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In [OPE-L:2040] Chaion wrote:
>
> I can at least enumerate some examples of measures where the unit of
measure is not composed of the same substance as what is being measured.
>
> First, we can measure the temperature with the height of mercury. The
mercury did not have the temperature but only has it transferred from the
measured.
>
> Second, in astronomy, we measure the distance with the yard stick that
has the same substance of the so-called length. The dispersion of light
replaces the yard stick.
>
> Third, we measure the weight of a thing with a spring scale, which has no
weight but only has the elasticity in responce to the weight of the
measured.
>
> Fourth, we can measure the blood pressure with an electronic measure that
has no pressure in itself but only responses to the outside pressure.
>
> Most astronomical measures and medical measures and electronical measures
are the cases.
>
The examples presented by Chaion show that the discussion of magnitudes and
its measurements requires closer consideration. The statement that *the
unit
of measure needs to be composed of the same substance as what is being
measured* doesn't seem to be acceptable. Measures may refer either to the
material substance of objects or to a single attribute of them. What is
measured is magnitudes, i.e., the extent or the size of some attribute of
objects. It seems to me that the measure of extension is the simplest
example. A standard object with a standard extension is confronted with the
extension of other objects, irrespective of the material substance of the
later. What is measured is the attribute *extension* of the objects. Other
measures refer to the effect of the relation between objects. Weight is not
a substance, but an attribute of every object on earth, that of being
subject to the attraction of gravity. It is not properly an attribute of
the
object, but of its relation with the Earth. Thus, measuring weight consists
of measuring the magnitude of the effect of gravity upon the objects. The
example of the spring scale is very good, because it shows the complexity
of
the measuring devices, in terms of the creation of devices derived from the
basic process or device of measure. Weight is measured by comparing the
effect of gravity suffered by an object to the effect suffered by a
standard
amount of a well defined standard object. In this case the unit of measure
and the object being measured possess the same attribute. The spring scale
is a derivative device: after the effect of the conventional unit of the
standard of weight upon the spring is determined, any other object that
produces the same effect corresponds to the same weight as the unit of
weight. It seems to me that one could not build a spring scale without
proceeding in this way.
The measurement of the temperature with the height of mercury follows the
same principle. The attribute to be measured is the effect of the amount of
calories upon objects. First an arbitrary origin on a mercury column of
well
defined dimensions has to be determined, and after that the effect of an
arbitrary change in the amount of calories is marked on the mercury column
and called the unit of temperature. After that, all the objects that cause
the mercury column to stop at the same point are said to be equally warm or
cold, or to possess the same temperature. In this case the proceedings are
a
litle more complicated because it is necessary to find a range of change,
which has been defined as the one between the points of freezing and of
boiling of water. In this case too, it seems to me that the attribute is
being measured by a standard possessing the same attribute, which is the
effect of the amounts of calories.
The measure of the labor content of the commodities follows the same
principle. It is impossible to measure directly the amount of social or
abstract labor time, in the same way as it is impossible to measure
directly
the expression of gravity or the amount of calories. But the effect of
labor
time can be measured indirectly: an arbitrary amount of a regular product
of
labor is taken as the standard unit. Thus, a commodity which is exchanged
for one of such units is said to be the product of the same amount of
labor.
In this case too the unit of measure and the objects measured possess the
same attribute. There is, however, a big difference in the process of
measuring, because in the case of value it is not a physical process, but a
social one, which complicates the understanding of it, but doesn't change
its nature.
Claus Germer
cmgermer@sociais.ufpr.br
Departamento de Economia
Universidade Federal do Paraná
Rua Dr. Faivre, 405 - 3º andar
80060-140 Curitiba - Paraná
Brasil
Tel: (041) 360-5214 - Ufpr
(041) 254-3415 Res.
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