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Coherence (units of measurement)
A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.
A coherent derived unit is a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units, with the proportionality factor being one.
If a system of quantities has equations that relate quantities and the associated system of units has corresponding base units, with only one unit for each base quantity, then it is coherent if and only if every derived unit of the system is coherent.
The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association. The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (SI) was designed in 1960 to incorporate the principle of coherence.
In the SI, the derived unit m/s is a coherent derived unit for speed or velocity but km/h is not a coherent derived unit. Speed or velocity is defined by the change in distance divided by a change in time. The derived unit m/s uses the base units of the SI system. The derived unit km/h requires numerical factors to relate to the SI base units: 1000 m/km and 3600 s/h.
In the cgs system, m/s is not a coherent derived unit. The numerical factor of 100 cm/m is needed to express m/s in the cgs system.
The earliest units of measure devised by humanity bore no relationship to each other.[citation needed] As both humanity's understanding of philosophical concepts and the organisation of society developed, so units of measurement were standardized—first particular units of measure had the same value across a community, then different units of the same quantity (for example feet and inches) were given a fixed relationship. Apart from Ancient China where the units of capacity and of mass were linked to red millet seed, there is little evidence of the linking of different quantities until the Enlightenment.
The history of the measurement of length dates back to the early civilization of the Middle East (10000 BC – 8000 BC). Archaeologists have been able to reconstruct the units of measure in use in Mesopotamia, India, the Jewish culture and many others. Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as Ancient Egypt, multiples with prime factors aside from 2, 3 and 5 were sometimes used—the Egyptian royal cubit being 28 fingers or 7 hands. In 2150 BC, the Akkadian emperor Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of which the only prime factors were 2, 3 and 5; for example there were 6 she (barleycorns) in a shu-si (finger) and 30 shu-si in a kush (cubit).
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Coherence (units of measurement) AI simulator
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Coherence (units of measurement)
A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.
A coherent derived unit is a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units, with the proportionality factor being one.
If a system of quantities has equations that relate quantities and the associated system of units has corresponding base units, with only one unit for each base quantity, then it is coherent if and only if every derived unit of the system is coherent.
The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association. The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (SI) was designed in 1960 to incorporate the principle of coherence.
In the SI, the derived unit m/s is a coherent derived unit for speed or velocity but km/h is not a coherent derived unit. Speed or velocity is defined by the change in distance divided by a change in time. The derived unit m/s uses the base units of the SI system. The derived unit km/h requires numerical factors to relate to the SI base units: 1000 m/km and 3600 s/h.
In the cgs system, m/s is not a coherent derived unit. The numerical factor of 100 cm/m is needed to express m/s in the cgs system.
The earliest units of measure devised by humanity bore no relationship to each other.[citation needed] As both humanity's understanding of philosophical concepts and the organisation of society developed, so units of measurement were standardized—first particular units of measure had the same value across a community, then different units of the same quantity (for example feet and inches) were given a fixed relationship. Apart from Ancient China where the units of capacity and of mass were linked to red millet seed, there is little evidence of the linking of different quantities until the Enlightenment.
The history of the measurement of length dates back to the early civilization of the Middle East (10000 BC – 8000 BC). Archaeologists have been able to reconstruct the units of measure in use in Mesopotamia, India, the Jewish culture and many others. Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as Ancient Egypt, multiples with prime factors aside from 2, 3 and 5 were sometimes used—the Egyptian royal cubit being 28 fingers or 7 hands. In 2150 BC, the Akkadian emperor Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of which the only prime factors were 2, 3 and 5; for example there were 6 she (barleycorns) in a shu-si (finger) and 30 shu-si in a kush (cubit).