measurement

=Measurement=

toc Read here about measurement and how it relates to studies of scale.

=Overview= Measurement is
 * the determination or estimation of ratios of quantities (John Wallis, Isaac Newton, Euclid's Elements)
 * the correlation of numbers with entities that are not numbers (additive conjoint measurement in positivist representational theory, Stanley Smith Stevens)
 * A set of observations that reduce uncertainty where the result is expressed as a quantity (information theory).
 * collapse of the wavefunction (quantum mechanics)

=Defining measurement=

Classical Definition
In the classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton, and was foreshadowed in Euclid's Elements.

Representational theory definition
In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers". The most technically elaborate form of representational theory is also known as additive conjoint measurement. In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens, numbers need only be assigned according to a rule. The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of the requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy the necessary criteria.

Information Theory Definition
Information theory recognizes that all data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the mean and statistics of the measurements. In practical terms, one begins with an initial guess as to the value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. Note that in this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between estimation and measurement. Ascertaining the degree measurement error is also a basic facet of metrology, and sources of errors are divided into systematic and non-systematic.

Quantum mechanics definition
In quantum mechanics, a measurement is the collapse of the wavefunction. The unambiguous meaning of the measurement problem is an unresolved fundamental problem in quantum mechanics.

=Links And Citations=

See Metrology

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