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05-24-2019, 11:11 PM (This post was last modified: 05-30-2019 11:38 AM by SlideRule.)
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An extract from The Quality of Measurements: A Metrological Reference, A.E. Fridman, DOI 10.1007/978-1-4614-1478-0_1, © Springer Science+Business Media, LLC 2012

Chapter 1 Basic Concepts in Metrology
1.1 Introduction

1.2 Properties and Quantities
It will be convenient to begin our discussion of metrological concepts with the concepts of property and magnitude. A property of an object is one of its distinguishing traits or characteristics. Heavy, long, strong, bright – these are all examples of properties of various objects. In philosophy, property is defined as a philosophical category, which expresses that aspect of an object that determines whether it has something in common with other objects or is different from other objects. Properties are qualitative characteristics, and many of them cannot be expressed quantitatively. Other properties can be expressed quantitatively. Such properties are called quantities. A quantity is a property that many objects (states, systems, and processes) have in common on a qualitative basis, but the quantitative value of the property for each object is specific to that object.
An extremely general classification of quantities as a concept is shown in Fig. 1.
Quantities are initially divided into real quantities and ideal quantities. An ideal quantity is any numerical value. It is, by its very essence, an abstraction, not associated with any real object. Therefore, ideal quantities are studied in mathematics rather than metrology.
Real quantities are divided into physical quantities and ideal quantities. Non-physical quantities are introduced, determined, and studied in information science, the social sciences, economic sciences, and humanitarian sciences (e.g., sociology or linguistics). Examples of non-physical quantities are as follows: Amount of information in bits, amount of financial capital in dollars, and a variety of ratings determined using sociological surveys. The physical quantities that metrology deals with are the properties of tangible objects, processes, and phenomena. Unlike non-physical quantities, they exist in the tangible world around us in an objective manner, independent of human desires.
Physical quantities are divided with respect to the method used for quantitative determination into measured quantities and estimated quantities. The distinguishing feature of a measurement is the presence of a measuring instrument – a special piece of equipment that stores the magnitude of a unit and is used to determine the value of a quantity. The process of estimation primarily refers to expert assessments and organoleptic assessments (i.e., assessments using human sensory organs) of quantities, such as, for example, determination of distances “by eye.” In such cases, there is no piece of equipment in which to store the magnitude of a unit, meaning that there is no assurance that the estimate obtained meets accuracy requirements. The magnitude of the standard length dimension maintained by a person in his consciousness varies substantially from one individual to another, and this value can also vary for a single individual depending on his psychological and physical condition. Thus, such an estimate is inaccurate and unreliable, and there is no guarantee that the result of the estimation process will be objective. Only a piece of equipment not subject to human deficiencies is capable of providing such a guarantee. This is in fact the reason that measurements are the highest form of quantitative estimation.
The history of metrology indicates that all physical quantities follow what is essentially an identical path. Following discovery and identification of a new property and determination of a physical quantity: first, a method for quantitative estimation of the quantity is developed, and then, as knowledge increases, estimation is replaced by indirect measurements. Measures and approaches for direct measurements of this quantity will then be developed and used as a basis for establishment of a system for metrological traceability of the new form of measurements. For example, this was the path followed by measurements of color: from color atlases to a form of measurement – colorimetry, including equipment and measurement techniques, as well as metrologic traceability of said measurements. Acoustic measurements and salinity measurements followed a similar path. Measurement techniques will obviously be developed for many other physical quantities that are currently estimated via expert or organoleptic methods, such that said quantities become measured quantities.
The above analysis enables us to draw a clear boundary between measured and estimated quantities: Measured quantities are physical quantities for which measurement techniques already exist, and estimated quantities are physical quantities for which measurement techniques have yet to be developed.

1.3 Magnitude and Value of a Quantity. Units of Measurement for Quantities. Reference Scales for Quantities
In actual fact, it is not the quantities themselves, but the quantities associated with specific objects, phenomena, or processes, i.e., quantities with specific dimensions, that are measured. Strictly speaking, measurement is the act of estimating the magnitude of a quantity using specialized equipment (*). The magnitude of a quantity is understood to be a quantitative determination of a quantity related to a specific tangible object, system, phenomenon, or process.
Upon comparing the magnitude of some quantity to the unit for that quantity, we obtain the value of the quantity. Thus, the value of a quantity expresses the magnitude of a quantity in the form of some number of the units adopted for that quantity. In formal notation, this is written as follows:
X = x × [X] (1.1)
where X is the value of the quantity,
[X] is the unit of measurement for the quantity,
x is an abstract number occurring in the value of the quantity. It is called the numerical value of the quantity.
Equation (1.1) is called the fundamental equation of measurement.
Setting x = 1 in (1.1), we find that: X = x × [X]. This then implies the following definition of a unit:
A unit of measure (or, briefly, a unit) is understood to be a quantity of specific magnitude that is arbitrarily assigned a numerical value of 1 and is used for quantitative expression of homogeneous quantities. For example, the unit of length is 1 m (m) and the unit of mass is 1 kg (kg).

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