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Why are numbers so hard?

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Raincrowlee
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 Message 33 of 51
22 March 2011 at 3:23am | IP Logged 
Cainntear wrote:
Raincrowlee wrote:
Then there's how the numbers get declined as singular genitive when it ends in 2-4, but a plural genitive when 5-9.

Ah, no it's not the singular vs the plural, it's the paucal vs the plural. If you call it singular it makes absolutely no sense, because 4 isn't "single".

"Paucal" is related to "paucity", and the French "peu" -- it means a low quantity.

"Plural" is related to "plus", so it means "more". "More" than what? More than whatever else there is that is smaller, whether that's singular, dual, trial, paucal, whatever.


No matter what you name it, the complexity is still there. And the terminology I used was simply the categories given to me by the Russian textbooks I used. Their accuracy is the concern of the grammarians who wrote it, not me.
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Cainntear
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 Message 34 of 51
22 March 2011 at 11:11am | IP Logged 
Chung wrote:
While it is true that one can think of 2-4 in Russian as paucal from a certain approach (it basically evolved as a way to cope for the loss of the dual), it doesn't make that much sense to downplay the fact that nouns modified by 2 to 4 take on the declensional endings of the genitive singular (or if you want to split hairs, the endings of a putative paucal quantity in modern Russian have merged with those of the genitive singular).

But neither of your explanations gets rid of the feeling that this is nonsensical.

"take on the declensional endings of the genitive singular"
No, they take "the same endings as the genitive singular".

This may really seem like splitting hairs, but we're talking psychology now, not technical facts.

The paucal is not singular, and saying it takes singular endings causes an immediate reaction of "this is wrong -- 3 is not singular" in most people. Telling people that they are different, but that they actually look the same, doesn't provoke the same reaction. It doesn't make it immediately easy, but it stops people being quite as resistant to the idea.
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Chung
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 Message 35 of 51
22 March 2011 at 3:17pm | IP Logged 
Cainntear wrote:
Chung wrote:
While it is true that one can think of 2-4 in Russian as paucal from a certain approach (it basically evolved as a way to cope for the loss of the dual), it doesn't make that much sense to downplay the fact that nouns modified by 2 to 4 take on the declensional endings of the genitive singular (or if you want to split hairs, the endings of a putative paucal quantity in modern Russian have merged with those of the genitive singular).

But neither of your explanations gets rid of the feeling that this is nonsensical.

"take on the declensional endings of the genitive singular"
No, they take "the same endings as the genitive singular".

This may really seem like splitting hairs, but we're talking psychology now, not technical facts.

The paucal is not singular, and saying it takes singular endings causes an immediate reaction of "this is wrong -- 3 is not singular" in most people. Telling people that they are different, but that they actually look the same, doesn't provoke the same reaction. It doesn't make it immediately easy, but it stops people being quite as resistant to the idea.


I fail to see why you're delving into psychology. I'm not saying that your approach yields the wrong conclusion, but we're splitting hairs. I also get the sense that the interpretation is nonsensical to you, and that you're railing against this interpretation by other people.

If it bothers you when the term "singular" is being associated with something non-singular, then I'm curious if you'd angrily challenge teachers of Polish who describe the ending -o below as a neuter singular rather than as a paucal (which I have never heard or seen anywhere outside a specialized monograph on Polish linguistics)

e.g.

- Kilka tysięcy osób umarło w Japonii. "Several thousand people died in Japan."

Several thousand [genitive plural] person [genitive plural] died [neuter 3rd person singular] in Japan [locative singular].

Would you insist that umarło is wrongly described as a neuter singular ending on the l-participle?

Or would you be indignant when confronted by one of these phrases?

- The government are taking steps to bring their citizens home from the war zone.
- The government is taking steps to bring its citizens home from the war zone.

Do you think that it's wrong or misleading to use "are" in the first phrase? In turn would you disagree vehemently with someone who identifies "are" here as being the 3rd person plural present tense form of "to be"?
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Abdalan
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 Message 36 of 51
22 March 2011 at 3:56pm | IP Logged 
Not only the numbers, but (much more) the math operations are quite difficult in
foreign languages. The intimate relationship between language and mathematics is
illustrated by the fact that in World War II, anti-Nazi forces in Europe believed that
the enemies was sending spies to report their activities. Some of them claimed to be
natives when in fact they were really Germans well trained in languages. The real test
was to ask them to solve a math problem out loud. If the person was not a native
speaker, he had a tremendous difficulty to do it out loud and that would cost his head.

