... on seeing Mark's
orientation of that "Anti-Lee's Link" I realized that ::
take Lee's Link BWL, and reduce the knot to a joint;
then use the opposite S.Part of that joint (to what LL's uses)
and one has what I call "Doubly HAH!" ("HAH" for "Happy
As Harry (Asher)" !! --this, a working of my inchoate
viewing of knots as loadings of **tangles**.
To clarify : my images of
Doubly HAH! are with the eye knot
oriented horizontally (which isn't something I always do, but
in this particular case have done). With Lee's Link BWL shown
vertically, I didn't look at it well enough to make the connection;
but the horizontal image grabbed me! Yes, there it was,
DlyHAH!,
fore<=>aft'd, so to speak.
Put a knot as a Tangle --all "ends" (S.Part(s), Tail(s), (eye legs))
run off from knot & outside the Tangle boundary. I'm pretty much
only musing about "2-Tangles" --of simple joints & eye knots,
mostly, with 2 pieces of knotted material ID'd as "1-2" entangled
with "A-B" (1, B, 2, A the 4 "ends").
Canonically, see an eye knot as a 2-tangle with S.Part end "1"
loaded in opposition to outgoing eye leg "2" & other-piece's
end "A" --and note that we don't really need to say that
"2" is fused into "A" : just that the two ends are loaded
in opposition to end "1"; "B" is the tail.
So, take either
Lee's Link or
Doubly HAH! and back
off of either of the eye knots to view as tangles, and there is
the joint 1-vs-A. I worked from "1" qua S.Part, Xarax "A"
(actually, he saw the obvious variation to
Lee Zep of tucking
through turNip and so on).
(The
sheet bend is often seen as having the
BWL as its
naturally corresponding eye knot; but as the SB is asymmetric,
there is a "natural" connection to be made from the U-fold's
S.Part of this joint --which, sure, isn't so good. But, then,
there are other ways of correspondence of ends joints
& eye knots to explore.)
--dl*
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