On Aug 7, 2009, at 10:11 AM, Lieberman Joshua wrote: (01)
> Not sure I agree. Anything which is a unit at least implies that there
> could be a multiple of that unit (theological concepts aside), which
> implies counting which is a form of measurement.
> (02)
True, but hardness does not have a 'unit' in this sense. The various
hardness scales are all simply orderings, and a hardness measure is a
point in the ordering. No other arithmetical structure need be assumed
for these scales: in particular, it does not follow that something
with RHC 6 is 'twice as hard" as one with RHC 3, in any precise sense.
As the necessary ideas of total ordering, being a group, etc., are all
well understood and available off the mathematical shelf, we can be
liberal in our ontology of measuring scales and allow these 'merely
ordered' cases. (Seems to me that the weakest condition on a measure
scale should be that it is totally ordered: does everyone agree?
Anyone want to defend a non-total partial order?) (03)
> On the other hand, getting into concepts of measurement and
> observation themselves will bloat an ontology of units beyond
> recognition. (04)
Agreed. (05)
> Certainly there are methods of measurement for properties
> such as hardness which are only faintly comparable in detail, but I
> would hope that concepts such as scales / coordinate systems would
> help with this, since some of those can be mapped precisely from one
> to the other, but not all of them even if they purport to represent
> the same property. (06)
While I agree with the general point, the fact is that the various
scales all called 'hardness scales' do not all measure the same exact
physical property. This is widely acknowledged in the relevant
technical literature, which also describes the circumstances in which
the various such scales are appropriate (some for metallurgy, some for
comparing carbide tools, some for very thin samples, etc..). Seems to
me that we should not try to get into the minutae of such a subfield,
but also not exclude it from consideration on account of its pragmatic
nature. We can simply allow all the various hardnesses to coexist, and
be agnostic regarding what it is they have in common. (07)
Pat H (08)
>
> Josh
>
> On Aug 7, 2009, at 9:30 AM, Mike Bennett wrote:
>
>> True, but we need to also remember that not all units are units of
>> physical measurement, i.e. not all measured amounts of something are
>> measured amounts of some physical thing. In particular, the concepts
>> of
>> "Amount", "Unit" and so on are applied equally to amounts of money
>> and
>> units of currency. Though you could argue that apart from the US
>> Dollar,
>> units of currency are defined by some process of measurement (the
>> rate
>> against the US Dollar).
>>
>> Therefore I would hope that the fundamental properties at the core of
>> this, are not prematurely committed to the physical world. Rather,
>> there
>> are amounts and units, and there are physical amounts and physical
>> units
>> which are kinds of these, as well as currency amounts and currency
>> units
>> which are kinds of these (and all the other interesting variations we
>> have seen). Perhaps things like hardness would fit into that kind of
>> framework more easily than if we pre-commit to a physical-only view
>> of
>> measurement and units.
>>
>> Mike
>>
>> John F. Sowa wrote:
>>> David,
>>>
>>> All units of measure are ultimately defined by some process
>>> of measurement. The meter was formerly defined by a comparison
>>> with a standard held in a vault in Paris. Now it's defined as
>>> a wavelength of light emitted by a certain type of atom under
>>> certain conditions.
>>>
>>> There is no difference, in principle, between the definition of
>>> 'meter' or the definition of 'standard candle':
>>>
>>> The Standard, or International, Candle is a measurement
>>> of light source intensity. It was originally defined as
>>> a one-sixth-pound candle of sperm wax, burning at the rate
>>> of 120 grains per hour. This intensity of light was standardized
>>> in 1921 in terms of incandescent lamps, and candles are no
>>> longer used for reference. (From Britannica online)
>>>
>>> The definition of 'hardness' by various methods is no different in
>>> principle from the definition of any other kind of physical unit.
>>>
>>> John Sowa
>>>
>>>
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>>>
>>
>>
>> --
>> Mike Bennett
>> Director
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> (09)
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