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"Un mot n'est pas la chose, mais un éclair à la lueur duquel on l'aperçoit"
Denis DIDEROT - Philosophe Français du Siècle des Lumières

“A word is not the thing, but a flash of lightning in the gleam of which  it is glimpsed”
Denis DIDEROT - Enlightenment French philosopher.

Of course Diderot warned  "...on ne peut s'intéresser qu'à ce qu'on croit vrai.'
"One can only take interest in what he believes to be true"

Diderot was compassionate enough to provide this consolation :
"Ce qu'on n'a jamais mis en question n'a point été prouvé"
"What has never been questioned has never been proved"

Keep in mind that he wrote too :  "Celui qui prendrait ce que j'écris pour la vérité serait
 peut-être moins dans l'erreur que celui qui le prendrait pour une fable"

" The one who would take what I write for the truth would be perhaps less in error
 than the one who would take it for a fable".

Diderot assures/reassures you that you will be safe when returning to
"The Masters"

"En passant de moi à mon bon maître, comme ils n'avaient rien appris, du moins ils n'avaient
 rien à désapprendre"

 "When passing from me to my good Master, as they had not learned anything,
at least they  had not anything to un-learn"

Read again in Page 3 of My Bat's belfry the 'Starting stance' of topic " REVERSE AND
MIRROR" of which here is a short graphical summary.

The way a "something" is designated, invoked, evoked, denoted rather stem from a
'parti pris' of commodity not to say sheer laziness and approximate thinking, all  that being
done to the prejudice and detriment of descriptive rigour.

I often feel, when reading (even some of my own writings), an extreme confusion is reigning
about the concept of  "sameness".

Following are only a few words my memory retained.
Much too often to my liking  imprecise use is made of them.


- Akin
- Alike / like
- Analogous
- Comparable
- Like
- Mirror
- Identical(ness)
- Indistinguishable
- Semblable
- Similar
- Resemblance


- Copy
- Different
- Duplicate
- Inverse
- Opposite
- Reverse
- Transposed / transposition

True synonymy is a figment of imagination  rooted in approximation of thought and language.


Some of these words imply a very partial notion of sameness which  in fact means it is
 absolutely no sameness at all. 

A sure thing for me is that  using, about a knot, a word in the left column with one in the right
column is rather to be avoided.

Same : only to be use as in 'the very same' uniquely defined individual identity.

So it is clear that a knot cannot logically be the same as another one but only to itself.

You may only use it as in " this is the same knife I lost yesterday " meaning it is the very same
one that was yours and not another one having an absolutely perfect resemblance.

Affinity : well it is certainly not sameness but a vague set of points of approximate likeness
that make one thought of...

Akin : certainly not sameness, only a 'parentage'

Writing words  like "it is the same in reverse", "it is the same except" " it is the same ....but
 for...", "it is the same only it has or has not...", 'it is the same though....' seems to me 
particularly improper .
It should be logically clear that they are in fact not 'same', not identical , not even similar but

Sameness cannot be gradually scaled : either 'it is' or 'it is not'.
It is an 'on" / "off" notion.
No "20% or 75% the same" can make any sense, and certainly not in a technical discussion
about  geometric entities. (knot/bend/hitch)

Entities :  elements that are completely defined in their nature, in their position in the space
of representation, and in parameters of external appearance, not to forget of their 'functioning'.

I think that it is well worth to take the time to read and ponder about the '
geometric transformations' that can be applied to knots or their representation.

A graphical summary with taking the SPart / WEnd identities on account and one without
taking them on account. SPart = Standing Part  , WEnd = Working End.

Of course these geometric transformations are "mental experience", in the Real World, with
knots in cordage, you cannot for example change the nature of crossings or exchange WEnd
for SPart instantaneously, you have to thread the knot anew!
Nevertheless as experiments with diagrams or 'in thoughts' they can be enlightening.

Now after theory some play with "real" objects :

- Turk's head knot inside-out
It is a cylinder of revolution , a tube opened at both end with both opening communicating
one with the other.
Inside-out changes values on all three axis x, y, z
It was possible to 'materially'  INVERSE this one. There a 'real' knot is transformed.
Note that there are two different ways to do the trick both passing through the ' mat shape
'offering a different face to observation, one would be 'heads' and the other 'tails' if it was a

- House cleaning rubber gloves. ( compare with hands inversion )
You can do an apparent INVERSE with hands supposed to be held in a vertical plane
- - right hand is held showing its back and tip of fingers is upwards.
- - left hand is held showing its palm and tip of fingers is downwards.

This make the left hand appear to be the inverse of the right but it is still materially a left hand,
held in a particular attitude, it is not a transformed right hand.

If you looks at the glove you will see that materially the inside out right hand glove can be
superposed to the left hand which can done it, but still it has green ( right) inside and show the
inside of a right or left glove, it is not really a left hand glove as found when opening
the package.
So it is not an INVERSE but a REVERSE with only 2 out of the 3 axis changed :
x is unchanged ( thumb is still on the same side ), z has changed : the inside is out now and
vice versa, y has changed tip of finger are now downwards. ( It your put the tips in the same
orientation as before  ( y has been restored ) you do it at the expense of changing the previously
unchanged x : thumb is now on the  other side.

- Vest inside out that is  'reversible' / 'invertible' in run of the day parlance.
What it is in fact ?
For run of the day parlance usage is now set, but if it were a knot the correct way would be to
say 'can be reversed'.  
Knots can be readily made to show their back but you cannot without rethreading them anew
or changing the way you put on the load, reverse SPart (load)  and WEnd ( 'free tail').
That is why I guess that this particular 'reverse' has its special own name : back view.

-Compare gloves and vest.  
REVERSE both but not with changing the same 2 axis : of course : vest is on a perpendicular
axis compared to the one of the gloves ( only arms are on the same orientation ( opening of
both are in the same direction.)
x is changed : left became right and vice versa, y is changed : it is an upside-down for arms
and for the fabric and its doubling, z is unchanged : collar is still in an unchanged orientation.

So vest or glove if for practical purpose you may say they are 'invertible' (at the expense of
the part being the 'observed one' : but that is what is wanted for a vest for example offering a
change in colour or for a glove : offering the possibility of a complete pair with 2 right ones or
with 2 left ones.) but it would be more correct to say  you can 'reverse' them as you cannot
readily 'inverse' them as a whole.

Sometimes it is necessary to make compounded manipulations to establish the way two
different knots can be 'related'.


                                             Go to page 7 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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