Re: definition of " metric" as a noun
"No Spam Mapson" wrote: The OED cites the following use of metric as a noun: 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the metric is defined by certain quantities ... >>> >>> A good example of bad usage: *what* metric, *what* quantities? >>> The reader should not be left hanging with those questions unanswered. >> >> This is not bad usage at all. In mathematics, the word >> "metric" as a noun refers to a general type of distance, >> not necessarily the type in common use. > > It is certainly bad usage, for the following reason: the phrase, > "the metric", implies that there is *one* metric function on > Riemannian geometry, which is false. This reason has nothing > to do with distance measure in general, as commonly understood, > or otherwise. It is not bad usage, because a PARTICULAR Riemannian geometry is given by a particular metric; in fact, by the local quadratic form defining the differential metric. >>> >>> It *is* bad usage, because it requires the type of exegesis you >>> have just provided to make it meaningful. >> >>Statisticians, of course, always use completely unambiguous terminology > > This is not about terminology; this is about usage. > No, this is about setting the world record for the longest string of ">"s. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
>>> The OED cites the following use of metric as a noun: >>> 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean >>> geometry of Riemann, the metric is defined by certain quantities ... >> >> A good example of bad usage: *what* metric, *what* quantities? >> The reader should not be left hanging with those questions unanswered. > > This is not bad usage at all. In mathematics, the word > "metric" as a noun refers to a general type of distance, > not necessarily the type in common use. It is certainly bad usage, for the following reason: the phrase, "the metric", implies that there is *one* metric function on Riemannian geometry, which is false. This reason has nothing to do with distance measure in general, as commonly understood, or otherwise. >>> >>> It is not bad usage, because a PARTICULAR Riemannian >>> geometry is given by a particular metric; in fact, by the >>> local quadratic form defining the differential metric. >> >> It *is* bad usage, because it requires the type of exegesis you >> have just provided to make it meaningful. > >Statisticians, of course, always use completely unambiguous terminology This is not about terminology; this is about usage. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
[EMAIL PROTECTED] (Neville X. Elliven) writes: > Herman Rubin wrote: > >> The OED cites the following use of metric as a noun: >> 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean >> geometry of Riemann, the metric is defined by certain quantities ... > > A good example of bad usage: *what* metric, *what* quantities? > The reader should not be left hanging with those questions unanswered. This is not bad usage at all. In mathematics, the word "metric" as a noun refers to a general type of distance, not necessarily the type in common use. >>> >>> It is certainly bad usage, for the following reason: the phrase, >>> "the metric", implies that there is *one* metric function on >>> Riemannian geometry, which is false. This reason has nothing >>> to do with distance measure in general, as commonly understood, >>> or otherwise. >> >> It is not bad usage, because a PARTICULAR Riemannian >> geometry is given by a particular metric; in fact, by the >> local quadratic form defining the differential metric. > > It *is* bad usage, because it requires the type of exegesis you > have just provided to make it meaningful. Statisticians, of course, always use completely unambiguous terminology that anyone can intuitively understand without need for exegesis --- like ``statistically significant at the 95% confidence level''... ;-) -- Gordon D. Pusch perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;' = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
Herman Rubin wrote: >The OED cites the following use of metric as a noun: >1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean >geometry of Riemann, the metric is defined by certain quantities . . A good example of bad usage: *what* metric, *what* quantities? The reader should not be left hanging with those questions unanswered. >>> >>>This is not bad usage at all. In mathematics, the word >>>"metric" as a noun refers to a general type of distance, >>>not necessarily the type in common use. >> >>It is certainly bad usage, for the following reason: the phrase, >>"the metric", implies that there is *one* metric function on >>Riemannian geometry, which is false. This reason has nothing >>to do with distance measure in general, as commonly understood, >>or otherwise. > >It is not bad usage, because a PARTICULAR Riemannian >geometry is given by a particular metric; in fact, by the >local quadratic form defining the differential metric. It *is* bad usage, because it requires the type of exegesis you have just provided to make it meaningful. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
