Have any lingering questions about knots? Want to hear more knot stories that didn’t make the cut? Derek and Emily (the writer/director of this video) will be hosting a livestream for our Patreons next week! Join our Patreon for more info and a link to the stream - ve42.co/VePatreon
Veritasium inspires me.. My parents said if i get 50K followers They'd buy me a professional camera for recording..begging u guys , literally Begging...
Veritasium's graphic designer would have become a physicist by now. It must take a lot of understanding on their part to learn the concept first and then visualize how to demonstrate it. It is just mind-blowing.
@@dburitto the face you see is Derek Muller. the animator is Fabio Albertelli, he also does graphical design (so probably also doing the graphical design for the videos). don't think they are the same person. Fabio Albertelli is well educated in science so he can work with the knowledge he already posseses.
I'm in awe at someone having the patience and skill to visually tie thousands of knots and distinguish duplicates. Thanks for another great story wonderfully told.
Very cool! I'm a graduate student in math learning algebraic topology. I'm working through Hatcher's right now. Its interesting enough right now, so we'll see if I end up focusing on algebraic topology.
As a non-Ph. D student in anything, topology and knot theory is, and has been, a very popular subject on science and mathematics themed channels for a very long time. It isn't "finally" getting the attention the subject deserves - you have only just now discovered it, apparently. Those are two very different situations.
@@watcherofwatchers I have not "just now discovered knot theory", however, I was merely trying to say that I am happy people are presenting it to the general public so more people can learn about these fields of mathematics.
I don’t think I’ve ever watched a video that I completely understood while, at the same time, I had no idea what you were talking about. It’s like a miracle. Fascinating subject!
Although I wouldn't in a hundred years choose to study knots, it never fails to inspire me how people take up these causes, pushing esoteric fields forward for nothing more than a pure love of the game until eventually their discoveries can be tied to other fields to make important scientific advances. Science really is humanities most collaborative sport.
The wonders of a deterministic universe People think its intelligent design, but it actually is thermodynamics, entropy, and life trying a better hand at making more "complex life" for energy dissipation
@@anthonymartial2832 I've heard that theory before, that life is an outcome that naturally extends from energy dissipation/entropy maximization, although for me it's still mostly theory. I don't think we've gathered enough information to know yet whether life is as prevalent in the universe as that theory would suggest. But it is a fascinating idea though.
Math is so incredible. People just study a phenomenon and it reveals a language that describes the world in ways we didn't know of before. Wonder what fields of maths exist that we have yet to study
Fun fact: making sure you're doing a square knot instead of a granny knot is also very important in surgery. They are taught to alternate the way they secure off the suture.
My understanding is the suture knot is similar to a square knot but with an additional 'under' at the first step so right over left and under and under, left over right and under. I read it was supposed to reduce scaring but looking how it performs it appears to lift the added knot mass off the surface perhaps making for easier removal. I suspect surgeons use a granny suture knot based on biological sex and age under... just for giggles.
@@tumekeehoa3121 The start of the 'surgeon's knot' is three twists so that it holds tension better while we get the next layer in place- or at least that was the explanation given to me. There's a lot of different types and thickness of suture material, but it's common for it to be smooth and springy, and you need to make sure it knots tightly around the blood vessel and not as a pointless loop with no tension.
Just to avoid potential confusion for those folks moving to a squar knot for tying their shoes, its actually isnt just clockwise or counter clock wise, it depends on how the first overhand knot you make is tied, whether its the left side going over then under or vice versa. It also depends on if you make the loop on the left or right side. So check to look if it actually appears like a squar knot to confirm.
Bingo! It was so frustrating the Derick didn't say this. Now people that were tying their shoes correctly may end up listening to his advice and getting granny's.
@repentandbelieveinJesusChrist2this literally has nothing to do with religion nor does it deny it. In fact, it's kind of like admiring the beautiful universe God created and its intricacies.
When it comes to avoiding knots in headphones, my easy way that I have used for years is to simply not allow the endpoints into the storage case. If it is a zippered pouch, just leave the earbuds and the plug hanging outside the zipper. You can just grab the entire length of cable and shove it in the zipper pouch as a massive wad if you want, just leave the ends outside the zipper, and you will have no knots. Same story if you put them in your pocket. Just leave the ends sticking out of the pocket and you get no knots.
You sir are legendary. I read ur comment when this video reach exactly 3:46 minutes. I tried this today when you post this, an entire day I follow ur instructions (I have a retro tape walkman) trying to have a walk the entire day in my town, visiting a caffe, meeting friends, work outside, bringing 4 cassette album from 2 legendary musician Daft Punk and Santana. And not a single accident of tangled knots occurred. Bless you for ur wisdom. Now I can resuming to watch this video to completion. Much love from Indonesia. 🎉🎉
I was going to comment something like "imagine not using wireless" But although I myself use wireless, even as the annoying internet troll that I often am, I just simply cannot deny the absolute genius of this.
