Nautile aka Charles Hamel's personal pages
or in French

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[ "Avoir une araignée au plafond" / " To have a spider on the ceiling"
is the French equivalent to "having a bat in the belfry"]

This is the place where I can freely be : " a bit touched you know".


You can not be troubled by what I write but only by your own judgement about it.

Point of importance to me is not having what I write approved (or rejected).
Point is rather to make you stop for a moment, having shed all pre-conceptions and 
having  put aside  
past 'read or heard' that you readily accepted without real examination. 
Just exercise your own thinking power in a critical ( intellectually that is, not affectively ) way.

To do that you will have to suspend all disbelief till having finished reading a whole topic and then
read it again having this time engaged you open and honest critical thinking.

Main point is having you, Reader, to go and shape your own personal view.

So again, please!,  do not fall back on 'automated, pre-digested, un-examined' response you have read
or heard elsewhere.

A much useful stance will be to be 'virginal' and think on your own as if you had never met the topic.

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You are not sure there is a difference that makes a difference ?

If by any chance it was not quite evident before it should be by now.

Knots are made using cordage ( we will by commodity put aside other materials ) that are
following a "self avoiding walk".
Please take note that it is knots / bends / hitches and not splices that are the point in case
Avoiding as in not 'truly intimately meeting' itself , not 'mixing' with itself.

This is a crossing (different level) , now  intersection (same level).

Think about it like that :
- when a highway is 'crossing' another one there is no risk of a collision,
- when two streets intersect each other you better be careful,
- electric wires are crossing and not intersecting with other wires or water ducts.

Another example : 
if one day not made like the other days, in Paris, le Métro were to go intersecting La Seine
(fleuve) or if in London the Underground were to go intersecting The Thames (river)  better
have a scuba gear in good working order handy.  
Fortunately, till now, both  underground railways are crossing (either under or over) their
respective body of water.

Note :
in a real knot there are crossings but in its planar projection, its diagram on a sheet of paper
(more so on your PC/Mac screen )  these crossings are represented by intersections. ( ink
can be admitted to be everywhere on the same level and not going under or over, though
one could conceive of the graphite layers left by the paper pencil as being on different
levels )


NOW SPLICES (in laid or in braided cordages) ARE DIFFERENT
No self-avoiding walk here for  the  cordage as a
'whole' even if strands or fibres
 are still avoiding each other and themselves.

In modern braided cordages splices are rather a 'confluence' where the cordage goes into
itself playing Orobouros.  ( confluence :  like a river meeting another river.)

By the way in English you seem to have only 'river', in French we have 'rivières' / river, that
is a body of running water meeting another one and we have 'fleuve', for which you do not
have the equivalent or I do not know it  : it is for a river that is ending in the sea .  

In spliced laid cordages the 'intersection' can be thought of as forming what topologists
call a 'double-point'  even if a splice diagram can be drawn without a double point !
( double point of crossing as there is  a top and a bottom crossing , a sort of piling up of

Double-point appear when you try to get "the unknotting number" that is modifying the
nature of crossings.

To go from a H to a L or from a L to a H crossing you have to go through a "double-point".
Making 'trambles' you can use them too.

Nevertheless pseudo or real double point can be made into a tool :
A 'double point' is 'totipotent',  it can resolve either in a "H" ( High) or in a "L" (Low)

Hence  the 'cordage intertwining' in my illustration can give rise to different knots depending
on the choice between "H" and "L".  

Illuminate it brightly and just look at the projected shadow taking care that each intersection
is not superposed on any of the other ones.

Question : which knots will produce identical shadow images.

We will come back to that again when looking  into  'shadow'.



D/d is the ratio between the larger diameter and the smaller one.

D/d ratio is quite important to keep in mind when imposing a curve to a cordage.

In particular while using a pulley it must never be forgotten : continued integrity of fibres
depends on a correct ratio being observed.

As for a hitch not only D/d play a role on the fibres of the cordage but has a direct influence,
that cannot be neglected, on the surface and friction.

By the way : fibres can be damaged by 'compression' and not only  by 'elongation'.
(more to come later in "ropes and cordages" pages )

Go to page 2 of  bat's belfry

Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

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