Re: Types of numerals
| From: | Tom Chappell <tomhchappell@...> |
|---|
| Date: | Monday, January 23, 2006, 22:42 |
|---|
On Wed, 18 Jan 2006 00:55:45 +0200, John Vertical
> <johnvertical@...> wrote:
> tomhchappell wrote:
> [snip]
>> 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.
So, then.
You agree with me that the pairs:
(tres, tria)-three, sex-six, and novem-nine
appear synchronically transparent.
(BTW Maybe I should change
my mind about novem-nine.)
And, you agree with me that the pairs:
quattuor-four, quinque-five, octo-eight, and
decem-ten
do not appear transparent synchronically.
But, you disagree with me that the pairs:
(unus, una, unum)-one, septem-seven, and
(duo, duae)-two
appear synchronically transparent.
I could see needing some slack for uni-one and
septe-seven; but to me duo-two is just too obvious.
Ah well, as the saying goes, "Your Mileage May Vary".
As far as Greek numbers go:
(Note that duo and octo are the same in both Classical
languages; and sex-hex, septem-hepta, decem-deka are
fairly close.)
I find _all_ of their numbers up to deka-ten, except
for duo-two and (treis, tria)-three, to be
non-transparent with synchronic Modern English. Note
that Greek uses "h" some places Latin and English use
"s" -- for six and seven, for instance. And, tessara
and penta aren't any closer to four and five than
quattuor and quinque are. Also, I don't think ennea
is as close to nine as novem is.
However I'm no longer sure novem is synchronically
transparently related to nine.
>>> 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.
_My_ linguistic intuition (which I don't assert is
better than yours; it's just that it's _mine_) doesn't
accept as "cardinal" any numbers other than "counting
numbers"; in fact, not even "zero" is "_intuitively_
cardinal", to me.
Zero and negative integers can be combined out of
"cardinal" numbers using only addition, subtraction,
and multiplication, so perhaps I feel they are
less-marked than other numbers.
Rational fractions can be achieved by including
division, so perhaps I feel they are less-marked than
irrationals.
But, even if you throw in "taking roots" as an
operation, you won't get all of the algebraic
irrationals (for instance, solutions to a general
quintic or sextic); and transcendentals, like e and
pi, can't be achieved by any algebraic means (they
aren't roots of any polynomial with rational
coefficients).
> If cardinals' "adjectival" and "pronominal" and
> perhaps other usages were split into different
> words, they could be made universally marked, too.
Which one would be marked, and which unmarked?
I think the adjectival use is less marked than the
pronominal use.
> Especially, if measures of mass nouns behaved
> differently from measures of count nouns, real
> numbers *would* end up as their own, non-cardinal
> category.
Since I think "measures of mass nouns" do indeed
behave differently from "measures of count nouns", I
feel the hypothesis of your conditional statement is
satisfied; so I accept the conclusion, that "real
numbers" are a category of their own, not included in
the category of "cardinal numbers".
>>>> 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.
Even granting that, I still feel that also changing
"any" to "many" would improve the statement's accuracy
(its "truthiness").
'... I doubt you're going to think of many useful
outside of mathematics.'
>>> 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.
That's not all.
That's an "unordered pair";
there are also "ordered pair"s.
Here come the details I withheld earlier:
Aside from "unordered pairs", mentioned above, here
are seven other mathematical uses;
http://mathworld.wolfram.com/AmicablePair.html
"An amicable pair consists of two integers for which
the sum of proper divisors (the divisors excluding the
number itself) of one number equals the other.
Amicable pairs are occasionally called friendly pairs
(Hoffman 1998, p. 45), although this nomenclature is
to be discouraged since the numbers more commonly
known as friendly pairs are defined by a different,
albeit related, criterion."
http://mathworld.wolfram.com/Ruth-AaronPair.html
"A Ruth-Aaron pair is a pair of consecutive numbers
such that the sums of the prime factors of and are
equal. They are so named because they were inspired by
the pair (714, 715) corresponding to Hank Aaron's
record-breaking 715th home run on April 8, 1974,
breaking Babe Ruth's earlier record of 714."
http://en.wikipedia.org/wiki/Pairing
"Pairing
>From Wikipedia, the free encyclopedia.
