- It is important in explaining why, before
Schaake discovered
it,
no one ever published a
Standard Herringbone knot with more than
TWO PASSES.
I did some computation of the probability of successful outcome when
not observing the
sequence rule . Not observing == using a fair coin and spinning it to
decide which way to go.
Up to PASS-3 included nothing can go wrong SEQUENCE-RULE-wise, even if
you
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 right and
complying
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
generation.
PASS-2 = there are 2
ways to make the PASS-2
( think modulo and disposed on
a circle circumference) 2
- 1 ( anti-clockwise) and
1
- 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 doomed
to failure.
It is plain to see that with A
A A
A disposed on a circle there
are 4 ways to
add a fifth 'A'
A A
A A A
A
A A
A A
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
'success'
Added
2010 June 26th
POUNDING THE NAIL OF THE ESSENtial
DIFFERENCES BETWEEN A
Standard HERRINGBONE
Knot
and a Standard
HERRINGBONE-PINEAPPLE Knot. See last topic in Turkshead_25
to
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
120
ways ( A!) or factorial A ) to get the HERRINGBONE-PINEAPPLE
right
Added
2010 July 3rd
ANOTHER
POUNDING (
dedicated to
'les tête de bois' ***
/ 'the heads made of wood'
as
goes the French popular expression)
ON THE NAIL
OF THE ESSENtial
DIFFERENCES (
NOT
SEMANTIC ! ) BETWEEN A
Standard HERRINGBONE
Knot
and a
Standard
HERRINGBONE-PINEAPPLE Knot. ***une
tête de bois or head of wood is a person rather...... 'thick-headed,
and
mulish'.
see topic of June 6th , last one in Turkshead_25.
in order to understand the background.
As
shown in this illustration using just elementary
observation of FACTS, 'plain
to see as
the nose in the middle of the face'.
Only someone totaly
devoided of any
power of observation will
insist on persevering in the propagation such an
idea as saying that
the differences
between
Standard HERRINGBONE
Knot
and a
Standard
HERRINGBONE-PINEAPPLE Knot are 'just semantics'.
( yes he spelled it
with 's' which just show that
the
poor guy does not even have a good handle on in own
mother tongue as
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 )
In
any case free speech need to be severely curbed (or so I
think) when
it
crosses the limit
and allows the deliberate
propagation of
utter
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
other's minds.
Well YES ! You are right ! I AM STILL ANGRY !
I cannot stand so-called
'ex-spurts', more ignorant than the persons wanting to
'learn',
propagating their
own blissful absence of solid knowledge, no beg your pardon!
it is much
more vicious
than
that : they do not propagate "absence of
knowledge" they propagate
'warped, distorted, false knowledge' .
That,
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
their readers.
*** semantics : the whole body
of
study while if one wants to refer to ' one word and the
meaning
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.
Just
to be sure I went to my trusted friend in such cases : The
Cambridge
International Dictionary of
English nest [SET]..... a set of
things that are similar but of different
size and
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
teaching !
So
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
single rim,
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 '...' ;-) )?
Added
2010 July 3rd
KNOTS
DIAGRAMS :
COMPARISON ISOMETRIC GRID versus SQUARE
ORTHOGONAL GRID
I find that the ISOMETRIC diagram is the
one respecting the
'relative proportion' between circumference in BIGHTs and 'length' in
LEADs.
Added
2010 July 4th
NESTED BIGHTS and NO-NESTED BIGHTS
PHASE
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.
No
need of being trained in rocket science or of being
of uncommon intelligence.
Simple average sense of
visual
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
being
happy with being taken for a ride (out of
hand half a dozen of names
immediately sprang to my mind coming from the past)
*** NESTED-bights
: there is NOPHASE
SHIFT between the components, you can
easily align the radii (more than one radius makes for that bizarre
spelling)
***
NO-NESTED-bights
as in Standard Herringbone knots : there is a PHASE
SHIFT
between any two components (here only two), you
cannot align the radii.
*** NESTED-bights
: 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
: several
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)
***
NO-NESTED
bights : NOSCALING
needed as the phase shift takes care of the
'distribution and spacing'
along a single
bight rim.
Added 2010 September 19th
PUTTING A
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
Processes
to
the actual
author of that
labelling.
I saw that and let time pass hoping such a
distressing
fact would be corrected with time.
Alas ! see
here
The author of the post declares "....is Tom HALL's "enlargement process
#1..."
Most sorry but that is taking away from the real author of the studies
and
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 I believe
this
posting*,
being
clear enough in the attribution of the credit of the
nomenclature
used.for all
readers to get it
right first time.
HALL
privately published Introduction
to Turks-Heads in 1996 while
SCHAAKE's Regular
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
Evolution Processes
JUST READ THE BRAIDER !
As we say in France better address yourself to God than to one of his
minors saints!
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. 2007-2012 -(each year of existence)
