2011 March Copyright Charles HAMEL aka Nautile
NO PERMISSION FOR ANYTHING ELSE THAN STRICTLY PRIVATE, NON-PUBLIC PLACE USAGE
ON HEAD HUNTER ‘s KNOTS (HHK)
In similar manner you may see a GAUCHO
Definition :
HEAD HUNTER KNOTS ARE REGULAR KNOTS
which are COLUMN-CODED.
THIS MEANS THAT THEY ARE SINGLE-STRAND
KNOTS MADE ON A TURK’s HEAD CORDAGE
ROUTE OR SHADOW with a particular
COLUMN-CODING ( horizontal mandrel
frame of reference) leading to a distinctive
pattern.
This simple definition should be quite
enough to prevent supposed ex-spurts
from uttering their usual pile of junk.
1-PASS KNOT of LEVEL ZERO in a 9L 8B THK
(see Fig 1)
Fig 1
Fig 2 is a 17L 8B 2-PASSes GAUCHO
----Digits, 1 to 9, take their meaning when in
a number thanks to 0, the null value, the
significant place holder.
Similar thing for knots :
The most basic knot is “the null knot” : a
piece of cordage with no knot in it.
Fig 2
So you may also look at a 4L 3B THK as
being a LEVEL ZERO HEAD-HUNTER.
2011 March Copyright Charles HAMEL aka Nautile
NO PERMISSION FOR ANYTHING ELSE THAN STRICTLY PRIVATE, NON-PUBLIC PLACE USAGE
Fig 3
You may have two conformations of the
(always distinguish the pattern
from the deep structure of the knot):
PATTERN
Fig 4
Either O2 – U2 – O2
or U2 – O2 – U2 for 2-PASSes 7L 4B
HHK.
Obviously they are strictly equivalent one
to the other and I will use any one of the
two conformations for illustration.
Again it is some posts found by pure
(un)luck on the Net that prompted the
writing of this document. Seems they are
not recent posts.
(in red the mistaken, in green the correct ;
I did not correct the original spelling)
----Goofy ONE (supposedly an acclaimed ex-spurt
but one who likes simpleton definition and
explanation IMO)) answered :
[OPEN QUOTE] ...Grant shows a single
string 2 pass & 3 pass headhunter braided
by pattern in his "encylopedia ppgs 410 415.
Tom Halls headhunter is an interweave of
two turksheads.
These are two ways of getting the same
structure for the knot with a different
number of bights versus parts. The only
thing that jumps out at me right now is that
7 is the minimum of parts for a two part
and 10 the minimum for a three pass, to
have room for the basic coding of each.
[END QUOTE]
These are two ways of getting the same
structure for the knot with a different
number of bights versus parts
This seems to me to be coming from a
rather foggy brain !
----Goofy TWO (knowledgeable, in other
domains but ignorant in this one)
answered :
[OPEN QUOTE] The smallest HeadHunter
knot of 2 pass is a 7 part 6 bight TH with
an over 2 under 2
over 2 coding. If you
expand it up the next
topolgy is a 7p 13b
and the next larger
one is a 7p19b and so
on. All of these have
the O2,U2,O2 coding.
Fig 5
For a 3 pass HeadHunter the smallest
topology is a 10p9p with a coding of over 3
under 3 over 3 . When this knot is
expanded the topologies are 10p19b and
the next larger will be a 10p28b and so on.
Again all of these knots have the
O3,U3,O3 coding.
Realizing of couse the compimentary
codings are possiblites also
ie) U2,O2,U2 and U3,O3,U3 respecively
[END QUOTE]
----So many egregious statements coming
from persons who should have known
better, if only how to keep mum.
Let me demonstrate.
braided
I have long ago demonstrated that a THK
route knots are NOT BRAIDS. I just let it
pass as just being an affectation of speech
that some like to keep so, “braided”… let
us forget.
headhunter is an interweave of two
turksheads.
This just show the utter ignorance of what
a Heads-Hunters knot is = SINGLE-STRAND
because it is a Standard Regular Knot and
as usual Hall’s theoretical mumbo jumbo is
best forgotten, just keep the drawings.
-----
2011 March Copyright Charles HAMEL aka Nautile
NO PERMISSION FOR ANYTHING ELSE THAN STRICTLY PRIVATE, NON-PUBLIC PLACE USAGE
The smallest HeadHunter knot of 2 pass is
a 7 part 6 bight TH ( Fig 6)
Fig 6
with an over 2 under 2 over 2 coding
(one must be careful to distinguish the
enlargement of the cordage route and the
enlargement of the knot while complying
with its pattern)
9L 8B cannot be a 2-PASSes HHK, nor a
3-PASSes
A 19L 16B makes a HHK (Fig 9)
Fig 9
!