My great aunt (Mary Gertrude haseman) was one of the founders of knot theory (after tait) (incidently her brother got his ph.d under Hilbert). She worked out a subset of 12 crossings in the early 1900w. After ph.d she became a housewife and knots were ignored until around the 80s mostly
Do you ever have Impostor Syndrome or feel pressure to do better or on par with your ancestors? Very cool family tree you've got there but I know I would've felt depressed trying to live up to it.
This video changed my life. I don’t have to double knot my shoes now. I tied them the other way and they didn’t come undone all 12 hours running around at work. Amazing.
Knot theory, and particularly the Alexander- and Jones polynomials, were my first foray into mathematics research in 2013. So happy to see algebraic topology getting a spotlight on your channel, and the incredible applications!
Oh man, I got excited when Conway showed up. It's fascinating every where and every time he shows up. In this one he just pops in, does something in an afternoon that no one had done before and then we don't hear from him anymore. I'm very grateful for all the footage we have of him.
We need a follow-up video on what all this knot theory means regarding conquering the practical, real-world, problem of detangling a mess of wire/rope/line the most efficient way possible.
My initial reaction was "So what? I wear slip-on shoes.". I then became slightly interested by the mathematics underlying knot theory and ended up floored by the practical applications of this area of study. An excellent video as always.
0:00 Intro 0:24 Knot Theory 1:17 What is a knot? 3:40 Knot equivalence problem 4:32 Other famous knots in history 5:20 Vortex theory of the atom 8:25 On Knots paper (the first seven order of knottiness) 9:52 Reidemeister Moves 10:51 Haken’s Unknot Theorem (and upper bound and crossing number) 13:01 Knot invariant 14:13 Tricolorability 16:37 p-colorability (and polynomials) 21:34 Perko pair 22:32 n-crossings knots 24:21 Molecular knots 28:31 How You Should Knot Your Shoes :) 29:40 Doug Smith & Dorian Raymer experiments 32:00 Knot Theory's Potential 33:15 Outro (and video sponsor Brilliant)
This is why everyone should have a copy of the Ashley Book of Knots in their library. Study 'marlinspike seamanship' for even a few days, and you quickly see how important knots are, and how seemingly complex knots are often just simple knots built upon each other. Clifford Ashley was documenting knots before knots were cool!
20:50 In grad school I took a class with Jozef Przytycki on Graph Theory and Knots, and he was also on my oral exam committee. It's so cool to see him pop up in a Veritasium video! This has to be one of the best, if not THE best, video on knot theory on TH-cam. Amazing job as always, Veritasium!
In southern India, everyday women create knot diagrams called 'Kolam' in their front porches . The more complicated the knotting the more skilled the person drawing it. This video is when I realized that many such Kolams are actually super complicated, challenging to create, un-knots! So cool to know there is a whole sub branch of math around this! Unknowingly it sounds like these women have been practicing Reidemeister moves on a daily basis in attempts to create ever more complicated knot diagrams! And instead of the p-colourability, these Kolams care more about the areas between the loops which are denoted by simple points. The points are actually laid out first and the knot emerges as a line diagram around them .
That's super interesting. Now I have to go read more about what those women are doing and what they know. But also, the description in your last paragraph sounds just like how my knot theory research represents the knots with graphs (graph theory kind), nodes representing the loops and the lines represent crossings. I wouldn't be surprised if someone in math academia lifted the ideas from the Kolams.
Another way to prevent cords from tangling is to loop them like normal, but leave enough uncoiled to then feed it through the middle, out around the outside, through the middle, over and over, making sure to space each loop so all of the coiled cord is wrapped with that extra length you started with. I do this for computer cable management, headphones wires, chargers, etc… it has never failed me and it puts less strain on the wire than Veritasium’s stiffening method
As a knitter and never heard of this is so fascinating. As someone who hated math but use basic arithmetic for knitting; but this field of math wants me advanced my math knowledge and thinking.
I’ve been a rock climber for over five years and this was a great video. I’ve spent a lot of time wondering about knot mechanics. and you spent a lot of time explaining knots, and I really appreciate that. I learned a lot.
when I was six and extremely bored, I had a habit of tying hair bands into as many knot combinations as I could think of. I also realized that they behaved differently than if I tied a knot with a normal string, and I've always been curious to find out why. This was super informative and kept my attention the whole way through, great video!
I was very surprised when Derek, a scientist, missed a very important piece of the shoe tying equation. You would only tie your shoes (bows) clockwise if you first tied the base knot counter clockwise, otherwise you are just tying a "lefthanded" granny knot. Clockwise or counter clockwise makes no difference, a proper knot involves one of each. Eg. left over right + right over left = good knot. You can't just finish correctly if you've started wrong in the first place.