"Robert J. MacG. Dawson" wrote: > Actually, there *is* essentially one canonical metric function on > Riemannian geometry. In either model of absolute geometry there is, up > to a multiplicative constant, only one metric preserved by reflection. > In hyperbolic geometry, moreover, there is an absolute distance scale > based on angular defect. I should, of course, have said "one metric which is additive along lines". The discrete metric (for instance) is preserved by reflection. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
Emord Nila Palindrome wrote: > It is certainly bad usage, for the following reason: the phrase, > "the metric", implies that there is *one* metric function on > Riemannian geometry, which is false. This reason has nothing > to do with distance measure in general, as commonly understood, > or otherwise. Actually, there *is* essentially one canonical metric function on Riemannian geometry. In either model of absolute geometry there is, up to a multiplicative constant, only one metric preserved by reflection. In hyperbolic geometry, moreover, there is an absolute distance scale based on angular defect. Obviously, you can put a different metric on the points of the hyperbolic plane (or on any set); but this is a vacuous observation. Only one metric is actually a metric for the plane rather than its underlying set. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
The phrase 'the metric' is being used here to signify the type of its class. This is perfectly ordinary usage, with no implication that there is only one member of the class. E.g. "The pen is mightier than the sword." On Sat, 22 Sep 2001 03:09:55 GMT, [EMAIL PROTECTED] (Neville X. Elliven) wrote: >Herman Rubin wrote: > The OED cites the following use of metric as a noun: 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the metric is defined by certain quantities . . >> >>>A good example of bad usage: *what* metric, *what* quantities? >>>The reader should not be left hanging with those questions unanswered. >> >>This is not bad usage at all. In mathematics, the word >>"metric" as a noun refers to a general type of distance, >>not necessarily the type in common use. > >It is certainly bad usage, for the following reason: the phrase, >"the metric", implies that there is *one* metric function on >Riemannian geometry, which is false. This reason has nothing >to do with distance measure in general, as commonly understood, >or otherwise. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
In article <9ogurt$d79tc$[EMAIL PROTECTED]>, Neville X. Elliven <[EMAIL PROTECTED]> wrote: >Herman Rubin wrote: The OED cites the following use of metric as a noun: 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the metric is defined by certain quantities . . >>>A good example of bad usage: *what* metric, *what* quantities? >>>The reader should not be left hanging with those questions unanswered. >>This is not bad usage at all. In mathematics, the word >>"metric" as a noun refers to a general type of distance, >>not necessarily the type in common use. >It is certainly bad usage, for the following reason: the phrase, >"the metric", implies that there is *one* metric function on >Riemannian geometry, which is false. This reason has nothing >to do with distance measure in general, as commonly understood, >or otherwise. It is not bad usage, because a PARTICULAR Riemannian geometry is given by a particular metric; in fact, by the local quadratic form defining the differential metric. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
Herman Rubin wrote: >>>The OED cites the following use of metric as a noun: >>>1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean >>>geometry of Riemann, the metric is defined by certain quantities . . > >>A good example of bad usage: *what* metric, *what* quantities? >>The reader should not be left hanging with those questions unanswered. > >This is not bad usage at all. In mathematics, the word >"metric" as a noun refers to a general type of distance, >not necessarily the type in common use. It is certainly bad usage, for the following reason: the phrase, "the metric", implies that there is *one* metric function on Riemannian geometry, which is false. This reason has nothing to do with distance measure in general, as commonly understood, or otherwise. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
