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iando
Guest
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| Posted: Mon Nov 07, 2005 8:07 am
Post subject: Two geometries |
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Generally speaking nouns expressing subjects like geometry, geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Is this plural use of "geometry" generally acceptable?
If so, can you apply this usage to other nouns? Furthermore can you apply to
other abstract nouns like symapthy,hatred, love,...?
For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete mathematics.
Thanks
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Aaron Davies
Guest
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| Posted: Mon Nov 07, 2005 8:07 am
Post subject: Re: Two geometries |
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iando <iando@abox.so-net.ne.jp> wrote:
| Quote: | Generally speaking nouns expressing subjects like geometry, geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Is this plural use of "geometry" generally acceptable?
If so, can you apply this usage to other nouns? Furthermore can you apply to
other abstract nouns like symapthy,hatred, love,...?
For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete mathematics.
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It's a fairly common acadmeic useage, which shows up particularly often
in philosophy and social sciences. It's not at all uncommon to speak of
"feminisms" and the like. Personally, I consider it an annoying pomo
affectation.
--
Aaron Davies
Opinions expressed are solely those of a random number generator.
Magnae clunes mihi placent, nec possum de hac re mentiri.
Ho! Ha! Guard! Turn! Parry! Dodge! Spin! Thrust! |
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Jim Lawton
Guest
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| Posted: Mon Nov 07, 2005 4:16 pm
Post subject: Re: Two geometries |
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On Mon, 07 Nov 2005 05:14:08 GMT, aaron@avalon.pascal-central.com.invalid (Aaron
Davies) wrote:
| Quote: | iando <iando@abox.so-net.ne.jp> wrote:
Generally speaking nouns expressing subjects like geometry, geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Is this plural use of "geometry" generally acceptable?
If so, can you apply this usage to other nouns? Furthermore can you apply to
other abstract nouns like symapthy,hatred, love,...?
For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete mathematics.
It's a fairly common acadmeic useage, which shows up particularly often
in philosophy and social sciences. It's not at all uncommon to speak of
"feminisms" and the like. Personally, I consider it an annoying pomo
affectation.
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Why? You have Euclidian Geometry, you have another sort. You have two
geometries. What do you want to say?
--
Jim
the polymoth
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Don Phillipson
Guest
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| Posted: Mon Nov 07, 2005 8:06 pm
Post subject: Re: Two geometries |
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"iando" <iando@abox.so-net.ne.jp> wrote in message
news:newscache$qrhkpi$wxd$1@news01c.so-net.ne.jp...
| Quote: | For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete
mathematics. |
This is not a reliable example because "hard cases
make bad law." The point of difference is that:
1. The various geometries (plane, spherical, etc.) have
conflicting axioms, thus different characters (e.g. number
of degrees in a triangle.)
2. There are not two chemistries: all varieties of chemistry
(pure or applied, organic and inorganic) are based on the
same set of axioms and principlels. They differ only in
either social purposes or specialized subject-matter.
--
Don Phillipson
Carlsbad Springs
(Ottawa, Canada) |
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CDB
Guest
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| Posted: Mon Nov 07, 2005 9:10 pm
Post subject: Re: Two geometries |
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"iando" <iando@abox.so-net.ne.jp> wrote in message
news:newscache$qrhkpi$wxd$1@news01c.so-net.ne.jp...
| Quote: | Generally speaking nouns expressing subjects like geometry,
geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Is this plural use of "geometry" generally acceptable?
If so, can you apply this usage to other nouns? Furthermore can you
apply to
other abstract nouns like symapthy,hatred, love,...?
For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete
mathematics.
|
Generally speaking, an uncountable noun "X" can be used in the plural
to mean "kinds of X". Two rices, arborio and basmati; two geometries,
as in the example you gave. In cases where the word is already plural
in form, like "mechanics" and "mathematics", it would be better to say
"kinds of mathematics", since the listener will otherwise have to
pause to consider and reject the possibility of one mathematic; in the
case of "mechanic", you can even find such a beast, though you might
find him rude. |
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John Lawler
Guest
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| Posted: Tue Nov 08, 2005 6:45 am
Post subject: Re: Two geometries |
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CDB <unbellecd@sprint.ca> writes:
| Quote: | "iando" <iando@abox.so-net.ne.jp> writes
Generally speaking nouns expressing subjects like geometry,
geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Is this plural use of "geometry" generally acceptable?
|
Absolutely. See below.
| Quote: | If so, can you apply this usage to other nouns? Furthermore can you
apply to
other abstract nouns like symapthy,hatred, love,...?