The concept of pairing treated here occurs in
mathematics.
Definition
Let R be a commutative ring with unity, and let M and
N be two R-modules.
A pairing is any R-bilinear map e:MxN->R. That is, it
satisfies
e(rm,n) = e(m,rn) = re(m,n)
for any r in R. Or equivalently, a pairing is an
R-linear map e:MxN->R
where MxN denotes the tensor product of M and N.
A pairing can also be considered as an R-linear map
Φ:M->Hom(N,R), which matches the first definition
by setting Φ(m)(n): = e(m,n).
A pairing is called perfect if the above map Φ is
an isomorphism of R-modules."
http://en.wikipedia.org/wiki/Ordered_pairs
"Ordered pair
>From Wikipedia, the free encyclopedia.
An ordered pair is a collection of two objects such
that one can be distinguished as the first element and
the other as the second element. An ordered pair with
first element a and second element b is usually
written as (a, b)."
http://en.wikipedia.org/wiki/BN_pair
"(B,N) pair
>From Wikipedia, the free encyclopedia.
In mathematics, a (B, N) pair is a structure on groups
of Lie type that allows one to give uniform proofs of
many results, instead of giving a large number of
case-by-case proofs. Roughly speaking, it shows that
all such groups are similar to the general linear
group over a field. They were invented by the
mathematician Jacques Tits, and are also sometimes
known as Tits systems.
Definition
A (B, N) pair is a pair of subgroups B and N of a
group G such that the following axioms hold:
G is generated by B and N.
The intersection H of B and N is a normal subgroup of
N.
The group W = N/H is generated by a set of elements wi
of order 2, for i in some non-empty set I.
If wi is one of the generators of W and w is any
element of W, then wiBw is contained in the union of
BwiwB and BwB.
No generator wi normalizes B.
The idea of this definition is that B is an analogue
of the upper triangular matrices of the general linear
group GLn(K), H is an analogue of the diagonal
matrices, and N is an analogue of the normalizer of H.
The subgroup B is sometimes called the Borel subgroup,
H is sometimes called the Cartan subgroup, and W is
called the Weyl group.
The number of generators wi is called the rank."
http://en.wikipedia.org/wiki/MMS_pair
Maris-McGwire-Sosa pairs
>From Wikipedia, the free encyclopedia.
Maris-McGwire-Sosa pairs or MMS pairs are two numbers
that when you add the digits of the numbers and the
digits of its prime factorization, they are equal.
MMS pairs are so named because in 1998 Mark McGwire
and Sammy Sosa both hit their 62nd home runs for the
season, passing the old record of 61, held by Roger
Maris. American engineer Mike Keith noticed this
property of these numbers and named pairs of numbers
like this MMS pairs."
http://en.wikipedia.org/wiki/Pairing_function
"Pairing function
>From Wikipedia, the free encyclopedia.
In mathematics a pairing function is a process to
uniquely encode two natural numbers into a single
natural number.
Any pairing function can be used in set theory to
prove that integers and rational numbers have the same
cardinality as natural numbers. In theoretical
computer science they are used to encode a function
defined on a vector of natural numbers f:N^k → N
into a new function g:N → N.
Definition
A pairing function is a bijective function
pi from N cross N into and onto N"
That's eight uses in mathematics, not counting
"couple" and words formed from "couple".
Below are two other scientific and technical uses that
may, arguably, not be "mathematical" (although they
may arguably be "mathematical"; Wikipedia categorizes
them as "statistics").
http://en.wikipedia.org/wiki/Ranked_pairs
Ranked Pairs
>From Wikipedia, the free encyclopedia.
Ranked Pairs (RP) or Tideman (named after its
developer Nicolaus Tideman) is a voting method that
selects a single winner using votes that express
preferences. RP can also be used to create a sorted
list of winners.
