Without the
freedom to make critical
remarks, there cannot exist sincere
flattering praise - Beaumarchais.
Tom HALL
Introduction to
Turk'sHead Knots, privately
published, can be
obtained (despite all
I may express here you would be throwing the baby with the
water of
the bath if you don't buy this book ! discard
the silly theorizing he gives
but by all means do use the practical side ) at Martin COMBS '
WARNING
:
this
is my OPINION honestly given and NOT INCONTROVERTIBLE FACT.
I
am no great admirer of the *manner* the brains has of expressing themself
that is for sure,
but that does not prevent me from admiring the
craft the hands deploy and anyway
from respecting the human being separated from the work.
This is used with the sincere intent of being a FAIR QUOTE of the 3
pages ( out of a 141
pages book)
evoking the coding .
IMO it is done in a manner rarely understood by readers if I take on
account the
many
questions raised and asked to me from here and there.
The
"recipe" given is not really profoundly (only half-baked) justified
on mathematical or
logical ground.
It stays, alas, at the, most usual in knots quarters alas, simplistic
level of a regurgitated,
handed down
recipe.
Even that regurgitation is not even done at the clearest level IMO
(that is
not entirely the
fault of Tom HALL,
it is the way it is with "recipes", they have no real flesh and brain,
they
are only a dismantled deformed skeleton.)
We
will see much later how we can use what has been exposed in the pages
preceding this
one to clarify the matter a bit.
As it stands in the book it is an hopeless task, for me at
least ( and I know for sure for
several knots tyers ! ) , it must be
erased and built anew if I want to stand a chance of
really understanding
it.
This bring huge changes as can be easily seen with the
2 frames being compared
(already addressed in the page
before that one : see table at bottom of page 7)
Please
make a careful note of the fact that HALL is numbering BIGHT
in his drawing p27
in continuous sequence from one RIM to the other : THE NUMBER SEQUENCE
IS
SHARED BY THE 2 RIM OF BIGHTs ( he call them cycles just as
he
calls PARTs what
I call LEAD ) while Nautile has been numbering BIGHT or
"summit of period"
independently for the 2 RIMs.
the remainder of 5 / 4 is = 1 or if you want we can
write 5 - ( 4 * 1) = 1
if instead of 4 it is 2 then
5 modulo 2 = 1
remainder of 5 / 2 = 1 or if you want ( - (2 * 2 ) = 1
B - (L modulo B) = 4 - (5 mod 4) = 4 - 1 = 3 in fact this
corresponds to L - 2 (as in
computing the JUMP )
Having FOUR bight to contend with you put .
. . .
four points in line on which you STEP ( circular permutation
or
modular progression ) 3 by 3
staring from the leftmost point that is
marked as
"ZERO"
I will use"#" instead of a point to avoid an ugly presentation
0
# #
# #
4 BIGHT to place. and counted not from 1 to 4 but from 0 to 3.
---------------------------------------------------------------
0
1
# #
# #
third step toward right (→) from zero
---------------------------------------------------------------
now you make AS IF 0
1
0
0
1
# #
# #
rewind to #
#
#
#
or
Then out of the vast blue yonder, without so much as a polite
introduction,
on page 19- line 6, like a magician pulling a white coney from his hat
the bolt strikes :
THIS IS OUR
COMPLEMENTARY CYCLIC BIGHT-NUMBER
Well , err, please to meet you I am sure, but who the hell are you,
where do you come
from?
This is the trouble with handing down recipes !
Well it is complementary ( using 3 ) of 3 0
1 2
because when you add the two lines you realize they
complement to 3
0 3 2 1
3 0 1 2
___________
3 3 3 3
this 3 0 2 1 you magically
get by reading as in Arabic from RIGHT TO LEFT
the 0 3 2 1
( recipe recipe recipe again as this is not a "reasoned"
justification
but just a sleight of hand that "works")
All of a sudden ( I always give a mental somersault when being
so victimized by
unreasoned assertion ) appear \
/ \ /
said ( without any justification, just stark naked and unashamed
affirmation :
this is "the coding
of our 5 Part 4 Bight so-called """casa""" knot".
Casa is just a not really useful and notreally intelligent
"proprietary" label for a THK
in particular for a "foundation THK " or "base THK" in an assembly of
THK. \
/ \ / is
supposed to represents "the coding of a so-called """casa"""
knot
is Over-one,
Under-one, so the coding will be alternating slashes and
back-slashes".
I don't know about you but I fail to grasp with the
explanation given
why U
Under-one Over one == \ /
\
/ being use in such a way even if I
understand
that a true THK is Over one- Under Oner ( or vice versa )
Once
again, handed down recipe oblige, without any procedural
justification, we just
get a Grand Master interjection : THAT IS THE WAY IT IS!
We are
told to put NOT 0 3
2 1 as
we would have naively believed but rather
3 2 1
0 ; that is you put 0 at the other end !
and
not 3 0 1 2 but 0
1 2 3 that is you push 3 at the other end.
No justification given either for putting one Above and the other Under.
" at the bottom of
this coding we write the cyclic- number ( me , that is 3
0 1 2 ) going
from left to right( me : OK , usual way to read) starting
at the second number ( me :
why is that ? justify please,
well sort of justification just follow ). The zero
(0) would be
over the left hand bight column that does not have a
coding so we don't need it
. On
long knots with more parts than bights we just keep repeating the
cyclic bight numbers ( ???
