!? I don't follow the "opposite direction" assertion : they are of
like handedness, which IMO is same direction.
This actually depends on ones perspective. And I think we are talking about 2 different things here... although we both understand the underlying concepts.
In terms of handedness, yes they do have the same chirality.
But, when tying #1415 double fishermans, you do have to do one of 2 things:
1. Tie the first strangled double overhand knot then -
perform a 180 degree rotation before tying the opposite strangled double overhand knot
2. Alternatively, hold the ropes statically (no rotation) - tie the first strangle, then tie the other (but you will have to
reverse the direction of one of the strangles from
your perspective.
I'm sure that you are aware of this..when teaching new knot tyers to tie #1415, a common error is that they end with one of the strangled knots tied in the wrong direction (very common error).
EDIT: Added a photo showing typical tying error (one of the strangled knots is tied in the
wrong direction...its all a question of perspective)... OR another way to describe this is 'Reference frame'. When tying this knot - you need a
reference frame to be able tie each
strangled double overhand knot in the appropriate direction, otherwise you will end up with the wrong geometry (per attached photo below). Beginners make this mistake all the time (and I even noticed the same error with a bunch of climbing guides earlier in the year - where virtually all their 'prusik loops' had the #1415 double fishermans knot incorrectly tied).
Mark G