International Guild of Knot Tyers Forum

General => Knotting Concepts & Explorations => Topic started by: Stagehand on July 29, 2015, 11:41:32 PM

Title: The model of all hitches and lashings is Mathematical Knots of two or more links
Post by: Stagehand on July 29, 2015, 11:41:32 PM
The model of all hitches and lashings is Mathematical Knots of two or more links.  In this model the Clove Hitch is identified with the Solomon's Knot and in this case one of the links of the Solomon's Knot is the object that the Clove Hitch is tied to.  10** is the first ordered two line knot without twists.  As a hitch, expect it to have features like other knots without twists like Carrick Bend and Turks-head Knots.  The first ordered lashing without twists is provided by Borromean Rings.  In faith with the polyhedra form, Borromean Rings provides other knots in the working range.
Title: Re: The model of all hitches and lashings is Mathematical Knots of two or more links
Post by: xarax on July 30, 2015, 09:49:00 AM
   I had tied and tried the **10 hitch, and all the other hitches I could derive from the Borromenean rings. No good practical knot emerged. It seems that Mathematical "knots" can rarely, only, serve as an inspiration for Practical knots - because the most important characteristic of the former is topology, while of the later is geometry - and there is no bridge in between those two Lands.
   In Practical knots, we start from one of the few geometrical configurations, which is stable because it utilizes the friction of ropes - we do not start from one of the many topological configurations of the Mathematical "knots", which will become stable knot if it utilizes ropes with friction.
   Many of the best Practical knots I know are TIB, that is, topologically equivalent to the un-"knot", to the un-"knotted" line. What could emerge if one would had tried to figure out Practical knots starting from the mental image of an unknotted line ?  :)
   ( Tie the Double Cow hitch, or the TackleClamp hitch shown in the attached pictures, which are based on the implementation of the opposing bights locking mechanism, to see what I mean. )