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reply to reply to Whitehead
Mike Lieber (U28550@UICVM.BITNET)
Tue, 10 Jan 1995 13:52:28 CST
Gotcha. I will have to disagree with you on ethnographic grounds. There are i
ndeed cases where you have rank differences without any necessary hierarchical
level, such as group membership, that contextualize those differences. My best
example is that of pre-Christian Kapingamarangi, where age stratification segr
gated men on the island, the lagoon, the reef, and the deep sea. Any older man
had the right to order any younger man to run an errand, help with a project,
etc.. These were not age sets, however. Old men did not form a group of any s
ort as opposed to, say middle-aged men. Now, you could say that this is an exa
mple of a category-to-member relation and get hierarchy in that way--old man A
is a member of the category of 'old men' (for which there is a term), while a y
ounger man is a member of the category 'younger men'. I'm not sure that this
would be an example of the *valid* point you are making, however. My point is
a simple one--rank and hierarchy are conceptually distinct. I proceed from
that point to a question about your point, which I understand to be one of
the logic of the relations between rank and hierarchy. Is there more than
one possible logic by which they can be combined or is there but one possible
logical relation. I have in mind a very thorny logical problem that has been
bugging me for years.
Susan Freeman and others working in Spain and France (Bill Douglas, Bob
Greenwood, and others) have described egalitarian turn taking neighborhood
organizations whereby each year, particular households are responsible for such
things as burial of the dead, care of the village commons, and the like. It
doesn't seem to matter who lives in the house or for how long. When it is
that house's turn to do a job, whoever lives there has to do it. Now this
sort of egalitarian order exists within a highly ranked and hierarchical
social order. Now, ifyou try to represent this ordering schematically, the
easiest way to do it would be using digraphs. But this is a wrong way to
represent it, since digraphs presuppose diads, and this is not a diadic
organization at all. Susan Freeman suggests that the way to represent it is
as a hierarchical order with households on one level and the village charter
on the next higher level. I've asked her to explain it, and she hasn't been
able to come up with an argument. It's more of a gut feeling. I'm trying to
recruit a mathematician friend to try a couple other representations to try
out on Susan. Any ideas?
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