If there is a candidate who is preferred over the
other candidates, when compared in turn with each of
the others, RP guarantees that that candidate will
win. Because of this property, RP is (by definition) a
Condorcet method. It is closely related to another
Condorcet method, the Schulze method.
Ranked Pairs is currently used by the Ice Games design
competition."
http://en.wikipedia.org/wiki/Paired_Comparison_Analysis
"Paired comparison analysis
>From Wikipedia, the free encyclopedia.
(Redirected from Paired Comparison Analysis)
In paired comparison analysis, also known as paired
choice analysis, similar items are compared one
against the next and the results are tallied to find
an overall winner. A paired choice matrix or paired
comparison matrix can be constructed to help with this
type of analysis."
Below are eleven other scientific and technical uses
that are probably not "mathematical".
http://en.wikipedia.org/wiki/Live_pair
"Live pair
>From Wikipedia, the free encyclopedia.
In the Senate and House of representatives, live pairs
are informal voluntary agreements between Members, and
are not specifically authorized or recognized by House
or Senate rules. Live pairs are agreements which
Members employ to nullify the effect of absences on
the outcome of recorded votes. If a Member expects to
be absent for a vote, s/he may "pair off" with another
Member who will be present and who would vote on the
other side of the question, but who agrees not to
vote. The Member in attendance states that s/he has a
live pair, announces how s/he and the paired Member
would have voted, and then votes "present." In this
way, the other Member can be absent without affecting
the outcome of the vote. Because pairs are informal
and unofficial arrangements, they are not counted in
vote totals; however paired Members' positions do
appear in the Congressional Record."
http://en.wikipedia.org/wiki/Pair_creation
Pair production
>From Wikipedia, the free encyclopedia.
Pair production refers to the creation of an
elementary particle and its antiparticle. This is
allowed, provided there is enough energy and momentum
available to create their mass and motion, because
they have opposite quantum numbers (which are
therefore conserved in the process)."
http://en.wikipedia.org/wiki/Minimal_pairs
Minimal pair
>From Wikipedia, the free encyclopedia.
In phonology, minimal pairs are pairs of words or
phrases in a particular language, which differ in only
one phoneme, toneme or chroneme and have a distinct
meaning. They are used to demonstrate that two phones
constitute two separate phonemes in the language."
http://en.wikipedia.org/wiki/Shared_pair
Shared pair
In chemistry, a shared pair is a pair of electrons
bonding two atoms together by being shared by the two
atoms.
See Also
covalent bond"
http://en.wikipedia.org/wiki/Lone_pair
"Lone pair
>From Wikipedia, the free encyclopedia.
A lone pair is an electron pair without bonding or
sharing with other atoms. It often exhibits a negative
polar character with its high charge density. It is
used in the formation of a dative bond, for example,
the creation of the hydronium, H3O+, ion occurs when
acids are dissolved in water and it is due to the
oxygen atom donating a lone pair to the hydrogen ion."
http://en.wikipedia.org/wiki/Lewis_pair
"Lewis pair
>From Wikipedia, the free encyclopedia.
A Lewis electron pair is a pair of electrons with
opposite spins located in a molecule. The pair of
electrons can comprise either a covalent bond, or a
lone pair, localized in a mostly non-bonding molecular
orbital.
See also
Lewis acid
Lewis base
Nucleophile
Retrieved from
"http://en.wikipedia.org/wiki/Lewis_pair"'
http://en.wikipedia.org/wiki/Base_pairs
"Base pair
>From Wikipedia, the free encyclopedia.
In molecular biology, two nucleotides on opposite
complementary DNA or RNA strands that are connected
via hydrogen bonds are called a base pair (often
abbreviated bp). In DNA, adenine (A) forms a base pair
with thymine (T), as does guanine (G) with cytosine
(C). In RNA, thymine is replaced by uracil (U). As DNA
is usually double-stranded, the number of base pairs
given for a particular DNA strand is the number of
nucleotides in one of the strands."
http://en.wikipedia.org/wiki/Twisted-pair
Twisted pair
>From Wikipedia, the free encyclopedia.
