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{{MitoPedia | {{MitoPedia | ||
|abbr=''U''<sub>''X''</sub> [x] | |abbr=''U''<sub>''X''</sub> [x] | ||
|description=An elementary unit ''U''<sub>''X''</sub> [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, 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 The International System of Units (SI) |Bureau International des Poids et Mesures 2019)]]. | |description=An elementary unit ''U''<sub>''X''</sub> [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 The International System of Units (SI) |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 number of atoms), then the entity is the single assembly but not the particle. A number of defined elementary units ''U''<sub>''X''</sub> is a [[count]], ''N''<sub>''X''</sub> = ''N''ยท''U''<sub>''X''</sub> [x], where ''N'' is only a number and as such ''N'' is dimensionless. The elementary unit ''U''<sub>''X''</sub> has the [[dimension]] U of the [[count]] ''N''<sub>''X''</sub>. The elementary unit ''U''<sub>''X''</sub> has the same unit [x] as the count ''N''<sub>''X''</sub>, 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''<sub>''X''</sub>ยท''U''<sub>''X''</sub><sup>-1</sup>. The unit ''u''<sub>''N''</sub> of a count can neither be the entity ''X'' nor a number. The elementary entity type (''X'' = electrons, ions, molecules, cells, organisms, events) defines the identity ''X'' of the elementary unit ''U''<sub>''X''</sub> with unit ''u''<sub>''N''</sub> termed 'counting-unit' with the simplified symbol [x]. Since a count ''N''<sub>''X''</sub> is the number of elementary units, the elementary unit ''U''<sub>''X''</sub> is not a count (''U''<sub>''X''</sub>; it is not identical with ''N''ยท''U''<sub>''X''</sub>). | If an object is defined as an assembly of particles (a party of two, a molecule as the assembly of a number of atoms), then the entity is the single assembly but not the particle. A number of defined elementary units ''U''<sub>''X''</sub> is a [[count]], ''N''<sub>''X''</sub> = ''N''ยท''U''<sub>''X''</sub> [x], where ''N'' is only a number and as such ''N'' is dimensionless. The elementary unit ''U''<sub>''X''</sub> has the [[dimension]] U of the [[count]] ''N''<sub>''X''</sub>. The elementary unit ''U''<sub>''X''</sub> has the same unit [x] as the count ''N''<sub>''X''</sub>, 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''<sub>''X''</sub>ยท''U''<sub>''X''</sub><sup>-1</sup>. The unit ''u''<sub>''N''</sub> of a count can neither be the entity ''X'' nor a number. The elementary entity type (''X'' = electrons, ions, molecules, cells, organisms, events) defines the identity ''X'' of the elementary unit ''U''<sub>''X''</sub> with unit ''u''<sub>''N''</sub> termed 'counting-unit' with the simplified symbol [x]. Since a count ''N''<sub>''X''</sub> is the number of elementary units, the elementary unit ''U''<sub>''X''</sub> is not a count (''U''<sub>''X''</sub>; it is not identical with ''N''ยท''U''<sub>''X''</sub>). | ||
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ย Communicated by [[Gnaiger Erich]] (2020-05-20) last update 2020-07- | ย Communicated by [[Gnaiger Erich]] (2020-05-20) last update 2020-07-04 โ Stave II in the [[MitoFit_2020.4.v0#XX-mass_carols |'''''XX''-mass carols''']] of '''A ''X''-mass Carol'''. | ||
Revision as of 11:28, 4 July 2020
Description
An elementary unit UX [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 number of atoms), then the entity is the single assembly but not the particle. A number of defined elementary units UX is a count, NX = NยทUX [x], where N is only a number and as such N is dimensionless. The elementary unit UX has the dimension U of the count NX. The elementary unit UX has the same unit [x] as the count NX, 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 = NXยทUX-1. The unit uN of a count can neither be the entity X nor a number. The elementary entity type (X = electrons, ions, molecules, cells, organisms, events) defines the identity X of the elementary unit UX with unit uN termed 'counting-unit' with the simplified symbol [x]. Since a count NX is the number of elementary units, the elementary unit UX is not a count (UX; it is not identical with NยทUX).
