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Surely the whole point of a measure is that its unit should be something
other than the thing being measured?
Suppose I have some wheat: it's not very informative to know that it is
identical in some respect (e.g. weight, volume) to some other *particular*
heap of wheat. What I want is some external standard of weight or volume
(etc.) to which any and all possible heaps of wheat can be compared.
That said, I share Jerry's sense that his examples don't quite capture the
point (see comments interpolated below).
> How do you measure the power of an engine? Horse-power, right? Yet, an
> engine is by no means composed of the same substance as a horse.
> Yeah, I know, that's probably not a good example.
Horses are flesh and blood and engines are metal, but they also have
one common substance, namely the ability to perform work (in the mechanical
sense) measured by time, mass and distance (if I recall correctly).
> The unit of measure for direction has been historically the magnetic
> compass. Yet, a magnetic needle is composed of a a different "substance"
> than what it is used as a proxy to measure (relative direction).
> That's probably not a good example either.
I think here Jerry is here (and also above) confusing the unit with
the technique of measurement. The "unit" of direction is the degree of
difference from some reference direction; the compass needle points out this
reference direction and the dial allows one to read off the difference of
one's own direction.
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