Is a Bowline with an added half hitch to the tail a Variant knot or a New knot?
I'd call that an extension, and I guess a variation of the Bowline.
So, we've recently explored a lot of Bowline extensions in seeking something
adequately secure for kernmantle ropes. The Cowboy & Common Bowlines
I'd say are maybe "versions" of each other; the former might offer some significant
resistance to the sort of capsizing-into-Pile-Hitch-Noose I showed in the YONN... thread
just now. Drawing the line gets more tricky with the Mirrored Bowlines variations.
(And consider how their presentation to a knowledge base lacking the Janus Bowlines
would seem a greater departure than it does with the other variations in awareness.)
Does it first have to be published and does it count ...
"Does it
count " thoughts shift the discussion to one of some kind of
recognitionor
claim to fame --and this for now should be put aside as not so intellectually
interesting or meritorious. If the stakes are low--and some might argue against
knot invention even having
stakes (!)--, we can lower the bar on credibility.
Does the publication have to be written in English or translated that way?
We can consider the case of the so-called Heaving-line Bend (i.e., a messenger-line
bend, of thin-2-thick ropes) attributed by Ashley to Ohrvall, where in fact the knot was
presented by O. as something found in a museum to secure an instrument string to
an anchor bight (which knotted structure is FAR more interestingly intricate!); and
then that O.'s illustrating daughter botched the drawings (or O. himself did so in
his sketches of record), so that the knot was really an orphan at birth--an image
of nothing-real was put into print and later misinterpreted to be . . . a messenger-line bend!
How to give any "credit" there, huh? --just laughs all around, I think.
As for topology, I assume then you would be agreeable to a sheet bend and a bowline being described as the same?
Firstly, "topology" has mathematical connotations that aren't helpful in practical dealings,
and are best left out of the discussion. (Schake has tried to put math in to the practical,
but I'm unfamiliar with his presentation.)
And this example is a good one to highlight senses of "knot". I do NOT describe them as
the same, no.
Re "topology", in the mathematical sense, I've discovered some of what I call
"Symmetric Figure 9" knots; they are topologically equivalent to that form
sometimes misconstrued for the (confusingly named) "Stevedore's Knot" (stopper),
and are, to my perception, closely related to Ashley's #425 (not "a"), although this
bend is of interlocked Overhands--see them as degenerate Fig.9s (one less turn).
I'd say I've broken new ground, but one could argue a case from #425 at least to
provide
proximity to "prior art" (a patent term).
And although the ("a"?!) "Figure 9" eyeknot is known, I've not encountered mention
(beyond maybe my own) of putting it in
reverse, which might have appeal.
(I think I have such a base in cord I'm half sitting upon (rear pocket) now, forming
a twin-eyes knot via the insert-bight-&-*backflip*, Bowline on a Bight way.)
... structure [read: constituent parts] remains unaffected, but we do have some ends joined that were not previously.
By my inclination re "knot", I take the opposite view in both cases: that the
knotsdiffer because of the loading profile,
and that the connection of ends (to make an eye) is irrelevant.
--at least that is a case worth considering: the looks-like-a-bowline AT THE KNOT of
this tow-line to a barge (big, spaced eye, you think),
but on inspection it's found that in fact the "eye" is the end of the tow line cleated
on port side, and a separate (but disguisedly similar) rope cleated on starboard side.
The *knot* is otherwise in all senses a bowline (we could even say it was exactly
that, and then the eye was put in cleats, and then somehow the part between cleats
got cut by falling cargo--and then became clearly separate ropes).
If we enforced a rigor that every *knot* coming to attention of this knowledge-center
IGKT were put to a loading-profile check--that is, the given *knot* was generalized
into a **tangle** and that was enumerated into all possible *knots* that it could
generate (itself a problematic challenge, in light of what constitutes allowable
transformation/deformation (mathematical topology has no bounds!)),
then we could be more sure of "newness" of incoming candidates--i.e., that they
couldn't be something we'd previously encountered but taken with different loading.
(But such rigor just spoils the fun of "invention", don't it?)

(E.g., Asher "invented" Shakehands bend, but saw that Ashley has the same, er,
**tangle** as an eyeknot; I, before Harry, had also discovered the bend, and for
me, the obvious eyeknot was loaded on the other end qua SPart than what Ashley
shows. The difference in behavior might be worthwhile; clearly, the *reach* to get
from one to the other is minor--but it's something.)
-------
I'd thought of a tact in which one would conceive a
tangle,
which would be just the general "topology"--as SR is using it above--;
and then from that one would define
knots, which would be specific
loadings of the
tangle . But the problem arose in fixing the
tangle ,
as it has SOME implied loadings/directions/angles from the start,
but lacks hard boundaries on how much change can come to them.
(E.g., should we see the Pile-Hitch noose hitch in the general owline
tangle? Is the Lapp bend really indicated there (much different angle
for what was the bowline's SPart) ?! --and the Marlinespike Hitch,
and Slip-Knot/Overhand Noose?
--dl*
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