Twisted pair cabling is a common form of wiring in
which two conductors are wound around each other for
the purposes of canceling out electromagnetic
interference which can cause crosstalk. The number of
twists per meter make up part of the specification for
a given type of cable. The greater the number of
twists, the more crosstalk is reduced. Twisting wires
decreases interference because:
The loop area between the wires (which determines the
magnetic coupling into the signal) is reduced as much
as physically possible.
The directions of current generated by a uniform
coupled magnetic field is reversed for every twist,
canceling each other out. "
http://en.wikipedia.org/wiki/Pair_gain
"Pair gain
>From Wikipedia, the free encyclopedia.
In telephony, pair gain is a method of transmitting
multiple POTS signals over a single traditional
subscriber line used in telephone systems, in effect
creating additional subscriber lines. This is
typically used as an expedient way to solve subscriber
line shortage problems by using existing wiring,
instead of installing new wires from the central
office to the customer premises.
A pair gain system consists of concentrators or
multiplexers which combine the separate signals into a
single signal which is transmitted through the
existing copper pair. The signals are then separated
into individual subscriber lines at the customer
premises. The pair gain unit which performs the
multiplexing can be as simple as providing two
telephone connections over a single subscriber line
(called an Analog Multi-Line Carrier) in circumstances
where a customer wants to add a new phone line for a
fax machine or dial-up internet connection. Some pair
gain units can expand the number of subscriber lines
available over a single copper pair to as many as
thirty-four."
http://en.wikipedia.org/wiki/Bit_pairing
"Bit pairing
>From Wikipedia, the free encyclopedia.
In telecommunication, bit pairing is the practice of
establishing, within a code set, a number of subsets
that have an identical bit representation except for
the state of a specified bit.
Note: An example of bit pairing occurs in the
International Alphabet No. 5 and the American Standard
Code for Information Interchange (ASCII), where the
upper case letters are related to their respective
lower case letters by the state of bit six.
Source: From Federal Standard 1037C and from
MIL-STD-188
Retrieved from
"http://en.wikipedia.org/wiki/Bit_pairing"'
http://en.wikipedia.org/wiki/Married_pair
"Married pair
>From Wikipedia, the free encyclopedia.
On railroads, a married pair is a set of two railroad
cars which are permanently coupled and treated as if
they were a single unit. On passenger railroads, light
rail, and monorail services, married pairs may have
machinery necessary for full operation of the cars
split between them. (For example, one car may contain
a propulsion system, while the other contains an HVAC
system.)
For many models of New York City Subway cars, a
married pair consists of one car with an operator's
cab and one without."
>>>> 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.
Because the part of your remark after the hyphen
sounds to me like you _agree_, rather than disagree,
with what I _meant_ to say, I think you might have
misunderstood me.
I meant that, when I referred to a language having
"its own special word" for something, that that
"special word" would _not_ be part of any productive
paradigm; it would be irregular; (or, possibly,
"quasi-regular"?, if part of a non-productive
paradigm?).
So, what I wanted to revise my original remark to,
might be something like this;
Among natural languages which have monolexemic,
irregular-or-quasiregular words
for 3/2 (i.e. 1+(1/2)) and for 2/3;
for any natural number n>2;
if the language also has a monolexemic,
irregular-or-quasiregular word for 1/n,
then it probably has a monolexemic
irregular-or-quasiregular word
for each of (n+1)/n (i.e. 1+(1/n))
and for (n-1)/n (i.e. 1-(1/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 symbol [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 case you didn't get it from my earlier reply
(since I wasn't explicit):
No, in RP and SAE all apostrophes represent
"_elision_"; they are not necessarily pronounced at
all, but if they are pronounced, in RP and SAE they
will be pronounced as "hiatus".
And:
Yes, there is a _risk_ of running into _dialectal_
glottal stops; but RP and SAE do not have glottal
stops that actually have to be _written_in_ anywhere.
