LATEST SADDENING NON-SENSICAL PROPOSAL (
up a heap of absurd and mistaken notions and that I
canNOT countenance despite liking the person intellectual
curiosity because it is
minds. ) :
TURK'S HEAD KNOT
The THK nature is NOT GRADABLE :
EITHER it IS
A THK OR
it IS NOT
A THK but there is ABSOLUTELY NO
possible QUASI-THK just as
there is no quasi positive number or quasi-even number.
is no quasi THK except if deliberately ignoring the structural
characteristics of THK and deciding to call THK just about
This soap box ranting of mine is in relation with a
post from friend
Struktor in the
IGKT- forum of which some ( surprised by the notion ) persons
apprised me after I got a private mail from Struktor asking me a
question but not telling of this post.
Struktor went public then I will answer in my site in the hope
will be saved from adhering to absurd notions.
To this question I must make some observations
( I was away from home
for a few days and could not immediately respond to Struktor
directly but learning of
his public post I deem necessary to answer on a place accessible to public to try and
block some poor souls from being contaminated with such notions as are exposed.)
That Struktor diagram seems to me to be specially
'gauche' or , may be though I doubt it, specially made to trick the observer by obscuring essential
Obscuring due to the very outlandish * topology* used. Not
but it makes the tyer's work a lot more difficult
necessary : looks to me more like a Art Nouveau wrought iron project than a grid for a knot.
I was trained in sciences and in "experimental method" so to get a
reasoned and factual answer I had to find a moment to lay cordage along that tracing
and as I suspected
from the first half second of seeing it that the result, laid
as opposed to the grid TOPOLOGY, is different from
what the grid seems to show.
No offence meant but I ( and a number of my correspondents with me)
wondered if Struktor is simply a
polymath just dabbling now and then with knots but without
any in depth and really extensive
practical experience with them or
if he has several hundreds of knots in his hands as
like most of those I deal with in a regular fashion.
Why that interrogation ? : this intelligent person has a real knack to
draw the most unfriendly grids for a "practical" knot tyer ;-)
Conical or cylindrical
How to describe this knot? [end quote]
Struktor question to me, as it stands, is really without any possible
answer as it
(at least for me...)
First point : friend Struktor is not showing a KNOT (geometry)
diagram of a knot (topology) which
make two entirely different logical planes that must not be
one with the other.
It is impossible to have a meaningful discussion if logical planes get
mixed up as this create perfect misunderstanding through total absence
of possible common ground.
I just hope that he did not even test his creation in the cordage
because that would show a surprising lack of knowledge of Schaake's work and of Ariane for
someone saying that he has the mastery of The Braider main points ! (well after years of
regular study I cannot even begin to boast that)
If from his question I understand :
How to describe this knot's GRID?
***Then he must know as well as me that the question is "meaningless"
is without any answer since the grid shows the topology and not the
It is meaningless to describe a topology when one want to
discuss the geometry, the 3D real life structure is geometry*not* topology like the gris is.
Has is well known any NESTED-BIGHT CYLINDRICAL KNOTS can cover a
cylinder OR a sphere or other volume so there is no
definite answer unless one refers to the fact that the
cordage rouge during its laying can be put on a cylinder.
This route and coding can certainly be laid on a cylinder so in that
particular restricted meaning it can be said "cylindrical" which is not really a
*** if the question put to me is "does this grid represents a
"cylindrical" Knot as
theorised by Schaake then the answer to be given in a reasoned factula
fashion will have to wait for the *geometry* of it to appear in my hands.
Let us see several hypothesis.
If I understand the question as meaning:
How to describe this knot once it is laid in cordage but not yet
dressed and set ?
Then there is still uncertainty as we may be speaking of
TOPOLOGY if the cordage is still on its
laying support with the pins still in place, or we may be speaking
of GEOMETRY if
--- the laid cordage route has been taken off its support ,
slack has been taken off almost in totality without being
really hard set.
If I understand the question as meaning
How to describe this knot once it is laid in cordage *and*
Then it is still without answer since we do not know what will appear
if we give it a core or if we let it "somehow collapse" in
some "natural" shape.
It was IMPERATIVE for me to put it in cordage to reveal the GEOMETRY of
awfully cumbersome TOPOLOGY.
It is now QUITE EVIDENT that this is an ASYMMETRIC
It is 7 LEAD yes but certainly not 8 BIGHT since it is 16 BIGHT/ On one KNOT EDGE
--- 4 bight on BIGHT-RIM N°1
--- 4 bights on BIGHT-RIM N°2
--- 8 bights on BIGHT-RIM N°3
On the other KNOT EDGE
--- 8 bight on BIGHT-RIM N°1
--- 8 bights on BIGHT-RIM N°2
ASYMMETRIC : the Number of BIGHT-RIM is different in the two
one has 3 BIGHT-RIM, the other has 2.
For me, (in the vertical cylinder frame of reference with BIGHT-BORDER
at TOP and BOTTOM) the ODD-numbered Half-Period go
and EVEN-numbered Half-Period go
/ from TOP-RIGHT
If you observe attentively the picture of the real
knot you will see
that its geometry clearly shows HALF-PERIODS that have their 'summit pin' inside
the knot itself :
NESTED-BIGHT ; the changing in direction of a
Half-Period which goes upward or downward before getting to the
opposite Bight-border sign the
nature of EVEN or ODD Half-period which does not begin or end on one of
the outermost Bight-Rim.
First I compared the two grids and found ( would be astonishing to get
the same number of crossings just by chance) the same number of crossings in both :
56 crossings all told , 24 in the
Nested-Bight zone and 32 (different repartition in the two grids) for
the remaining contingent. Struktor's Nautile's
By all means do ( for exploration ) this knot in several diameter of
cordage ( from 3 mm to 15 mm ) as the rendering of a knot dependends on the size of the
cordage, try it to in flat lace ( gutted paracord and hard
a core ( to flatten it ).
If you are not sure that a knot is cordage diameter diameter ( and
support diameter ) then I suggest :
a Constrictor knot with kitchen string on a pencil
a Constrictor knot with kitchen string around a 1 liter bottle
a Constrictor knotin 15 mm string around a glass
a Constrictor knott in 15 mm string around a 50 cm
tree trunk or a barrel
and see how they behave...
Ashley worked there following the principle " why make it simple when
you can make it complicated ?" and very ill advised he drew flat ( mat
grids for knot that really are "volume" and not mat as they are covers for the surface of some volumes.
Using the same process I have redrawn Struktor 'PENTA' conical knot for
use on a
cylinder as 98% of knots-tyers I know very much prefer that way of
doing thing (usual method, less deformation in the knot, no need to stress it to make it
go form "flat" to "relief...)
You have there the two grids. = the mat from Struktor and
the cylindrical from me.