Abbreviation: UX [x]
Reference: BEC2020.1 doi10.26124bec2020-0001.v1
Communicated by Gnaiger Erich (2020-05-20) last update 2020-07-04 โ Stave II in the XX-mass carols of A X-mass Carol.
Elementary entity-type 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 โ 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 UNX. 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", mce [kg]. In contrast, X = body in the context of body mass and body mass index (BMI) is used in dual-message code, mbody. Body mass with dual-message code means the mass of all entities of entity-type human body, mbody [kg], divided by the number of bodies, Nbody, which leads to the explicit canonical expression MUbody = mbodyยทNbody-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", NX = NยทUNX-1. Similarly, in the term "O2 flow per cell" IO2/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 abstract unit uQ Symbol for unit uQ [*] elementary entity *,$ UX U elementary unit x count *,$ NX = NยทUX X elementary unit x amount of substance *,ยง nX = NXยทNA-1 N mole mol charge *,โฌ Qel = zXยทeยทNX IยทT coulomb C = Aยทs length l L meter m mass m M kilogram kg time t T second s electric current I I ampere A thermodynamic temperature T ฮ kelvin K luminous intensity Iv J candela cd
- [*] SI units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments, related to iconic symbols.
- * For the elementary quantities NX, nX, and Qel, the entity-type X of the elementary entity UX has to be specified in the text and indicated by a subscript: nO2; Nce; Qel.
- $ Count NX equals the number of elementary entities UX. 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)). An elementary entity UX is a material unit, it is not a count (UX is not a number of UX). NX has the dimension X of a count and UX has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
- ยง Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA.
- โฌ 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. zX is the charge number per elementary entity UX, which is a constant for any defined elementary entity UX. Qel = zXยทFยทnX
References
Bioblast link | Reference | Year |
---|---|---|
Brown 2018 Metrologia | Brown RJC (2018) The evolution of chemical metrology: distinguishing between amount of substance and counting quantities, now and in the future. Metrologia 55:L25. https://doi.org/10.1088/1681-7575/aaace8 | 2018 |
Brown 2021 Metrologia | Brown RJC (2021) A metrological approach to quantities that are counted and the unit one. Metrologia 58:035014. https://doi.org/10.1088/1681-7575/abf7a4 | 2021 |
Cooper 2012 Synthese | Cooper G, Humphry SM (2012) The ontological distinction between units and entities. Synthese 187:393โ401. https://doi.org/10.1007/s11229-010-9832-1 | 2012 |
Gnaiger 2020 BEC MitoPathways | Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-0002 | 2020 |
Gnaiger 2020 MitoFit x | Gnaiger E (2021) The elementary unit โ canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprints 2020.04.v2. https://doi.org/10.26124/mitofit:200004.v2 | 2021 |
Gnaiger 2024 MitoFit | Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3. https://doi.org/10.26124/mitofit:2024-0003 | 2024 |
BEC 2020.1 doi10.26124bec2020-0001.v1 | Gnaiger E et al โ MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/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 elementary UX elementary unit [x] UX, UB; [x] not in SI count NX elementary unit [x] NX, NB; [x] not in SI number N - dimensionless = NXยทUX-1 amount of substance nB mole [mol] nX, nB electric current I ampere [A] A = Cยทs-1 time t second [s] length l meter [m] SI: metre mass m kilogram [kg] thermodynamic temperature T kelvin [K] luminous intensity IV candela [cd]
- Fundamental relationships
- ยป Avogadro constant NA
- ยป Boltzmann constant k
- ยป elementary charge e
- ยป Faraday constant F
- ยป gas constant R
- ยป electrochemical constant f
- Fundamental relationships
- SI and related concepts
MitoPedia concepts:
Ergodynamics