2006/8/23, Neil Harris neil@tonal.clara.co.uk:
The problem is different senses of 'subcategory': there's [1] "the set of objects in B are a strict subset of the set of objects in A", which is loop-proof, and [2] 'B is a topic that is usually discussed in the context of A'
For example:
London -[2]-> Thames Valley -[1]-> London, comes to mind
Russia -[2]-> Soviet Union -[1]-> Russia, as well.
Also, another entirely reasonable cycle would be:
Universe -[contains]-> Human beings -[who have]-> Human thought -[which includes]-> Philosophy -[which studies the]-> Universe
Doing a search of cycles, I found that there must be thousands if not more of them on the English Wikipedia. Yours differ somewhat from the average by being short. I chose a category more or less at random (it was [[Category:Waves]]). It had 999 supercategories, and was part of 6 cycles (counting only elementary cycles):
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Systems -> Dynamical systems -> Waves
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Applied sciences -> Engineering -> Mechanics -> Dynamical systems -> Waves
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Applied sciences -> Education -> Education by subject -> Physics education -> Introductory physics -> Waves
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Applied sciences -> Education -> Academia -> Academic disciplines -> Mathematics -> Dynamical systems -> Waves
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Applied sciences -> Education -> Academia -> Academic disciplines -> Mathematics -> Differential equations -> Waves
Waves -> Sound -> Music -> Music events -> Music competitions -> Eurovision Song Contest -> Eurovision host cities -> Rome -> History of Rome -> Ancient Rome -> Ancient Roman religion -> Ancient Roman Christianity -> Patristics -> Heresy -> Heretics -> People executed for heresy -> Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies -> Museology -> Anthropology -> Linguistics -> Proper nouns -> Organizations -> Educational organizations -> Schools -> School subjects -> Biology -> Tree of life -> Eukaryotes -> Animals -> Chordates -> Tetrapods -> Synapsids -> Therapsids -> Theriodonts -> Mammals -> Primates -> Apes -> Humans -> Technology -> Applied sciences -> Education -> Academia -> Academic disciplines -> Mathematics -> Equations -> Differential equations -> Waves
Interestingly, checking out your examples, I found none of them (I checked London, Russia and Universe, with 1060, 1013 and 1001 supercategories) is currently part of a loop.
For Jesus on the other hand, there are 39 different cycles, which however all start with: Jesus -> Doctrines and teachings of Jesus -> Nonviolence -> Peace -> Social justice -> Community organizing -> Protests -> History of social movements -> Critical theory -> Cultural studies