Construct · 2 fields · 3 citations

Where does genus collide?

One name. Different field. Different construct. One map.

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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to genus is species.

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genus2 CONSTRUCTSGenus (logic)ARISTOTLE · GENERAL KINDGenus (topology)RIEMANN · SURFACE HANDLES

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Logic and philosophy

A general kind divided into species

In logic, a genus is a general kind under which more specific kinds, the species, fall, and it is marked off from those species by a differentia, the feature that divides the genus into them. Aristotle set out this structure in his Categories and Topics (ca. 350 BCE), where a definition states a thing's genus and then the differentia that narrows it, and Porphyry's Isagoge (ca. 270 CE) fixed genus as one of the five predicables alongside species, differentia, property, and accident. The referent is a place in a hierarchy of predication, a class more general than the species beneath it, not a group of organisms named by a naturalist or a count of holes in a mathematical surface.[1][2]

Unit
One general class standing above its species in a hierarchy of kinds
Recovery means
Not applicable
Measured by
Identified by logical analysis of a definition into its genus and differentia

Mathematics and topology

A surface's number of handles

In topology, the genus of a surface is the number of handles it has, equivalently the largest number of closed cuts that can be made without splitting the surface into separate pieces: a sphere has genus 0, a doughnut-shaped torus has genus 1, and a two-holed surface has genus 2. Riemann introduced this measure of connectivity for surfaces in Theorie der Abel'schen Functionen (1857), where the number of independent cuts classifies a surface and constrains the functions that can be defined on it. The referent is a whole-number invariant that counts holes and stays the same under continuous deformation, not a kind in a logical hierarchy or a rank of related organisms.[3]

Unit
A single non-negative whole number assigned to a surface
Recovery means
Not applicable
Measured by
Found by counting handles, or from the Euler characteristic as genus equals two minus the Euler characteristic, divided by two, for a closed orientable surface

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Nearby collisions

taxonomy4 fields · 6 citationsjingle · one word, four constructstopology4 fields · 6 citationsjingle · one word, four constructsdifferentiation4 fields · 4 citationsjingle · one word, four constructs

References

  1. Aristotle. (ca. 350 BCE). Categories and Topics (J. L. Ackrill & W. A. Pickard-Cambridge, Trans.). In J. Barnes (Ed.), The complete works of Aristotle: The revised Oxford translation. Princeton University Press.
  2. Porphyry. (ca. 270 CE). Isagoge (E. W. Warren, Trans.). Pontifical Institute of Mediaeval Studies.
  3. Riemann, B. (1857). Theorie der Abel'schen Functionen. Journal für die reine und angewandte Mathematik, 54, 115–155. https://doi.org/10.1515/crll.1857.54.115

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