Up to PASS-3 included nothing can go wrong SEQUENCE-RULE-wise, even if
make them in a random order.
So up to PASS-3 you get 100% success 4
in 4 possibilities
BUT after that things change drastically for a randomly made sequencing
PASS-4 33.33% success
in fact 4 in 12 possibilities
PASS-5 8.33% success
in fact 4 in 48 possibilities
PASS-6 1.67% success
in fact 4 in 240 possibilities
PASS-7 0.28% success
in fact 4 in 1440 possibilities
PASS-8 0.04% success
in fact 4 in 10080 possibilities
Easy to compute : you will NEVER get more than 4 'success' in
all the opened possibilities in a given PASS-N !
Open possibilities for PASS-(N) = Open possibilities for
PASS-(N-1) * (N-1)
open possibilities for PASS-6 = 48 * 5 = 240
Why never more than 4 success ?
--- Once a Mistaken Knot
has been made ALL its successor will be
mistaken even if after that the Sequence Rule is complied with.
--- If the knot in generation PASS-(N-1) is a success then only ONE of
its descendants will also be a success as there is only one way to be
with the rule.
As PASS-3 has 100% success that is 4 successful outcome out
of 4 possible outcome
it follows that you will be stuck with only 4 success in the whole of
any of the successive generations.
PASS-2 = there are 2
ways to make the PASS-2
( think modulo and disposed on
a circle circumference) 2
- 1 ( anti-clockwise) and
- 2 ( clockwise )
PASS-3 = there are 4
ways to make PASS-3 2
- 3 - 1 3 - 2 - 1
1 - 2 - 3
1 - 3 - 2
only 2 - 4 - 3 - 1
3 - 4 - 2 - 1
1 - 2 - 4 - 3
1 - 3 - 4- 2
may hope to give birth to a successful descendant all the other
lineages being already
It is plain to see that with A
A disposed on a circle there
are 4 ways to add a fifth 'A'
A A A
A A A
A A A
there are as many 'slots' as there are PASSes already in place (
problem of posts and intervals on a circular fence ) and so on...
so PASS-5 has 12 ( number of possibilities in
PASS-4) time 4 = 48 and only 4 can be
2010 June 26th
POUNDING THE NAIL OF THE ESSENtial
DIFFERENCES BETWEEN A
and a Standard
HERRINGBONE-PINEAPPLE Knot. See last topic in Turkshead_25
understand some allusions. Another illustration lay here
compare those two STRUCTURALLY VERY DIFFERENT sorts of knots ( examples
given : PASS-5 size) :
Only 2 ways
to get the HERRINGBONE right
ways ( A!) or factorial A ) to get the HERRINGBONE-PINEAPPLE
2010 July 3rd
'les tÍte de bois' ***
/ 'the heads made of wood' as
goes the French popular expression)
ON THE NAIL
OF THE ESSENtial
SEMANTIC ! ) BETWEEN A
HERRINGBONE-PINEAPPLE Knot. ***une
tÍte de bois or head of wood is a person rather...... 'thick-headed,
see topic of June 6th , last one in Turkshead_25.
in order to understand the background.
Only someone totaly
devoided of any
power of observation will
insist on persevering in the propagation such an
idea as saying that
HERRINGBONE-PINEAPPLE Knot are 'just semantics'.
( yes he spelled it with 's' which just show that
poor guy does not even have a good handle on in own mother
with 's' it pertain generally to the science (a noun) and
is not an adjective ***)
What an astronomical level of...of....of...
I cannot even find a word
strong enough and still polite.
This is not a question of "freedom of speech" .
(freedom of speech is abused when used to throw stupid things
in the air )
any case free speech need to be severely curbed (or so I
crosses the limit and allows the deliberate
stupidity that 30
seconds of attentive observation and the use of a modicum of
intelligence would have avoided, and when the end result in polluting
Well YES ! You are right ! I AM STILL ANGRY !
I cannot stand so-called
'ex-spurts', more ignorant than the persons wanting to
own blissful absence of solid knowledge, no beg your pardon!
it is much more vicious
that : they do not propagate "absence of
knowledge" they propagate 'warped, distorted, false knowledge' .
in my book, is a crime just
as attempted murder is a crime because it is attempting to murder the
intelligence, the learning stance, the acquisition of knowledge in
*** semantics : the whole body
study while if one wants to refer to ' one word and the
attributed to it - which is clearly the semantic
content of that guy's words ;-) - it is without 's'.
semantics: the whole body of study of meaning in a language
semantic ( or semantical) : the meaning value/content
attributed to a word
It seems to me he does not even know the meaning of nest / nested.
to be sure I went to my trusted friend in such cases : The
International Dictionary of
English nest [SET]..... a set of
things that are similar but of different
have been designed
to fit inside each other.
