Re: Co-optation Today

r norman wrote:
On Wed, 09 Jan 2008 17:08:53 GMT, John Harshman
<jharshman.diespamdie@xxxxxxxxxxx> wrote:

r norman wrote:
On Wed, 09 Jan 2008 16:20:28 GMT, John Harshman
<jharshman.diespamdie@xxxxxxxxxxx> wrote:

r norman wrote:
On Tue, 08 Jan 2008 19:51:20 -0800, John Harshman
<jharshman.diespamdie@xxxxxxxxxxx> wrote:
Here: a nested hierarchy is a set of groups in which each group has one of two relationships with each other group; either the two groups are wholly disjunct, or one group is entirely included within the other. Partially overlapping groups are right out. Phylogenies can further be described as natural nested hierarchies: only one hierarchical arrangement of groups will work.
Actually a nested hierarchy is simply a directed rooted tree
structure, that is, an connected graph without cycles where each node
has no more than one parent (edge directed toward the node) and has
zero or more children (edge leaving the node). Such trees are
commonplace in programming.

No, a nested hierarchy can be *represented* as a tree structure. It can be represented in other ways too, for example by Venn diagrams. Programming structures are not natural nested hierarchies, i.e. they are imposed by fiat rather than arising out of the characteristics of the elements. One could rearrange those elements freely into a different hierarchy. As such, it's similar to any arbitrary division. The geologic time scale is a nested hierarchy too, with eons, eras, periods, epochs, and ages. But it's not a natural one. We do make nested hierarchies all the time, but they just don't have the features of a natural hierarchy, the sort that results from common descent.
We can disagree about the nature of reality vs. representation for a
completely abstract structure or concept. I would argue that every
nested hierarchy can be so represented and that every such tree
represents a nested hierarchy.
I agree with the first part, but not every tree represents a nested hierarchy. Some identical trees represent non-nested hierarchies. A company organizational chart is one such. The CEO node has descendant nodes -- CFO, COO, etc. -- but the CFO is not part of the CEO. The correspondence of trees and nested hierarchies is not one-to-one.

I don't want to get into a protracted UC-like exchange. But I do
think you are misinterpreting the meaning of the nodes. The CEO node
is not the individual who occupies the CEO position but represents the
part of the organization for which the CEO has responsibility. In
that sense, the tree is indeed nested; each level has reduced levels
of responsibility.

In other words, every tree can be interpreted to be a nested
hierarchy. You have to do the same with phylogenetic trees. The
nesting requires that a node be associated not only with the species
that occupies that node but with the clade descended from that
species.

I agree. Every tree *can be interpreted* as a nested hierarchy. Or it could be interpreted as a non-nested hierarchy. That's why I say that a tree is a representation of the hierarchy, not the hierarchy itself. This is not a big deal. But a nested hierarchy is best understood and defined in terms of sets, not trees. And of course a natural nested hierarchy is best *explained* by a tree.

.

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