🚀 go-pugleaf

If you take a HyTime PATHLOC, which maps a tree to a 2-D matrix
by making each column a nodelist from root to leaf, one for each
leaf, and generalize it into n dimensions, something interesting
happens.  Nodes, and especially leaves, have a new property,
polarity.  Polarity in this sense is the measure of the number
of directions a given node exists in.  Try this at home:

1. Draw a simple tree of three or four levels with some leaves
   indicated by letters and some by numbers.

2. Imagine that the numbered leaves extend above the page
   vertically (the Z direction).

3. Create a PATHLOC table for this tree.  It will have one
   column in the X direction for each lettered leaf and
   one plane in the Z direction for each numbered leaf,
   forming a rectangular solid as deep as the deepest path.

The numbered leaves should not be in the same plane as
the lettered leaves, and thus they have a polarity of "Z",
while the parents of leaves that have both lettered and
numbered leaves have a polarity of "ZX" because they are in two planes.

This property of polarity for n-directional PATHLOC allows
multiple independent elements to exist in the same path
space.  I think this could be used to model CONCUR, by
assigning a different direction to each different concurrent
DTD.  Uni-directional elements would not interact with
other uni-directional elements with the same parent.  Polarity
could also be used as a filter by constraining the directions
you can currently "see". At least I think this might work.

Is this a useful insight?  Not being grounded in any formal
or analytical science, it seems interesting, but I'm wondering
if this sort of way of viewing trees and such is used
elsewhere?  It seems like there are some potentially useful
applications for n-D pathloc, but I'm not sure what they
might be.

Eliot Kimber                      Internet:  drmacro@ralvm13.vnet.ibm.com
Dept E14/B500                     IBMMAIL:   USIB2DK9@IBMMAIL
Network Programs Information Development     Phone: 1-919-543-7091
IBM Corporation
Research Triangle Park, NC 27709