Theiling Online    Sitemap    Conlang Mailing List HQ   

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; "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." "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." "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 &#934;:M->Hom(N,R), which matches the first definition by setting &#934;(m)(n): = e(m,n). A pairing is called perfect if the above map &#934; is an isomorphism of R-modules." "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)." "(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." 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." "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 &#8594; N into a new function g:N &#8594; 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"). 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." "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". "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." 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)." 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." 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" "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." "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 ""' "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." 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. " "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." "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 ""' "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: 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. 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. 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... 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. 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. 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 ? 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. - 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. 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". '... 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!” ...' "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,..." '"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."' "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 or ) "Whence and Whither" also occur in philosopy: "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." '"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 ...' "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 ... - 36k - Cached -
> Still, I've browsed thru >\ > Phonological_history_of_the_English_language > a few times and there's nothing on the topic > there.
I'm sorry to say I can't find it any more, either. However says: "English may have the labiodental approximant as a realisation of /r/. Although traditionally regarded as an idiosyncrasy, speech defect, or infantilism, use of labiodental /r/ is increasing in many accents of British English (see papers in Foulkes and Docherty 1999). As a realisation of /r/, it may not always be labiodental: bilabial and velarised labiodental realisations have been reported (see Foulkes and Docherty 1999, Wells 1982). English speakers may also use it to pronounce place names in languages that do use it, such as Hawai‘ian Wahiawa." And a source I found the first time I responded to you (the lost response), said it was used this way by "older speakers of upper-class British dialects".
>>>> 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 __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around