TRANSPOSITION (exploring the concept)

[agent_smith]

NEW TOPIC THREAD   TRANSPOSITION

I had introduced the term 'transposition' to describe a condition where the S.Part(s) and Tail(s) have changed identities.

In a transposition, the geometry of the core of the knot remains unchanged (ie the geometric configuration of the core remains unchanged - ignoring the effect of load).
Here I use the word 'core' (in lieu of nub) to denote the part of a knot that is central or principal to its existence or character.

A good example of a transposition is in relation to Ashley #1047 Figure 8 eye knot.
When we speak of a transposition, it can only have meaning if it is relative to something.
With respect to #1047 F8 eye knot, you need 2 F8 eye knots side-by-side, and then you show which segments have been transposed.
It is theorised that in one orientation of a F8, there is better resistance to jamming (I had shown this in another topic thread).

Refer to attached image below for general outline of concepts.

per Dan Lehman:

(Interestingly, the Reverse of the Fig.8 EK changes the
Interior/Exterior loading --S.Part & Tail being opposite in this.)
For the e2e Joint, "reverse" = "Tail-loaded",
but not for Eye Knots.

When you say "reverse of the Fig 8 eye knot" - this has no meaning.
Your statement can only have meaning if it is relative to something.
You need to show 2 F8 eye knots side-by-side where one version is the transposition of the other.
I have already done this in another topic thread.

With regard to your comment:

For the e2e Joint, "reverse" = "Tail-loaded",
but not for Eye Knots.

Again, the word 'reverse' implies a transposition (where the geometry of the knot core does not change).
And your comment; "but not for Eye Knots" - not sure what you mean?
Words have meaning - but there needs to be context/images something that is relative to assist in understanding.
In a #1047 F8 eye knot, there are different ways to tie it.

Note: It is possible to tie and use an F8 so that it has 2 S.Parts.
In fact, Ashley at illustration #1047 does not show a tail!
He shows his F8 with 2 S.Parts (dual leg loading).
Obviously, we also know that an F8 eye knot can have single leg loading (climbers do this routinely).

Therefore, in the case of an F8 with dual leg loading (ie 2 S.Parts), a transposition would make no sense!
The transposition can only make sense where an F8 eye knot has one (1) S.Part.

Interesting point:
With respect to #1415 Double Fishermans bend, the transposed version is completely unstable.
Transposing the S.Parts with the tails results in a knot that pulls apart.

EDIT 1 (additional images and text)
I have added some images of #1010 Simple Bowline (with tail tuck).
The great Xarax long ago showed us that most 'Bowlines' can be made 'TWATE' with
a simple tail tuck through the collar.
TWATE (Tiable Without Access To an End).

EDIT 2
I have added the Simple #1010 Bowline (no tail tuck).
Showing a transposition... although it is completely unstable.
I am showing it for purely academic reasons.
This is an example where a transposition results in something unstable or illogical.

[Dan_Lehman]

NEW TOPIC THREAD   TRANSPOSITION
per Dan Lehman:

(Interestingly, the Reverse of the Fig.8 EK changes the
Interior/Exterior loading --S.Part & Tail being opposite in this.)
For the e2e Joint, "reverse" = "Tail-loaded",
but not for Eye Knots.

When you say "reverse of the Fig 8 eye knot" - this has no meaning.
Your statement can only have meaning if it is relative to something.
You need to show 2 F8 eye knots side-by-side where one version is the transposition of the other.
I have already done this in another topic thread.

With regard to your comment:

For the e2e Joint, "reverse" = "Tail-loaded",
but not for Eye Knots.

Again, the word 'reverse' implies a transposition (where the geometry of the knot core does not change).
And your comment; "but not for Eye Knots" - not sure what you mean?
Words have meaning - but there needs to be context/images something that is relative to assist in understanding.
In a #1047 F8 eye knot, there are different ways to tie it.

Why did you omit (reading & comprehending, apparently)
copying my entire statement, which begins exactly with
my definition you so want --to wit :

For an EyeKnot, I define "reverse" to swap the loadings of
each of the 2 pieces in the 2-Tangle, after cutting apart the loop
  (well, my *Tangle* never connected it and joining
    the old S.Part & Tail),
and thus the 1-2 piece will shift from 100%-&-50% to 50%-&-100%,
and the A-B piece likewise goes from 50%(RELeg) -&- 0%.
(Interestingly, the Reverse of the Fig.8 EK changes the
Interior/Exterior loading --S.Part & Tail being opposite in this.)
For the e2e Joint, "reverse" = "Tail-loaded",
but not for Eye Knots.

