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ABOUT PINS LABELLING, PINS POSITIONNING, TABLE OF HALF-PERIODs CODES, FORM OF DIAGRAMS, TRACING PAPER USED
in existing “tutorials” documents for THE TRANSMITION OF AN ORNAMENTAL KNOT
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CONTENTS Page 3 INTRODUCTION Page 6 SOME SIMPLE MINDED REMARKS ABOUT PINs IN CYLINDRICAL KNOTS
Page 7 FRAMES of REFERENCE FOR CYLINDRICAL KNOTS Page 9 The EXISTENT Published literature Page 10 Paul N. HASLUCK Hjalmar ÖHRVALL George Russel SHAW Chas L. SPENCER Page 11 Raoul GRAUMONT & John HENSEL Clifford ASHLEY Cyrus Lawrence DAY Bruce GRANT Richard H. GRAVES Mario BIGON & Guido REGAZZONI Eric FRANKLIN Page 12 Ron EDWARDS Tom HALL Page 13 Georg SCHAAKE and John C TURNER Charles WARNER Des PAWSON Gordon PERRY Geoffrey BUDWORTH Page 14 John SHAW (BUDWORTH is hiding behind that name) Richard HOPKINS Lindsey PHILPOTT Don BURRHUS
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Page 16 Special category : software Charles HAMEL Douglas VARNEY Tim ALLWINE Claude HOCHET Page 17 NOW LET US SHOW AN ‘IDEAL’ NOTATION : SCHAAKE’S Page 22 NOW LET US SEE WHAT HAPPEN WHEN SOMEONE THINKS IT IS A GOOD DECISION TO NOT FULLY OBSERVE THIS RIGOUR Page 23 Claude HOCHET Page 25 Jan VOS Page 26 John RICHINGS Page 27 Michel SINCE Page 28 Charles HAMEL Page 29 ABOUT THE OBJECTION THAT LETTERS ARE LIMITED TO THE 28 LETTERS OF THE EUROPEAN ALPHABET A TO Z Page 31 PERSONAL CONCLUSION Page 33 ANNEXE. Part ONE : PIN JUMP PIN STEP Page 38 ANNEXE. Part TWO : How to position or number the PINs Page 42 ANNEXE. Part THREE : Mandrel versus Cylinder
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INTRODUCTION I want to state very clearly that I do not *** wantonly practise the fallacy (logical fault) of believing that ad hominem is a valid argument, I *never*, intent to harm, or dismiss, or demean, or attack persons. Most certainly I will attack * their acts and only their acts* (words and thoughts are ‘acts’ in that context). The personal NAMES I name here (mine included) are just identifying LABELS attached to the WORK I am speaking about and it does not constitute a nominal attack (or approval) of anyone but it is simply a pragmatic referencing of the work. Some of the persons named are good friends who along the years have enriched my pages. Without them these pages would have been sadly autistic. Thanks are given to each of you again mes amis. Those friends are good enough to share. To be able to share they gave much time and brains to their tutorials, diagrams, tables of HP by HP coding, inspiring work. They are their own independent agents and keep the full ownership of their works and the entire responsibility for the way they go about their sharing. When someone is friendly enough to share I make no judgement on the “theoretical complying” of that shared work. I readily publish it “as is”, even when by happenstance it may contradicts some of my tenets and/or some of my writing. Diversity is very desirable. I do believe I have a mind large enough to accommodate my own contradictions. So any one thinking that I am criticizing those friends is deeply mistaken ; I am just ‘dissecting’ their work using what I have for certain knowledge but also, of course, with all my biases ! *** That I use words in a rather ‘restricted’ way with no demeaning or insulting connotation(s) that may have been attached to those words by some persons or some cultures. So here are the meaning I attach to some words : Aberrant ==which contradict reality or the way things are set by external reality; the usual normal (statistical meaning and not judgemental meaning) way. Ignorant==the state of one who does not (yet) know something or thoughtlessly discarded it either as too demanding on the brains or as uninteresting. Brainless recipe==one recipe which will not demand of the user that (s)he engages their brain. Brains were already fully engaged by the author of said recipe who used all their best abilities to provide, in a friendly spirit of sharing, an easy “paint by the number” way to produce something satisfying but devoid of any intellectual labour. This is for users “to be doers” and not “to be thinkers”
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This stage of “being exclusively a doer” is an unavoidable NECESSITY when beginning to acquire experience but IT MUST BE VERY SHORT LIVED. The balancing wheels on a children bicycle are necessary but must be, as soon as possible, taken off. This transitory phase has to quickly give way to a more balanced mix between “brute, thoughtless experience” and “theoretical” (what a grand word to mean : use your own brain to go beyond procedures and appearance, to see the structure and the reality!). I am of the opinion that one of the silliest sentences ASHLEY wrote is (ABoK#127) No amount of theoretical knowledge in any of the arts or handicrafts can compensate for lack of practical experience. What ASHLEY clearly show here is that he utterly failed to understand that THEORETICAL (in craftsmanship or in sciences) COMES FROM EXPERIENCE. From experience BUT from an experience SYSTEMATICALLY (using a ‘system’) APPLIED, ANALYZED, TESTED, EXPLORED, INTELLIGENTLY EXAMINED. All that going from the particular to the general. EXPERIENCE ACCUMULATED WITHOUT DISTILLING IT INTO THEORETICAL OR, IF YOU PREFER, INTO FORMALIZED PROCESSES AND PROCEDURES WITH A “DEEPLY THOUGHT ABOUT HARD CORE is strictly limited in scope and interest.
This is just my opinion and not a universal truth set in stone. Unaware==with a rather loose perception of what is ”there in the real world” and not using their critical thinking mode (in the honest meaning of open mind but attentively examining what is proposed to them) (opposite == focused and “brain being wide awake”) Stupid== under just average intelligence, quite dull. Silly==wanting in judgement or thought, the gentle “empty mind full of void”. This long ‘dissertation’ is EN-TI-RE-LY Friend Jan VOS fault, great fault ! ;-) he made me do it Mum! Not my fault. We were discussing the NOTATION of PINS in reference to the 1776 FACEs diagram that Jan made with the diagram invented by NONO (Norbert TRUPIANO) . Jan was anxious about missing letters if Nono is to go on higher and higher. I think it is now time to make good rules, before it is widespread over the internet. To which my first response was [open self-quote]There you sorely hit a nerve my friend ! [end self- quote] I went on with my rambling which I latter decided to transform into a piece for my web pages. make good rules ?!, well SCHAAKE already did that, guided by logical systematic analysis and those “ways of doing things properly” is used in publications of good standing such as those by Ron EDWARDS. EDWARDS and SCHAAKE& al are the only ones worth speaking of as far as printed publications on Cylindrical Knots are concerned. No one else –till today 2011 Jan
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14th- ever wrote something of real interest to me on Cylindrical Knot -save Bruce GRANT in a circumscribed way-). I do feel there is no urgent need to try and perpetually reinvent the wheel. Wheel has been invented a while ago : NAME THE PINS WITH NUMBERS AND CLOCKWISE ORIENTATION with ODD-numbered HalfPeriods that are going from BOTTOM RIM to TOP RIM of cylinder. In my opinion the use of LETTERS is good only for personal or between friends ' expedient pragmatic coding but not for impeccable expression of a technical matter… I do think that there is enough, too much really, mistaken ideas going around without needing to destroy what intellectually solid system already exists. Destroy it just to be able to introduce in the “theory» a vastly inferior system is not a plan I favour. This vastly inferior system has its place only in a rather limited "expedient" and informal space, ideally restricted to personal and private use. To say the truth I never understood why Claude, Jan or Michel ever used this bizarre system. If the intent is being patient with persons who do not want to use their brain and giving them some easy to use recipes while at the same time hoping that some persons will become interested and go further then I do think that this is not the best way to go about things. My easy counter-argument to this intent is : Then it is better to give a proper tool which complies with established conventions (not to say any thing of our neuro-motor en psychological organization and development) while at the same time allowing the acquisition of thinking methods. It is as easy (and much more rigorous and general) to use NUMBERS than to use LETTERS. Over that using NUMBERS is an attempt at education while LETTERS only favour laziness and ignorance. It is all very well to give fishes it is much better to teach correct fishing methods. I think that persons at large must be strongly warned against all those disparate methods. Those methods have their limits and lifting those limits only makes things worse and more difficult. Persons ignorant of the reality of the red hot iron bar will hurt themselves, the perfectly informed will be able to manipulate it without hurting themselves ; that is my thinking.
