"...
Several methods are in use for braiding SHPK.
Most of these methods involve the memorising of "sequence patterns" in
the braids. These
methods may be fine for those who regularly braid only a very small varietyof SHPK ;
however, the
serious braider is strongly
advised against using such restrictive
methods ( my note =
memorizing
"sequence patterns" ), since they
invariably lead,
sooner or latter, to misconception and
erroneous conclusions.
For example, there exists literature which deals only with the two
types ( me : that indeed
do no more that speaking about two types
really ) of the 2-PASS SHPK ; and it wrongly refers
to four types, when there are only 2 . There are ,indeed, in
case of
2-PASS
SHPK, two ways to braid each type, so there are four methods of
braiding them ;
but only two different types of these knot
result . This is the
kind of misconception
that can arise when very restrictive
set of members of an infinite family is studied or written
about."
Wonderfully put!
Putting in bold
face is my doing.
Now that we have been fully warned we can go on.
HOW TO DETERMINE
AND DENOTE THE TYPES ?
Once again refer to illustrations given.
'S1'
will denote the SHPK with a first ODD numbered H-P STARTING
on LEFT
BIGHT RIM PINS LINE 1
and ARRIVING on RIGHT
PINS LINE 1
'S2' will
denote the SHPK with a first ODD numbered H-P STARTING on LEFT
BIGHT RIM PINS LINE 1
and ARRIVING on RIGHT
PINS LINE 2
I will leave you work the rest.
.... 'SA' will
denote the SHPK with a first ODD numbered H-P STARTING on LEFT
BIGHT RIM PINS LINE 1
and ARRIVING on RIGHT
PINS LINE A
So in a generalised formulation :
Sa2
(remember a2 is the second SET of component THK in a "true"
pineapple.)
denotes the TYPE of a SHPK with an ODD numbered first H-P ( left to
right )
STARTING
on the LEFT1
and arriving one RIGHTa2
A simple "translation" when a2 is empty, worth zero, does not exist, is
to write SA
instead of Sa2
Understanding to the fullest this simple summary will prevent
the useless utterance of wildly
mistaken notions, that even
in the case of experts if I believe some stupendous
things read
in posts ! (the same goes for the next topics
and so-called ex-spurts too !)
THE "TYPE"
IS DETERMINED BY
THE ODD NUMBERED H-P THAT STARTS ON THE LEFT BIGHT RIM ON
PIN
LINE N°1
AND
ITS ARRIVAL LINE ON THE RIGHT
BIGHT RIM;
Please do your
utmost when making a post on forums to abstain from propagating
erroneous notions about " TYPE OF A PINEAPPLE" (it
is already enough to speak
of PINEAPPLE that
are
not really PINEAPPLE !) by mistaking the TYPE with the
number of
braiding methods or with something quite different from TYPE .
It does not do any good to pass on false notions and concepts without
warning others
that you are only expressing personal concepts that have no validity
whatsoever in the
external reality.
turksheads_28.html
Added 2012 Sept 23rd
: see little simple worded summary in Turksheads_28
A FREQUENT
EGREGIOUS MISTAKE ABOUT PINEAPPLE
I know I will anger many ego but I know it will be good for said
ego to
shut-down in shock and allow the brain to engage. ;-)
Imaginary dialog very real , believe me : a "summary" of what
I
have
read in
the last 5 years on forums ! )
Two guys are
discussing a beautiful, really beautiful knot, one
very neatly and
cleanly made,a
really top notch spider performance if you will .
I want to heap
compliment upon compliment so as not to be mistaken for a
character
assassin. It is the visual rendering
given by the coding that prompt the high
interest . No coding is given for each
PASS at this stage.
Arrive the moment the other
guy inquire
" so the PASS are to be made in that order "
the maker very gently but assertively (not one iota of doubt in him
even if he is
full of... !
) insist :
"Err
well in fact it should be made in that other order really "
THAT IS
LAUGHABLE ; WELL AND TRULY LAUGHABLE.
The more so if they are discussing a 6 or 7 PASS
knot since respectively there
are 720 and 5040 CORRECT
DIFFERENT WAYS
to get the knot
tied really.