>> 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 don't understand what you mean by a "checked vowel".
I looked it up in Wikipedia, and if what they say
there is what you meant, then I suppose the answer is
"yes". "Se'ennight" is not a very modern word, so it
wouldn't necessarily be part of SAE or RP, which have
few open syllables ending in "checked vowels"
according to Wikipedia.
OTOH an apostrophe is often used by phonologists and
phoneticians to indicate the "checked"ness of a
"checked consonant". The apostrophe is also used to
indicate that the consonant is "ejective", that is,
produced with a glottalic-egressive air-stream.
RP and SAE have no phonemically checked consonants;
but certain accents do allophonically "check" certain
sounds, especially for instance utterance-final
voiceless stops; and this is the source of replacing
the "checked" sounds with what you called "dialectal
glottal stops", which will be non-phonemically written
as an apostrophe in literature meant to record the
accent as it sounds, rather than as it is meant.
> I've never heard of /E/ occuring before other
> vowels; does it become /eI)/ or
> (non-rhotic 'lects only) /E@)/?
1) Not in "se'ennight", IMO; but,
2) for all I know it could. I don't know enough to
say yes or no; but it sounds plausibly possible, to
me.
>> there is no glottal stop in "chaos", nor
>> in "vacuum".
>
> "Vacuum" has a third syllabe?
It depends on the accent or 'lect; maybe even on the
register or genre.
> I just say "vacume".
As do many people.
>>>> 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. :]
"hence" means "from here"
"thence" means "from there"
"whence" means "from where" or "where from"
"hither" means "to or toward here" or "this way"
"thither" means "to or toward there" or "that way"
"whither" means "to or toward where" or "where to" or
"which way".
These words are falling out of use.
People tend to use "here" instead of "hither", "there"
instead of "thither", and "where" instead of
"whither".
People tend to use "from here" instead of "hence",
"from there" instead of "thence", and "from where" or
"where from" for "whence".
Ruth 1:16-17 illustrates "whither" and the contrast
between "whither" and "where".
As I remember it (IIRC) it goes:
"Entreat me not to leave thee, nor to return from
following after thee. Whitherersoever thou goest
thither also will I go, and wheresoever thou lodgest
there also will I lodge. Thy people shall be my
people, and thy God shall be my God. Wheresoever thou
dwellest there also will I dwell; and wheresoever thou
diest there will I die, and there also will I be
buried beside thee. The LORD do thus to me, and more,
if aught but death part me from thee."
Here are the various translations I found online:
http://www.preceptaustin.org/ruth_114-22.htm
1:16 But Ruth said, "Do not urge me to leave you or
turn back from following you; for where * you go, I
will go, and where you lodge, I will lodge. Your
people shall be my people, and your God, my God.
English of Septuagint: And Ruth said, Intreat me not
to leave thee, or to return from following thee; for
whithersoever thou goest, I will go, and wheresoever
thou lodgest, I will lodge; thy people shall be my
people, and thy God my God
KJV: And Ruth said, Entreat me not to leave thee, or
to return from following after thee: for whither thou
goest, I will go; and where thou lodgest, I will
lodge: thy people shall be my people, and thy God my
God:
Young's Literal: And Ruth saith, 'Urge me not to leave
thee -- to turn back from after thee; for whither thou
goest I go, and where thou lodgest I lodge; thy people
is my people, and thy God my God.
BBE: But Ruth said, Give up requesting me to go away
from you, or to go back without you: for where you go
I will go; and where you take your rest I will take my
rest; your people will be my people, and your God my
God.
GWT: But Ruth answered, "Don't force me to leave you.
Don't make me turn back from following you. Wherever
you go, I will go, and wherever you stay, I will stay.
Your people will be my people, and your God will be my
God.
NLT: But Ruth replied, "Don't ask me to leave you and
turn back. I will go wherever you go and live wherever
you live. Your people will be my people, and your God
will be my God.
