the.com/transitivity
the logic that if A beats B and B beats C, A wins by association.
means The property of a relation whereby, if it links A to B and B to C, it must also link A to C — true of 'greater than,' 'equals,' and 'ancestor of,' but not of 'is friends with.'
from From Latin transire, 'to go across or pass over' (trans-, 'across,' plus ire, 'to go') — the same root that gives us 'transit' and 'transient.' The mathematical sense names a relation that lets you pass through a middle term to reach the far end; the formal noun 'transitivity' settles into logic and grammar in the 19th century, when mathematicians and grammarians alike grew fond of naming the exact behaviors of their relations.
- math root
- Defines orderings, equalities, and most relations we trust
- breaks often
- Rock-paper-scissors mocks it with elegant cycles
- social proof
- Friend-of-a-friend networks assume it, then disappoint
- voting paradox
- Group preferences can loop despite individuals being rational
- grammar twin
- Verbs are transitive when they demand an object
sports rankings — college football: team a beat team b, team b beat team c, but team c beat team a (happens every season)
medication interactions — drug a interacts with drug b, drug b with drug c, but a and c together are safe (breaks transitivity in pharmacology)