Let us begin…
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SOME SIMPLE MINDED REMARKS ABOUT PINS IN CYLINDRICAL KNOTS In order to be able to understand the solid reasons underlying a number of things that will be said, were done, are done or should be done or not done, we make, in the following pages, a quite necessary review of a number of FACTS.
HANDEDNESS AND HOW HUMANS FUNCTION : (It would be to your advantage to read bats_belfry_10 page if you find the following paragraphs difficult) Handedness is a neuro-psychological preference for the use of one of our two hands. In the general population the prevailing lateralization is RIGHT HANDEDNESS (85% to 90%). However interesting the remainder of the population is, the 10 to 15%, ONE IN TEN to ONE IN SEVEN, of LEFT HANDED cannot serve as base for a formalized notation. From now on we will speak from a RIGHT HANDED perspective. From very early on in the development of a new born human (about 15 months if I recall correctly) the entire psycho-motor organisation is AXIPETAL. This means that the whole of the organization is made taking the body axis as a reference landmark. Body axis : imagine a long arrow entering between the shoulders blades of a standing person, going out in front between the 2 upper limbs held horizontally and parallel to each other in front of the body. Our RIGHT ‘field’ is organized from the RIGHT to the LEFT.
Our LEFT ‘field’ is organized from the LEFT to the RIGHT. So both fields are “going toward our central axis” ; that is the meaning of AXIPETAL
Opposite = AXIFUGE, “going away from the axis”. Now lets us take the position of neutral rotation of the hands : Arms held straight alongside the thorax, elbow bend to 90° so as to get the forearms at horizontal level, both hands opened flat vertically with thumbs up, palms facing each other, both looking at the body axis. Let us make an “inside rotation” with both hands, that is an ANTI-CLOCKWISE rotation with the RIGHT HAND and a CLOCKWISE rotation with the LEFT HAND. The palms are now facing DOWNWARD (we can also start with the elbows completely bent, hands in neutral position, after the “inside rotation” the palms will be facing OUTWARD in front of ourselves, or we can start with elbows straight along the body and after the rotation palms would be facing BACKWARD).
We just made a PRONATION move. PRONATION == TAKE A HOLD ON (as if “by the scruff”) Now starting again from the neutral rotation position we impose an “outside rotation to both hands. RIGHT hand rotates CLOCKWISE and LEFT hand rotates ANTI-CLOCKWISE. The palms are now facing UPWARDS. We made a SUPINATION move. This is the SUSTAINING move or holding something in the cup of the hand (See the very last page of this document)
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The LEFT hand is the hand maintaining, fixing, taking a hold on. This is the hand holding the SHIELD
Our anatomy and physiology make for the fact that the easiest way of holding those two tools is usually :
The RIGHT hand is the one “that does the work”, it is the SWORD hand.
- PRONATION (palm facing DOWNWARD or away from you) for the MANDREL
Now let us speak of SPONTANEOUS NATURAL moves (as opposed to EDUCATED, TRAINED, ACQUIRED, TAUGHT moves.)
or
-SUPINATION (palm facing UPWARD or toward you) for the CYLINDER (see the very last page of this document)
We are not here speaking of gestures learned for a procedure as this training often violate the “natural” slope, hence the very necessity of being taught and of learning, of being trained.
The working hand is the RIGHT hand holding and laying the cordage.
There is a severe risk of being led astray when going to an inferior source and in consequence of that, of acquiring improper, aberrant ways. All this misleading goes on with the subject being quite UNAWARE of what is happening because of ignorance of reality. Good sources feel ethically obliged to destroy ignorance and they certainly do not to promote it and/or feed their ego or purse on it.
If the task is “to wind a length of cordage” around the chosen tool then the most often seen gesture (spontaneous, untaught, unlearned, which can be ‘maimed’ by a bad habit previously caught from a ‘bad’ source or by wanton training) is :
FRAMES OF REFERENCE FOR CYLINDRICAL KNOTS. For such knots can be defined TWO easy to use frames of reference : (considered as having a large diameter filling a good proportion of the handhold, with a length containing only a very few times the diameter). VERTICAL CYLINDER
(considered as having a small diameter, broom handle like, with a length containing many diameters). Mandrel is a word used mainly by persons working with leather lace and using a small number of BIGHTs. HORIZONTAL MANDREL
or MANDREL is maintained in the desired position by the LEFT hand. CYLINDER
= winding starting from the part nearest to the LEFT hand (BOTTOM of CYLINDER), going away (toward what is, psychologically and unconsciously, experienced as the axis, so complying with AXIPETAL direction and AXIPETAL organisation of LEFT field) HORIZONTAL MANDREL
From there the RIGHT hand is WINDING IN A CLOCKWISE direction : starting BELOW the level of the mandrel, going UP in front of the mandrel, after the TOP going DOWN on the other side of the mandrel and so on (This is why the logical choice is for the ODD-numbered Half-Period to go from BOTTOM LEFT to TOP RIGHT in the diagram of the MANDREL) VERTICAL CYLINDER = winding from the part nearest to the LEFT hand , the BOTTOM of the CYLINDER), going away
(toward what is symbolically the axis
Copyright Charles HAMEL aka NAUTILE
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for the working hand, so complying with AXIPETE direction and axipetal organisation of LEFT field as the holding hand serve as reference.) From that LEFT hand hold the RIGHT hand is WINDING IN A CLOCKWISE direction : starting at BOTTOM, going UP AND LEFT to the TOP (This is why the logical choice is for the ODD-numbered Half-Period to go from BOTTOM RIGHT to TOP LEFT in the diagram of the cylinder). Just for this once, the perspective seen from the LEFT handed point of view. IT IS A STRICT MIRROR IMAGE of RIGHT.
This minority of ONE OUT OF TEN cannot be taken in account by the publisher of a book (or the publisher needs to clearly warn potential buyers that it is made from the LEFT handed perspective) that is logically supposed to address the overwhelming majority of potential buyers, the RIGHT handed ; unless you are an inept businessman or a sly one preying on a herd of RIGHT handed customers. The working hand is the LEFT hand holding the cordage. CYLINDER or MANDREL is maintained in the desired position by the RIGHT hand.