In article <9nh0a7$7brv4$[EMAIL PROTECTED]>, Neville X. Elliven <[EMAIL PROTECTED]> wrote: >Richard Wright wrote: >>On Thu, 23 Aug 2001 04:33:44 GMT, [EMAIL PROTECTED] >>(Neville X. Elliven) wrote: >>I don't feel that the practise (where the adjective takes the place >>of the adjective + noun) is regrettable. This is one of the ways by >>which languages evolve into conciseness. >Wrong, Wright; *you* wrote that. I feel that it's one of the *worst* >ways the language can be made more concise [evolution be damned] >because it comes at the cost of a loss of clarity, as experienced by >Stephen Dubin. >>Anyway, it is a bit late to be regretting the examples you give. >It's never too late to regret bad usage. >>The OED cites the following use of metric as a noun: 1921 Proc. R. >>Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the >>metric is defined by certain quantities . . . which are identified by >>Einstein with the potentials of the gravitational field." >A good example of bad usage: *what* metric, *what* quantities? >The reader should not be left hanging with those questions unanswered. This is not bad usage at all. In mathematics, the word "metric" as a noun refers to a general type of distance, not necessarily the type in common use. As an adjective, it refers to an object for which there is a metric which is connected to the properties of that object, or where there is a definite metric involved. It is usage as a noun which comes first, with the adjective usage being based on that. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
On Mon, 10 Sep 2001 00:17:54 GMT, [EMAIL PROTECTED] (Neville X. Elliven) wrote: >Context? 1587 Fleming Contn. Holinshed III. 1379/1 At hir being in Cambridge . . thus did an academike write in praise of the forenamed earle. 1671 Milton P.R. iv. 277 Mellifluous streames that watered all the schools Of academics old and new. 1848 Dickens Dombey i, The family practitioner opening the room door for that distinguished professional. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
Richard Wright wrote: >On Thu, 23 Aug 2001 04:33:44 GMT, [EMAIL PROTECTED] >(Neville X. Elliven) wrote: > >I don't feel that the practise (where the adjective takes the place >of the adjective + noun) is regrettable. This is one of the ways by >which languages evolve into conciseness. Wrong, Wright; *you* wrote that. I feel that it's one of the *worst* ways the language can be made more concise [evolution be damned] because it comes at the cost of a loss of clarity, as experienced by Stephen Dubin. >Anyway, it is a bit late to be regretting the examples you give. It's never too late to regret bad usage. >The OED cites the following use of metric as a noun: 1921 Proc. R. >Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the >metric is defined by certain quantities . . . which are identified by >Einstein with the potentials of the gravitational field." A good example of bad usage: *what* metric, *what* quantities? The reader should not be left hanging with those questions unanswered. >As for the other examples, 'professional' as a noun was good enough >for Dickens. Milton (1671) uses 'academic' as a noun. Context? = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
> As for the other examples, 'professional' as a noun was good enough > for Dickens. Milton (1671) uses 'academic' as a noun. And Shakespeare, "mechanical". -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
On Thu, 23 Aug 2001 04:33:44 GMT, [EMAIL PROTECTED] (Neville X. Elliven) wrote: I don't feel that the practise (where the adjective takes the place of the adjective + noun) is regrettable. This is one of the ways by which languages evolve into conciseness. Anyway, it is a bit late to be regretting the examples you give. The OED cites the following use of metric as a noun: 1921 Proc. R. Soc. A. XCIX. 104 "In the non-Euclidean geometry of Riemann, the metric is defined by certain quantities . . . which are identified by Einstein with the potentials of the gravitational field." As for the other examples, 'professional' as a noun was good enough for Dickens. Milton (1671) uses 'academic' as a noun. >The word in that setting refers to a metric *function*, with the noun in >the phrase left out; a common, if regrettable practise, seen in the use >of words such as "professional" and "academic". A metric function on a >suitable topology provides a measure analogous to distance. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
i think some of the posts about what "metric" as a noun means are going a bit beyond reality and trying to inculcate nuances that just don't have to be sure, there is the metric system ... where the term metric is a specific adjective to system ... but, the KEY term there is system which does not have to be defined as metric ... or even anything related to distance my old dictionary says as one definition of metric as: of, involving, or used in measurement another version says: in mathematics, the theory of measurement so, it seems to me that metric, as a noun, SIMPLY means that there is SOME system of measuring something ... could be the way we represent volumes, or lengths, or pressures, or hardness of rocks ... just something that is systematic applied to measuring some object, or phenomenon that it has to meet some highly rigid set of constraints seems rather irrelevant to me _ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
definition of " metric" as a noun
Stephen Dubin wrote: >I often see (and use) the term "metric" as a particular kind of >measure. However, I have had difficulty in finding a clear definition. >This is made more difficult because of the more common use of >"metric" as an adjective denoting the system of measurement units. >Please tell me what I mean when I call something "a metric." The word in that setting refers to a metric *function*, with the noun in the phrase left out; a common, if regrettable practise, seen in the use of words such as "professional" and "academic". A metric function on a suitable topology provides a measure analogous to distance. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
