Talk:Entity

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

The big box is the system

The counting unit [x] is invariably one entity. Define one entity X=U as a Unit-container U of fixed volume V_NU [L·x^-1] per Unit-containter full of particles E with fixed volume V_NE [L·x^-1] per particle E. Add a number N_U [x] of Unit-containers U into a system (the big box) of volume V = V_NU·N_U [L]. The Unit-container carries an average number of particles E per Unit-container, N_NE = N_E·N_U^-1 [x·x^-1=1]. The object (= entity 'Unit-container') of our study contains N_E·N_U^-1 particles per Unit-container, whereas the system in which the objects with the particles E are enclosed contains N_E = N_U·N_NE [x] particles.

1. Note that the entity Unit-container U does not contain a number of entities N_E of particles E. Only the system contains entities U or E, which are counted either as Unit-containers U or particles E.
2. Note that the system does not contain N_U·N_E particles, which would have the dimension X² [x²]. N_E [x] is the number of particles contained in the system, whereas N_NE [x·x^-1=1] is the number of particles E per entity U.

The entity U is the system

Now we do not care about a big box, we focus strictly on the Unit-container as the system. This means, that the Unit-container U is not an entity X, since the system contains entities X. But if the Unit-container is defined as the system, then the systen cannot (or can?) contain itself: system = U. The system as defined contains a number N_E of countable objects X, which now are the particles E. Then X = E.

The particle E is the system

On this level, we do not care about a Unit-container, we focus strictly on the particle E as the system. This means, that the particle E is not an entity X, since the system contains X. The system contains itself. This self-referential condition is appreciated by the definition that the entity is refered to itself as a count for a count of x=1. This is appreciated further by considering the dimension X of the quantity 'count' at a level above all dimensions of physicochemical quantities.

Biological and chemical entities — 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 N_X=N_ce. 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.