A New Binding Knot?

[InTension]

   Great scientific theories ...come out of the minds of men

   And where did t h o s e men come from ? Have you met anybody ? ( because I have not...)
   Why they were born 1800 years before the time they "normally" would ? ( Archimedes was, intellectually, contemporary to Newton and Leibniz ).

My short list of more recent Greats:
   Charles Darwin
   James Clerk Maxwell
   Michael Faraday
   Werner Heisenberg
   Albert Einstein
   Norbert Wiener
   Alan Turing
   John von Neumann
   Ivan Sutherland
   James J. Gibson (I met his wife, who also did good research.)
   Vernon Mountcastle
   Hubel & Wiesel (I met Wiesel.)

   Jumps between similar knots are shorter than those between dissimilar knots.

   You still do not get it.
   There is no comparison, no linear relation, no "similarity" between common and great knots, and, of course, not between great knots.

The real question is "Is this knot great?" because that's the only superlative you deal with in art.

   There is no comparison, no linear relation, no "similarity" between common and great knots, and, of course, not between great knots. Gleipnir is not "similar" to the bowline and to the Sheepshank,

Forgive me if I'm telling you something you may already know: Gleipnir-like knots exhibit the principle of 'tensegrity', in fact they are the simplest useful system that I've come across that does so.

Wikipedia:
"Tensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially.
The term tensegrity was coined by Buckminster Fuller in the 1960s"

In Gleipnir-like knots, the cords inside the nub are elements under compression within a circuit of continuous tension; thus these binds apply 'tensegrity' inside a very simple structural arrangement. Tensegrity structures are usually built with struts as compressive elements & cables as tensional elements, but there's no reason to confine the principle to apply only to struts & cables.

I hear it coming:

A f t e r  it [Gleipnir] has been discovered, and only b e c a u s e it has been discovered, we can scratch our heads and try to figure out ad-hoc "similarities", and sort / "explain" everything in a simple, "comprehensible" way that will make us feel good...

That's how science works. Sometimes people make new observations and check to see if preexisting theories & principles account for it. At other times, people make predictions & run experiments to verify them. It's called the scientific method.

My take is that Gleipnir's author had an intuition that: 'Hey, this might just work.' He tied the knot & started testing it (running an experiment) and was amazed by how well it worked. He was not a research mechanical engineer specializing in knots, so his initial idea was based on intuition, derived from experience working with knots, rather than an engineering theory. Since the knot was not derived from theory it was only natural for him & others to seek out a better understanding of how it worked, after the fact.

Personally, I am somehow modest regarding this, when I declare that I would nt been able to discover Gleipni even after 1000 years !

You're either being humble, over estimate what it takes to see things in a different way, or are over awed by the Gleipnir.

Biologists didn't stop making great discoveries just because Darwin came out with the (awesome) Theory of Evolution, they drove forward to crack the genetic code which explained the internal mechanism driving evolution.

You never know when your next attempt at discovery will fail badly, fail but provide a new insight, work as expected, work well and provide a new insight, work great, or work great and provide a whole new set of marvelous insights. The day the Gleipnir was invented it's author did not say to himself: "Now I am ready to construct the greatest knot seen over the last few millennia." Just keep learning, thinking, & trying out new things, and maybe, just maybe...

I am not immune to awe & wonder

   I am sure you are not - but we are all "spoiled", somehow, by the contemporary "politically correct" ideology of collective inventions and discoveries, of the gradual, non-revolutionary way everything in nature and society evolves, and the desperate need we feel to "explain" and "predict" phenomena, far more complex than our models and our processing powers enable us to do.

I did not say that most inventions are made collectively. I paraphrased Newton when he said in effect that: "If I have seen further it is by standing on the shoulders of giants."

In saying: "science is mankind's collective discovery of the laws of nature." I was simply pointing out that science is the sum of all the scientific theories and discoveries garnered to date.

   Why the Gleipnir was not discovered 2000 or 4000 years ago, is a mystery - and it will make no harm to us to accept that there will always remain some mysteries out there !

You never know "what's just around the corner" in knot-space. - That keeps it interesting!

[xarax]

   I think that the five first persons of your list will remain there for a long time. Alan Turing s life became a movie because nobody would go to see a movie on Kurt Godel.   ( I do not know anything about the four persons at the end of the list ).
   Gleipnir is a great knot. The bowline, the fig.8 bend/loop, the Fisherman s knot and the Zeppelin bend, too - and perhaps a few, only, more.
   Great things have a great disadvantage : they are few !
   I do not believe we can say that any knot is a "tensegrity structure" : even the simplest knots are much more complex than them.
   The so-called "scientific method" can not explain why the author of Gleipnir was not born 2000 or 4000 years ago. And it can not predict when the next great knot will come - or if there will be any other such great knot like the ones we have, ever, if there will be anything other around any other corner...
   Great scientists do not follow any "scientific method" : they were born such, and they follow their heart. 
   I am awe by the Gleipnir, indeed - thanks KnotGod !    

