred seventy-five"
A hundred hundreds, or 10,000, is "tolok". Then thousand ten thousands,
or 100,000,000, is "tolok tolok".
All in all, a somewhat exotic system by English standards, but nevertheless
quite reasonable, I think.
Matt.
Danny Wier
Dirk A. Elzinga wrote:
>In a book by Leanne Hinton, _Flutes of Fire_, there is an interesting
>essay on the number systems of a sample of California languages. In
Yuki,
>an octal system is used with the relevant "counters" being the _spaces_
>between the fingers. Here's what Kroeber had to say about it in the
>_Handbook of California Languages_:
Well I did learn something! If one does count the spaces of the fingers
along with the tips, couldn't one also develop a nonary (base 9) or
octadecimal (base 18) system as well, at least theoretically? (Or the
spaces could represent halves...)
Danny
Danny Wier
Joel Matthew Pearson wrote,
>Awhile back I posted on the counting system in Tokana. Here's a
summary
>of that post:
>
>The Tokana count using a base ten system, but (as in some natlangs)
there
>are underived words for "eleven" and "twelve", from which names for
larger
>multiples may be derived.
I notice that! The use for distinct terms for "eleven" and "twelve",
are they limited to Germanic languages or do they come from somewhere
else?
For Tech, I'm debating with myself on whether to use underived terms for
the numbers one through twelve and twenty (which would work fine for its
quinary/duodecimal fractional system -- I decided to add a base-5
element to fractions recently) and "-teen" forms for thirteen through
nineteen, or use all underived terms for the numbers one through twenty
(again the language is base-20 for whole numbers).
Ever notice that the Arabic word for "thousand" (_?alf_) is similar to
the German word for "eleven" (_elf_)?
>Adding the suffix "-ta" multiplies these by ten (except that 100 is a
>separate word, "kunma").
What I'll do is a derivation of the numbers "two", "three", and "four"
for the numbers "forty", "sixty", and "eighty".
Also, I just might do something that is done in Sanskrit for numbers
like 19, 29, 39, 49, etc.: for a word that means more or less literally
"twenty less one", "thirty less one", etc. Russian has _vosem'desjat_
for "eighty", _devjanosto_ for "ninety", and _sto_ for "hundred" --
which looks like a similar case, "ninety" looking more like "nine of
hundred" or something. In both cases, it sounds like the protocol for
Roman numerals ("nine" after all is written as IX and not VIIII).
>To form the numbers 13-19, 21-29, 31-39, etc., compounds are formed
using
>the linker "-pa(h)", which is related to the word "pama", meaning "on
top
>of":
I think that's how Welsh and Scots (not Irish) Gaelic form numbers like
21-39 ("one on twenty", "two on twenty"... "nineteen on twenty"),
likewise 40-59, 60-79, and 80-99. German says "one and twenty", "two
and twenty"), but thirty-one is "one and thirty" not "eleven and
twenty".
>(Note that "elhupatam" = "eleven-on-ten" and "huoipatam" =
"twelve-on-ten"
>are also acceptable for 21 and 22...)
>("Elhupakunma" = "eleven-on-hundred" and "huoipakunma" =
"twelve-on-hundred"
>are also acceptable here...)
Reminds me of when Tolkien talked about Bilbo Baggins' "eleventieth
birthday". There's another idear...
>Note that there is no word for "thousand" in Tokana. You count tens of
>hundreds instead:
Can't think of any natlangs that lack a word for "thousand", but then
again, I don't know everything. Greek has "thousand" (_khilios_) but
knows no native number word greater than "ten thousand" (_muriados_);
for "two hundred million" Revelation 9:16 has "two myriad myriads".
(Modern Greek has borrowed "million" and "billion" from Latin however.)
Sanskrit and its daughter languages have "thousand" but not "million";
instead, it has "hundred thousand" (_lakh_). (Even modern Hindi numbers
are written not in the format 53,942,806, but as 5,39,42,806.).
Large numbers in Tech (as I said in an earlier post) are base 10,000
instead of 1,000: "million" is literally "hundred myriad" and "billion"
(US meaning) is "ten myriad myriads".
Or I could use an entirely new construction for exponents -- the analogy
of "billion", "trillion", "quadrillion", etc., which in the UK and
France mean "million" to the second power ("bi-"), third power ("tri-"),
etc. (in the US "billion" however is not a million millions but a
thousand millions). Except the base again would be ten thousand, not
one thousand. A possible construction would be a reflexive one,
something like "myriad on itself twice" for "hundred million".
>A hundred hundreds, or 10,000, is "tolok". Then thousand ten
thousands,
>or 100,000,000, is "tolok tolok".
Cute! So is sixteen hundred in Russian "sorok sorok"? Actually that
would be "sorok sorokov" wouldn't it? (_Sorok_ is "forty" in Russian.)
>All in all, a somewhat exotic system by English standards, but
nevertheless
>quite reasonable, I think.
Erotic is good. (Oops, Freudian slip there; I meant "exotic".)
Danny
Fuscian
In a message dated 1/21/98 7:23:19 PM, you wrote:
>Ever notice that the Arabic word for "thousand" (_?alf_) is similar to
>
>the German word for "eleven" (_elf_)?
And Hebrew "elef" (or 'elef, or whatever). But are they actually related?
JTR
Danny Wier
Fuscian wrote:
Probably not; ever heard the apocryphal story where elves from Egypt
sneaked off to Germany in 1591 and altered all the dictionaries where
"eleven" and "twelve" was _einzehn_ and _zwo"zehn_?
No? Neither have I.
(Seriously, that would probably be a case of coincidence. But I thought
it was an interesting similarity.)
Danny
Douglas Koller
Time for Ge'arthnuns to weigh in:
Numbers follow the easy pattern mentioned earlier: 22 = 2-10-2, 246 =
2-100-4-10-6, and so on.
The only thing that I find remotely neat is that each power of ten has
its own word; the sequence never repeats, so that "ten-thousand" is not
an option.
0 - ngau
1 - si'r
2 - punge
3 - tou
4 - sebut
5 - palav
6 - rhal
7 - zho"she
8 - be's
9 - ngareth
10 - mno"
100 - kashad
1,000 - pe'r
10,000 - i'asa
100,000 - o"
1,000,000 - ngefu"
10,000,000 - gate
100,000,000 - lam
1,000,000,000 - go"i (our favorite sound again!)
10,000,000,000 - erho"u
100,000,000,000 - au
1,000,000,000,000 - rhovi'
10,000,000,000,000 - azve
100,000,000,000,000 - tu"ko"r
1,000,000,000,000,000 - ouz,i'
That ought keep even astromers and economists occupied. If I _ever_ need
higher numbers, I'll coin them (Chinese fizzles out after a trillion).
365 - toukashad rhalmno" palav
5,879 - palavpe'r be'skashad zho"shemno" ngareth
897,554,824,136 - be'sau ngaretherho"u zho"shego"i palavlam palavgate
sebutngefu" be'so" pungei'asa sebutpe'r kashad toumno" rhal
A bit taxing on the memory, I'll grant you, but _I_ like it. Outside of
counting and math expressions, numbers become adjectives.
Fractions are formed by adding the suffix -baks to the denominator; the
numerator is an adjective:
1/3 - su" toubaks si'rek
2/5 - su"k palavbaksu"p pungeku"p
Ordinals are formed by adding the adjectival ending -fi'b to the
number:
1st - si'rfi'b
25th - pungemno" palavfi'b
Kou