--dl*
====

[agent_smith]

To Dan:
Take a breath... no conspiracy here.
The last part of your commentary in the previous post appeared
to contradict the first part (" but not for eye knots").

The same can be seen with your apparent irritation with my
use of the phrase "counter claim".
The word "counter" is not conspiratorial.
It simply means that Alan made an original claim - and then
you also made a claim. This is where the word "counter" means
to rebut or contradict a previous claim.
That is, Alan made a claim of originality.
You then stated that you had discovered the knot prior to Alan.
How are people supposed to interpret this?
(as you point out, there are no awards or ceremonies for knot discoveries!).
I would comment that there are some people in this forum who do
believe in the concept of originality and see no harm in acknowledging
that a particular person claims title to discovery.

Also in this topic thread (which I started) - the theme is transposition.
In my view, the term transposition is more precise and meaningful than "reversal".

Reversal could be taken to mean a physical exchange of position or some
may interpret it in other ways depending on subject matter.
The word reversal could also be problematic in discussions about chirality.

Transposition - for me - means no alteration of the core geometry.
Key to understanding is the change of identity, without
disturbing the core geometry.

...

NOTE:
A transposition can occur with End-to-End joining knots ('bends'),
and it can also occur with Eye knots (ie 'loop knots').
A transposition is not limited to End-to-End joining knots alone.

...

BACK ON TRACK

TRANSPOSITION OF CARRICK BEND (Ashley #1439)

What happens in a transposition of the Carrick bend?
Is the resulting transformation equally stable as the original form?
(NOTE: A Carrick bend undergoes transformation when tied in the typically depicted way,
which is a 'dressing state' that is unstable).
For example, see this link for a typical tying method: https://www.animatedknots.com/carrick-bend-knot

Of course, we can tie a Carrick bend directly using #206 Crossing hitches.

[Dan_Lehman]

The last part of your commentary in the previous post appeared
to contradict the first part (" but not for eye knots").

But it actually points do a difference between the act
and effect :: that "Reverse (e2e)" gets same result/knot
as "Tail-load (e2e)", but not so for Eye Knots (where the
Reversal gives 2-v-1+B and Tail-loading gives B-v-2+A
--the Tail "B", swapped in for former S.Part "1").

The word "counter" is not conspiratorial.
It simply means that Alan made an original claim - and then
you also made a claim. This is where the word "counter" means
to rebut or contradict a previous claim.
That is, Alan made a claim of originality.
You then stated that you had discovered the knot prior to Alan.
How are people supposed to interpret this?

Yes, but I exactly did neither; rather, YOU have taken
these notes of facts as in a contest for prize *FIRST!*,
whereas we have merely passed along notes about our
travels in the Knot Universe --for which information
about our aims & pathways can be of interest.

Also in this topic thread (which I started) - the theme is transposition.
In my view, the term transposition is more precise and meaningful than "reversal".

In such technical discussion key terms are defined.
("transposition" has ample generalities too --and esp.
 re altering physical positioning.)

The word reversal could also be problematic in discussions about chirality.

But those familiar with the concept of chirality would
have trouble with your recent images of a BWL tied
beside its mirror image with claims of differing chirality
when a savvy knot tyer fines one in a line with ends
out of play and yet transposes it into the other
--which chiral knots can't do!

NOTE:
A transposition can occur with End-to-End joining knots ('bends'),
and it can also occur with Eye knots (ie 'loop knots').
A transposition is not limited to End-to-End joining knots alone.

I think this is said re my "but not for Eye Knots";
I hope that that misunderstanding is now erased.

--dl*
====

[agent_smith]

Quote from: agent_smith on September 29, 2024, 11:05:44 PM
The last part of your commentary in the previous post appeared
to contradict the first part (" but not for eye knots").

Quote from Dan Lehman: But it actually points do a difference between the act
and effect :: that "Reverse (e2e)" gets same result/knot
as "Tail-load (e2e)", but not so for Eye Knots (where the
Reversal gives 2-v-1+B and Tail-loading gives B-v-2+A
--the Tail "B", swapped in for former S.Part "1").