This stand for any sequential assemblies of component knots ! not only
for true
SHPK aka Pineapple.
If you will allow me to quote myself in my Turkshead-4 page
[begin quote -
Turkshead page 4 ] The
'gestalt' of
the knot lies in its SHADOW or
"cordage route" and
certainly not in the nature of
its
crossings and their
sequence.
One "proof" I can propose that the cordage route (SHADOW) is much more
important than the crossing sequence as recorded, not as by
my H
&
L system
along the way of the making, but on the finished
knot, following the SPart-WEnd
vector and tallying the crossing s and when they are
encountered is
the following
fact follows :
while NO CROSSING has been altered in its
nature, no rethreading was done,
we can have 2 really
physically different knots that the topology recognize as
equivalent (
which is quite a bit different from "identical" ).
Unchanged crossings but
different cordage route.
No crossing physically re threaded and yet two quite individualized
knots : The SHADOW (cordage
route) is more important than the crossings as usually
noted in the
order they are met in the finished knot. ( quite different
from the
sequence of crossing as use in my H & L system which
is in fact the "crossings
route" so to speak ) [end quote]
I wonder why people are so blind to the notion of "shadow", "cordage
route"
( S
& T
string run )
and are so critically (as in "terminally fatal !) obsessed by " coding"
of "coding of
crossings".
That alone explain to me why a 'spider' (my name for
knot-tyer, from just average to brilliant
in manual skill but dull
theoretically) can insist that
the
PINEAPPLE he is speaking of should
be done in that order and that one only and that any other is
mistaken.
This just show abysmal absence of knowledge and deep thinking.
An "A" PASS PINEAPPLE CAN BE MADE IN A! ( factorial 'A' ) WAYS
so A = 2 then 2 * 1 = 2 ways
A =3 then 3 * 2 * 1 = 6 ways
A= 5 then 5 * 4 * 3 * 2 * 1 = 120 ways
A = 7 then 7 * 6 * 5 * 4 * 3 * 2 * 1 =
5040 ways
ABSURD IT IS TO INSIST THAT ONLY ONE IS ""THE""" CORRECT ONE !
Look a A BC
I can spell this word in 3!
3
* 2 * 1 = 6 different ways.
A
B C
B C A
C A B
A
C B
B A C
C B A
this is EXACTLY what happen with a 3 PASS PINEAPPLE
THERE ARE 3 * 2 = 6 WAYS TO SPELL IT IN CORDAGE.
Want to look at FMPT that is 4 so 4!
spelling or ' 4 * 3 *
2 * 1 = 24 as you use each
letter once only.
F M P T M P T F
P T F M
T F M P
F M T P M T P F
T P F M P F M T
F P M T P M T F
M T F P T F P M
F P T M P T M F
T M F P
M F P T
F T M P T M P F
M P F T
P F T M
F T P M T P M F
P M F T M F T P
Instead of losing time writing (and making mistakes and forgetting
some) it is slightly
more astute to use factorial !
A small practical example :
I want to make a PINEAPPLE with 4 BIGHT NEST on each RIM :
a 2 PASS one with 8 LEAD in the finished knot
PIBU ( PIneapple BUilder HP-RPL program that I
wrote) to get the specifications for me :
Different ways = 6
Distance x = 6
First set [ a1] = 1 ( 1
elementary component THK )
S = 5
B* = 4
Second set [a2] = 1 ( 1 elementary
component THK ) S = 3
B* = 4
It should be as
plain as 3 + 5 == 5 + 3 that the two ways are
quite equivalent and
that it is
of ABSOLUTELY NO IMPORTANCE whether you get 8 by adding
3 to 5 or by
adding 5 to
3.
The only importance it can have is just "personal preference"
or
"subjective practicality" of
one way compared to the other.
As it is plain to see the
intrinsic coding of each component THK cannot be altered
by the order in which they are put to use.
More ! the
coding of their mixing interlocking THK, (I can
even accept
the
, to me
shocking,'inter-braiding' as this does not correspond to the technical
process of
braiding ) cannot be changed
either by the order in which they are put to use.
