Concept System
A four-level hierarchy across three parallel axes — quantity, entity, and measurement. Each level adds constraints, from abstract kind to specific measurement.
See it live — follow the rod measurement →Source Table
Reproduced from Pendrill (2024), Table 1.1 — the authoritative 7-column layout.
| Level | Quantity term Dybkaer (2010) | Example | Entity term | Example | Measurement term Pendrill (2019) | Example |
|---|---|---|---|---|---|---|
| 0 | kind of quantity | space | — | — | — | — |
| 1 | quantity, Q = X | length (X₁ − X₂) | kind of entity | physical body | — | — |
| 2 | entity quantity [Sachgrösse] | length of rod | entity | rod | — | — |
| 3 | instantiation | length of rod AB | entity instance | rod AB | quantity as measured | 1.234 m |
Pendrill, L. R. (2024). Quantities and units: order amongst complexity. De Gruyter. doi:10.1515/9783111036496-002
What Each Term Means
Plain-language definitions for every concept in the table, grouped by axis.
The most abstract category — a grouping of quantities that can be compared, added, and subtracted because they share the same dimension. "Space" is not a quantity itself; it is the kind to which length, width, wavelength all belong.
A named, defined concept expressed as Q = {Q} · [Q]. This is the level ISO 80000 defines. Every entry in the standard is a Level 1 quantity.
A quantity bound to a specific kind of entity. Coined by Fleischman (1960). "Length of rod" is not abstract length — it is length as applied to rods.
A particular quantity value of a particular entity at a particular time. This level exists in reality, not in standards.
The abstract category of things that quantities can characterize. Other kinds include substance, field, wave, system.
A specific type of physical thing. Entities are what the dedicated quantity is about. "Mass of electron" characterizes the entity "electron".
A particular physical object that exists in reality at a specific time and place. This is what a metrologist actually picks up and measures.
The measurement result — a numerical value paired with a unit, obtained by a measuring instrument acting on an entity instance. This is the only level with a numerical value.
How the Table Maps to This Site
Each cell in the concept hierarchy informs a specific feature of the ISQ Browser.
Derived automatically from unit dimension analysis. Every quantity whose primary unit reduces to the same dimension vector belongs to the same kind.
The primary content of the dataset. Each ISO 80000 entry (e.g., t3-1.1 "length") is a Level 1 quantity concept.
Derived semi-automatically. The quantity "sound particle displacement" is the "displacement" quantity bound to the "particle" entity.
Modeled in the ontology: isq:QuantityInstantiation and isq:MeasuredQuantity (Qm = {Q}·[Q], with GUM uncertainty), realized by the worked example. Real measurement data belongs to measurement databases and laboratory information systems.