Operative words here are: DESIGNED TO FIT
INSIDE EACH OTHER
Not knowing the semantic value of words in his own
language is poor communication and very poor
here Wooden Head goes netherwards to an abyss of black
ignorance and decided
that in Standard
HERRINGBONE K.) the bights ( of knots of
identical size) which are in fact staged along a
behind or in front of the others as is the
case, are 'nested' .
How does that measure on the scale of .... ( chose your semantic value
for the '...' ;-) )?
2010 July 3rd
COMPARISON ISOMETRIC GRID versus SQUARE
I find that the ISOMETRIC diagram is the
one respecting the
'relative proportion' between circumference in BIGHTs and 'length' in
2010 July 4th
NESTED BIGHTS and NO-NESTED BIGHTS
SHIFT AND SCALINGas neither a simpleton's explanation nor
semantics bla bla bla ( French for Blah blah blah ;-)
) or semantical personal quirk but
as evident, objective, immediately perceptible FACTS.
need of being trained in rocket science or of being
of uncommon intelligence.
Simple average sense of
observation is more than sufficient, unless, alas for you, you
happen to be
one of a certain ex-spurt (see 2 topics above) misguided and
uncritically admirative disciples that was led astray and
happy with being taken for a ride (out of hand half a dozen of names
immediately sprang to my mind coming from the past)
: there is NOPHASE
SHIFT between the components, you can easily align the
radii (more than one radius makes for that bizarre
as in Standard Herringbone knots : there is a PHASE
SHIFT between any two components (here only two), you
cannot align the radii.
: there is a SCALING
in the components : they do not all have
identical dimensions (here 3
sets of dimensions so NOT a HERRINGBONE PINEAPPLE that have only 2 sets
-one being 'empty' if need arise- ) but this scaling
allows the 'nesting' in absence of phase shift. SCALING implies
bights rims = some 'outer', some 'inner' .In case of all
components being of the same size in L
& B the role of the SCALING
is taken by TRANSLATION.
( sliding or going crab-like)
bights : NOSCALING
needed as the phase shift takes care of the
'distribution and spacing'
along a single
Added 2010 September 19th
MIS-ATTRIBUTION STRAIGHT as I dislike seeing
someone - the
more so someone who cannot defend his property- he is
dead- robbed ( even if involuntarily and with no intention to do harm
by an otherwise nice and honest
person ) of his work to see it attributed to
an author who was not clear enough in his writing to unambiguously
attribute the credit of the labelling of Enlargement
author of that labelling.
I saw that and let time pass hoping such a
fact would be corrected with time.
Alas ! see
The author of the post declares "....is Tom HALL's "enlargement process
Most sorry but that is taking away from the real author of the studies
creator of the
nomenclature of the enlargement processes : namely GEORG SCHAAKE.
Enlargement Process #1 and #2 refer to the SIDE of the
SPart-WEnd vector the
enlargement is done : right side for #1 and left side for #2. This
labelling is Schaake's
in THE BRAIDER.
Tom HALL was just using it in one of the
books he committed ( Gallicism; some book can be said
"il a commis ce livre" , just as the same way we say he " il
a commis un meurtre") on the Turk'sHeads knots without, *apparently if
being clear enough in the attribution of the credit of the
readers to get it right first time.
privately published Introduction
to Turks-Heads in 1996 while
Knot Tree and ENLARGEMENT PROCESSES was
published by the DEPARTEMENT of MATHEMATICS and STATISTICS of the
UNIVERSITY of WAIKATO in 1991 (FIVE YEARS EARLIER!) and
in 1992 it was An introduction to
JUST READ THE BRAIDER !
As we say in France better address yourself to God than to one of his
Wrong attribution put right .
As they also say in France " don't undress Paul to dress Jacques "
Copyright 2005 Sept - Charles
Hamel / Nautile -
Overall rewriting in August 2006 .
Copyright renewed. 2007-2014 -(each year of existence)