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Without the freedom to make critical remarks, there cannot exist sincere
flattering praise
- Beaumarchais.

PINEAPPLE ( S H P K ) AND THEIR TYPES .

This is no use if you have not fully internalised the previous pages on (PINEAPPLE 'SHPK)

You will need to look again at those illustrations

of bight boundaries
- of "sets"


"... 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 variety of 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 LEFT 1 and arriving one RIGHT a2

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.

Some of my old attempts, (2007 - well before meeting SCHAAKE & TURNER's
writings)  at clarifying  :
- COMPARED ANATOMY ONE
- COMPARED ANATOMY TWO

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.

This the case of the Fig-9  and #925 that I solved and show in another page.
picture one - picture two -picture three - picture four

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.

Evident it is that the SHADOW ( cordage route ; string run; the knot in fact ! ) will be
identical in both cases

Now let us add the worshipped coding : it will not change one iota the outcome :
whatever the way the final knots are identical


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.

Have a long studious look at this illustration  to convince yourself that " all the trails lead to
Rome "  ( this is very much adapted from S & T )

Another way to convince yourself is to study this document about the coding of
the two ways to get at a  2 PASS 8 BIGHT (4 + 4 )  8 LEAD ( 5 + 3 )


***** 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 packaging BUT 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 C         A C A       C A A
A
C A         A A C       C 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)

Url : http://charles.hamel.free.fr/knots-and-cordages/