"Metric" as a noun is well established, though I sense that it's being used in this way more frequently than before. Check some dictionaries. A very good one online is http://www.m-w.com/cgi-bin/dictionary , which gives 3 definitions for the noun; the one you're referring to sounds like "2 : a standard of measurement " Jerrold H. Zar, Professor Department of Biological Sciences Northern Illinois University DeKalb, IL 60115 [EMAIL PROTECTED] >>> Dubinse <[EMAIL PROTECTED]> 08/21/01 06:56AM >>> I often see (and use) the term "metric" as a particular kind of measure. However, I have had difficulty in finding a clear definition. This is made more difficult because of the more common use of "metric" as an adjective denoting the system of measurement units. Please tell me what I mean when I call something "a metric." Thanks. Stephen Dubin VMD http://www.hometown.aol.com/dubinse [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
[EMAIL PROTECTED] (Dubinse) writes: > I often see (and use) the term "metric" as a particular kind of > measure. However, I have had difficulty in finding a clear definition. > This is made more difficult because of the more common use of > "metric" as an adjective denoting the system of measurement units. > Please tell me what I mean when I call something "a metric." It is difficult to say without seeing an example; however, one possible meaning would be any function on pairs of elements of a set that satisfies the four formal mathematical axioms of a ``distance'' function: positivity, symmetry, non-degeneracy, and the triangle inequality. Alternatively, it has regrettably become trendy to abuse the word ``metric'' to mean a ``quantitative measure'' (e.g., ``can we find some sort of performance-metric for that?''). -- Gordon D. Pusch perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;' = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: definition of " metric" as a noun
[EMAIL PROTECTED] writes:
>
>I often see (and use) the term "metric" as a particular kind of
>measure. However, I have had difficulty in finding a clear definition.
>This is made more difficult because of the more common use of
>"metric" as an adjective denoting the system of measurement units.
>Please tell me what I mean when I call something "a metric."
>
>Thanks.
>Stephen Dubin VMD
>http://www.hometown.aol.com/dubinse
>[EMAIL PROTECTED]
>
>
>=
>Instructions for joining and leaving this list and remarks about
>the problem of INAPPROPRIATE MESSAGES are available at
> http://jse.stat.ncsu.edu/
>=
To qualify for a measure of distance to be called metric, one popular way
is to
see if the measure satisfies 'metric axioms,' which consist of the
following:
(1) d(jj)=0 ; the distance from point j to itself is zero.
(2) d(jk) is greater than or equal to zero; the distance is non-negative
(3) d(jk)=d(kj); the distance is symmetric.
(4) d(jk) is less than or equal to d(jp)+d(kp)' the triangular inequality,
that is,
the sum of any two segments of a triangle cannot be smaller than the
remaining segment.
(5) that d(jk)=0 means j=k; if the distance between the two points is zero,
the two points are the same.
If all the above are satisfied, the measure is called metric.
But, not all measures satify all of them.
(a) it is pseudometric if it satisfies only (1), (2), (3) and (4)
(b) it is semi-metric if it satisfies only (1), (2), (3) and (5)
(c) it is semi-pseudometric if it satisfies only (1), (2) and (3)
(d) it is ultrametric if (4) is replaced by (6), where
(6) d(jk) is less than or equal to the larger of d(jp) and d(kp).
There are a family of metrics for continuous variables, called the
Minkowski power metric,
d(jk)(p)={the sum of |x(ij)-x(ik)|, raised to the power p, over i}
provided that p is equal to or larger than 1.
When p=1, it is called the city-block metric.
When p=1 and the variables are binary, it is called the Hamming distance.
When p=2, it is the Euclidean distance.
I hope the above is sufficient as an answer to your inquiry.
Nishi
Shizuhiko Nishisato, Professor Emeritus, Measurement and Evaluation
Program,
CTL, OISE/UT, 252 Bloor Street West, Toronto, Ontario, Canada M5S 1V6
[EMAIL PROTECTED]
(Tel): 416-923-6641, X2696
http://fcis.oise.utoronto.ca/~snishisato
http://fcis.oise.utoronto.ca/~icmma
=
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definition of " metric" as a noun
I often see (and use) the term "metric" as a particular kind of measure. However, I have had difficulty in finding a clear definition. This is made more difficult because of the more common use of "metric" as an adjective denoting the system of measurement units. Please tell me what I mean when I call something "a metric." Thanks. Stephen Dubin VMD http://www.hometown.aol.com/dubinse [EMAIL PROTECTED] = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