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direction and AXIPETAL organisation of RIGHT field) From there the LEFT hand is WINDING IN AN ANTI-CLOCKWISE direction : starting BELOW the level of the mandrel, going UP in front of the mandrel, after the TOP going DOWN on the other side of the mandrel and so on (This is why the logical choice here is for the ODD-numbered Half-Period to go from TOP RIGHT to BOTTOM LEFT in the diagram of the MANDREL) VERTICAL CYLINDER = winding from the part nearest to the RIGHT hand , the BOTTOM of the CYLINDER) and going
away (toward what is symbolically the axis, so complying with AXIPETE direction and axipetal organisation of RIGHT field as the holding hand serve a reference.) From that RIGHT hand the LEFT hand is WINDING IN AN ANTI-CLOCKWISE direction : starting at BOTTOM, going UP AND RIGHT to the TOP (This is why the logical choice is for the ODD-numbered Half-Period to go from BOTTOM LEFT to TOP RIGHT in the diagram of the
cylinder). ANY OTHER WAY THAN THOSE TWO JUST EXPOSED CAN BE CONSIDERED ABERRANT FOR BOTH TYPE OF (firmly set) HANDEDNESS. EITHER
If the task is “to wind a length of cordage” on the chosen tool then the most often seen (spontaneous, untaught, unlearned, that can be ‘maimed’ by a bad habit previously caught from a ‘bad’ source or by wanton training) gesture is : HORIZONTAL MANDREL = winding from the part nearest to the RIGHT holding hand (BOTTOM of CYLINDER) and going away (toward what is psychologically and unconsciously experienced as the axis, so complying with AXIPETAL
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(in the cylinder diagram ) ODD-
\
numbered HP go from BOTTOM-RIGHT to TOP- LEFT
/
they go in that diagram from BOTTOM-LEFT to TOP-RIGHT OR
ANY OTHER WAY RUNS AGAINST HOW WE ARE BUILT AND HOW WE NATURALLY FUNCTION.
A choice that can be made, of course, but let me give my mind : this choice bears the stamp of ignorance of our nature .
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RULE FOR TRANSFORMING ONE FRAME OF REFERENCE INTO THE OTHER : Going from HORIZONTAL MANDREL held in LEFT hand to VERTICAL CYLINDER held in LEFT hand is accomplished by a Pi/4 or 90° rotation in the ANTICLOCKWISE direction Going from VERTICAL CYLINDER held in LEFT hand to HORIZONTAL MANDREL held in LEFT hand is accomplish by a Pi/4 or 90° rotation in the CLOCKWISE direction
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(cylinder), in a CLOCKWISE rotation. Choosing to go from TOP to BOTTOM (cylinder) in ANTI-CLOCKWISE rotation for an ODD numbered HP is indeed either the sign of poor thinking or more probably the sign of a defective acquisition of lateralization which is not firmly set, neither fish nor fowl. TOP LEFT
Doing so in a book(s) will lead to the contamination the unawares (they are legion) in his population of readers. The way to dispose the LETTERS or the NUMBERS will of course follows the direction of the rotation of the HalfPeriods and LOGICALLY the notation whether using LETTERS or NUMBERS will begin at the start of the first ODD numbered HP (LEFT for MANDREL, BOTTOM for CYLINDER) We will see the details later.
THE EXISTENT: For now let us take what is a mandatory step in any study : doing a quick survey of the “existent” in the published literature. The VERY few Authors really tackling Regular Knots and Cylindrical Knots of other types are HIGHLIGHTED . Some authors even give only a single simple one, may be two
FIG 1
Readers were given enough to realize that the only “natural” way for a RIGHT handed person to lay the ODDnumbered Half-Periods is : starting from BOTTOM LEFT to TOP RIGHT (mandrel) or from BOTTOM RIGHT to
There is NOT A SINGLE French book worth speaking about !
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Paul N. HASLUCK Knotting and Splicing Ropes and Cordages First edition 1904
FIG 2
Drawings, with a few places in the drawing labelled with LETTER but NO PINS or BIGHT NUMBERING
Hjalmar ÖHRVALL Om Knuttar First edition 1908 (also 1916 edition)
FIG 4
NO notation of PINS : only beautifully clear drawings. Chas L. SPENCER Knots, Splices and Fancy Work First edition 1934 Drawing with some ‘landmarks’ pointed to by arrows designated with a LETTER
FIG 3
NO notation : only naked drawings George Russel SHAW Knots Useful and Ornamental First edition 1924 (also the 1933 edition)
FIG 5
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Raoul GRAUMONT& John HENSEL Encyclopedia of Knots and Fancy Rope Work(1939) NO real notation only letters designing some places in the knots.
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Richard H. GRAVES Knots and lashings (1952) Use drawings with NUMBERS pointing to the order to follow.
Clifford W ASHLEY ABoK (1944) NO notation, drawings. Cyrus Lawrence DAY The Art of Knotting and Splicing (1947) NO annotation, Black & White photography with annotated arrows, very clear, very intelligent.
FIG 7
Bruce GRANT Leather Braiding (1950)
Mario BIGON & Guido REGAZZONI The Morrow Guide to Knots (1982) NO notation, photography.
NO notation of PINS.
Eric FRANKLIN Turks Head The Traditional Way (1985)
FIG 6
Numbers on the mandrel corresponding to FACEs of mandrel for orientation : here a 5 BIGHTs and a mandrel with 4 numbered FACEs FIG 8
Drawings and NUMBERED NOTATION of PINS.
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Ron EDWARDS (IMO the second best after Schaake and Turner) Turk’s Heads (1988) Drawing and NUMBERED NOTATION
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Round Knots and Braids –Advanced Leatherwork – Volume 2 (2006) Drawings and NUMBERED NOTATION
FIG 9
FIG 13
Tom HALL (alias for HICKEY) The third best, probably one for raw beginners) 1996 Introduction to Tuk’s-Head Knots NO notation but drawings FIG 10
Turk’s-Head Workbook
FIG 11
FIG 14
FIG12
NO notation, drawings and codes for each Half-Period given.
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Georg SCHAAKE and John C, Turner UNSURPASSABLE BY A LONG CHALK ! THIS IS THE VERY BEST NOTATION OF PINS. (it is GENERAL and so it can be directly used in computations)
BOOKS, PAMPHLETS
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Braiding Standard Herringbone Knots (1992) The Braiding of Row-coded Regular Knots (1993)
The Braider (1600 pages or about – published from 1995 February to 2009 November - last issue : N° 60)
Edge Lacing – The Double Cordovan Stitch
Plus may be some other publications that I forgot !
Braiding Application – Horse Halter
Charles WARNER A fresh Approach to Knotting and Ropework (1992) NO notation, drawings.
