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.
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