Talk:Entity

Entity and count [x] as a self-referential quantities

Define the big box as the system

The counting unit [x] is invariably one entity. Define entity X=C10 as the Container C10 of fixed volume VUC10 [LΒ·x-1] per containter full of particles E with fixed volume VUE [LΒ·x-1] per particle E. Add a number NC10 [x] of Containers C10 into a system (the big box) of volume V = VUC10Β·NC10 [L]. The Container carries an average number of particles E per Container, NNE = NEΒ·NC10-1 [xΒ·x-1=1]. The object (= entity Container') of our study contains NEΒ·NC10-1 particles per Container, whereas the system in which the objects with the particles E are enclosed contains NE = NC10Β·NNE [x] particles.
1. Note that the entity Container C10 does not contain a number of entities NE of particles E. Only the system contains entities C10 or E, which are counted either as Containers C10 or particles E.
2. Note that the system does not contain NC10Β·NE particles, which would have the dimension U2 [x2]. NE [x] is the number of particles contained in the system, whereas NNE [xΒ·x-1=1] is the number of particles E per entity C10.

Define the entity C10 as the system

Now we do not care about a big box, we focus strictly on the Container C10 as the system. This means, that the Container C10 is not a unit entity UX, since the system C10 contains a number NE of unit entities E. But if the Container is defined as the system, then the systen cannot (or can?) contain itself: system = C10. The system as defined contains a number NE of countable objects X = E.

Define the particle E as the system

On this level, we do not care about a Container, we focus strictly on the particle E as the system. This means, that now the particle E is not a countable entity X; Otherwise we obtain the self-referential loop: the system E contains the entity E β the system contains itself. This self-referential condition is appreciated by the definition that the single (unit) entity is not a count of one entity (for which we would write NE = 1 x), but the unit entity is a separate quantity UE. The system E does not contain itself as NE entities (at NE = 1 x), but the system as defined as a single (unit) entity is the quantity 'unit entity' UE. This is appreciated further by considering the dimension U of the quantity 'count' NE and 'unit entity' UE at a level above all dimensions of physicochemical quantities.

Biological and chemical entities β and count

Countable biological objects are entities. An organism can be defined as an entity and counted, to obtain a count of organisms. This is simple for many but not all types of organisms. Think of counting humans or fish versus corals or multicellular algae. The single cell ce is the entity X=ce of the cell count NX=Nce. A cell count can be obtained for a suspension of cells using a cell counter. If the cell counter detects structurally defined elementary entities as cells, then a homogenate of the same cells does not contain a cell count, but it still contains the equivalent of a previously determined cell count. If the cell count was not determined before homogenization, alternative elementary entities may be defined to obtain a cell count, in which case a particular entity is the marker of a single cell. If the single cell of a particular cell type contains one nucleus, then the single nucleus is a marker of the cell. In principle, the same concept holds for molecules.
If a molecule is stable under a set of conditions, such as O2 or C6H12O6 at room temperature, then the pair of oxygen atoms or the atomic composition of glucose defines the entity 'oxygen molecule' or 'glucose molecule'. Typically we do not use an oxygen or glucose counter to measure the number of molecules, but charge or mass are markers of the number of molecules using electrochemical or gravimetric methods. The markers thus define the format and units of an entity, and the conversion between different formats is achieved by constants, such as the Avogadro constant, elementary charge, and Faraday constant.