Septuagint (LXX): eipen (3SAAI) de Routh me apantesai
(2SAMM) emoi tou katalipein (AAN) se e apostrepsai
opisthen sou hoti su opou ean poreuthes poreusomai kai
ou ean aulisthes aulisthesomai o laos sou laos mou kai
o theos sou theos mou
1:17 "Where you die, I will die, and there I will be
buried. Thus may the LORD do to me, and worse, if
anything but death parts you and me."
English of Septuagint: And wherever thou die, I will
die, and there will I be buried: the Lord do so to me,
and more also, if I leave thee, for death only shall
divide between me and thee
KJV: Where thou diest, will I die, and there will I be
buried: the LORD do so to me, and more also, if ought
but death part thee and me.
Young's Literal: Where thou diest I die, and there I
am buried; thus doth Jehovah to me, and thus doth He
add -- for death itself doth part between me and
thee.'
GWT: Wherever you die, I will die, and I will be
buried there with you. May the LORD strike me down if
anything but death separates you and me!"
ICB: And where you die, I will die. And there I will
be buried. I ask the Lord to punish me terribly if I
do not keep this promise: Only death will separate us.
NLT: I will die where you die and will be buried
there. May the LORD punish me severely if I allow
anything but death to separate us!"
Septuagint (LXX): kai ou ean apothanes (2SAAS)
apothanoumai (1SFMI) kakei taphesomai (1SFMI) tade
poiesai moi kurios kai tade prostheie (3SAAO) hoti
thanatos diastelei (3SFAI) ana meson emou kai sou
As for "whence", Psalm 121:1-2 illustrates that.
http://www.bartleby.com/108/19/121.html
The Holy Bible: King James Version. 2000.
The Psalms
121
The LORD Is Thy Keeper
A Song of degrees.
1 I will lift up mine eyes unto the hills,
from whence cometh my help.
2 My help cometh from the LORD,
which made heaven and earth.
http://beliefnet.com/prayeroftheday/sec_prayerslst.asp?paid=52
I will lift up mine eyes unto the mountains: from
whence shall my help come?
My help cometh from HaShem, who made heaven and
earth...
http://www.farsinet.com/bible/psalms/psalm121.html
Psalm 121 - The LORD is my Protector - A song of
ascents.
Psalm 121 (New King James Version - NKJV)
1 I will lift up my eyes to the hills.
From whence comes my help?
2 My help comes from the LORD,
Who made heaven and earth.
http://www.geocities.com/Baja/Canyon/3778/Mythmyst/Hills.html
I will lift up mine eyes unto the hills:
>From whence cometh mine help.
My help cometh even from the Lord:
Who hath made heaven and earth.
http://www.findarticles.com/p/articles/mi_qa3942/is_200501/ai_n9465668
The second half of verse one can be read as a
declaration of faith, as in the King James
translation: !will lift up mine eyes unto the hills,
from whence cometh my help. Or with the New Revised
Standard version, we can hear the verse as a question
addressed to God: / lift up my eyes to the hills-from
where will my help come ?
http://www.rockydawuni.com/home.html
Psalm 121
A Song of Degrees
I will lift up mine eyes unto the hills from whence
cometh help.
My help cometh from the Lord, which made heaven and
earth.
http://256.com/cgw/service/program.html
- I will lift up mine eyes unto the hills; from whence
cometh my help?
- My help cometh even from the Lord, who made heaven
and earth.
http://www.godweb.org/prayersforhope.htm
The Lord Is Thy Keeper
I will lift up mine eyes unto the hills.
>From whence cometh my help?
My help comes from the Lord, who made heaven and
earth.
