Re: Co-optation Today

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.

.

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