A new theory of braiding (RR1/1) (1988) A new theory of braiding (RRI/2) : algorithms for regular knots (1988) New and Automatic Methods for Constructing Knots and Braids Regular Knots (1988) Braiding Regular Fiador Knots (1990) Introducing grid-diagrams in braiding (1991) The regular knot tree and enlargement processes (1991) indeed, contrary to what some misinformed persons have been propagating here and there, the naming of the enlargement processes and their formalizing are NOT Hall’s BUT SCHAAKE’S. An introduction to flat Braid Braiding Standard HerringbonePineapple Knots (1991) An introduction to evolution processes. (1992) The Braiding of Column-coded Regular Knots (1992) The Braiding of Long Column-Coded Regular Knots (1992)
Des PAWSON Pocket Guide to Knots and Splices (2001) NO notation, photography (by the way, IMO, PAWSON’s books are not hyperbolically titled in a silly way and are *always* good value –safe and sound practical, no theory). Gordon PERRY Knots First edition 2006 NO notation, drawings only. Geoffrey BUDWORTH The Ultimate of Knots and Ropework. (how laughable such hyperbole can be, this just measures the vanity of Author and bears absolutely no relation to the value of the content IMO – he is not, alas, the only one using such silly titles- The good Lindsey PHILPOTT does not less with his “Complete” and “Ultimate” !) NO notation, photography. The book of knots (with Jason DALTON) (2002) NO notation, drawings.
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John SHAW (BUDWORTH ; a slick way to trick buyers –I was (tricked) ! and do not take too kindly to that! –and make more money I guess . The Directory of Knots (2003) NO notation, just drawings.
Well you would be, as I was, sorely disappointed. NO intelligent advancement! Just a simple cost saving expedient (surely benefits enhancing too, I suppose).
Richards HOPKINS Knots (2003) NO notation, just drawings.
[open quote] In this volume, a new recipe format is presented that SAVES
Lindsey PHILPOTT Knots, a complete Guide (2004) NO notation, photography. Pocket Guide to Knots (2006) NO notation, photography. Don BURRHUS : Interesting case : aberrant* notation using LETTERS with INDEXES in NUMBERS, begins at the TOP and goes DOWNWARD ANTI-CLOCKWISE (ODDnumbered HP) (*aberrant = straying from the correct or normal way). The TurksHead Cookbook Vol 2 (2007)
CONSIDERABLE SPACE ON THE PAGE
[end quote] How is that for a pedagogic stance? After that I never bothered to buy VOLUME 1.
Buying that one seems quite superfluous because it was already child play to do your own creations with paper and pencil but with RKnot Builder it is ‘infinity’ being opened before you as you can do any SINGLE STRAND knots of whatever coding that can be made on a THK cordage route. No need for books for those willing to use their brain, knowledge and imagination. You will have noted of course that ALL AUTHORS QUOTED HERE SAVE THE EXCEPTION OF BURRHUS use a NON-aberrant winding orientation
FIG 15
Aberrant notation and orientation, well never mind! What I find staggering is the offered “why”? You would think, surely this decision was taken after an intelligent theoretical work improving on Schaake?
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FIG 16
FIG 17
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In The Globe Knots Cook book – 2008 (another aberrant notion resides in there: globe (or ball) is the volume, the sphere is the area. So it is really spherical covering (most have a CORE so an INSIDE VOLUME). It is a signature of ignorance of reality to speak of globe knots (unless they are indeed without any core) instead of spherical covering Knots (with a core, or a ball or a globe - think the globe of a breast : clearly that is referring to volume and not to area!-). (EVEN THE POSITION of the PINs is aberrant, as it is in the Turkshead Cookbook! -see annexe part 2) Persons unaware and ignorant of those facts will be kept ignorant by those books !
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I seem to recall that in 2008 Doug had some captures of Worksheets on THK coding. EXCEL WORKSHEET on Standard Herringbone Pineapple Knots and Enlargement of THK – I bought several CD and offered The Braider to Doug. Tim ALLWINE Gridmaker (2008) good, limited in scope. Does COLUMN-coded Regular Knots and leaves entirely untreated ROW-coded, NEITHER row NOR columncoded and ENLARGEMENTS. Claude HOCHET RKnot Builder (Oct 2010) is polyvalent and complete -really, not hyperbolically- for Regular Knots. Can do any type of coding for Regular Knots, also compute Enlargements.
The most GLOBE KNOT COOKBOOK is offering at the moment of this writing is 176 FACEs – Geee! almost 1/10th of Norbert TRUPIANO’s 1776 FACEs, less than the 360 FACEs by the same Nono’s-)
SPECIAL CATEGORY : SOFTWARES Charles HAMEL HP48GX programs on THK, ROWcoded, LONG-Column-coded, COL’UMN-coded, NEITHER Row NOR Column-coded, STANDARD HERRINGBONE-PINEAPPLE knots, STANDARD HERRINGBONE Knots, Enlargements,etc…(2008-2009) EXCEL WORKSHEET (2009) idem IsoGridMaker and HP by HP for Regular Knots (July 2010) Douglas VARNEY
This software has high capabilities drawing wise and code publishing wise. So it does effectively replace many books. ALL of those programs strictly conform with numbering and orientation of HP as is “natural” for those who are 9/10 to 6/7 of the humans, the RIGHT handed persons, and as seen in the most masterly publications of all : SCHAAKE and TURNER’s. Indeed Turkshead Cookbook and Globe Knots are a sore, fortunately isolated, sight. Nevertheless those titles succeeded** in contaminating unaware persons with aberrant, to a RIGHT handed person, notation. (**much influence : the more ignorant the reader is of reality the more influence he will be under)
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NOW LETS US SHOW AN ‘IDEAL’ NOTATION : SCHAAKE’s FIG 18
Look on the right side of FIG 18 to see how the 2 PASSes are perfectly specified by the two STRINGRUN. (Read each from LEFT to RIGHT and from BOTTOM UP.) You get the BIGHTRIM to use ; it only remains to give the CODES for EACH HALF-PERIOD in the PASS. IMPORTANT NOTE: the NUMBERING for the BIGHT-RIM that you have to use the NUMBERING SEEN IN A COMPLETE OR FINISHED DIAGRAM of the knot. FIG 19
BIGHTs-RIMs
are easy to
number. Note that they are SYMETRICALLY NUMBERED from the OUTSIDE to the INSIDE, on both KNOT-EDGEs.
is
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FIG 20
FIG 21
In FIG 20 please note on the right side of the illustration the FIVE STRING-RUN that perfectly specify the PASSes using the BIGHT-RIM NUMBERS as seen in a COMPLETE DIAGRAM of the knot.
Fig 21 shows a “temporal unrolling of the BIGHTRIM along the process of laying the PASSes”. It is the STRUCTURAL, FIXED, FINISHED numbering that must be use to specify the STRING-RUN.
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Armed with that knowledge let us see how SCHAAKE’s communicate a knot diagram and the crossings coding for each Half-Period. From personal experience I can tell you that there is much to be gained by understanding and using this way of doing things.
The knot is: SET-ONE is ONE THK 7L 4B a 2-PASS 12L 8B Type S1 (ONE) FIG 22
FIG 23
SET-TWO is ONE THK 5L 4B STANDARD HERRINGBONE-PINEAPPLE KNOT
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Page 21 sur 45 Fig 24 HOW IS THAT FOR CLARITY, NEATNESS, ECONOMY and COMPLETENESS ?
could be suppressed, yet it would still remain enough !
