Ashley's Stopper knot is a member of the "Overhand Knots" family because you make it with an overhand knot, and I've said from the beginning my criteria is knot construction, not topology. There is nothing arbitrary about this. You may charge me with being random and arbitrary in other selections, but I think you get the idea where I'm going in this topic.
But you
have been arbitrary, at least in regard to what
you have seen as "figure 8" structures: as I remarked above,
the Fig.8 knot is a knot that withstands loading on both
ends (and is sometimes accidentally tied by anglers, casting
-- "the wind knot"); you have likened that "McLoughlin knot"
and the "Dble.Fig.8 hitch" to it although these knots do not
contain a proper "Fig.8" structure, but only looks-like-an-'8'
shapes; so, too, then, that "Tricorn" eye knot in Budworth's books.
[edit to add...:]
If that "Dbl.Fig.8" qualifies as a "fig.8" family member, then one
should include the
single version of it -- viz., the
Clove hitcth !
Perhaps this makes my point clearer about the "fig.8"ness issue?
You're saying the Overhand knot is only vaguely figure eightish? Yes, it's definitely not a figure eight.
Why you say there is no figure eight involved in the Double Figure Eight Hitch, I don't understand.
They look like two perfectly healthy figure eights to me.
In your referenced binder, there is no knotted structure at all, until putting the ("8-ish"-laid) cordage around an object (as are Clove & Constrictor
non-knots w/o an object).
Yes, it's a natural law that all knots that can be untied without withdrawing an end can be tied in the bight.
Well, look:
a Fig. 8 canNOT be tied without ends -- period.
If you tie
with a bight (as is often done for the eye knot), yes, one
hasn't used ends, but has used the doubled rope as a single one and its
bight-end as an "end". That binder "hitch" has no proper Fig.8 in it,
just the 8-like Overhand form base of the "Tricorn" isn't a Fig.8. But
you're including one and not the other. (I'm assuming that your Budworth
book shows the "Tricorn" eye knot.)
Also, you seemed to think about taking vectors of like
tyingmethods, which is an idea worth trying in teaching knots; but this
would suggest something at least sometimes different than having
a common knot structure: e.g., those so-called "Dragon" eye knots
are very like --
in one tying method-- the venerable
Angler's/Perfection
Loop, with this latter simply knot entailing the simple twist of a bight
as was done for Asher's Prusik variation for a bottle (does this
help, in that case, btw?). So, there, one has a knot w/Overhand
among others w/o, but justifiably grouped for a common tying method.
-- there are many inter-relations that can be found.