ALL THE END
RESULTS OF EACH WAY , BE THEY 5040 or more WILL ALL BE IDENTICAL AND
YOU WILL BE QUITE UNABLE TO SPECIFY WHICH OF THE ,
SAY
5040, recipes WAS ACTUALLY USED.
That is the power of "shadow" or "cordage route"
over "coding.
Yet something has to be paid to be allowed to use A!
different ways to make the knot :
but it is so evident that not many see it and
so mistakenly chose to "blindly obey an imaginary
compulsory order in
the
making"
Now for important statements :
******
When planning to do a knot you may freely choose among the A!
different and
correct ways to assemble the components ( provided the
component obey a set of
rules - included in PIBU - that make the S-H-P-K *possible* )
When you have decided upon the order of the PASS then you will have to
find for
each PASS ( PINAPL or PINAPL2 programs do that for you ) the coding of
each
HALF-PERIOD in it.
IT IS THE
CODING OF THE HALF-PERIOD THAT MUST BE MODIFIED WHEN YOU
MODIFY THE ORDER OF THE MAKING OF THE PASSES.
***** When you are "handed-down" (a superior level toward an
inferior
level is implied
in this and that quite displease me as in that there is no "superior"
and no
"inferior" , still
that may be one unconscious motive to insist
on "handing-DOWN") an ALREADY
DECIDED UPON ORDER OF PASS then in fact they arrange to
have you hemmed
in a
prison not of your
choosing as you cannot chose not to comply to that order if you want to
be able to use
the "coding" that is going with it.
So the insistence on OBEYING the sequence of PASS that one
give to you
is just the
'HANDER'-DOWN taking power on you DOWN-THERE and forcing you to adopt
HIS
OWN way.
Not a good teaching stance in my experience !
I
love St Ignatus of Loyola stance : it is not so
important to make
someone else follows your own trail than to help them find and follow their OWN
trail.
Handing-down saying "the order of making is mandatory" is bad
teaching and a lie too.
It
should be ;
" the order of PASS is mandatory in
the frame of reference of the
half-period coding I
am giving you in the same packagingBUT you can chose any order in
the
A!
available
but you will have
to work the coding of H-P for that one "
Even for a bowline the coding *for the making* is not
important at all (that is why there
are several ways to tie a perfect bowline : if this
sort of coding was all important it would
be impossible to have 2
different ways to tie one ) what is important is :
THE CORDAGE ROUTE TO BE
MADE. THAT cordage route ONCE IT HAS BEEN
MADE AND FINISHED WILL HAVE A UNIQUE STRUCTURAL CODING
: THE
ONE FOR THE BOWLINE.
Once again mixing logical planes such as "process coding" and
"structural coding" will
lead to something silly.
Unique structural coding = in the finished knot put "flat" and showing
all its
useful crossing
and no superfluous crossing when following the SPart -
WEnd directional arrow
(vector)
you will get that sequence of coding just as with knot made on a THK
shadow you are
asked for the coding sequence "seen" by the first half-period in the finished knot.
AVOID TAKING "
BLADDER FOR LANTERN" as goes the French saying :
Be fully brain-enabled.
A B C or
3 PASS PINEAPPLE
if you use one colour per PASS : 3! or 6
ways to make it.
A B C
B C
A C A B
A C B
B A C
C B A
which will APPARENTLY, SEEMINGLY become if 2 colours only
are
used
it will be falsely 3 ways
A A CA CAC A A
A C A
A A CC A
A
BUT in fact it is
A A1 C
A1 C
A C
A A1
A C A1
A1 A C
C A1 A
and if one colour is used it will be seemingly (
but falsely !
) only one way
A A A every where so one way
BUT in fact THIS IS MISTAKEN, EGREGIOUSLY SO !
it will be IN FACT
A A1 A2
A1 A2
A A2 A A1
A A2 A1
A1 A A2
A2 A1
A
Take it as you like 3 PASS give 3! different ways to make the assembly.
Copyright 2005 Sept - Charles
Hamel / Nautile -
Overall rewriting in August 2006 .
Copyright renewed. 2007-2012 -(each year of existence)