Fig 22
Even suppressing Fig 23 it would still be enough for those with a BASIC BUT SOUND knowledge of those knots. (THK and computation of PINSTEPS and Standard Herringbone-Pineapple PATTERN)
FIG 25
Unfortunately ignorance has ubiquity and many knots tyers will think all the preceding not enough and will feel more at ease being given FIG 25 25 and 25bis
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------------------------(NOW TAKING AGAIN USING THE 2-PASS NOW LET US SEE WHAT HAPPEN SHPAK let us see what other persons WHEN ONE THINKS IT IS A GOOD could have proposed : here when I do DECISION TO NOT FULLY not show their own documents I OBSERVE THAT RIGOUR. pastiche, as faithfully as possible ,their Here is a *compounding* of what may ways. appear in a knot you will have to Roy CHAPMAN communicate. Use the most monachal hand-drawn diagram, no superfluous indication beyond cordage route, crossings and place of PINs like FIG 26BIS. Roy add a photo of the finished knot.
FIG 26BIS
FIG 26
In this compounded case (parts taken from knot diagrams I have) it should be as plainly easy to see, “as the nose in the middle of the face”, that any PIN NOTATION with LETTERS (indexed or not with NUMBERS) will be hopelessly cumbersome and ONLY the NUMBERS NOTATION will be easy, the more so if using SCHAAKE’s way shown previously. FIRST REMARK : IN WHAT FOLLOWS THE GENERALLY CHOSEN FRAME OF REFERENCE IS THE VERTICAL CYLINDER.
JIMBO Use photos and detailed worded instructions explaining what the photos show and how to get the result.
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
Benoit VIGIER Donald WRIGHT Those two use series of photos with or without some accompanying words Norbert TRUPIANO aka NONO The simplest and quite efficacious even if he uses a square tracing :
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So Don WRIGHT, Roy CHAPMAN, JIMBO, Didier MURAT, Norbert TRUPIANO, Benoit VIGIER,Jimmy R.WILLIAMS are perfect examples of “handing out’ friendly tutorials transmitting their own way to make a knot without using any special or complicated notation. Claude HOCHET had spontaneously chosen the aberrant anti-clockwise and starting at the top prior to meeting with BURRHUS He was just confirmed in his ways let himself be contaminated with the PINs notation. Burrhus has the worst way you can find IMO : ---From TOP LEFT to BOTTOM RIGHT – ANTICLOCKWISE ---Notation : LETTERS with INDEX NUMBER ----and added to that an aberrant
disposition of PINS. FIG 27
Don WRIGHT uses Nono’s knot diagrams directly on a cylinder and bother with nothing else. The crossings are indicated in a Nono’s diagram. Barry BROWN , a rather top of the barrel apple, will simply use the TABLE of HP by HP code he will have derived from the diagram or been given. Jimmy R. WILLIAMS Jimmy made a beautiful 3-colours monkey-fist tutorial using no notation but very explicit photos with some words as prop. Didier MURAT without any special annotation but with cartoon/comics made with photos and words is sharing a solid tutorial about chest beckets. See his web site : http://www.sailorschest.com/home.htm
Not a single bad trick missed. Fig 16 this 9L 8B THK has an aberrant placing of the PINS which do not respect the necessary shift for an ODD number of LEAD. Not respecting that induced useless tension in the cordage that are difficult or impossible to correct during fairing, dressing, tightening. Fig 16 also
shows an aberrant positioning of the PINS.
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2010 Dec 26th
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shows an isometric (the only one that respect equivalence of length, hence of tensioning) diagram of the 9L 7B THK and Fig 29 the globe knot
Fig 28
Fig 30 Fig 30 shows
the aberrant position of the pins in one face given in Fig 16
Fig 31 Fig 28
Fig 31 shows
the correct position
Fig 32 Fig 29 This is HOW the knot in Fig 17 SHOULD HAVE BEEN PROPERLY DRAWN.
Fig 32 shows the given in Fig 17
aberrant position
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2010 Dec 26th
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Claude does show a proper RELATION between the PINS on the knot edges which is more than BURHHUS does. Here is how his TABLES are done He gives the PINS positioning like in Fig 34 Fig 34
Fig 33
For the foundation knot the TABLE OF CODE would be thus given:
Fig 33 shows a more proper position for the PINS than the one given in Fig 17
Now let us see how much Claude HOCHET is …err…”unusual” ( that was well before he studied SCHAAKE & TURNER and wrote RKnot Builder which contains no aberrant notation) in orientation of the HP,
notation of the PINs and positioning of the PINs. Let us keep the example taken from Schaake dispenses altogether with giving diagrams in his tutorials, he uses the diagrams to built a TABLE of the HP with their crossings.
HOCHET
Unfortunately, in my view, HOCHET propagates the aberrant orientation of the HP and numbering of the PINS. The way Claude uses is much more astute than what you can see in Fig 17.
Fig 35
Those tables are much neater than the ZIG-ZAG in the Globe Knot Cookbook, alas they remain with the original sin of their origin : aberrant orientation. They do not respect the most frequent neuro-psychological organisation, our anatomy and so are a disaster in ergonomic for the well lateralized person.(RIGHThanded or LEFThanded!)
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
Jan VOS You will have to look at one of his latest tutorials to get a “ VOS original” but they will tend to look like that. With my eyesight I do not find them very easy to use.
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VOS gives the HP by HP codes for the knots in his tutorials This is a VOS original in Fig 38 Jan VOS also shows “in situation’ photos. He can also do Tables of that type : N° of HP – L to R – codes for this HP N° of HP – R to L – codes for this HP
Fig 36
Here is a “VOS original” (Fig 36)
Fig 38
Fig 37 Fig 37
is my pastiche of Jan’s way.
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
John RICHINGS John is 73 years old, new comer to my page but not to knots. I am speaking here of his Standard HerringbonePineapple. Illustrations in this paragraph are John’s own.
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not do to say that this is not a receivable ‘formal tutorial’. *** John uses ‘unusual’ ways but he always makes sure to built “a common background”. That is more than so called “advanced or ex-spurts” do ! *** the way he sets the BIGHTs, with a SHIFT (ODD-number of LEADs as in any proper Standard HerringbonePineapple) to LEFT of the BOTTOM KNOT-EDGE relative to the TOP KNOTEDGE. That is more than so called “advanced or ex-spurts” do ! BIGHTs are numbered 1 to n (here PINS on INTERNAL BIGHT RIMS are labelled with LETTERS.
4)
John decided to put aside letters that are prone to be confused with digits, for example ‘I’ and ‘O’ (but why not as the stance “novice to novice’ was clearly stated) :
WHAT IS STRONGLY UNUSUAL
--- the fact that the PINS for the foundation THK are NOT labelled as if this was *not* PASS-1 in this 8-PASS SHPAK.
3 *very good* points for John : *** RICHINGS does take the greatest care to set his stance as “A tutorial for a novice by a novice”. That is more than most do. Difficult to state more clearly that this is *not* a formal paper and that it is in the frame of friendly hand-out to persons interested in seeing this HerringbonePineapple Knot explained to them in simple and workable terms. So it would
--- the way he indicates the numbers of the PINS to use. Usually it is the PER KNOT-EDGE number of pins that is indicated. John goes for “wholesale” ! (a) Insert 14 additional rows of pins: To be used for the bights of the nested Turks Heads (Passes 2 to 8) Unusual as this ’14’ is the sum total of the PINS to set BETWEEN the NO-NAME PINS for the Foundation THK. Unusual it is but perfectly clear.