For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete
mathematics.
|
It depends. See below.
| Quote: | Generally speaking, an uncountable noun "X" can be used in the plural
to mean "kinds of X". Two rices, arborio and basmati; two geometries,
as in the example you gave. In cases where the word is already plural
in form, like "mechanics" and "mathematics", it would be better to say
"kinds of mathematics", since the listener will otherwise have to
pause to consider and reject the possibility of one mathematic; in the
case of "mechanic", you can even find such a beast, though you might
find him rude.
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(Actually, in that case, I'd sanction 'mechanicses' and 'mathematicses',
just to be clear -- as well as eccentric, which is a prerequisite for
philosophical discussion. [Warning: Closed clause and professorial
linguist. Don't try this at home.])
CDB is right; and it works both ways. That's how you countify a mass noun
-- by types; but you can also massify a count noun:
o a lot of car for the money
o after the explosion at the faculty meeting,
there was professor all over the place
o there's a bit too much two-year-old
in the President's responses
Wherever there is a distinction produced automatically by the grammatical
system, there is some semantic or pragmatic convention to exploit it.
Sometimes several, depending usually on socioeconomic group.
-John Lawler ** Linguistics @ umich.edu & wwu.edu
------------------------------------------------
"Overrated, anyway, those complete sentences."
-- Chris Waigl |
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Mike Lyle
Guest
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| Posted: Tue Nov 08, 2005 7:31 am
Post subject: Re: Two geometries |
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Don Phillipson wrote:
[...]
| Quote: | 2. There are not two chemistries: all varieties of chemistry
(pure or applied, organic and inorganic) are based on the
same set of axioms and principlels. They differ only in
either social purposes or specialized subject-matter.
|
But then, as I understand it, we would often use "chemistries": I
don't know if it's acceptable, as I'm not a scientist, but I've
certainly heard it in things like (to invent an example I haven't
actually heard) "Brain and plant chemistries are very different".
--
Mike. |
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Stewart Gordon
Guest
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| Posted: Tue Nov 08, 2005 6:15 pm
Post subject: Re: Two geometries |
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iando wrote:
| Quote: | Generally speaking nouns expressing subjects like geometry, geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
|
Non-Euclidean isn't a geometry. It's a general term for all geometries
other than the Euclidean.
| Quote: | Is this plural use of "geometry" generally acceptable?
|
Yes, IMX. Similarly, there are many sciences.
| Quote: | If so, can you apply this usage to other nouns? Furthermore can you apply to
other abstract nouns like symapthy,hatred, love,...?
|
Good question.
| Quote: | For example,
mechanics: We have two mechanics: classical and quantum mechanics.
chemistry: We have two chemistries: pure chemistry and applied
chemistry.
mathematics: We have two mathematics: continuous and discrete mathematics.
|
Doesn't really sound right. Rather, if there's any such thing as a
"mathematic", then it would seem to be talking about two of those.
(FTM, have any of you Americans out there tried pluralising "math" to
"maths"? Doesn't work here in Britain, where "maths" is a singular
subject.)
Case in point: a "statistic" is a single value calculated from some
statistical formula. (Is this a back-formation?) So "two statistics"
means two such values.
Stewart.
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Mike Lyle
Guest
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| Posted: Wed Nov 09, 2005 12:39 am
Post subject: Re: Two geometries |
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Stewart Gordon wrote:
| Quote: | iando wrote:
[...]
If so, can you apply this usage to other nouns? Furthermore can
you
apply to other abstract nouns like symapthy,hatred, love,...?
Good question.
[...] |
We can, though not all in the same way.
In "My sympathies are with the victim" or "a woman of Republican
sympathies", the plural seems to me meaningless, though it's very
common. The singular versions "My sympathy is with the victim" and "a
woman of Republican sympathy" seem to mean exactly the same as the
plural ones. I'd actually say that "Republican sympathy" is rather
uncommon.