I knew the difference between a granny knot and a square knot as a kid. In college, a girlfriend pointed out that I was tying my shoes with a granny knot - that was a real blow to my manhood. I couldn’t seem to change how I tied the top knot, but it was relatively easy to change the bottom knot and now I try my shoes with a square knot even though I did not change how I actually tie the bunny ear part.
@@faroukhashim3862except that's only clearer if everyone else assumes the same starting position. And that can be pretty bad communication if you don't make the starting position clear A week or so after people watch this, they're not going to remember the details of the diagrams or the animations, but they'll remember that he said that clockwise knots stay together better than anticlockwise knots. That's not a great lesson to teach, IMHO, not without the clarification
As a budding molecular biologist, I know think that it is essential and indeed impossible to venture into the field without having a thorough grasp of knot theory first. Thanks Veritasium, truly eye-opening.
these videos are cool because at the beginning i understand nothing and by the end i still understand nothing but it's cool that there are people that do.
I seriously love this channel, seems like these videos take a LOT of effort to build but the quality and completeness and depth is unmatched all in one place.
The fix for turning your granny knots into reef knots is really simple. When you start to tie your shoes, pay attention to which lace you place over the other. This is a habitual action and people do it the same way every time. If your habit is to start by placing your left lace over the right, simply reverse that step, go right over left instead. Then just finish tying your knot the same way you always do. Your hopeless granny knot will become a perfect reel knot. It may take a few times of consciously reversing that initial step, but it will quickly become your new habit and your shoes will never come untied again.
I'm not a matematician with fine expertise on knots... but i know something about storage of audio matherial. I could clearly hear those hearbud's chord screaming for mercy! The first thing you want to avoid is twisting cables, that's why it is most commonly stored in circular or "8" shape takeing care to gently twist it between your finger while coiling up so the core is kept straight. To prevent further mess there are chord holders or just use some tape. Confineing in a restricted area as a bag is a good advice anyway.
Tip to get used to tying shoe laces stronger: don't change the complex movement that finishes the tying, but the first simple knot. The effect is the same Happy side effect of the secure knot is that the loops stay perfectly perpendicular to the shoe so it's also prettier
The added advantage is that when you untie your shoe laces, as long as they're not too short, the 1st knot can often remain tied for next time, so you don't have to remember to tie the 1st part 'backwards' relative to what you've spent all your life doing - just tie the 2nd part which requires the more complex movement as you've always done.
@@richardjones38 sadly my laces are short(or I have to undo them in hiking boots) but after a short amount of time, even though the first knot still feels "backwards" I do it without thinking it
I find the easiest way to tie a square knot in my shoe laces is to use the "bunny ears" method, where the second knot is just an overhand knot of two loops. Then, tying your shoes is just two overhand knots. Make sure to tie the two overhand knots in opposite directions, and you've got your square knot.
@@manolismarinakis8444 I spent a couple of months trying to teach myself to tie the 2nd part of the knot 'backwards', but still regularly kept tying it the way I always have. This was when wearing boots in the winter, so I had to re-tie both parts each time. Then when the summer came around and I wore lighter shoes I noticed I often left the 1st part tied without even thinking. I guess my Vans just had the right length laces, so reversing the 1st part if the knot effectively 'lasts longer' between my forgetting and tying it the way I've always done. Once I wear boots in the winter again it'll be interesting to see how often I forget and tie it the old way!
As a contractor and a math enthusiast, I quickly learned that isolating the two free ends of a long extension cord would make any wrapping process into an unknot. Many of us know the braid, which I believe is a type of sailor’s way of keeping a rope from tangling. I also knew IT people who’d use similar strategies for long cat-5 cables. It would be interesting to me to see how tradespeople and sailors had long ago “discovered” these theories by trial and error. Incidentally, I’ve tied my shoes with a square knot since I was a teenager, and my young kids know the difference between the granny and square. When they try to teach their friends they’re usually met with blank stares. 😂
Great video as usual from this channel, but sometimes he does make some more controversial proposals. His idea at 31:23 of twisting the headphone cables are kind weird to me. It is the last thing i would do at work to avoid knots in a electrical cable. Just imagine how much the wires inside the cable will suffer with everyday twist and untwist. The control of the ends of the cable and a good "snug space" to keep it should be the main priorities, to which each of us will add their own learned experience.
@@estranhokonstathe practicality within certain contexts is questionable when other properties need to be preserved, like stress on an electrical cable, nonetheless, whatever works with the minimal applied work/force is the definition of mastery in a given domain. Some task may require these higher level of application, so judge each task as individual and use as little skill as required to achieve the desired outcome. A simple metaphor I use is Jimi Hendrix's guitar playing style, effect the maximum amount of change, with the minimum work required, the graph at the end of the video (the knots in a box experiment) outlines a representation of the point of diminishing returns.
