Author Topic: For What is a Knot??  (Read 3314 times)

DerekSmith

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For What is a Knot??
« on: April 18, 2008, 05:50:54 PM »
The Knot Drawing (cypher) utility continues to be enhanced and is now becoming a handy sketching and editing tool, this aspect seems to be eclipsing its initial design function as a means to create and exchange small, reliable text based knot files.  Already the list of proposed enhancements for Version 5 includes - adjustable cord thickness, Copy/Paste, Drag/Drop, Zoom, Multiple tabbed drawing grids and rigid Spar elements; all very much aimed at making a more usable knot drawing tool, the cypher bit was fun but seems not as useful as the drawing functionality.

And when you use the utility, you start to understand why.  Creating a knot diagram by pen and paper can quickly become untidy as you realise that bits are heading in the wrong direction or you have not left enough space.  With the drawing utility, change is easy and relatively fast and can quickly lead to experimentation with the knot structure.  This in turn leads inexorably to the topic so often raised amongst knotters - Just what is it that makes a knot work? which, after a significant preamble, brings me around to the gist of the subject line -"For What is a Knot??"

The following blue diagrams show the evolution of twists and turns from a straight cord to something which looks much like the OH knot. 



Except that in the red OH knot, just one junction has been transposed (shown in green) from the blue close equivalent.

One transposition from 'over' to 'under' makes a round turn into the familiar Overhand Knot.

What has changed in this simple example?  If we 'pull' on the blue Round Turn, nothing is obstructed and the turn simply straightens out and the structure falls apart.  But in the red OH knot, every loop is locked against another by crossing it from above to below (or v.v.), so it cannot flow unobstructed.

So could we define a knot as 'A LOCKED CORD STRUCTURE' ? or perhaps 'A SELF LOCKED CORD STRUCTURE' ?

Can we identify these locking structures and describe a knot with them?  Can we start to describe what a knot is by describing its active components?

Derek

Dan_Lehman

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Re: For What is a Knot??
« Reply #1 on: April 22, 2008, 09:11:48 PM »
Creating a knot diagram by pen and paper can quickly become untidy as you realise that bits are heading in the wrong direction or you have not left enough space.
Sounds like "operatERror", IMHO!   :P

Here's a tip:  (in pencil, or otherwise insignificantly reletive finished strokes)  make some
position & orientation/direction marks as you hold a tied specimen oriented as you wish
to present it; then you fill in the bulk of the sketch from that.  This can work pretty well,
and if you're doing an initial sketch in pencil (to be overdrawn in ink and then pencil
erased, and then yet touch-up w/ink) you'll have another chance to improve the work
a little, filling in on the inside of a parallel-line part here, outside there, to bring
things into better alignment, et cetera.  Sometimes one can compromise on showing
the structure in an exploded form (which would clearly show positions of parts) by
putting rope-flow sequencing numbers/letters (mixture, for a bend!) on parts to
disambiguate a more like-it-looks-drawn-up image.  (I almost never bother to
show more than one side.)

As for "For What is a Knot??", I've tried to get my mind to a grip on that, and have
in this forum offered some sort of high-minded definition ("a curvilinear structure that ..."
(though I recently had the musing of a planar (!!) knot)), but am not entirely satisfied.

In the case of an Overhand (and many other) mid-line stopper, where both ends are tensioned,
friction can be lost completely, yet the knot cannot evaporate; but in most practical circumstances,
friction is essential.  And there is, esp. with our modern variety of cordage (meaning by c.
"knottable media"), the "YMMV" aspect of variability on what is stable qua *knot*.

But the idea of specifying component parts can be useful.  Consider some catalogue of knots
in which one has an index of starting components, and then can build upon them by specifying
additional component parts in sequence ... !?  Hmmmm.

--dl*
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