I make no claims about...
You make no claims about insignificant matters, who discovered what, but you do make claims about most important issues - as if two
topologically equivalent knots are
identical knots.
If you follow this most erroneous reasoning, you will claim that Mike s bend, a symmetric BEND, is the same knot as the "coming and going" bowline - a TIB EYE-KNOT - two things that are geometrically, formally, structurally and functionally different ! Would you go so far as to claim the same thing for the two knots shown in the thread about "bi-stable knots"
And, as if you had solved this "easy" issue, you are quick to proceed (= jump ) into a more difficult one...
OK, I will try to answer as I can : Supposing that the chopstick remains immovable in space, the second knot tied around it is a HITCH, while the first one is a BEND. Moreover, the distribution of tensile forces inside the two knots is much more different - if we could "see" those tensile forces running through the ropes, we would had realized it at once. So, the structure of the two knots is different. Different forms, different functions, different structures, what else do we need to declare two things different ? If we start disregarding such differences, we would arrive at a world with very few things, in no time !
Is the slipped version of a knot the same as the un-slipped one ? Is a very loose knot, where the strands can re-arrange themselves almost randomly /freely into the knot s nub, the same as a tight one ? I have no idea ! We should be careful not to disregard important characteristics, but also to understand that that there are "things" out there, indeed, that have primary and secondary qualities - although they may differ in many, or even all, of their secondary qualities.
Which are the primary, and which are he secondary qualities of an object ? Good question !
The answer is very easy, although it is not evident : The primary qualities of an object are those which we have to distinguish, in order to
use this object for our own purposes - and, at the end of the day, in order
to survive. When a tiger is
coming after you - or if you are
going to it - you do not have to distinguish the number of stripes, or nails, or teeth, to decide what is this thing, and then act accordingly. A tiger is a tiger, and, for you, it is the same tiger, even if it has fewer stripes, nails or teeth ( as long as it has enough to eat you alive ). If you fail to sort the thing you see under the label "tiger" = "run the hell away from it", because it has fewer stripes, nails or teeth, you will not survive - and so there will be no descendant of you, who, some day in the future, will claim that a knot does not exist
per se, and it is only "knotted material" !
Although in most cases the geometry of a knot can have no severe consequences, its structure and/or its function always does - so each of them is most important for us, so we consider both of them as primary qualities, belonging to something different from the rest of the Universe, an object we call a knot. For the worm, an apple is nothing but the edible material around it which it will devour, but for us it is an isolated, individual object we call apple, and its existence is not depending on the worm, the apple tree, the theory of universal gravitation, or the apple pie the mother of the physicist who discovered it by watching the apple falling from the tree is going to make for her beloved son.
Of course, if you call the bend and the eye-knot with the same name, you are not going to die ! But if you start to think it is the same thing, you will not proceed much further in order to
understand how those rope-made mechanism work, you will soon be driven to the erroneous belief that everything that "works" is OK, and that you do not need anything else, you will start to avoid any effort to understand even one thing...and that may well kill you one day ! We are the descendants of human beings that isolated some characteristics of the physical world around and inside them, labelled them as essential or primary, sorted the totality of their experiences into individual "objects", and used the model of the world that was generated by this division of the whole into parts in a way that helped them survive ! If you see the World as a unified soup, with apples, worms, apple pies, forms of knots, strictures of knots, knotted materials, bends, hitches eye-knots, knot tyers, the girl friends of the knot tyers, the loans of the knot tyers, the cats, mice and monkeys or whatever else is pounding the knot tyers keyboard,...then the odds you will be killed at the next turn of the road are multiplied....
We do not wish to examine things and distinguish different qualities in them in a detailed way, just as a pass time.. We do it because we first want to distinguish the real from the imaginary objects, then we want to separate the one World into many individual things / objects that we can use, then to understand how those things / objects are related to others, then to understand the World...Why ? Because understanding the World helped our ancestors to survive, so we, just like them, we are curious about it. OK, somebody will say, suppose we have understood the World, and we have managed to survive...What for ? THAT is the most easy question to answer, indeed !
To tie knots !
(
what else ? )