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
For the code in each Half-Period John goes classical while not using the table format. To get his HP code John makes ISOMETRIC grids of the knot ; John is an Pass Half Period No. No. 2
1 2 … 4
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artist at ‘spying’ and he made his own grids of Nono’s spherical covering by ‘reading’ Don WRIGHT laid cylinders.
From Pin
To Pin
Btm2 U2 – O1 – U1 – O1 – U1 4G U1 – O1 – U1 – O1 – U1
4G 1Q
3G
6Q
U2* - O1 – U1 – O1 – U1
… ----In his 800 Faces (from a Nono’s diagram) John RICHINGS changed tack : now BIGHT-RIM are identified with NUMBERS and BIGHT-NEST by LETTERS.
Michel SINCE Another contaminated through Claude HOCHET whose tables of crossings he admired. This hideous contagion progresses at a fast pace ! On the bright side : contrary to BURRHUS, Michel SINCE, as Claude HOCHET does, properly positions the PINS on the two KNOT-EDGE. Also worthy of note is the inspiring NEATNESS of his cordage lay on the cylinder. On the darkness side is this aberrant anticlockwise winding with ODDnumbered HP going from TOP-LEFT to BOTTOM-RIGHT ; EVEN-numbered for them go from BOTTOM-LEFT to TOPRIGHT. BIGHTs are labelled with LETTERS BIGHT-RIM with NUMBERS.
and
See his 63 Faces tetrahedral tutorial for details. IMPORTANT = ALL those persons authored tutorials that WORK PERFECTLY for those needing EASY AND GOOD RECIPES
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
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Charles HAMEL Yes indeed! I am quite ashamed to say that I let myself go down and tried to use LETTERS. BLUSHING CRIMSON ! Fortunately that document is not yet in the public space and its draft was shared only with friends. I am, for honesty sake, giving here a fac-simile for this knot
Fig 41
Of course it is also possible to put LETTERS where the NUMBERS are and vice versa while keeping a PROPER ORIENTATION of the HPs. In which case the table is as in Fig 41. The Bottom/top and External/internal for the labels of the BIGHT RIMS are more interesting to have in some complex knots with this kind of rhythm Fig 39
Here is the first proof that I can also go into an aberrant loop after being contaminated by my friends !
Fig 40
Fig 42
Still NEVER those silly notations will allow STUDY of knots, COMPARISON between them, or the making of a mathematical formula allowing the writing of command lines in a
Copyright Charles HAMEL aka NAUTILE
2010 Dec 26th
programs with the ease provided by Schaake and Turner’s way. In my mind map those notations are just acceptable in handed out tutorials between friends (never hand down ANY thing, that is insufferable delusion of grandeur and insulting to the person receiving it.). it should be seen as an obligation** to keep the ORIENTATION OF THE ODD-numbered Half-Periods from BOTTOM to TOP whether the cordage is wing CLOCKWISE as for RIGHT-HANDED persons (or ANTI-CLOCKWISE for the LEFT-HANDED)
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5
6 7 1
2
3 4 5 6 7 1 2 3
NOW SAME EXERCICE WITH LETTERS
E + 4 = what? So you have to count Start PIN 5 ABCDEF Once again you have to count to find the arrival PIN A B C D E F G
STILL
** unless when writing a software in which case it would be really nice to have the user choosing the start edge and the rotation.
Note : one case where it would be perfectly acceptable to mix CLOCKWISE and ANTI-CLOCKWISE in the same tutorial for a knot is to avoid the pulling through of a large length of cordage. In which case one would begin at the middle of the length and go CLOCKWISE with one half and ANTICLOCKWISE with the other. ABOUT THE OBJECTION THAT LETTERS ARE LIMITED TO THE 26 LETTERS OF THE EUROPEAN ALPHABET A to Z.
This mirage of limitation is of nil import compared to the fact that you cannot compute with LETTERS without having to count on your fingers to know ‘the result’ Imagine = PIN-STEP = 4 Using NUMBERS Start PIN = 5 B= 7 for modulo B 5+4=9 9 modulo 7 = 2 so Arrival PIN = 2
C D E F G A B C D E F G A B Imagine that exercise with B= 5 and PIN-STEP = 12 It is immediate with NUMBERS Say Start PIN = 4 4 + 12 = 16 16 modulo 5 = 1 Arrival PIN is 1 after 3 wraps of 360° It is IMMEDIATE 1 2 3 4 5 Now how about LETTERS : start counting on your fingers while keeping track of the WRAPs ! ABCDEABCDEABCDEABC DEABCDE Of course ‘spiders’ persons always using received recipes and thinking they “really made the knot all by themselves”, never inventing or exploring anything will not try to see the point. The person either simply curious or wanting to approach the crafts(wo)man state will immediately see what I am pointing to. Obviously they will need to know what a PIN STEP is, how to compute it, what is its use…
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2010 Dec 26th
Stating that there is a limitation in the number of PIN’s labels available with LETTERS is as good as saying that for NUMBERS we are limited to the 10 DIGITS, 0 to 9.
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26 + 676 = 702 is the number of labels you can make with the notation using exclusively LETTERS Plus you can mix LETTERS and NUMBERS as HOCHET and others do.
A,B, C………X, Y, Z 26 This will leave you using NUMBERS without any of the advantage of them ; BUT AA, AB, AC…..AZ , BA, BB, it is as difficult to use PIN STEPs or to BC…..WZ,…….,ZA, ZB, ZC,……..ZZ compute a BIGHT-INDEX Number or a This is 26 * 26 = 676 BIGHT Number with A1 B1 C1 D1 E1 than with A B C D E xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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PERSONAL CONCLUSION : IF one is writing with the pedagogical intent of propagating “proper methods and procedures”, promoting guardedly formalized and verified knowledge, awakening curiosity, inviting to exploration of what is lying beyond the visual appearance, of being less of “the doer” and more of the “thinking creature” then there is NO SALVATION WHEN USING ANYTHING ELSE THAN NUMBERS and this ORIENTATION OF THE HALF-PERIODS : *** from BOTTOM to TOP VERTICAL CYLINDER
for the
*** NEAREST THE HAND HOLDING IT to THE OTHER EXTREMITY for the HORIZONTAL MANDREL *** CLOCKWISE WINDING for the RIGHT-HANDED (or may be ANTI-CLOCKWISE if exclusively written for LEFT-HANDED persons)
The more sober GRIDS DIAGRAMS and TABLES of CODING can be made, the better it is. Always go for being 100% EXPLICIT and 0% IMPLICIT Picture quoted from http://patrick75.voila.net/vermeer_atelier.jpg
This is like trying to gives lessons in linear perspective, colour mixing, colour perspective, light and shade….to someone wanting to be an “AU-TO-NO-MOUS” painting artist. This is using a NON PERSONAL, NON WHIMSICAL, NON PARTICULAR BUT GENERAL, SYSTEM. Formalized publications need to strictly comply with the system TILL IT IS DESTROYED USING LOGICAL ARGUMENTS AND NOT USING PERSONAL PREFERENCES OR WHIMS and THEN REPLACED BY A LOGICALLY IMPROVED NEW SYSTEM THAT IN TIME MAY BE DESTROYED USING……..
