Author Topic: Spooky way to find knots  (Read 3440 times)

DerekSmith

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Spooky way to find knots
« on: June 18, 2006, 01:00:20 PM »
  You know, Schrodinger was lucky not to have had the RSPCA on his case for doing that to a cat !!

Still, back in 1935 he would probably have got away with explaining that the cat was lucky to be enjoying all the amazing combinations of its possible nine lives and deaths both simultaneously and severally.

Willeke, please wait a moment before reaching for your red correcting pen - I am getting to the point, and yes it is knotting related.

Ever noticed how the pieces of 'fiddling string' you keep in your change pocket (Aha! so I am not the only saddo anorak around here) are always knotted when you take them out for a twiddle?  Well, I say knotted, perhaps most of us are more likely to grumble and say 'effin tangled'.  But there is probably a lot more in that seemingly disorganised tangle than perhaps at first meets the eye.  Perhaps because you have to undo that 'tangle' before you can start purposeful twiddling, you may just be closing your eyes to a miracle of nature and a highly functional extension to quantum mechanics.

Consider for one moment these three environments:-

1. Schrodingers cat in it's box.
2. Old hags tealeaves in a cup.
3. Cord in a loose change pocket.

What do you see?

They are all closed quantum systems.
They all contain something, which can have superposition, and which will collapse to a single state when the system is opened.
And finally, they all have input conditions and perturbation energy.

Is there just an outside chance that you are looking at three wonderful examples of natural Quantum Computers?

You put the string and the problem into your pocket.  You add perturbation energy (fiddling for your loose change amongst all that ruddy string!!) whilst thinking about the problem.  Then, Hey Presto !  When you pull the cord from your pocket, all the superpositions collapse into one possible solution of the problem you are trying to solve.  Then of course, without looking at the amazing solution to our knotty problem, we cuss and start to unpick the quantum computers hard work, without even giving a moments notice to what it has created.

Talk about - "There's none so Blind....." - because we are expecting a tangle that's not only what we see, its also what we get.

OK, so what has got me cranked up and thinking in this way?  Well, I had been working on the problem posed by Josh for his drum tensioning knot.  The problem needs a little device which allows cord to flow through it in one direction, then locks up when the cord attempts to flow in the opposite direction.  Then, if we construct two of these back to back, we might have a stayput knot which solves his requirements.  I had been tying slip/grip hitches back to back (without success because the whole thing was just too big) and had given up in order to let the minds eye mull over the problem for a while.

This morning, I pulled out the cords for my twiddling fix, and this time the customary tangle was strangely tidy.  Instead of just undoing it, I looked a little closer to see what 'knots' nature produces.  To my surprise, this tiny little tangle was really quite neat {OI-8:12}.  It was a bend comprising a loop passing through an & shape.  If it isn't already named I would probably call it the Ampersand bend.  

So what did it do?  Well, it has four ends, so I started to see if it was stable, locked up, ran through - whatever.  With two particular opposing ends it locked up very efficiently.  The non opposing end however, tipped the knot backwards and allowed the loop line to feed through with ease. A against D slips, B against D locks.  A against C locks, B against C slips.  Grab hold of knot and A or B slip through easily.

I tend to steer clear of fickle knots like this, get the wrong end and you are left holding nothing but a piece of string - oops!

Then suddenly I realised, this could be the knot I was looking for:- pull one end and the knot tips forward and locks, pull the other end and the knot tips back and unlocks.  WHOA !!  SPOOKY !! THE POCKET KNEW WHAT I WAS LOOKING FOR AND CAME UP WITH AN ANSWER !!  

As I don't believe in ghosts, it could only be quantum mechanics at work (Einstein famously derided entanglement as "spooky action at a distance)

Anyway, what does it look like and how can you tie it?



or here

To tie the beast, hold ends A and D and work with ends B and C.
Start as if you are going to tie a left hand Granny i.e. B over C, under and up.  Then C over B, but instead of passing C under and up through the hole, pass C under outside of itself then back over itself and down through the hole and that's it.

Well folks, has this thing got any previous?

KnotNow!

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Re: Spooky way to find knots
« Reply #1 on: June 19, 2006, 11:09:48 AM »
Hi Derek,
 I hope the post exists for a day or two.  Just long enough for me and others to determine the worth of the knot... or not.  Happy Fathers Day to you. (might be a USA "only" holiday, for all I know).
 As to cats and violin strings I do not know what we might have done in 1935, nor do I care.  Today... a reference to knots without  the "notes to the past" might be better.
 Where am I to use this knot?  What is the worth to me?  How can I tie it rapidly?  Why would I care?
 Simple questions from a simple man.
 As to my Webmistress... I alwasy support her judgement.   She keeps me from looking really stupid.  She keep others from looking beyond stupid.
ROY S. CHAPMAN, IGKT-PAB BOARD.

DaveRoot

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Re: Spooky way to find knots
« Reply #2 on: June 19, 2006, 09:34:02 PM »
Derek,

Looks like an interesting twist on a Sheet Bend (no pun intended).  I'll play around with this thing...

I think I even got the OI and the Saturation correct this time, so maybe I'm not totally hopeless after all!   ;D  (Did you see my recent post in the Overs Index topic?)

Dave

DerekSmith

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Re: Spooky way to find knots
« Reply #3 on: June 20, 2006, 12:00:47 AM »
Quote
Where am I to use this knot?  What is the worth to me?  How can I tie it rapidly?  Why would I care?


PABPRES,

I was kinda hoping that you and other KM's on this forum might turn their minds to exactly those questions.  Any thoughts?

Dave,

Charles (Nautile) has contacted me and let me know that this little beastie has been to this forum before at this thread

If I can find it I will bump it up here.  I have contacted twentythree, the original poster to see if there have been any developments on it and will post this onto the WKI page for Ampersand

On the topic of the Overs Index, both you and Jimbo raised some important issues that I have to admit have been worrying me as well.  I was preparing a reply when this little beastie popped out of my pocket and stole my attention.  However, I will respond to the issues and hopefully we can progress again.

Dan_Lehman

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Re: Spooky way to find knots
« Reply #4 on: June 20, 2006, 10:14:41 AM »
Quote
Charles (Nautile) has contacted me and let me know that this little beastie has been to this forum before at this thread

These aren't the same--look at how the ends of the non-U-shaped rope relate
to the U part (they're on the same side of it here, on opposite sides there).

I find the knot to be unstable in soft, silky, flexible nylon solid braid; I don't
see any great appeal to it.  (And, of course, I fiddled something else in the
process--but my fiddling comes outside of the pocket, spook free. :o)

--dl*
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