All languages are potentially able to communicate any idea, and particular features of
other languages may alert us to mathematical nuances that are hidden in world languages
like English. Examining language gives us new insights into a number of things; I read
a paper that impressed very much:

It is known that both, Dhivehi and Turkish decline their nouns. Thus, in Dhivehi, the
word for five has several different forms: "Fas mas" (five fish) is the adjectival
form, and is used when speaking of the digit 5, but:

- Tinek ehkuran fahek ehvarey ashakaa (Three and five is eight).
- Hayek fahekaa ehkuray (Add six to five).
- Fanarayakee fahekuge gunaeh (Fifteen is a multiple of five).
- Tinek fahekun kendeema ehvarey dek (Three subtracted from five equals two).

But even in English:

1 - Three fives - Five threes --> (The plural form ‘fives’ indicates that
this is a ‘group of five’ and that there are three of them, or vice versa).

2 - Three multiplied by five - Five multiplied by three --> (the word ‘by’ indicates
that the role of the three is different from the role of the five, despite the form of
the words being the same.)

3 - Three times five - Five times three --> (is actually similar, but does not look
like it. The ‘times’ here refers to how many times it occurred: “three occurrences of
five”. But young children often say “times it by five” showing they think of “times” as
a verb.)

In Dhivehi the number words change in the first and second cases because the different
role played by the two numbers is embedded in the structure of the word. There is no
equivalent to “three times five” in Dhivehi.

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Cainntear
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 Message 37 of 51
22 March 2011 at 6:49pm | IP Logged 
Chung wrote:
I fail to see why you're delving into psychology.

Because the difficulty is psychological. A structurally correct explanation clearly isn't good enough if people still have difficulty with it.

Quote:
I also get the sense that the interpretation is nonsensical to you, and that you're railing against this interpretation by other people.

Calling 2, 3 or 4 "singular" is objectively illogical.
Saying it uses a the same form as the singular gives the same structural conclusion, but doesn't go against logic.

Quote:
If it bothers you when the term "singular" is being associated with something non-singular, then I'm curious if you'd angrily challenge teachers of Polish who describe the ending -o below as a neuter singular rather than as a paucal (which I have never heard or seen anywhere outside a specialized monograph on Polish linguistics)

Many people on this forum feel that many teachers do a bad job. I am one of them.

The problem is that teachers confuse terms with concepts.

The term "paucal" isn't much use to the casual Polish learner, but the concept is. So I don't really care how the paucal is labelled, just that the concept is clear. Calling it "singular" obscures the concept, which is the opposite of what good teaching does.
Quote:
Or would you be indignant when confronted by one of these phrases?

- The government are taking steps to bring their citizens home from the war zone.
- The government is taking steps to bring its citizens home from the war zone.

Do you think that it's wrong or misleading to use "are" in the first phrase? In turn would you disagree vehemently with someone who identifies "are" here as being the 3rd person plural present tense form of "to be"?

Why would I have a problem with either of those? They're both good English after all.

I can imagine a learner might have a problem with the collective-as-plural usage, and that concept needs to be explained properly. Nothing more.
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Chung
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 Message 38 of 51
22 March 2011 at 8:37pm | IP Logged 
Cainntear wrote:
Chung wrote:
I fail to see why you're delving into psychology.

Because the difficulty is psychological. A structurally correct explanation clearly isn't good enough if people still have difficulty with it.
I for one haven't had a problem with it

Chung wrote:
I also get the sense that the interpretation is nonsensical to you, and that you're railing against this interpretation by other people.

Cainntear wrote:
Calling 2, 3 or 4 "singular" is objectively illogical.
Saying it uses a the same form as the singular gives the same structural conclusion, but doesn't go against logic.


The parsing of "logic" is problematic since languages are often "illogical" depending on your point of view (and which I suspect you're well aware of).

Hungarian is probably more stark about mixing singularity with plurality (especially from a certain Indo-European point of view) whereby Hungarian nouns modified by any numeral are in singular. Grammar is not a reflection of some unalloyed "logic" (however some of us conceive it). Logic is relative especially when accounting for the different languages that can provide one's "logical background".

E.g.

Egy ember fut.
"One person is running."

Két/Három/Négy/Öt/Hat/Száz ember fut.
"2/3/4/5/6/100 people are running."

BUT: Az emberek futnak.
"The people are running."