Here is the proof in a 7L 2B (Fig 7) and in
the 7L 3B (Fig 8)
HOW ABSURD
Fig 7
Same lot of rather dumb considerations for
the 3-PASS
For a 3 pass HeadHunter the smallest
topology is a 10p9p (Fig 10)
Fig 8
Goofy Two goes on and writes : smallest
HeadHunter knot of 2 pass is a 7 part 6
bight TH as if HHK were THK.
Some things really stagger me.
That guy must be confounding the
cordage route and the knot itself.
How on earth could that person have been
so mistaken ?
The silliness did not stop at that :
If you expand it up the next topolgy is a 7p
13b and the next larger one is a 7p19b
and so on.
Compounding mistakes !
Fig 10
with a coding of over 3 under 3 over 3
Poor soul is again mistaken !
You may have a much smaller HHK 3PASSes with this 10L 3B. (Fig 11)
Not aesthetic or useful may be but
perfectly possible.
A 7L 8B or 7L 9B or 7L 10B or 7L 11B or
7L 12B are perfectly possible before being
at 7L 13B.
Fig 11
7L 6B THK cordage route expands first
to 9L 8B via Type I enlargement process
and
To 19L 16B via Type II enlargement
process.
A 9L 8B THK cordage route is *not*
readily amenable to being coded in a HHK
Some bizarre consideration about the
“expand “ or rather the ‘enlarge’ :
is a 10p9p with a coding of over 3 under 3
over 3 . When this knot is expanded the
topologies are 10p19b and the next larger
will be a 10p28b and so on
2011 March Copyright Charles HAMEL aka Nautile
NO PERMISSION FOR ANYTHING ELSE THAN STRICTLY PRIVATE, NON-PUBLIC PLACE USAGE
A 10L 9B THK cordage route does not
enlarge to a 7L 13B but to a 12L 11B by
TYPE I enlargement to a 28L 25B by a
TYPE II enlargement process.
Why wait for 10L 19B when you can easily
have 10L 11B , 10L 13B, 10L 17B .
THIS IS NOT INVOLVING ANY ROCKET SCIENCE
! I CANNOT FATHOM THE DEEP OBSCURITY
REIGNING IN SUCH MIND.
----I made up this “”formula”” for a HHK ( a
simple one, there are much more complex
ones possible) : (columns are ‘read’ left to
right on an horizontal mandrel ; BIGHT RIMs
on the left side and right side)
n time (O(1*P) ; U(1*P) )
followed by
( O(1*P) ; U(1*P) ; O(1*P)
) )
or
n time (U(1*P) ; O(1*P) )
followed by
( U(1*P) ; O(1*P) ; U(1*P) )
which
for n = 0 and P = 2 is
;;;;;;; O2 – U2 – O2 (or U2 – O2 – U2)
LEADS = 6+1 = 7
BIGHTS= any ODD or EVEN number
complying with GCD=1
for n = 0 and P = 3 is
;;;;;;; O3 – U3 – O3 (or U3 – O3 – U3 )
LEADS = 9+1 = 10
BIGHTS= any ODD number complying with
GCD=1
For n = 1 and P = 2
O2 – U2 – O2 – U2 – O2
LEADS = 10+1 = 11
BIGHTS= any ODD or EVEN number
complying with GCD=1
For n= 2 and P = 3
O3 - U3 - O3 - U3 - O3 - U3 - O3
LEADS = 21 + 1 = 22
BIGHTS= any ODD number complying with
GCD=1
I hope that even before you read you had
seen that if NUMBER of PASSes is ODD the
Number of LEADs is EVEN and vice versa.
If NUMBER of PASSes is ODD then NUMBER
of BIGHTs MUST BE ODD.
-----
2011 March Copyright Charles HAMEL aka Nautile
NO PERMISSION FOR ANYTHING ELSE THAN STRICTLY PRIVATE, NON-PUBLIC PLACE USAGE
Just put some brain cells in gear to try and
see some of the “relations” existing
between some Column-coded Regular
knots.
This does not ask for high levels of
intelligence or/and education, just for
“good observation”.
I am most probably ”battering down open
doors” as goes the French expression as I
would be very much surprised if you have
not seen years ago that :
A GAUCHO knot ( Standard Regular Knot
Column-Coded (that even the inferior Grid
Maker can manage (vastly inferior to
RKnotBuilder that does ALL the coded
types) can be seen as related
to a FAN knot
or to HEAD HUNTER knots
A FAN knot
A GAUCHO amputated to get a HHK
A GAUCHO amputated to get a FAN
A GAUCHO amputated to get a HHK