Certain nautical sayings frequently had both "whence"
and "whither".
http://etext.library.adelaide.edu.au/t/twain/mark/paine/chapter259.html
'... Of course the little skipper popped into the
shrouds and squeaked out a hail, “Ship ahoy! What ship
is that? And whence and whither?” In a deep and
thunderous bass the answer came back through the
speaking-trumpet, “The Begum, of Bengal—142 days out
from Canton—homeward bound! What ship is that?” Well,
it just crushed that poor little creature’s vanity
flat, and he squeaked back most humbly, “Only the Mary
Ann, fourteen hours out from Boston, bound for Kittery
Point— with nothing to speak of!” ...'
http://www.kellscraft.com/Steerage/ModernSteerage.html
"Now it is not so easy a matter as one might think to
ship as a third-class passenger. At the ticket office
you have to give an account of yourself, tell who you
are, whence you come, whither you intend to go, your
age, whether married or single, your occupation,
whether an anarchist or not; and in accordance with
your answers you are pretty carefully scrutinized and
sized up by the emigration authorities. Then there are
the doctors to pass,..."
http://www.yesterdaysisland.com/04_articles/satire/barzillai.html
'"Late night for one so young to be prowling the
docks, young master."
Barzillai, blinking the glare away, clambered to his
feet. "Yes, sir. I’m late of Vineyard Haven, having
come to Nantucket to seek my fortune. I’ve no berth
for the night, and find myself entirely destitute."
The older man drew on his pipe, the cherry glow
lighting his face. His eyes narrowed as he listened to
Barzillai’s plight. "Peculiar choice of words there,
lad. Tell me, how old are you?"
"Twenty-one years, sir."
"And are you a travelling man?"
"Indeed I am."
"Whence and whither?"
"From West to East and East to West again."
"What do you seek?"
"That which was lost," said Barzillai, and gripped the
older man’s hand thus.
"My brother!" exclaimed the man with the pipe, "I have
lodging for you this eve. My name is Francis Brown,
captain of the sloop Charming Sally that lies behind
me. Follow me aboard, and we’ll stow your gear for the
night."'
http://www.sacred-texts.com/neu/eng/child/ch285.htm
"285A.3 They had not sayled leagues two or three
Before they spyed a sail upon the sea.
285A.4 ‘O hail, O hail, you lusty gallants,
From whence is your good ship, and whither is she
bound?’
285A.5 ‘O we are some merchant-men, sailing for
Safee:’
‘And we be French rebels, a roving on the sea.'"
(The ballad of the George Aloe can also be found at
http://www.bartleby.com/243/131.html
or
http://sniff.numachi.com/~rickheit/dtrad/pages/tiGALOESW.html
)
"Whence and Whither" also occur in philosopy:
http://www.mystudios.com/treasure/gauguin/where_review.html
"Paul Gauguin
Whence Come We? What Are We? Whither Go We?
1897
Oil on canvas 55x148in
Museum of Fine Arts, Boston
This is Gauguin's largest work and he completed it in
less than a month's time. Gauguin completed this work
just before he attempted suicide with an overdose of
arsenic, although he was saved when his body violently
rejected the poison. He intended it to be a suicide
note that would, he hoped, slow down the decay of the
western world."
http://www.lafcadiohearn.jp/articles/InYokohama.html
'"Yes," I made answer; "and I think that in Western
countries there is more unhappiness than in Japan. For
the rich there are larger pleasures, but for the poor
greater pains. Our life is much more difficult to
live; and, perhaps for that reason, our thoughts are
more troubled by the mystery of the world."
The Priest seemed interested, but said nothing. With
the interpreter's help, I continued: ---
"There are three great questions by which the minds of
many men in the Western countries are perpetually
tormented. These questions we call `the Whence, the
Whither, and the Why,' meaning, Whence Life? Whither
does it go? Why does it exist and suffer? Our highest
Western Science declares them riddles impossible to
solve, yet confesses at the same time that the heart
of man can find no peace till they are solved. All
religious have attempted explanations; and all their
explanations are different. I have searched Buddhist
books for answers to these questions, and I found
answers which seemed tome better than any others.
