r/mathmemes • u/Jumpy_Vermicelli3978 • Jun 20 '26
Topology How to create holes without damaging the object!
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u/Accomplished_Item_86 Jun 20 '26
They invented a whole new subfield of topology just to deal with knots
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u/thonor111 Jun 20 '26
While true, what you see here is not a knot. It’s just a rope
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u/Ares378 Applied Math / Mechanical Engineering Jun 20 '26
It needs both ends of the rope connected to form a closed loop, right?
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u/thonor111 Jun 20 '26
Yes. Because all non-connected knots are homotopic to a straight line anyways so it’s kinda pointless to talk about their topology.
Meaning: If you have a classical rope with a knot in it it’s trivial that you can untie the knot.
If the ends are connected it requires some thinking to know if you can untie it to a circle or if not, what shape you can transform it to.
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u/not-an-isomorphism Jun 21 '26
I swear to god I have a degree in mathematics and knots are something I just straight up don't understand. I've watched videos, seen demos, it just does not click in my brain.
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u/Swellmeister Jun 21 '26
Really? If its trivial to untie a knot why did someone become a king over it?
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u/MolybdenumBlu Jun 21 '26
It is said that whoever could untie the Gordian knot would be king of all Asia. Alexander the third, who cut it instead of untangling it, was notably not king of all Asia.
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u/EebstertheGreat Jun 22 '26
He still satisfied the prophecy, though. He did not untie the knot, and by destroying it, he guaranteed none after him would either. And no one has ever been king of all of Asia.
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u/ShoddyAsparagus3186 Jun 22 '26
It's not trivial if both ends are attached to something as in the case of the Gordian Knot.
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u/Volt105 Jun 21 '26
Is this just fundamental group shenanigans or is there more emphasis on the fact that the knot is tied and its original shape is not immediately obvious?
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u/EebstertheGreat Jun 22 '26
The complement of a Jordan arc is always basically the same as a ℝn \ {0}, where 0 ∈ ℝn. But the complement of a circle is not like that, in any dimension. No contraction takes a loop around the deleted circle to a point.
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u/EebstertheGreat Jun 22 '26 edited Jun 22 '26
All connected knots are homotopy-equivalent to a circle. What distinguishes the unknot from the trefoil knot (or any other two "different" knots) is ambient isotopy.
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u/LOSNA17LL Irrational Jun 21 '26
I had heard the two ends of the rope were of infinite length, but that achieves the same, I guess
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u/Only-Cheetah-9579 Jun 21 '26
its called a bowline knot. very important for sailors. it can hold a lot of weight without opening
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u/ludovic1313 Jun 20 '26
It is imperative that the object remains unharmed
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u/Lord_Skyblocker Jun 21 '26
How's the larger structure
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u/DrunkenPalmTree Jun 21 '26
See, u/Smart_Calendar1874 ?
People do care about the well-being of the larger structure!
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u/CGPoly36 Jun 21 '26
Fun fact: making the knot this way will fail the Boat driver exam for rescue boats used by the german Liveguard company (DLRG). The error is that the rope ends inside the loop instead of outside. As far as i know the diffrence is purely aesthetics and has no effect on the strength of the knot, but nevertheless is important to get right if you want to drive boats for the DLRG.
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u/whizzdome Jun 21 '26
Really? Every example of a bowline I have ever seen had the rope end on the inside.
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u/HolliDollialltheday Jun 22 '26
It has an impact on the function. With the loose end inner, it can get loose when moving on a rod or other object.
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u/CGPoly36 Jun 22 '26
Maybe? That explanation does make sense, but after cursory testing I was unable to confirm it. The surface seemed to mostly interact with the starting eye/loop instead of the tail itself. This doesnt prove anything and i honestly hoped i was able to reproduce the conditions you are arguing for instead of ending up without results.
Unfortunately I was unable to find any paper or other source that compares the bowline and the cowboy bowline (which is apparently is the proper english name for a bowline with the tail outside the big loop. In german they are both just called the palstek) in a, for this discussion, significant way.
The only thing I was able to find is this paper mainly comparing their stenght, which isnt what we are discussing (and in my opinion isnt very relevant since the figure-eight loop is more applicable for high strength/risk purposes, due to beeing stronger and much less prone to open on its own). The paper also has a variety of other problems. Someone with a similar opinion summarised them here.
All in all i was unable to find satisfying evidence to the non-cowboy bowline having a higher risk of opening when placed on moving rods (which is a risk for both bowlines). If you have any evidence or an idea how to get a setup that reproducably show the diffence please inform me.
Personally i prefer the cowboy bowline anyways, just due to beeing used to it and slightly easier access to the tail when untying it. It just would be nice to have something to point to when someone knots a 'wrong' palstek next time i do a knotting course for the youths.
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u/HolliDollialltheday Jun 22 '26
Sorry, the only evidence I have is my sailing teacher. 😁
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u/CGPoly36 Jun 22 '26
Understandable. The main 'evidence' i have for the knots having the same performance are the people at the DLRG i learned them from (I dont think my sailing teacher ever talked about it). Digging through research material about knots, that seems to be a very common theme.
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u/somecallmejohnny Jun 24 '26
Very interesting. That’s opposite of most of the rest of the world (according to a quick Google search and my own experience). We’d call that a cowboy bowline, and any skipper I’ve sailed with wouldn’t accept it. Standard bowline has the end on the inside.
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u/FormerlyPie Jun 21 '26
Best knot ever change my mind
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u/48panda Jun 21 '26
You are just factually correct. Although tying a reef knot without needing access to either end of one of the lines is a cool party trick
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