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
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