Gits & Gambits

[Jon Awbrey]

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Arisbeans, SemioCompères, SUOphists, TMesians, & SeqFanFolders ...

I would that I could not be held responsible for the
hasty way that I will have to be pudding this today,
but, of course, nobody ever escapes responsibility
for anything, and especially the half-baked loaves.

I have been trying to rely as much as I can on my 'archives',
as I was so much sharper then than I'll ever be again, but
I do not see how I can avoid treading on the haziness of
trying to force a fresh thought on this point or edge.

Aside to Graham:  I do not see much chance that I can do anything
about most of the annoyances and irritations that you mention, as
they are parts of what I need to keep even this barest semblance
of organization, myself, but I do see that a continuing fraction
of the discontinuity you experienced is due to the circumstance
that I have always been disposed to think and to work in what
one might call "overlapping neighborhoods of thought" (ONOT's),
as a consequence of which I'll often be trying to make some
contributary to one "watershed of thinking" (WOT) when out
of the blue it will appear to me that some of it might be
pertinet to some other group that is weighing on my mind --
I am often disieved by my illusions of pertinets, sure,
but the raveling of that is always a post hoc matter --
anyway, with that pre-rumble, here is the message that
preceded the one you seized up on -- oh, wait, it will
probably be less distracting to e-mit it separately:

| Cf:  "This Is The Forest Primeval ..."
| Now Serving At Two Locations, No Waiting:
|
| http://stderr.org/pipermail/arisbe/2001-July/000690.html
| http://www.infoloom.com/pipermail/topicmapmail/2001q3/001161.html

To continue, I want now to introduce the family
of 'graph-theoretical data structures' ("gits")
that I know as "gambits", for reasons that will
soon be manifest.  Structures like these always
come in two forms, the text and the graph forms,
like the phenotypic 'alternation of generations'
that I remember from a biology course lang syne.
I will present the two variations on this theme
in the parallel paradigmatics that follows here.
Nota Bene.  The at-sign "@" denotes a root node.

¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤
|   Definition                                                                  |
¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤
|                                       |                                       |
|   Blank " " is a gambit.              |   @ is a gambit.                      |
|                                       |                                       |
¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤
|                                       |                                       |
|   If i is a gambit and                |   If i is a gambit and                |
|   if j is a gambit,                   |   if j is a gambit,                   |
|                                       |                                       |
|                                       |        i j                            |
|   then ij is one too.                 |   then  @  is one too.                |
|                                       |                                       |
¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤
|                                       |                                       |
|   If i is a gambit and                |   If i is a gambit and                |
|   if j is a gambit,                   |   if j is a gambit,                   |
|                                       |                                       |
|                                       |         i   j                         |
|                                       |         o---o                         |
|                                       |         |                             |
|   then (i(j)) is one too.             |   then  @     is one too.             |
|                                       |                                       |
¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~¤

In Step 1 of this recursive scheme, the
notation "ij" denotes the concatenation
of i and j, id est, just the writing of
string i and string j one after another.
The associated graphical notation means
that one joins tree i and tree j at the
root in order to construct the new tree.

In Step 2 of this scheme, i is called the "index"
and j is called the "exponent" of the gambit that
is constructed there.  The notation "(i(j))" says
to place the strings for i and j in the indicated
places of the frame "(_(_))".  The parallel graph
notation enjoins one to graft the tree i and then
to graft the tree j at the pair of sites that are
severally indicated, merging their roots with the
nodes that are currently sited in the underlying
gambit, in passing erasing their status as roots.

The glyphing of that basic constructor, the rooted path of length 2,
in the form of a 'gamma' is the source of the family name, but that
is little more than a conventional way of scribing it that is often
convenient.  In actuality, except for their roots, gambits are free
trees, not embedded in the plane or unnaturally crooked or anything.

That is the basic construction of gambits,
contingent on my remembering it all right.

Four days till Stratford ...
Until we all get a break ...

Jon Awbrey

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Incidental Musements:

http://www.stratfordfestival.ca/

"Succor The Arts!"

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