Note also how not only is the noun singular when preceded by a numeral, but the verb conjugation is in singular - reinforcing that the numerals are not unequivocally plural (manifested as they are per the standard or "accepted" grammar).

Finnish will probably throw a loop too in this insistence that numerals greater than one cannot be singular (or even interpreted in that way in grammar), since relevant Finnish "experts" from hum-drum language teachers to high-powered linguists writing reference manuals state that Finnish nouns and adjectives just modified by numerals greater than one are declined in partitive singular with the associated verb also being singular. I'm not sure if they would appreciate being told that it's conceptually wrong or psychologically damaging to look at it this way (i.e. mixing singular with plural) and certainly they wouldn't insist that their students must refer to this as paucal in order to suppress any connection between the numeral greater than 2 and "partitive singular"

E.g.

Yksi ihminen juoksee. (ihminen is nominative singular)
"One person is running."

Kaksi/Kolme/Neljä/Viisi/Kuusi/Sata ihmistä juoksee. (ihmistä is partitive singular of ihminen)
"2/3/4/5/6/100 people are running."

If there were a plural demonstrative pronoun modifying the numeral then the verb would become plural, but the noun remains in partitive singular.

Tämä yksi ihminen juoksee.
"This one person is running."

Nämä kaksi/kolme/neljä/viisi/kuusi/sata ihmistä juoksevat.
"These 2/3/4/5/6/100 people are running."

Cainntear wrote:
Chung wrote:
If it bothers you when the term "singular" is being associated with something non-singular, then I'm curious if you'd angrily challenge teachers of Polish who describe the ending -o below as a neuter singular rather than as a paucal (which I have never heard or seen anywhere outside a specialized monograph on Polish linguistics)

Many people on this forum feel that many teachers do a bad job. I am one of them.

The problem is that teachers confuse terms with concepts.


There's no doubt in my mind about this (see my post about Dutch teachers who tried to teach Finnish direct object as if it were like the accusative in most Western European languages). However (mis)labelling a paucal as genitive singular seems hardly detrimental nor the most far-reaching blunder that a teacher can commit when teaching a language.

Cainntear wrote:
The term "paucal" isn't much use to the casual Polish learner, but the concept is. So I don't really care how the paucal is labelled, just that the concept is clear. Calling it "singular" obscures the concept, which is the opposite of what good teaching does.

Chung wrote:
Or would you be indignant when confronted by one of these phrases?

- The government are taking steps to bring their citizens home from the war zone.
- The government is taking steps to bring its citizens home from the war zone.

Do you think that it's wrong or misleading to use "are" in the first phrase? In turn would you disagree vehemently with someone who identifies "are" here as being the 3rd person plural present tense form of "to be"?

Why would I have a problem with either of those? They're both good English after all.

I can imagine a learner might have a problem with the collective-as-plural usage, and that concept needs to be explained properly. Nothing more.


With these examples I was trying to show that what one counts as singular depends and trying to fit "logic" to fit grammar isn't that helpful since the "logic" or definition of such varies on whom you ask. For sure both of these English forms are correct. Just as you detect that Russian can only be marking a paucal with something that by accident matches the genitive singular, Raincrowlee, various Russian grammarians interpret it as the coexistence of a genitive singular with a non-singular modifier. Neither approach is "wrong", and to boot, when I learned BCMS/Serbo-Croatian (which also declines noun in genitive singular after 2 to 4) I didn't blow a fuse, write an angry letter to the course's author or get hopelessly befuddled by seeing a singular concept linked to a non-singular one. I just learned it and made sure to keep using it when dealing in the language.

This kind of splitting of hairs reminds me of some teachers who insist that the periphrastic future in Polish is formed with the "l-participle" instead of the "past participle". I actually learned it from my teacher and textbooks as "past participle" and only later saw reference in specialized literature to "l-participle". In any case a terminological imprecision wasn't harmful since I merely made it a point to learn that the Polish periphrastic future is constructed with future of "to be" plus a participle that I had indeed learned of as the "past participle" (when tackling the Polish past tense) or infinitive. "L-participle", "past participle": it makes no difference to me what people want to call it. The important result is to use the construction in a way that is understandable, grammatically correct AND acceptable for the target audience. Decrying the description, (mis)naming or (mis)classification has little effect if people still use the construction in question consistently and in a way that they deem to be unambiguous or "correct".
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leosmith
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 Message 39 of 51
23 March 2011 at 1:05am | IP Logged 
Just answering the title question, without reading anything (sorry about that). Because you learn a formula, or set of
rules when you learn numbers. You have to run through this when you want to speak, instead of just repeating a
word you memorized. QED :)
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Cainntear
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 Message 40 of 51
23 March 2011 at 6:24pm | IP Logged 
Chung wrote:
Cainntear wrote:
Because the difficulty is psychological. A structurally correct explanation clearly isn't good enough if people still have difficulty with it.
I for one haven't had a problem with it

Good students learn despite bad teaching.
Bad students fail because of bad teaching.

