# Measure

(Redirected from Measured)

From Middle English mesure, from Anglo-French, from Latin mensura, from mensus, past participle of metiri to measure; akin to Old English mǣth measure, Greek metron

• Date: 13th century

## Definitions

• 1 a (1) : an adequate or due portion (2) : a moderate degree; also : moderation, temperance (3) : a fixed or suitable limit : bounds <rich beyond measure>
b : the dimensions, capacity, or amount of something ascertained by measuring
c : an estimate of what is to be expected (as of a person or situation)
d (1) : a measured quantity (2) : amount, degree
• 2 a : an instrument or utensil for measuring b (1) : a standard or unit of measurement — see weight table table (2) : a system of standard units of measure <metric measure>
• 3 : the act or process of measuring
• 4 a (1) : melody, tune (2) : dance; especially : a slow and stately dance
b : rhythmic structure or movement : cadence: as (1) : poetic rhythm measured by temporal quantity or accent; specifically : meter (2) : musical time
c (1) : a grouping of a specified number of musical beats located between two consecutive vertical lines on a staff (2) : a metrical unit : foot
• 5 : an exact divisor of a number
• 6 : a basis or standard of comparison <wealth is not a measure of happiness>
• 7 : a step planned or taken as a means to an end; specifically : a proposed legislative act

— for good measure : in addition to the minimum required : as an extra

## Description

### Classical

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, which it is 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[1].

### Representational

In the representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers"[2]. The strongest 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

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."[3]. 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 a continuum between estimation and measurement.

### Quantum mechanics

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.

## References

1. Michell, 1993
2. Ernest Nagel: "Measurement", Erkenntnis, Volume 2, Number 1 / December, 1931, pp. 313-335, published by Springer, the Netherlands
3. Douglas Hubbard: "How to Measure Anything", Wiley (2007), p. 21