Abok #1059 continued
The notion of correlation between “TIB knots” might designate a TIB route transition from one to the other, without access to ends, on condition that there would be no unknotted line throughout this transformation procedure.
Beyond that, there is no other geometrical or functional correlation, since the slightest geometrical change, leads to a completely different knot, from a functional perspective.
Of course, there is also the notion of topological equivalence between two knots, which i would conceptualize as a “linear transformation process” that encompasses only core manipulation, with absolutely no impact on knot’s complexity/ order.
On the flip side, if eye manipulation would be intergrated in the TIB transition process, by way of eye collapsing or eye reeving, that i would mark as a “non-linear transformation”, with significant effect on initial knot’s complexity/order/and functionality by extension.
Xarax would had provided a more meaninful description or definition of this concept, therefore, an example is more needed than ever for a more thorough understanding.
More specifically, the following attached image, illustrates the linearly configured, end of line instance, derived from Enhaut’s wheel inline knot, using only core maneuvering in order to progress from the inline, to the end of line field.
Now, feeding the eye through the collar, as the white arrow indicates, that would, non-linearly, simplify the knot to the minimum complexity level of Αbok#1051 or parallel, linear progression to the inline level of 1050.
In conclusion, if one has been following all these consecutive posts about 1059, he might be able to establish a TIB route, between 1053 butterfly knot and 1050 harness , through linear or non-linear transformation methods, additively or reductionally, in terms of the induced complexity.
The reduction method, as much more easier, would be realised descriptively with the following consecutive transformation stages….
- Start with 1053 butterfly knot, and feed the eye through the nearest overhand to get Abok#1044 (non-linear).
- Dress 1044 as 1059 rearranging the eye legs appropriately (linear).
- Feed the eye through the overhand link of 1059 to get the first wheel inline knot(non-linear).
- Move the complexity to the other link using only core manipulation in order to get the second wheel, Enhaut’s inline knot (linear).
- Get the harnessque end of line form of previous wheel knot (linear).
- Feed the eye through the collar to get 1051 (non-linear).
- Progress to the inline field of 1050 (linear).