Many people drop out of studying Russian. More people have problems than don't.

Quote:
Cainntear wrote:
Calling 2, 3 or 4 "singular" is objectively illogical.
Saying it uses a the same form as the singular gives the same structural conclusion, but doesn't go against logic.


The parsing of "logic" is problematic since languages are often "illogical" depending on your point of view (and which I suspect you're well aware of).

Yes, most things in language are only logical from a certain point of view.
The job of a teacher is to describe the language in a way that makes sense to the learner.
Certain descriptions are inherently illogical, and create problems for the learner. Saying "3 is 1" is illogical to every rational person. "Singular" means "1". There is a better way to describe the language.
Quote:
Hungarian is probably more stark about mixing singularity with plurality (especially from a certain Indo-European point of view) whereby Hungarian nouns modified by any numeral are in singular. Grammar is not a reflection of some unalloyed "logic" (however some of us conceive it). Logic is relative especially when accounting for the different languages that can provide one's "logical background".

No, but each language is internally logical, and teaching the language means teaching the logic.

Saying that "Hungarian nouns modified by any numeral are in singular" does not appeal to the learner in any understandable way.

You don't need to think of it as "singular", but simply as a base form. Then you can say that you only need to mark once for number -- hence it stays in the base form where there's an explicit number, and only needs to be plural-marked when there's no explicit number.
Quote:
Finnish will probably throw a loop too in this insistence that numerals greater than one cannot be singular (or even interpreted in that way in grammar), since relevant Finnish "experts" from hum-drum language teachers to high-powered linguists writing reference manuals state that Finnish nouns and adjectives just modified by numerals greater than one are declined in partitive singular with the associated verb also being singular. I'm not sure if they would appreciate being told that it's conceptually wrong or psychologically damaging to look at it this way (i.e. mixing singular with plural) and certainly they wouldn't insist that their students must refer to this as paucal in order to suppress any connection between the numeral greater than 2 and "partitive singular"

You're obviously not listening, because that's not even what a paucal is!

It's similar to the situation with Hungarian (for obvious reasons) but the partitive gives us an extra level of marking.

But in both cases, it's a matter of marking for plurality in a different way from other languages.

In both languages, 3 is still a plurality. It is not a singularity. So again it does not appeal to any logic or sense to call it "the singular". "The same as the singular" is OK, "the singular" is not.

The problem here is analogous to what you're trying to accuse me of.
You say I'm trying to pin the language to a logic that doesn't fit, but the "experts" are trying to pin the language to a Latinate grammatical model that doesn't fit.

I'm trying to identify the logic within the language and describe the language in terms of that logic.
Describing the language in terms designed to describe Greek and Latin is the wrong way to go.
Quote:
However (mis)labelling a paucal as genitive singular seems hardly detrimental nor the most far-reaching blunder that a teacher can commit when teaching a language.

So, what... we shouldn't improve the little things that are easy to improve? We should wait until someone has fixed all the "big" things first?

All the little things can accumulate to one big mess of confusion. We certainly should fix them.

Quote:
With these examples I was trying to show that what one counts as singular depends and trying to fit "logic" to fit grammar isn't that helpful since the "logic" or definition of such varies on whom you ask.

You seem to be assuming that logic is external to the language.
I'm a descriptivist, so I'm not trying to impose logic on the language, and am looking for the logic that is inherent to the language.
Quote:
Neither approach is "wrong", and to boot, when I learned BCMS/Serbo-Croatian (which also declines noun in genitive singular after 2 to 4) I didn't blow a fuse, write an angry letter to the course's author or get hopelessly befuddled by seeing a singular concept linked to a non-singular one. I just learned it and made sure to keep using it when dealing in the language.

Again, the success of a minority of learners does not prove the efficacy of teaching when held up against the failure of the majority. You didn't have a problem with it -- many more do.


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