Dimension (metadata)

Last updated

In metadata, a dimension is a set of equivalent units of measure, where equivalence between two units of measure is determined by the existence of a quantity-preserving one-to-one correspondence between values measured in one unit of measure and values measured in the other unit of measure, independent of context, and where characterizing operations are the same.

The equivalence defined here forms an equivalence relation on the set of all units of measure. Each equivalence class corresponds to a dimensionality. The units of measure "temperature in degrees Fahrenheit" and "temperature in degrees Celsius" have the same dimensionality because given a value measured in degrees Fahrenheit, there is a value measured in degrees Celsius with the same quantity, and vice versa. Quantity-preserving one-to-one correspondences are the well-known equations Cº = (5/9)*(Fº  32) and Fº = (9/5)*(Cº) + 32.

Units of measure are not limited to physical categories. Examples of physical categories are linear measure, area, volume, mass, velocity, and time duration. Examples of non-physical categories are: currency, quality indicator, and colour intensity.

Quantities may be grouped together into categories of quantities which are mutually comparable. Lengths, diameters, distances, heights, wavelengths, and so on would constitute such a category. Mutually comparable quantities have the same dimensionality. ISO 31-0 calls these quantities of the same kind.

See also

Related Research Articles

Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.

<span class="mw-page-title-main">Fahrenheit</span> Temperature scale

The Fahrenheit scale is a temperature scale based on one proposed in 1724 by the European physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit as the unit. Several accounts of how he originally defined his scale exist, but the original paper suggests the lower defining point, 0 °F, was established as the freezing temperature of a solution of brine made from a mixture of water, ice, and ammonium chloride. The other limit established was his best estimate of the average human body temperature, originally set at 90 °F, then 96 °F.

<span class="mw-page-title-main">Physical quantity</span> Measurable property of a material or system

A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol. Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.

<span class="mw-page-title-main">Thermodynamic temperature</span> Measure of absolute temperature

Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.

<span class="mw-page-title-main">Metric system</span> Metre-based systems of measurement

The metric system is a decimal-based system of measurement. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela.

<span class="mw-page-title-main">Parts-per notation</span> Set of units to describe small values

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million, parts-per-billion, parts-per-trillion and parts-per-quadrillion. This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.

<span class="mw-page-title-main">Zeroth law of thermodynamics</span> Physical law for definition of temperature

The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized.

The term degree is used in several scales of temperature, with the notable exception of kelvin, primary unit of temperature for engineering and the physical sciences. The degree symbol ° is usually used, followed by the initial letter of the unit; for example, "°C" for degree Celsius. A degree can be defined as a set change in temperature measured against a given scale; for example, one degree Celsius is one-hundredth of the temperature change between the point at which water starts to change state from solid to liquid state and the point at which it starts to change from its liquid to gaseous state.

<span class="mw-page-title-main">Dry-bulb temperature</span> Temperature of air as measured by a thermometer shielded from radiation and moisture

The dry-bulb temperature (DBT) is the temperature of air measured by a thermometer freely exposed to the air, but shielded from radiation. DBT is the temperature that is usually thought of as air temperature, and it is the true thermodynamic temperature. It is directly proportional to the mean kinetic energy of the air molecules. Temperature is usually measured in degrees Celsius (°C), kelvins (K), or degrees Fahrenheit (°F). If expressed in kelvins, then the symbol Ta, if expressed in Celsius or Fahrenheit, then the symbol is ta. When measuring dry-bulb temperature care should be taken to prevent the sensor from being subjected to radiation from neighbouring heat sources.

<span class="mw-page-title-main">Elementary mathematics</span> Mathematics taught in primary and secondary school

Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense, algebra, geometry, measurement, and data analysis. These concepts and skills form the foundation for more advanced mathematical study and are essential for success in many fields and everyday life. The study of elementary mathematics is a crucial part of a student's education and lays the foundation for future academic and career success.

ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It was intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by ISO 80000-1. Other parts of ISO 31 have also been withdrawn and replaced by parts of ISO 80000.

<span class="mw-page-title-main">Metrication in Canada</span> Adoption of the metric system of measurements in Canada

Metrication in Canada began in 1970 and ceased in 1985. While Canada has converted to the metric system for many purposes, there is still significant use of non-metric units and standards in many sectors of the Canadian economy and everyday life. This is mainly due to historical ties with the United Kingdom, the traditional use of the imperial system of measurement in Canada, interdependent supply chains with the United States, and opposition to metrication during the transition period.

<span class="mw-page-title-main">Degree day</span>

A degree day is a measure of heating or cooling. Total degree days from an appropriate starting date are used to plan the planting of crops and management of pests and pest control timing. Weekly or monthly degree-day figures may also be used within an energy monitoring and targeting scheme to monitor the heating and cooling costs of climate controlled buildings, while annual figures can be used for estimating future costs.

<span class="mw-page-title-main">Celsius</span> Unit of measurement for temperature

The degree Celsius is the unit of temperature on the Celsius temperature scale, one of two temperature scales used in the International System of Units (SI), the other being the closely related Kelvin scale. The degree Celsius can refer to a specific point on the Celsius temperature scale or to a difference or range between two temperatures. It is named after the Swedish astronomer Anders Celsius (1701–1744), who proposed the first version of it in 1742. The unit was called centigrade in several languages for many years. In 1948, the International Committee for Weights and Measures renamed it to honor Celsius and also to remove confusion with the term for one hundredth of a gradian in some languages. Most countries use this scale.

<span class="mw-page-title-main">Kelvin</span> SI unit of temperature

The kelvin, symbol K, is the base unit of measurement for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts from 0 K, the lowest possible temperature, then rises by exactly 1 K for each 1 °C. The Kelvin scale was designed to be easily converted from the Celsius scale. Any temperature in degrees Celsius can be converted to kelvin by adding 273.15.

<span class="mw-page-title-main">Temperature</span> Physical quantity of hot and cold

Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.

Scale of temperature is a methodology of calibrating the physical quantity temperature in metrology. Empirical scales measure temperature in relation to convenient and stable parameters or reference points, such as the freezing and boiling point of water. Absolute temperature is based on thermodynamic principles: using the lowest possible temperature as the zero point, and selecting a convenient incremental unit.

In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and kB. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.

References