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Difference between revisions of "Entity"

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{{MitoPedia
{{MitoPedia
|abbr=''U''<sub>''X''</sub> [x]
|abbr=''U''<sub>''X''</sub> [x]
|description=A '''unit-entity''' ''U''<sub>''X''</sub> [x] of elementary 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, 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=A '''unit-entity''' ''U''<sub>''X''</sub> [x] of elementary 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)]].


If an object is defined as a group of particles (a party of two), then the entity is the single group but not the particle. A number of defined unit entities ''U''<sub>''X''</sub> is a [[count]], ''N''<sub>''X''</sub> = ''N''·''U''<sub>''X''</sub> [x], where ''N'' is only a number and as such ''N'' is dimensionless. The unit entity ''U''<sub>''X''</sub> has the [[dimension]] U of the [[count]] ''N''<sub>''X''</sub>. The unit entity ''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 unit entities (''U'') of elementary type ''X'', it follows that count divided by unit entity is simply a number, ''N'' = ''N''<sub>''X''</sub>·''U''<sub>''X''</sub><sup>-1</sup>. The elementary entity type (''X'' = electrons, ions, molecules, cells, organisms, events) defines the identity ''X'' of the unit entity ''U''<sub>''X''</sub>. Since a count ''N''<sub>''X''</sub> is the number of unit entities, the unit entity ''U''<sub>''X''</sub> is not a count (''U''<sub>''X''</sub> is not identical with ''N''·''U''<sub>''X''</sub>).
If an object is defined as a group of particles (a party of two), then the entity is the single group but not the particle. A number of defined unit entities ''U''<sub>''X''</sub> is a [[count]], ''N''<sub>''X''</sub> = ''N''·''U''<sub>''X''</sub> [x], where ''N'' is only a number and as such ''N'' is dimensionless. The unit entity ''U''<sub>''X''</sub> has the [[dimension]] U of the [[count]] ''N''<sub>''X''</sub>. The unit entity ''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 unit entities (''U'') of elementary type ''X'', it follows that count divided by unit entity is simply a number, ''N'' = ''N''<sub>''X''</sub>·''U''<sub>''X''</sub><sup>-1</sup>. The elementary entity type (''X'' = electrons, ions, molecules, cells, organisms, events) defines the identity ''X'' of the unit entity ''U''<sub>''X''</sub>. Since a count ''N''<sub>''X''</sub> is the number of unit entities, the unit entity ''U''<sub>''X''</sub> is not a count (''U''<sub>''X''</sub> is not identical with ''N''·''U''<sub>''X''</sub>).
|info=[[BEC2020.1 doi10.26124bec2020-0001.v1]]
|info=[[BEC2020.1 doi10.26124bec2020-0001.v1]]
}}
}}
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__TOC__
  Communicated by [[Gnaiger Erich]] (2020-05-20) last update 2020-06-11
  Communicated by [[Gnaiger Erich]] (2020-05-20) last update 2020-06-30
 
[[File:NUCE-kaleidoscope.jpg|right|360px|link=Number#Does_a_number_make_sense.3F]]
== Entity-type and unit-entity ==
== Entity-type and unit-entity ==
:::: 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 '''N'''umber, '''U'''nit, '''C'''ount, '''E'''ntity — NUCE (''in nuce''), which remains a CASE to this day (CASE represents the '''C'''ounting-'''Assembling'''-'''S'''orting '''E'''xperience).   


:::: Entity-type ''X'' is distinguished from unit-entity ''U''<sub>''N''<sub>''X''</sub></sub>. 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''<sub>ce</sub> [kg]. In contrast, ''X'' = <span style="color:red">body</span> in the context of [[body mass]] and body mass index (BMI) is used in dual-message code, ''m''<sub><span style="color:red">body</span></sub>. <span style="color:red">Body</span> mass with dual-message code means the mass of all entities of entity-type human body, ''m''<sub>body</sub> [kg], divided by the number of bodies, ''N''<sub>body</sub>, which leads to the explicit canonical expression ''M''<sub>''U''<sub>body</sub></sub> = ''m''<sub>body</sub>·''N''<sub>body</sub><sup>-1</sup>.
:::: Entity-type ''X'' is distinguished from unit-entity ''U''<sub>''N''<sub>''X''</sub></sub>. 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''<sub>ce</sub> [kg]. In contrast, ''X'' = <span style="color:red">body</span> in the context of [[body mass]] and body mass index (BMI) is used in dual-message code, ''m''<sub><span style="color:red">body</span></sub>. <span style="color:red">Body</span> mass with dual-message code means the mass of all entities of entity-type human body, ''m''<sub>body</sub> [kg], divided by the number of bodies, ''N''<sub>body</sub>, which leads to the explicit canonical expression ''M''<sub>''U''<sub>body</sub></sub> = ''m''<sub>body</sub>·''N''<sub>body</sub><sup>-1</sup>.

Revision as of 22:12, 1 July 2020


high-resolution terminology - matching measurements at high-resolution


Entity

Description

A unit-entity UX [x] of elementary 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).

If an object is defined as a group of particles (a party of two), then the entity is the single group but not the particle. A number of defined unit entities UX is a count, NX = N·UX [x], where N is only a number and as such N is dimensionless. The unit entity UX has the dimension U of the count NX. The unit entity 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 unit entities (U) of elementary type X, it follows that count divided by unit entity is simply a number, N = NX·UX-1. The elementary entity type (X = electrons, ions, molecules, cells, organisms, events) defines the identity X of the unit entity UX. Since a count NX is the number of unit entities, the unit entity UX is not a count (UX is not identical with N·UX).

Abbreviation: UX [x]

Reference: BEC2020.1 doi10.26124bec2020-0001.v1

Communicated by Gnaiger Erich (2020-05-20) last update 2020-06-30
NUCE-kaleidoscope.jpg

Entity-type and unit-entity

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 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 = mbody·Nbody-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 = N·UNX-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

SI-units-elementary quantities.png
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 = N·UX X elementary unit x
amount of substance *,§ nX = NX·NA-1 N mole mol
charge *,€ Qel = zX·e·NX I·T coulomb C = A·s
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
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].
§ Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA.
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 = zX·F·nX

References

Bioblast linkReferenceYear
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:2020-00022020
Gnaiger E (2021) The elementary unit — canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. https://doi.org/10.26124/mitofit:200004.v22021
Gnaiger E et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/10.26124/bec:2020-0001.v12020


SI-units.png


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Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
Entity, count, and number, and SI base quantities / SI base units
SI-units.png
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 = NX·UX-1
amount of substance nB mole [mol] nX, nB
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 IV candela [cd]
Fundamental relationships
» Avogadro constant NA
» Boltzmann constant k
» elementary charge e
» Faraday constant F
» gas constant R
» electrochemical constant f
SI and related concepts
» International System of Units
» elementary unit x
» SI prefixes
» International Union of Pure and Applied Chemistry, IUPAC
» entity
» quantity
» dimension
» format
» motive unit
» iconic symbols



MitoPedia concepts: Ergodynamics