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IFF one is writing with the sole intent of being expedient, of giving friendly and relaxed help in the making of a knot rather than help in learning the deeper understanding, then in giving to friends the “brainless recipe” for one interesting and difficult knot (recipe is brainless for users but demands hard work and precious time from the giver) ANYTHING
GOES (whimsical decisions, personal preferences or quirks…) IF AND ONLY IF : *** IT DOES NOT CONTRADICT THE EXISTING SOLID PUBLICATIONS, in
other words the few rules mentioned just above about winding orientation and PINS positions. *** IT DOES NOT SURREPTITIOUSLY SOW OR PROMOTE BAD HABITS in the mind of the receiver. *** IT DOES MAKES IT OBVIOUSLY FAIRLY EASY for the interested person having no previous extended knowledge, and/or in a hurry, and/or lazy, and/or unable to think by themselves, and/or whatever…to get an acceptable result. *** IT AWAKEN a real curiosity that will lead to more structured learning.
This is akin to PAINTING BY NUMBERS which is certainly a pleasant activity but is not painting at all, just as a child dabbling on a piece of paper and being proud to show it to mother (mothers are usually indulgent persons thanks Heavens !) Picture quoted from http://justingibbs.com/wpcontent/uploads/2009/06/paintbynum_vermeer.lg.jpg
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ANNEXE PART ONE : PIN JUMP(ING) and PIN-STEP QUESTION : Do *you* know how to make a 17L 10B THK cordage route (you are not asked, for the moment, to put any type of crossings in place) in the cordage when being given : --- the necessary and sufficient length of cordage, --- 20 PINS, --- a cylinder / mandrel --- (let us charitably add paper and pencil for those who cannot compute mentally).
I bet many will be lost without the usual gris-gris or fetish : a brainless ready made recipe. Yet, it is a “no problem” answer. (Ingredients needed: just average intelligence and solid basic knowledge). This is the point where no amount of so-called experience can save the day ; for me that is a good occasion to laugh*** ! No amount of practical experience will save you here without the necessary “second leg” : the theoretical or formalized distillation made from experience. Two ways exist : ----- IFF you have ‘A REAL KNOWLEDGE’ of the ENLARGEMENT PROCESSES then you will just make a 3L 2 B. This 3L 2 B after a LEFT side enlargement will give you a 7L 4B In its turn this 7L 4B after a RIGHT side enlargement will give you your 17L 10B. DONE ! BRAVO ! ----- second way, easy as pie even for the none too favourable to so called ‘theory’, is to put 10 pins at the TOP EDGE, 10 pins at BOTTOM EDGE, then to take the cordage in hands. (PINs in the correct position please : 17L ; 17 is ODD so "shift" the BOTTOM PINs CLOCKWISE in relation with their equivalent on TOP) Now you are ready for a really easy direct making of the 17L 10B using the PINSTEPS.
If you lack both of those 2 tools (ENLARGEMENTS and PINs-STEPs) then you are in a difficult situation.. I could almost feel sorrow for you; almost only, as it takes a few minutes to free oneself. Knowing the PIN-STEPS (or instead, if you are so inclined, may be, the PINS-JUMPS) and the ultra simple CLOCK-ADDITION (MODULUS by its grand name) you can trace ANY THK cordage route ; it will only remain to add the CODING you want on it. (Ah! Yes! you do have to know the meaning of “the four types of coding”).
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CLOCK ADDITION
(12 HOURS AM , PM)( 12 for 'day', 12 for 'night’) 09:30 is 09:30 ( AM as there is no change in the numbers) 15:20 is 03:20 (PM as there is change in the writing of the numbers, one 360° worth 12 hours ‘round’ has already been ‘run’ ) note : when using modulo 24, so forgetting the 'convention' of AM, PM which being letters cannot translate into numbers, then 24:00 (midnight) is 00:00 and not 01:00 ( modulo N use 0 to N-1 and NOT 1 to N) Cannot be simpler really, yet it is a rare one (I have yet to meet one, either in person or on forums !) that seems to able to make a THK of any arbitrary L & B dimensions from scratch. Let us first see a method I don’t favour though it works all right and is ‘solid’. Simply I find that it feels cumbersome and that it does not comply economically with an easy algorithm. This is PIN-JUMPING or PIN-SKIPPING Computation of PIN JUMPING is quite easy. (Excellent diagrams are given there and you should not miss studying them at http://www.shurdington.org/Scouts/TurksHead.htm ) Remember that when laying a Regular Knot (RK**) on a VERTICAL CYLINDER using PINS (ONE BIGHT==ONE PIN) at the TOP and at the BOTTOM (or at the RIGHT and the LEFT if MANDREL held HORIZONTAL) you need to JUMP or SKIP PINS when going from one PIN situated on one border to another PIN situated on the other border when laying a Half-Period. **(RK means that it is made on a THK cordage route with a single strand) PINS JUMPS = (Number of desired LEAD – 2 ) / 2 = (Number of LEADS / 2) - 1 This gives you the NUMBER OF PINS you have to JUMP OVER JUMP
can be 0 to n ; note that JUMP=0 is ONE STEP.
*BUT* pins jumped over, IMO, is neither the most rational method, nor the one the more closely related to the structural mathematical facts that explain that it works. Fig A That is why I will not dwell on the subject (it is more than adequately treated on the site I just gave above) ; I prefer to spend time on the way more satisfactory to me, the PINS STEPS You will observe that if the square grid respects the symmetry and the PIN-STEPS it completely puts out of kilter the relation between the dimensions en LEADs and in BIGHTs.
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A 5L 3B should be, quite evidently, greater in height that in width which is not really the case in Fig A. This is why the square grid is inferior to the isometric grid for representing those cylindrical knots. (compare with Fig C) Fig B
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explain the “slicing” of one Half-Period into LEADs , really, here PARTs seems much better, by Half-periods of different direction. Note that in this case one Halfperiod makes TWO slicing.
Fig B
Fig C
Read and have a second attentive look at Fig C, in particular the shoes marks and the stepping stick figure. L/2 or PIN-STEPS My preference goes to PIN-STEPS which I find more immediately derived from the anatomical and mathematical structure of the THK than the JUMPS can be. and PINS STEPS are like the old pickets and intervals problem : either you count the pickets or you count the interval between *two* pickets. number of intervals = number of pickets (NP) minus one. PINS JUMPED OVER
2 pins JUMPs : start PIN is A then jumped are B and C, arrival pin is D. Hurdles jumped over.
