relative vs. absolute

[Mark Mandel]

"Relative" here is being used for an ordinal scale, which is more
meaningful than a nominal one but less than an interval or ratio
scale. There are four classes of value: nominal, ordinal, interval,
and ratio, in ascending order of rigor. (My mnemonic for them is
"noir".)

Nominal: Each value has a name, but there is no order or comparison
between them. E.g., for "nationality" you might have values like
France, UK, Trinidad and Tobago, Japan, USA, Philippines. I'd be
unwilling to call such a classification a "scale" at all.

Ordinal: The values are ordered, but there is no arithmetic comparison
between them. For example, cancer is "staged" in increasing order of
development and seriousness as I, II, III, IV, with substages like
IIIa and IIIb, but it's meaningless to ask whether Stage III is twice
as far from Stage I as it is from Stage II. The Mohs scale of hardness
is a classic example of an ordinal scale.

Interval: The values are ordered and can be subtracted, but not added,
multiplied or divided. The interval between Sept. 12, 2000 and Sept.
12, 2009 is 9 years, but "Sept. 12, 2000 + Sept. 12, 2009" is
meaningless. Similarly,   Jan. 1, 2000 isn't twice as (anything) as
Jan. 1, 1000,   100 degrees Fahrenheit isn't twice as hot as 50, and
40 degrees west longitude isn't four times as west as 10 degrees west,
except as measured from their scales' arbitrary zeros.

Ratio: The values can be treated as numbers: meaningfully subtracted,
added, multiplied or divided. $6 is twice as much as $3,   300 degrees
Kelvin is three times as hot as 100, and a person of 60 is twice as
old as a person of 30.   40 degrees north latitude is twice as far
north as 20 degrees north (and the equator, unlike the Greenwich
meridian, is not arbitrary).

Google gives about 18k hits for /+nominal +ordinal +integer +ratio/.
This one (http://tinyurl.com/qskmrh) is helpful:

Data mining: practical machine learning tools and techniques with Java
implementations
By Ian H. Witten, Eibe Frank
Edition: 2
Published by Morgan Kaufmann, 2000
ISBN 1558605525, 9781558605527
371 pages

--
Mark Mandel

On Tue, Jun 2, 2009 at 9:06 PM, Victor <aardvark66 at gmail.com> wrote:
>
> Perhaps I am overly influenced by mathematics and physics jargon, but I
> am having trouble figuring out in what sense "relative" is being used in
> a piece on "absolute hardness". Normal interpretation of "[measure] X
> [for Y] is relative" for me is that X is a measure of Y where Y is being
> compared to Z. If a "scale" merely gives some ranking of Y, Z and other
> "stuff", I would never consider describing such a scale as "relative".
>
> In the example here, I would consider the "absolute hardness" scale to
> be relative, in the sense that the tool that measures it, a sclerometer,
> does so by effectively comparing the test hardness to some reference
> measure. But the Mohr scale is simply a rank ordering of minerals in
> terms of hardness without any attempt to relate them, so using
> "relative" in this context makes no sense to me. And I don't just make
> that distinction in English--hopefully it's not some form of early senility.
>
> Do I need to get out more or is the following passage really odd with
> respect to its use of "relative"? My guess is that the author of the
> piece reinterpreted the modifier "absolute" to apply to "scale" rather
> than to "hardness" and recovered his meaning of "relative" from there.
>
> http://www.inlandlapidary.com/user_area/hardness.asp
>
> Absolute Hardness
> The Mohs Hardness Scale is relative. Fluorite at 4 is not twice as hard
> as gypsum at 2; nor is the difference between calcite and fluorite
> similar to the difference between corundum and diamond. An absolute
> hardness scale looks a little different than the relative scale. Using a
> piece of sensitive equipment called a sclerometer, a comparison of the
> absolute hardness of minerals can be measured. Most minerals are close
> in hardness. But as hardness increases, the difference in hardness
> greatly increases as seen in this  absolute hardness scale.
>
> Using an absolute scale you can say that corundum is actually 4 times
> softer than diamond, not half as soft as Mohs relative scale leads you
> to believe.
>
> Mohr's Scale: 1. Talc, 2. Gypsum, 3. Calcite, 4. Fluorite, 5. Apatite,
> 6. Orthoclase/Feldspar, 7. Quartz, 8. Topaz, 9. Corundum, 10. Diamond
> Absolute Hardness Scale: 1 Talc, 3 Gypsum, 9 Calcite, 21 Fluorite, 48
> Apatite, 72 Orthoclase/Feldspar, 100 Quartz, 200 Topaz, 400 Corundum,
> 1600 Diamond
>
> ------------------------------------------------------------
> The American Dialect Society - http://www.americandialect.org

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The American Dialect Society - http://www.americandialect.org