Word salad
Cause and effect?
Also, I had previously stated that I prefer to begin with an end-to-end joining knot,
and use that as a base from which to derive the corresponding eye knots.
I find it more logical and intuitive to adopt this approach.

One can of course begin with an eye knot, and then try to derive the
corresponding 'bends'. However, it is less intuitive and results in more
possible pathway variables.

Note that Double Fishermans bend (Ashley #1415) does not fare so well
in a transposition.


Obviously, I dont like the use of the term "reverse" or "reversal" in lieu of transposition.
I am of the view that 'reverse' leaves open too many edge cases and ambiguities.
The term 'transposition' locks the concept down nicely for me.

...

You have made it clear that you don't believe in prizes, awards, ceremonies,
academy awards, fanfare, or recognition, for making a new knot discovery.
That's fine.
I am of the view that there are some dedicated knot tyers who do believe in the merits
of awarding recognition of achievement.
Why don't you make a counter claim against all yChan's knots?
I reckon he will bark at you faster than you can say "counter claim" 

But those familiar with the concept of chirality would
have trouble with your recent images of a BWL tied
beside its mirror image with claims of differing chirality
when a savvy knot tyer fines one in a line with ends
out of play and yet transposes it into the other
--which chiral knots can't do!

The great Xarax reminded me that in all of the technical posts,
that I make, I have an audience of one (1)!
The word salad that you and I engage in pops up on virtually no one's radar screens.
Its just two knot geeks engaging in deep technical dives that interest very few people.

With regard to your comment above:
But those familiar with the concept of chirality would
have trouble with your recent images of a BWL tied
beside its mirror image with claims of differing chirality
I of course disagree.
There was nothing technically wrong with the images of simple Bowlines (#1010)
that I posted previously.
I showed #1010 Simple Bowline in both 'S' and 'Z' chirality.
I also showed the transposed images.
I drew a red line to clearly separate the differing chiralities.

The key concept is that the core of the knots do not change.
I use the term 'core' to denote the part of the knot that is central to its existence or character.
The chiralities shown were correct (one shown as 'S' and the other as 'Z').

Look - Dan - the fact is that most of this info is rarely (if ever) discussed or published.
With all of my work in relation to chirality, transposition, and correspondence between knots, it is
largely breaking new ground.
Whenever you break new ground, expect teething troubles.
Harry Asher briefly touched on some of these topics - but he never explored it in deep
technical detail. He only 'dipped his toes into the water' so to speak...

I think this is said re my "but not for Eye Knots";
I hope that that misunderstanding is now erased.

Well yes and no.
Its still a word salad
What you might have meant is this:
[ ] End-to-end joining knots usually tolerate a transposition (loading does not flip the knot - there is no 'eye' to flip)
[ ] Eye knots generally don't fare too well in a transposition (the 'eye' will be wrenched and loaded in an opposite direction).
This is where the use of the term 'reversal' can be complicated.
Although again, the Double Fishermans bend (Ashley #1415) doesn't tolerate a transposition.

[KC]

To me it has always been as like input/outputs reversed to same sum/or a 1way if not.
i also look at it like a reverse polarity of +/- ;
>>whereby the input is positive and the terminal as ground negative.
>>or antennae/force catcher to ground anchor termination type travel.
.
But must be of linear force inputs thru SPart, after witch force typically degrades via friction along travel of input to output.
But NOT of radial force inputs of radial binding, whereby force input is to side of rope and equivalent around
(vs. more typical end input of linear forces for Hitch and Bend then on degrading force travel onto round host).
Radials don't degrade force as travel around host until crossing nips.
.
Linear vs. Radial input, output, travel always makes big difference.
Linear force is focused to port thru 1 axis.
Radial is NOT focused, but rather radial is evenly dispersed to all axises by extreme contrast.
Thus radial can be folded , funneled , focused to 1 axis as increase
>>but linear diluted, dispersed from focused to dispersed.
Hand crank winch is radial dispersed focused into linear
>>lock crank to become single layer rope on drum can be bollard of focused linear input dispersed to radial.

[agent_smith]

per KC:

i also look at it like a reverse polarity of +/- ;

Yes, I too had originally considered the descriptive term "reverse polarity".
But then decided on a singular word: Transposition (one word instead of two words).

Conceptualising as a reversal of polarity might help some in understanding.