Still, they did not satisfy me, being incomplete. From
your own lips I hope to obtain some answers to the
first and the third questions at least. I do not ask
for proof ...'
http://www.maqom.com/may20_99.htm
"Akavya ben Mahalaleil says: contemplate three things
and you will not be susceptible to sin. Know from
whence you have come and whither you are going and
before whom you will have to give an account in the
future. From whence did you come? From a decaying
drop. Whither are you going? To a place of dust, worms
and maggots. And before whom will you have to give an
account [of your deeds] in the future? Before the King
of Kings, the Holy one Blessed be He. (Avot 3:1)"
The Holy Gospel of Jesus Christ, According to St. John
2
14 Jesus answered, and said to them: Although I give
testimony of myself, my
testimony is true: for I know whence I came, and
whither I go: but you know not ...
www.theworkofgod.org/Bible/NewTestm/John2.HTM - 36k -
Cached -
> 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.
Interesting and new, to me.
>> [snip]
>> 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.
Interesting and new, to me.
>>>> [snip]
>>>> 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.
Right you are.
> The syntax for the affix demands
I suspect _this_ (the above) is the key point.
> a form ending with a digit or power-of-10 numeral
> in basic form.
Thanks for letting me know.
>> "Percent" occurs frequently, but
>> "parts per thousand", "parts per million",
>> and "parts per billion" occur less frequently.
>
> And "perdeca" "°/" seems to be nonexistent. :)
You're right; usually "n out of ten" is used instead
of anything like 'perdeca'.
>> [snip]
>> 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.
For a pragmatic reason, I felt that an XOR of
more-than-two distinct arguments should mean "an odd
number of these arguments are true".
The pragmatic reason is, it is easy to say, using
other operations, each of the other meanings.
For instance, the most useful other meaning is
probably "at least one is true but not all are true
and at least one is false but not all are false". It
is easy to say that using AND, OR, and NOT, even if we
don't get to rely on "the Law of the Excluded Middle".
It is especially easy if we are allowed NANDs and
NORs; we could say
AND(OR({..}),NAND({..}),NOR(NOR({..}),AND({..})))
(where {..} stands for the set of the arguments.).
The second-most-useful other meanings are probably
"exactly one is true and the rest are false" and
"exactly one is false and the rest are true".
A meaning which is probably not very useful is "Before
Jan 23 2006, XOR({..}) means that an odd number of its
arguments are true; after Jan 23 2006, XOR({..}) means
that at least one of its arguments is true and at
least one of its arguments is false; and, on Jan 23
2006, XOR({..}) means 'bubblegum'.".
> If someone knows well a language which has an
> inclusive/exclusive "or" distinction, it would be
> interesting to hear how's the case there.
Latin had "aut" and "vel"; I don't know which was
AND/OR and which was XOR. We should ask some of the
Latin speakers on-list.
>> 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.)
OK, thanks; I _think_ I _might_ understand, now.
>>> draw attraction
>> You mean, "draw attention"?
>
> Aggh, sloppy writing. Yes.
"No biggie". Fuggeddabouddit.
>>>> 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 gave two meanings for each of "halve" and "quarter";
each has a meaning including "precisely equal", and
each has a meaning including "approximately equal". I
think the "divide into n equal parts" meaning is, in
fact, "directly reciprocal". The "divide into n
approximately equal parts" meaning is, as you say,
"not really directly reciprocal".
>>> I mean, if we assume it IS reciprocal,
>>> what would be the natural number equivalent?
>>> "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
I actually think all of them except "pair" do connote
conjoining along with their denotations and other
connotations: but not all to the same degree.
"Couple" has the strongest "conjoining" connotation;
"Mate" has the middle-strength connotation; and
"Marry" has the the weakest "conjoin" connotation.
(IMO).
> (and yes I know halving doesn't *have* to involve
> breaking), and "to halve" sounds like a more
> basic concept anyway.
Could be.
> Who knows, maybe it's the original root word
> and "half" was derived from it, and not the other
> way.
Could be; _I_ don't know.
> Also, thanks for all the interesting information
> that got snipped from this reply.
You're very welcome, and, the same back to you.
> John Vertical
Tom H.C. in MI
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