Loops : One overhand knot is ( more than ) enough

[jcsampson]

I was so into determining the labeling that I missed the labeling in the filename.

O(w): Over working end
U(w): Under working end
O(s): Over standing part
U(s): Under standing part

Using the appropriate one, of the above alternatives, we have this:

C(f)C(a)H(f)O(w)

Whaddaya think?

JCS

[jcsampson]

"X(f)"

Are you certain that X(f) and X(b) will be able to handle all of the possible situations?

O(w) means "working end over working end."
O(s) means "working end over standing part."

Does X(f) mean "working end crosses over whatever comes next in the eye"?
Does X(b) mean "working end crosses behind whatever comes next in the eye"?

JCS

[jcsampson]

Well, I see that you like the idea of "regions," and that what I presented before is inconsistent with that idea (i.e., broke from it).

So, in order to maintain the same high degree of detail that what I presented before has, but also to be consistent with your idea of regions, we could define the current working end as a type of region all its own:

W(f)
W(b)

These would be always for when the current working end is to cross ITSELF.

It could be argued that, before, my allowing for

O(s): Over standing part
U(s): Under standing part

is redundant and unnecessary, because the "collar" specifications already deal with the crossing of the standing part by the current working end. Right?

Alternatively, we could have these:

F(w)
B(w)

But these would be unnecessary:

F(s)
B(s)

Right?

JCS

[jcsampson]

"Perhaps the S(f), S(b), T(f), T(b), S for standing end, T for tail, should [replace] the collar notation [?] . . ."

Yes, I think that the above syntax would offer greater specificity to your notation. I've been throwing ideas at you in the hopes that you yourself would sense the need for something like the above syntax. The current notation is fairly good at sequentially describing a knotter's actions and the resulting structure itself, but I sensed a need for more describing power. I think that the above syntax would do it. You need to be the one to decide the syntax, because only you know where you will want to take it as it evolves and all the possible combinations that you will want to be able to handle with it.

S(f): In front of the standing-part region
S(b): Behind the standing-part region
T(f): In front of the tail region
T(b): Behind the tail region

I like it.

I AM interpreting it correctly, now, right?

JCS

[jcsampson]

Loop.L(b)H(f)C(a)H(f)X(b)L(b)X(b).JPG is a good example that clearly demonstrates your current notation.

The "greater specificity" that I described in the previous post has to do with a type of "user friendliness" that can be exploited to win over, more quickly, to your notation, those knotters who are new to your notation.

In other words,

L(b)H(f)S(b)T(b)H(f)T(b)L(b) is a little more user friendly than L(b)H(f)C(a)H(f)X(b)L(b)X(b).

See what I mean?

These are all ideas to make you think, because thinking is good!

JCS

[jcsampson]

". . . the C (C for collar) notation . . . cannot cover elongated, more complex knots, where we have the working end coming into play with the tail . . ."

Well, for those knots, all SPATIAL regions that come into existence as the knot is made have no associating syntactic representation; but, using the T specification, all crossings that occur BELOW the S region are officially in the T region. See? Most of the knot (except possibly for the crossing that touches the standing region) can be considered to be in the T region, since it was formed strictly by the tail's moving over and under itself. With the T specification, your notation will be able to accommodate the overs and unders of a tail's crossing over and under itself, for as long a sequence as is necessary to finish a knot. Since a practical knot can be only so big, the "sequence" will automatically be limited to a practical length.

Considering the possibilities of sequence, selection, iteration, and recursion, I'd say that sequence is the best choice!

". . . is it more natural for most people to tie the overhand knot in such a way that the tail emerges above the L bight (and the standing end below the H bight)?"

Yes, the notation needs to be able to handle all of the possibilities equally well.

When making a Bowstring Loop, I go under and over and under; when making a Butterfly End Loop, I go over and under and over. As if that weren't complicated enough, my father was left-handed, I am right-handed, and I use both hands when playing piano!

JCS

[jcsampson]

Here's an idea:

Consider adding to the notation a numerical syntax by which the SPATIAL regions that come into existence as a knot is made are automatically created (i.e., enumerated). Then, you'll have some serious specifying power for any situation. It could be complicated, because you'll need to formulate an algorithm that defines the creation of a type of "grid" system--the labeling of which will have to change dynamically--as a knot develops, since there could be a piling up of regions both vertically and horizontally as a knot develops. . . .

Something like . . . "row 1, column 1," etc., in the form "(1,1)," etc. The meanings of these would change dynamically as the notational sequence grows. . . .

By the way, sorry for my taking this thread into so many other directions.

JCS

[jcsampson]

Are you certain about that? I'd hate to lose a boat!

JCS

[SS369]

I'm wondering if along the way we've crossed over into the  Knot Theory & Computing Zone ?

[knot4u]

 Close "front" view of the three loops tied without overhand knots.

The knot in that first pic didn't jam (that bad).

By the way, if you're ever tying down a load for my ex, then I recommend you do her the honors of tying an overly complicated knot that requires you to pull out a knot book and study for awhile.

[jcsampson]

"By the way, if you're ever tying down a load for my ex, then I recommend you do her the honors of tying an overly complicated knot that requires you to pull out a knot book and study for awhile."

Would it be OK to pull out the ABOK? You know, all six hundred something pages?

"Hold on, Honey, I have to cross reference. We'll be on the road by twilight. I promise."

JCS

[jcsampson]

Very interesting presentation.

Although these final loop knots are very simple, they result in some of the most complex-looking knots I've ever seen; but, they work.

I find it very interesting that when the Overhand is removed, much of what I sensed as beauty is also removed: Somehow, an Overhand gives a type of body or skeleton to a structure, which, when removed, results in what can be seen as a body without a skeleton.

But it could just be that we are all conditioned to accept the familiar and to shudder at the unfamiliar.

I applaud your methodical thinking.

JCS