AH ! so 0
1 2 3
were Bight related and not LEAD related ???) until all the codings
have a
number over them. ( why is that ? no justification given
again, no need in a recipe!). On
a narrow knot with less parts than bights we just start with the second
cyclic
bight-number ( me : why again ? ) and go until we run out of
codings. The rest of the cyclic
numbers are not used ( me
: again , why is that ,)
3
2 1
0 \
/ \
/
0 1
2 3
and with that you get the soothing : "that completes our
algorithm-diagram"
NO
SO FAST PLEASE !
I am not a complete idiot and I heartily dislike handed
down half-baked recipes.
I want true "grande
cuisine" and that my intelligence be addressed rather than my
memory or my bowing to the fallacy of "authority".
QUITE
UNSATISFYING FOR ME.
Then
on page 20 to 23 Author goes trying to explain.
IMO it would have been better to
explain first and illustrated with a numbered
example in a second
phase,
that is the right way for training people or so I
believed
all
the years I taught(medicine, diving ) and was led to believe by
seeing
every other instructors applying that sequence.
Teaching cooking before teaching how to buy at the market and
how to make a
fire is the way of too many.
Then
when you have failed preparing an edible meal you are taught
about buying
and making a fire, but in another location ( with another
THK : no wonder people
get lost so easily )
Page 20
" the top row of
cyclic bight-numbers are used for the LEFT to RIGHT half-cycles so they
are read by going from left to right ( me I don't' see why
LOGICALLY one follow the other
, ). The bottom row
of cyclic
bight-numbers are used for the RIGHT TO LEFT half cycles,
so they are
read by going from right to left ( again I don't see why
LOGICALLY...) The
knot is tied in an upward direction, so the left to right half-cycles
cross the coding from
lower left to upper right..... The right to left
half cycles cross the codings going from
lower-right to upper
left...
Then the hilarious part " To
make it easier
to see we have written a "U' and "O" for the
unders and
overs above the top cyclic bight-numbers and below the bottom cyclic
numbers"
Now " the best way
to see how to use the algorithm-diagram is to do an example"
OH ! I thought it was the whole point of the preceding page
18 & 19.
How silly I am .
"This time we will
......7Parts 4 Bights so-called """casa""" knot."
Here goes again L/B = B*n +r
B-r = v n v = 4 - 3 = 1 so "our count
value" is 1 ( me : read your stepping value is )
then " we mark off
four (4) dots for
the number of BIGHT we have, and count off
our
cyclic bight-numbers 0 1
2 3" "
Then we mark off our so-called """casa"""-codings marks for
seven (7) Parts" so 7 LEAD "Which
will be
six (6) marks, (P-1)"
Note that (L-1) * B we know already as being the number of crossings (
or facets or faces,
or of "holes") in the true THK
\ / \ /
\ /
"going
from left to Right we write the cyclic bight-numbers above the coding
marks. Then
going from right to left we write the cyclic bight-numbers
under the coding marks."
In fact Hall use twice 'cyclic" when
one is cyclic ' and the other the "complementary-cyclic' if
I did not
miss something ; that does not
make for easy understanding !
1 2 3
0 1 2
\ /
\ / \ /
2 1 0
3 2 1
"Now
to make the overs and unders easier to see we write (O) or (U) above
and below the
cyclic bight-numbers for the overs (O) and (U)
"
U O U O
U O
1 2 3
0 1 2
\ /
\ / \ /
2 1 0
3 2 1
OU OU
OU
"Starting on
the left
side of the algorithm diagram we do half-cycle #1 which is a free run
(me :
what tell you that in the diagram ???) . Note : All ODD numbered
half-cycles go from LEFT
TO RIGHT, so we use the TOP of the
ALGORITHM-DIAGRAM.
Half-cycle #2
going from right to left using the BOTTOM CYCLIC-NUMBERS.
We
are looking for cyclic bight-number zero (0). Wherever we find a zero
(0) we look at the
coding to see if it is an under or an over. ( me why
? justification ? ). Where we have the "U's"
and "O's"
under the cyclic
bight-numbers we can just mark it with a line here we have
an
Over(0)
U
O U O
U O
1 2 3
0 1 2
\ /
\ / \ /
2 1 0
3 2 1
OU OU
OU "Half-cycle #3
......
U O U O
U O
1 2 3
0
1 2
\ /
\ / \ /
2 1 0
3 2 1
OU OU
OU
I will leave you do the rest till the end all by yourself, I
find this too boring for my patience.
Now I would like to attempt to make that just a wee bit neater and
clearer.
I
will prefer to stay with *my* frame of reference, as I find it too
boring to
try to make a
neater version of what HALL point to.
I am sure
that the source idea (SCHAAKE) must have been high level, may be above
HALL's,
may be above mine and that if was incompletely digested and
assimilated.
That is the only explanation I can find.
Plus using another frame of reference will pull
you out of the "ruts" you were set in by
HALL's text.
Sorry but you will have to comply or to desist ; most
sorry ( not really ;-) ) but not enough
to
change tack !
I gave the mean to "translate" one frame into the other at
the bottom of the previous
page 7 in : CAVEAT
This page is full of UNCLEAR POINTS ALL BELONGS TO Tom HALL AND NOT
TO ME! Please note that and keep it well in mind
OH! BLAST IT ! if you don't
want to use your brain the undoubtly HALL recipe may be just what you want
to
learn (even if itis hardly understandable du to essential parts being overlooked),
a half-baked
recipe to write
an algorithm and a coding.
I suppose that many will just want that so... HAIL HALL !
(will rather HAIL SCHAAKE myself)
Copyright 2005 Sept - Charles
Hamel / Nautile -
Overall rewriting in August 2006 .
Copyright renewed. 2007-2012 -(each year of existence)