[InTension]

   I think that the five first persons of your list will remain there for a long time. Alan Turing s life became a movie because nobody would go to see a movie on Kurt Godel.   ( I do not know anything about the four persons at the end of the list ).
   Gleipnir is a great knot. The bowline, the fig.8 bend/loop, the Fisherman s knot and the Zeppelin bend, too - and perhaps a few, only, more.
   Great things have a great disadvantage : they are few !
   I do not believe we can say that any knot is a "tensegrity structure" : even the simplest knots are much more complex than them.
   The so-called "scientific method" can not explain why the author if Gleipnir was not born 2000 or 4000 years ago. And it can not predict when the next great knot will come - or if there will be any other such great knot like the ones we have, ever, if there will be anything other around any other corner...
   Great scientists do not follow any "scientific method" : they were born such, and they follow their heart. 
   I am awe by the Gleipnir, indeed - thanks KnotGod !    

   Agreed!  & I do appreciate your enthusiasm.

[Dan_Lehman]

Where's Guass?!

In Gleipnir-like knots, the cords inside the nub are elements under compression within a circuit of continuous tension; thus these binds apply 'tensegrity' inside a very simple structural arrangement. Tensegrity structures are usually built with struts as compressive elements & cables as tensional elements, but there's no reason to confine the principle to apply only to struts & cables.

Calling the parts within the turNip's compression
"under compression" seems to miss that they are
principally in tension --and just held from movement
by the constriction, which is a far cry from Fuller's vision, IMO.

Now, whether I'll peruse the rest of this extended discussion
is a matter for later thought.

 

[InTension]

Where's Guass?!

Good point!

In Gleipnir-like knots, the cords inside the nub are elements under compression within a circuit of continuous tension; thus these binds apply 'tensegrity' inside a very simple structural arrangement. Tensegrity structures are usually built with struts as compressive elements & cables as tensional elements, but there's no reason to confine the principle to apply only to struts & cables.

I admit that I'm reaching a bit, seeking for a principle that applies to Gleipnir-like knots.

   I do not believe we can say that any knot is a "tensegrity structure" : even the simplest knots are much more complex than them.

Of course Xarax was correct, but a principle only needs to shed light on certain aspects of a phenomena to have value.

Calling the parts within the turNip's compression
"under compression" seems to miss that they are
principally in tension --and just held from movement
by the constriction, which is a far cry from Fuller's vision, IMO.

The coils (limbs) within the Draw Knot are under tension as they enter the turNip's, but the free ends (limbs) that exit are not. Certainly parts of the limbs within the turNip's are also under tension, but that's not the key factor locking (nipping) them in. The compression applied by the cove hitch under tension applies compression on the limb lines running though it. That compression increases the frictional force that nips the lines ("and just held from movement by the constriction"). The compression is critical to making the turNip's fulfill its function.

In these terms, the Draw Knot is simple because there is a fairly clear factoring between tension and compression. It?s the more minimal joining knots, like the square knot, where to lines wrap around each other that I do not really understand. Exactly how do the to lines of square knot interact to distribute their tension & compression in order to generate & direct the frictional forces necessary to hold them together? If you could refer me to a good reference explaining this mystery I would appreciate it.

"which is a far cry from Fuller's vision, IMO."

The definition of the principle of tensegrity appears to apply to Gleipnir-like knots. But in itself a Gleipnir-like knot is not a self-supporting rigid 3D structure, which has become so strongly associate with tensegrity. A Gleipnir-like bind needs a bundle to compress in order to maintain its rigid structure. I see no reason that the well defined principle of tensegrity must be confined to only apply to strut & cable constructions.

BTW, Bucky was big on knots. He described them as (I paraphrase):
' A knot is a regenerative pattern in the rope; a self-interfering pattern of energy and restraint that maintains its "patterned integrity." '

Now, whether I'll peruse the rest of this extended discussion
is a matter for later thought.

 

In retrospect, I find the most interesting observation to be that Xarax & I were seeking & emphasizing different features & functions of Gleipnir-like binders, which led us to appreciate & dismiss/neglect different variant types.

[InTension]

I'm taken aback that there seems to be so little known regarding the science of how practical knots work:

I got the following quote from:
      Knots and Physics: 53 (Series on Knots and Everything)
      by Louis H Kauffman  (Author)
      Kindle Edition
      Publication Date: November 9, 2012

      "It is important to come to some practical understanding of how these knots work.
       The facts that the square knot holds, and that the granny does not hold are best
       observed with actual rope models. It is a tremendous challenge to give a good
       mathematical analysis of these phenomena. Tension, friction and topology conspire
       to give the configuration a form - and within that form the events of slippage or
       interlock can occur.

       I raise these direct physical questions about knotting, not because we shall answer
       them, but rather as an indication of the difficulty in which we stand. A book on knots
       and physics cannot ignore the physicality of knots of rope in space. Yet all of our
       successes will be more abstract, more linguistic, patterned and poised between the
       internal logic of patterns and their external realizations."

Ouch!
---------
PS. I just found that dared posted the exact same quote in
      Re: testing physical theories of knots
      ? Reply #6 on: November 25, 2012, 04:16:51 AM ?