The way a "something" is designated, invoked, evoked, denoted rather
'parti pris' of commodity not to say sheer laziness and approximate
thinking, all that being
the prejudice and detriment of descriptive rigour.
I often feel, when reading (even some of my own writings), an extreme
confusion is reigning
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.
- Alike / like
Some of these words imply a very partial notion of
which in fact means
it is absolutely no sameness at all.
A sure thing for me is that using, about a
word in the left column with one in the right
column is rather to be
Same : only to be use as in 'the very same' uniquely defined individual
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
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
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
about geometric entities.
Entities : elements that are completely defined in their
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
summary with taking the SPart / WEnd identities on account
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'
can be enlightening.
Now after theory some play with "real" objects :
head knot inside-out
It is a cylinder of
revolution , a tube opened at both end with both opening
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
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
So it is not an INVERSE but a REVERSE with only 2 out of the 3 axis
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
unchanged x : thumb is now on the other side.
inside out that is 'reversible' / 'invertible' in
run of the day
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
or changing the way you put on the load, reverse
(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
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
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
as a whole.