In "A man of violent hatreds", though, there is a focus on a number
of objects of his hatred considered separately. The difference from
"A man of violent hatred" may be subtle, but it's a real one.
Similarly, plural "loves" isn't always the same as the abstract noun
"love": in "My great loves are baroque music and traditional jazz",
it refers to the things I love, not the feeling itself, though of
course the feeling is included. In "She was the last and greatest of
his loves", it again seems to refer more to persons loved than to the
feeling.
--
Mike. |
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John Lawler
Guest
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| Posted: Wed Nov 09, 2005 7:40 am
Post subject: Re: Two geometries |
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Stewart Gordon <smjg_1998@yahoo.com> writes:
| Quote: | iando writes:
Generally speaking nouns expressing subjects like geometry, geology,
mechanics, acoustics,.... are considered to be uncountable.
But I found the following expressions in a book.
We have two geometries : Euclidean and Non-Euclidean geometry.
Non-Euclidean isn't a geometry. It's a general term for all geometries
other than the Euclidean.
|
Well, actually, it's a general term for *both* geometries other than the
Euclidean. Until we get to Affine and Projective, which are at a different
level, there are only three types of Geometry: Ordinary Euclidean;
Hyperbolic non-Euclidean à la Gauss, Bólyai, and Lobachevski (GBL); and
Elliptic non-Euclidean à la Riemann. They differ in how they treat the
Parallel Postulate:
o Euclidean geometry posits one and only one parallel line to any given
line through any given point.
o GBL geometry posits an indefinitely large number of parallel lines;
that's the one that led to Minkowsky's 4-dimensional space that was
used for Einstein's general relativity.
o Riemann's geometry, on the other hand, posits no parallels at all;
that's the one with the spherical model that uses Great Circles for
'lines'.
Since the only ways to contradict the "one and only one" part of Euclid's
parallel postulate is to either deny the "one" (i.e, zero) or the "only
one" (i.e, many) parts, these are the only non-Euclidean geometries on the
same level of abstraction as Euclidean geometry.
There are those three geometries, but there are also other geometries,
like affine and projectional geometries, which have fewer axioms.
And then there's topology, which sits at the top of Klein's Erlanger
Programm. They're all geometries, as any mathematician will tell you.
But only mathematicians use 'geometry' in the plural.
-John Lawler www.umich.edu/~jlawler/geb.html umich.edu & wwu.edu
------------------------------------------------------------------
"Mathematicians are like Frenchmen: whatever you say to them they
translate into their own language, and forthwith it is something
entirely different." -- Johann Wolfgang von Goethe (1829) |
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Stewart Gordon
Guest
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| Posted: Wed Nov 09, 2005 6:25 pm
Post subject: Re: Two geometries |
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John Lawler wrote:
| Quote: | Stewart Gordon <smjg_1998@yahoo.com> writes:
snip
Non-Euclidean isn't a geometry. It's a general term for all geometries
other than the Euclidean.
Well, actually, it's a general term for *both* geometries other than the
Euclidean. Until we get to Affine and Projective, which are at a different
level, there are only three types of Geometry: Ordinary Euclidean;
Hyperbolic non-Euclidean à la Gauss, Bólyai, and Lobachevski (GBL); and
Elliptic non-Euclidean à la Riemann. They differ in how they treat the
Parallel Postulate:
o Euclidean geometry posits one and only one parallel line to any given
line through any given point.
o GBL geometry posits an indefinitely large number of parallel lines;
that's the one that led to Minkowsky's 4-dimensional space that was
used for Einstein's general relativity.
o Riemann's geometry, on the other hand, posits no parallels at all;
that's the one with the spherical model that uses Great Circles for
'lines'.
Since the only ways to contradict the "one and only one" part of Euclid's
parallel postulate is to either deny the "one" (i.e, zero) or the "only
one" (i.e, many) parts, these are the only non-Euclidean geometries on the
same level of abstraction as Euclidean geometry.
snip |
That actually isn't quite what Euclid postulated - see
http://en.wikipedia.org/wiki/Parallel_postulate
But anyway, what's your proof that:
- no geometry can be constructed by deviating from any of Euclid's first
four postulates?
- each of the above has only one version when you consider assumptions
beyond the five postulates (several of which exist in Euclid's work)?
Stewart.
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