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3 STEPs = start is PIN A, first step is on PIN B, second step is on PIN C, the third step arrives on PIN D. Japanese stepping stones The simple formula to get, in a direct fashion, the "count"to do in order to be on the NEXT PIN (instead of the awkward number of skipped pins between the 2 extremity pins that PIN JUMPS use) is : PIN STEPS = L / 2 ex 7 / 2 = 3. 5 so 3 and 4 (USING THIS DEMANDS A PROPER NUMBERING OF THE PINS ON BOTH KNOT EDGES AND OF ONE KNOT-EDGE RELATIVELY TO THE OTHER KNOT-EDGE – see annexe part 3-) --------------------------------------------------Let us take again our 17L 10B 17 / 2 = 8.5 8.5 so it will be 9 and 8 , 9 at the TOP , 8 for the BOTTOM DO NOT forget that MODULUS(B)=10
the pins go a merry go round so use MODULUS(B), here
Start is at the BOTTOM, ODD –numbered HP go from BOTTOM-RIGHT to TOP-LEFT (cylinder) and EVEN-numbered HP go from TOP-RIGHT to BOTTOM-LEFT. Note that you have the choice to number your PINS either 1 to 10 or 0 to 9. (no importance for "in the cord" but highly important when using formulas). So it is : start at BOTTOM PIN 1 go to TOP PIN 10 ( 1 + 9 = 10 ; 10 modulo(10) is ‘0’) go to BOTTOM PIN 8 ( 10 +8 =18 ; 18 modulo(10) == 8) go top TOP PIN 7 ( 8 + 9 = 17 ; 17 modulo(10) == 7) go to BOTTOM PIN 5 go top TOP PIN 4 go to BOTTOM PIN 2 go top TOP PIN 1 go to BOTTOM PIN 9 go top TOP PIN 8 go to BOTTOM PIN 6 go top TOP PIN 5 go to BOTTOM PIN 3 go top TOP PIN 2 go to BOTTOM PIN 10 go top TOP PIN 9 go to BOTTOM PIN 7 go top TOP PIN 6 go to BOTTOM PIN 4 go top TOP PIN 3 go to BOTTOM PIN 1 curve has closed on itself, the Working End meets with the Standing Part.
Now you know how to accomplish that horribly difficult feat (just jesting!) of making ANY THK CORDAGE ROUTE you want.
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PART TWO : HOW TO POSITION AND NUMBER THE PINS. Chosen frame of reference : a vertical cylinder. *** With an ODD number of LEADS the numbered pins are best laid in this manner (less deformation induced in the knot as tension are more balanced all over) : 0 0 NOT 0 0 NOT 0 0
5
4
3
2
1
5
4
3
2
1
5 5
4 4
3 3
2 2
1 1
5
4
3
2
1
5 4 3 2 1 == with ODD keep the oddness == SHIFT the pins
MNEMONIC
*** With an EVEN number of LEADS the numbered pins are best laid in this manner (less …) : 0 0
5 5
4 4
3 3
2 2
1 1
NOT 0 5 4 3 2 1 0 5 4 3 2 1 NOT 0 5 4 3 2 1 0 5 4 3 2 1 MNEMONIC == with EVEN keep the evenness == DO NOT SHIFT the pins The way the PINs seem disposed in computed grids makes sense ONLY if you see it as being A CIRCULAR disposition and NOT AS A LINEAR disposition. There is, apparently,’ a lesser difficulty in seeing that particular point when having, like Schaake did, ROW ZERO ANYWHERE BUT AT THE LOWERMOST LINE in the grid. Alas that can be somewhat impractical for a computer program, so it may be decided to go for standardization: ROW ZERO == lowermost. This makes for easier computing and also allows comparability between grids being constantly maintained. This illustration under (Fig D) is intended as a summary to be kept in mind after understanding it.
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The whole point of this is not to say that you will not be able to make knots but that if you do not comply with that you will induce deformations in your knots that will always be keep, despite dressing, fairing and tightening, vestigial remnants of that skewed laying.
Fig D Any perceived discrepancy is a mirage created by the fact that software like HP by HP or RKB *always* put ROW ZERO as the lowermost ROW while Schaake’s put this ROW ZERO *anywhere BUT* on the lowermost line. This choice was made for software for the sake of maintaining comparability between different grids AND for ease of writing the command lines but it may be hiding some points to the eyes of the inattentive. Fig E gives the ‘vertical cylinder perspective’.
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Fig E
*** People using PINS NUMBERS***………. You may dispense with PINS NUMBERS (except that you need then to know PINS STEPS) Then it suffices to know the START PIN on each BIGHT RIM and the PIN STEP(S)
Copyright Charles HAMEL aka NAUTILE
Fig F
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PART THREE : MANDREL versus CYLINDER Q: To me a mandrel is a tool and a cylinder is a shape. In my humble opinion it would be less confusing to use cylinder only with a qualifier of horizontal bight rims or vertical bight rims. I may be missing something here and would appreciate you enlightening me if you will.
A: No all this is a question of CONVENTION so ARBITRARY and to build a "common ground" accepted with a smile , it is just because it is easier with a word that does carry a precise "context" in it. Yet ARBITRARY should never be automatically equated with SENSELESS or WITHOUT GOOD REASON FOR... Here the MANDREL frame of reference is used so as not to perturb persons knowing Schaake’s work and because Australian Authors use it too. Mandrel (WITH A SQUARE SECTION or a CIRCULAR SECTION as they use the "faces" as orientation while braiding leather) as frame of reference and as material tool. MANDREL : word does not even figure in my CAMBRIDGE International Dictionary of English. I guess it is sort of pidgin to use ‘mandrel’ as in fact a mandrel is a part of a machine ( comes from old French word ‘un mandrin’ -40% or English word comes from French thanks to Normans- which is a piece for the lathe, but then “ throwing a knot” Just as “throwing a bowl on the lathe” is perfect English to “make a knot” so “turning a knot “ may be inspired the adoption of the noun ‘mandrel’ ). Fig To make things simple AND AS FAR AS KNOT AND BRAIDS ARE CONCERNED: Mandrel is SLIM and ‘stick-like’. It as a small diameter compared to its length. Its length is many diameters large so being “slim’ anatomically for the human hand the easiest gesture is to hold it palm downward (in pronation) and the ‘stick’ more horizontal than vertical. See Fig 18 fair quote from p371 of Bruce GRANT Encyclopedia of Rawhide and Leather Braiding/ ** yes Encyclopedia and not as it should be Encyclopaedia. Cylinder is STUBBY : its diameter is a large portion of its length so anatomically it is best to hold it palm going a bit ”upward” (in semi-supination) as shown in Fig 17 that is more vertical than horizontal.
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Whatever the name you use there WILL STILL BE TWO DIFFERENT FRAMES OF REFERENCE (VERTICAL & HORIZONTAL) AND IT IS GOOD DISAMBIGUATION TO ATTACH A DIFFERENT NAME TO EACH. An idea stolen from Jimbo The Kinky: [open quote]Perhaps to include the notion of "around the cylinder" vs. "along the cylinder"? Somehow? [end quote] It is considered nowadays that words may be accepted with reluctance (with a large shovel of salt IMO) as defined by their usage rather than by their meaning (to me this is anathema and leads to loss of culture). Some like myself much prefer to use a CYLINDER (it is an "old" reference) with a wide circular section as compared to its length ( a CYLINDRICAL short mandrel with a bigger diameter if you will) so anatomically easier to hold vertically in the hand. CYLINDER is called A MOULD in old texts. ***Fore example Australians don’t speak of LEAD but of PART Some insist on using xL yB to state a knot while others will insist on yB xL Before the introduction of BIGHT by ASHLEY they were called TURN, SCALLOP SCALLOP was perfect description so one may wonder why ASHLEY had to do the dog trick with that. LEAD was PART in UK text (Spencer, 1934) and so on. Words, in this domain, have to be accepted at the beginning of the discussion for the sake of “common ground” only, not to prevail one over the other. Here, all this ‘affair about words used’ is certainly not an academic matter and IMO never will but is just limited to “plain usage and habits” and no one want to change theirs! To avoid “breaking the communication” it is best before an exchange to explicitly state the “common ground”.
