A unit is defined as 'a single individual thing' in Euclid's Elements (Book VII). This defines the elementary entity UX of entity-type X (thing). The International System of Units defines the unit as 'simply a particular example of the quantity concerned which is used as a reference'. Then the value of a quantity Q is the product of a number N and a unit uQ. The symbols UX and uQ chosen here with U and u for 'unit': UX is the Euclidean or entetic unit ('eunit'), and uQ is the abstract unit ('aunit'). Subscripts X and Q for 'entity-type' and 'quantity-type' reflect perhaps even more clearly than words the contrasting meanings of the two fundamental definitions of a entetic versus abstract 'unit'. The term 'unit' with its dual meanings is used and confused in practical language and the scientific literature today. In the elementary entity UX, the unit (the 'one') relates to the entity-type X, to the single individual thing (single individual or undivided; the root of the word thing has the meaning of 'assembly'). The quantity involved in the unit of a single thing is the count, NX = N·UX [x]. In contrast to counting, a unit uQ is linked to the measurement of quantities Qu = N uQ, such as volume, mass, energy; and these quantities — and hence the units uQ — are abstracted from entity-types, pulled away from the world of real things. The new SI (2019-05-20) has completed this total abstraction of units, from the previous necessity to not only provide a quantitative definition but also a physical realization of a unit in the form of an 'artefact', such as the international prototype (IPK) for the unit kilogram. The new definitions of the base SI units are independent of any physical realization: uQ is separate from X. The classical unit of Euklid is the elementary unit for counting, entirely independent of measuring. Therefore, the quantity count is unique with respect to two properties: (1) in contrast to all other quantities in the metric system, the count depends on quantization of entities X; and (2) in the SI, the Number 1 is the Unit of the Count of entities — NUCE.
Abbreviation: UX [x]; uQ
Communicated by Gnaiger Erich (2020-07-06) last update 2020-08-14 in: Anastrophe XX Entity X and elementary unit x of X-mass Carol
MitoPedia concepts: Ergodynamics