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Entity
Description
A unit-entity U_{X} [x] of elementary entity type X is a single countable object (X = molecules, cells, organisms, particles, parties) or a single countable event (X = beats, collisions, emissions, decays, celestial cycles, instances, occurences, parties). "An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles" (Bureau International des Poids et Mesures 2019).
If an object is defined as an assembly of particles (a party of two, a molecule as the assembly of a stoichiometric number of atoms), then the entity is the assembly but not the assembled particle. A number of defined elementary units U_{X} is a count, N_{X} = N·U_{X} [x], where N is only a number and as such N is dimensionless. The elementary unit U_{X} has the dimension U of the count N_{X}. The elementary unit U_{X} has the same unit [x] as the count N_{X}, or more accurately it gives the count the defining 'counting-unit' [x]. From the definition of count as the number (N) of elementary units (U) of entity type X, it follows that count divided by elementary unit is simply a number, N = N_{X}·U_{X}^{-1}. The unit u_{N} of a count can neither be the entity X nor a number. The elementary entity type X defines the identity X of the elementary unit U_{X} with the unit 'counting-unit' with symbol [x]. Since a count N_{X} is the number of unit-entities, the unit-entity U_{X} is not a count (U_{X}; it is not identical with N·U_{X}).
Abbreviation: U_{X} [x]
Reference: BEC2020.1 doi10.26124bec2020-0001.v1
Contents
Communicated by Gnaiger Erich (2020-05-20) last update 2020-07-06 in: Anastrophe XX Entity X and the elementary unit x of A X-mass Carol
Elementary entity-type, unit-entity, and elementary unit
- In Euclid's Elements (Book VII) a "unit" is defined as 'a single individual thing'. Take 'individual thing' as equal to elementary entity. Then we see in Euclid's definition a kaleidoscopic imaging of Number, Unit, Count, Entity — NUCE (in nuce), which remains a CASE to this day (CASE represents the Counting-Assembling-Sorting Experience).
- Entity-type X is distinguished from unit-entity U_{X}. Dual-message code may lead to misunderstanding depending on context. For example, X = ce in 'cell mass' is normally understood as meaning "the mass of all entities of entity-type ce in a sample", m_{ce} [kg]. In contrast, X = body in the context of body mass and body mass index (BMI) is used in dual-message code, m_{body}. Body mass with dual-message code means the mass of all entities of entity-type human body, m_{body} [kg], divided by the number of bodies, N_{body}, which leads to the explicit canonical expression M_{Ubody} = m_{body}·N_{body}^{-1}.
- Colour code: Colour red may be used in X, indicating that the term entity or symbol X are used in dual-message code, meaning both entity-type and unit-entity. When specifying "single entity X" it is sufficiently clear that X is used in dual-message mode, and the term "number of X" is equally clear to meaning "number of unit-entities X", N_{X} = N·U_{X}^{-1}. Similarly, in the term "O_{2} flow per cell" I_{O2/ce}" it is sufficiently clear that ce is used in in dual-message code.
Base quantities and count
Quantity Symbol for quantity Q Symbol for dimension Name of SI unit Symbol for SI unit u_{Q} [*] length l L meter m mass m M kilogram kg time t T second s electric current I I ampere A thermodynamic temperature T Θ kelvin K amount of substance ^{*,§} n_{X} = N_{X}·N_{A}^{-1} N mole mol count ^{*,$} N_{X} X elementary unit x unit-entity ^{*,$} U_{X} U elementary unit x charge ^{*,€} Q_{X} = N_{X}·z_{X}·e I·T coulomb C = A·s luminous intensity I_{v} J candela cd
- [*] »SI base units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments.
- ^{*} For the quantities n, N, U, and Q, the entity-type X of the unit-entity U has to be specified in the text and indicated by a subscript: n_{O2}; N_{ce}; Q_{X}.
- ^{§} Amount n_{X} is an elementary quantity, converting the elementary unit [x] into moles [mol] using the Avogadro constant, N_{A}.
- ^{$} Count N_{X} equals the number of unit-entities U_{X}. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). A unit-entity U_{X} is not a count (U_{X} is not a number of U_{X}). N_{X} has the dimension X of a count and U_{X} has the dimension U of a unit-entity, and both quantities have the same unit, the 'elementary unit' [x].
- ^{€} Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge, e, or converting moles [mol] into coulombs [C] using the Faraday constant, F. z_{X} is the charge number of entity X, which is a constant for any defined entity X. Q_{X} = n_{X}·z_{X}·F
References
Bioblast link | Reference | Year |
---|---|---|
MitoFit 2020.4.v0 | Gnaiger Erich (2020) A X-mass Carol. Body Mass Excess and mitObesity. MitoFit Preprint Arch 2020.4.v0. | |
BEC 2020.1 doi10.26124bec2020-0001.v1 | Gnaiger Erich et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. doi:10.26124/bec:2020-0001.v1. | 2020 |
- Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
- Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment unit-entity U_{X} elementary unit [x] U_{X}, U_{B}; [x] not in SI count N_{X} elementary unit [x] N_{X}, N_{B}; [x] not in SI number N - dimensionless = N_{X}·U_{X}^{-1} amount of substance n_{B} mole [mol] n_{X}, n_{B} electric current I ampere [A] A = C·s^{-1} time t second [s] length l meter [m] SI: metre mass m kilogram [kg] thermodynamic temperature T kelvin [K] luminous intensity I_{V} candela [cd]
- Fundamental relationships
- SI and related concepts
MitoPedia concepts:
Ergodynamics