(moRE) SwampRat's Fig.8 Six Eyeknots

[Dan_Lehman]

After searching in vain for this thread --not seeing it because
of the unhelpful Subject (cf. the OP here :
http://igkt.net/sm/index.php?topic=3849.msg23147#msg23147
)--,
let me initiate an aptly named thread to continue,
which I do by presenting the set of six eyeknots
in my own sketches (which I think I got right, from
the SwampRatProductions video).

--dl*
====

[X1]

   It is the geometry, not the topology of the fig. 8 knot that is utilized here. Any S shaped knot can serve as a base for such a loop. So, instead of knots topologically equivalent to the fig. 8 knot, we can use simpler S shaped knots, topologically equivalent to the overhand knot, or even to the unknot. All we need is,
a : to form, as a base, a geometrically S shaped knot on the standing part, and,
b : to pass the working end through this knot two or three times ( two times, as at the # 0 and #4 loops, three times, as at the # 1, #2 and #3 loops).
   If we could possibly achieve essentially the same thing using a simpler base knot, which would be much easier to untie, why should we use the fig.8 knot ? An S shaped overhand knot would probably produce equally secure loops.

   (At the attached picture, one can see this idea driven to the extreme : the most simple S shaped knot base there is, topologically equivalent to the unknot, in fact nothing but an S form on the standing part (black line), and the working end that passes through this base three times (red line). The loop produced this way is a most simple, quite secure loop, yet it can be untied instantly, in just one step. It is called " Eskimo" bowline . 

[Dan_Lehman]

   It is the geometry, not the topology of the fig. 8 knot that is utilized here. Any S shaped knot can serve as a base for such a loop. So, instead of knots topologically equivalent to the fig. 8 knot, we can use simpler S shaped knots, topologically equivalent to the overhand knot, or even to the unknot. All we need is,
a : to form, as a base, a geometrically S shaped knot on the standing part, and,
b : to pass the working end through this knot two or three times ( two times, as at the # 0 and #4 loops, three times, as at the # 1, #2 and #3 loops).
   If we could possibly achieve essentially the same thing using a simpler base knot, which would be much easier to untie, why should we use the fig.8 knot ? An S shaped overhand knot would probably produce equally secure loops.

Without probing distinctions between "geometry" & "topology"
in knotting, here, suffice it to say that this set of knots arises
from working the commonly given fig.8 shape ("geometry")
into an altered form and then <... --variations of the set>.
Yes, one can do such general working with other bases,
but so what?  (Casting the Eskimo bowline into this shape I think
distorts that knot's real geometry more so than does this set's
use of the fig.8 .  The "S" is hardly essential, either, generally;
but it is particular to this set, and the idea set off upon in exploration.)
This fig.8 set has a characteristic enclosure of the SPart's
eyeleg exit/entry by the turn of the SPart that is lost, e.g.,
in that Eskimo bowline diagram.


I see (slowly) that a version that I verbally sketched in the OP's
thread is his #0 with the tail's path reversed; it's not all so clear
to me which should be preferred --#0 is surely better on ring-loading.
And both of these I think are better bets at easier loosening than
others --in that their brief entanglement of the tail allows it to be
used qua lever for loosening--, though I've not played much with
the full set.


--dl*
====

[X1]

Yes, one can do such general working with other bases, but so what? 

   As in it happens in the case of bowline, one would generally prefer a loop that can be untied in just one step, leaving no knot left on the standing part, a knot that , in its turn, should be untied in a second step... So, it would be better if a similar procedure can be be worked on a base topologically equivalent to the unknot.
   The fig. 8 knot provides an S shaped form with two bights, through which one can pass the working end two, or even three times. We can imagine that we can use an S shaped knot with a simpler topology, equivalent with the overhand , or even - which is the best case scenario - with the unknot. The shown tying method of the " Eskimo"  bowline is presented only as an extreme example of a stable, quite secure loop that uses only the S form of a most simple base knot- and nothing else ! I am not sure that the multiple twistings and the more complex topology of the fig. 8 knot are the essential elements of the SwampRat series of loops. The generated loops seem to be more complex than they could have been, and they contain elements that are redundant, and do not contribute to the security of the knots. And it can be further claimed that the quick tying methods of the bowlines- where we form a knot topologically equivalent to the unknot on the standing part, we pass the tail through it, and then we just pull the ends, and the bow, yet much simpler loops, able to be untied easier, in just one step. It should be expected that if we pass the tail two, or even three times  through such a base ( as we do here through the fig.8 knot), we would end up with more complex similar loops - but is this really necessary ?
   Do not get me wrong. The SwampRat series is a clever and an interesting method, that is able to produce interesting stable, secure loops. I only wonder if one could simplify this method more, and reach the holy grail of the loops - loops that can be untied in just one step, leaving no trace of a knotted rope on the standing part.
   The question of which one of all those loops is more secure, can be answered only with the help of detailed experiments, I guess...It seems very difficult to predict which knot would not suffer from a unwanted deformation, or a dangerous tail slippage, under heavy loading, without such tests.