The notion of "
Symmetric bends" is already debatable ( does it mean only bends where the one link is point- or line- ( = mirror-) symmetric to each other ? ), so imagine what the notion of "
Supersymmetric bends" would be !
In short, I characterize as "
Supersymmetric bends" those symmetric bends where :
1. The Tail Ends leave the knot s nub towards opposite directions.
2. They are "face-symmetric".
Note : Just a few words about what a "face" of a knot is / what we mean by this : Some simple bends ( in fact, most of them, but that is irrelevant for our discussion here ), even when they are tightened, ( i.e., not in any initial loose, but in their final, most compact form ) are more "flattened" in relation to one plane going through their axis { and more "rounded" in relation to another - we can easily understand this if we realize that the areas of their cross-sections in relation to all such planes should have a maximum and a minimum : the maximum corresponds to their "flat" section, and the minimum to their "round" section ). We call "face" the aspect they present when they are projected perpendicularly to the plane on which the area of their cross section is minimum. We can distinguish the two "faces", the "front face", which we choose to be the face which shows more details of the knot ( that is, more details of how the most important segments of the knot are related to each other at their mutual crossings ( "over" or "under" )), and the "rear" face. When the "front" and the "rear" faces are indistinguishable regarding their geometric form, the bend is "face-symmetric". ( Which should we name as the "front" and which as the "rear" face of the bowline, was something that proved to me how stupid can clever knot tyers become, when they are "talking" to each other ( = talking past each other ).
Now, it has been some time I had noticed something about all he "Supersymmetric bends" I know, which I present here in the form of a conjecture ( = precise but unproven statement ):
All Supersymmetric bends are either Zeppelin-knot like, or Fisherman-knot like. ( Note : In the later case, that of the
Fisherman-knot like bends, the two interpenetrating links can also be linked / hooked to each other, at their middle )
Trying to get an indication about the truth value of this conjecture, I have recently been examining again the pictures of the bends I keep in my files ( I keep only the simpler and more beautiful ones, but I am afraid that one has to actually
tie a knot, in order to become able to decide if it is really
"overcomplicated, which will never be taken up by mainstream users because of its complexity, when far simpler variants work perfectly well." (sic)
- and, in general ( so, by definition ) knot tyers are those who do not tie other people s knots !
)
So, what about the beautiful, most compact
& bend of the 20 shown in this thread ? At first sight, it does not seem to be
Fisherman-knot like - but that is true only
at first sight, and
sight alone does not help knot tyers, as it was proven over and over again !
One has to
TIE the knot, a number of times, to see if it is "
overcomplicated'(sic), or anything else he would had wished it to be...
It turns out that, before its final dressing, this
& bend is a
Fisherman-knot like bend, indeed ( and, although it is not very simple, it is not "
overcomplicated"(sic) either ! ). However, to start from
this loose form ( which reveals its simple topology at a glance - one can also start from the slightly different loose form shown in the previous post, which leads directly to the final compact form ) and dress it in its most compact form, passing through others, less compact ones, is an interesting knotting exercise. See the attached pictures, of the loose and the most compact form of this
& bend.
Therefore, the conjecture about the Supersymmetric bends was not
disproven - but that does not mean it was
proven, of course ! ( The antonym of the "simplest" is not "overcomplicated" !
)