@@Saturn_Enslaveda rudimentary explanation I believe is required at this point in order for most of the others to be able to keep up and utilize the information with which you were projecting for them to necessarily come up with the plan for them to have the same kind of outcome that is beneficial to themselves that previously wasn't necessarily beneficial to them based on the Simplicity of the explanation of such programming however there are ones that will be able to interpret to them later down the road I'm sure so hopefully the commentary at this point is in a complete loss but will be remembered and click in someday.
Huh in the Boy Scouts around here every kid learns and teaches the difference between square and granny knots at the most basic levels. It's all over the literature and even symbology in scouts, I thought it was pretty universal. Although, turns out that tying the 'sheet bend' is much stronger in many circumstances, there are some where it can not be used and the square knot can still shine.
The research for your videos must be absolutely insane! Not to mention figuring out and understand those scientific papers to really break it down for us
31:24 For every twist you introduce, you also introduce forces that will eventually snap the thin conductor inside. That's why you should not coil an electrical cable, or a braided climbing rope, like you coil a 3- or 4-strand rope. For your headphones, just doubling and redoubling them to a convenient length and then putting a clothespeg on them is just as efficient and gives you more use from them before you break them. 😊
A method I use is to wind my headphones in a figure eight. I don't remember where I heard about this, but since doing this, I can carry around my headphones in one of my backpack pockets without them getting tangled.
Or you can learn to properly coil cables, something pretty much every audio technician get taught. By introducing opposing twists, the cable doesn’t accumulate axial torque. It saves the cable from trouble and it greatly reduces knotting, since most of it in headphones is from the coil twisting, not the ends going through the loop.
I never knew knots would be so complicated and diverse in use! It is great to learn about their different uses and I am excited to see what the future could bring for knots!
A buddy of mine is studying knots in projective spaces, called like “knots in the shadow world”; he explained that you can’t necessarily get a well defined projection onto the plane for them (over/under crossings could be the same so you don’t really get a “drawing” of the knot in way that works well).
Does this have anything to do with virtual knot theory? There's similar things going on where they draw knots on non-simply connected surfaces of genus 1+2, which can't be "translated" to the plane without virtual crossings.
OMG it is uncredible that something so "common" like a knot would help us to develop ENORMOUS changes in science and technology like that. That's the reason I love science.
It's not whether you counter clockwise or clockwise tie the knot. It depends on the first step and whatever way you cross the strings, it must be the opposite in the second step.
@@YoeyYutchExactly what I did in my very late twenties after realising why my shoelaces didn’t want to stay in place across the shoe. ("Have I been doing it wrong for twenty years? Yes, I have.") When you learn to tie your shoes, it's going to be mostly random if you happen to start doing it wrong or not.
I've started to lace my shoes like this ~2 years ago when I realized its symetry and aesthetism, but never paid attention to its tightness. Thank you for this great video, as always !
I really liked how this video shows the benefits of "knowledge for knowledge's sake". That something with no obvious practical application can be worked on for centuries, and suddenly a breakthrough happens that turns the previously "useless" knowledge into something potentially world changing.
This is amazing. I am extremely happy, that this video found me today. I've loved knots since childhood. I was tieing knots and drawing them in my album for hours, I've tried to compare and replicate them. Is there any books abouts knots? I really want to explore its mathematic and scientific side
My all-time favorite knot to tie is the trucker's knot. My dad showed me how to form 2 trucker's knots in series when a lot of tension was needed over a long pull length. It's effortless to tie. It secures a load, and it can easily be untied even after great tensions are applied. One of my favorite books about knots is The Rigger's Apprentice by Brion Toss. It contains lots of useful knots and nice illustrations too.
This is such an inspiring example of the value of pure science and long-term benefits of pure intellectual curiosity. I wish this kind of story could land in the hearts of more people. The survival of our great grandchildren's civilization may depend on supporting today what seems to be pointless navel gazing.
FOR TYING SHOE LACES: You don't need to loop the other way for more security. You can just go around twice. Loop around twice. Not double knotting, but looping twice. It has more friction.
The shoes tying direction changes depending on how you tie the first half of the knot. The upper one must be a different direction than the lower one to form a square knot. This is one of the first things even amateur freshwater sailors learn - you do not want the rigging that holds your big strong sails and heavy pipes they are attached to unwinding because you tied a granny knot. Besides that great video!
Figured I'd look to see if anyone else picked up on this. As someone who always went clockwise, [I never learned the "bunny ears" method either] I never realized that it was supposed to be "better". But as it turned out, I had to slow down and pay attention to notice that I also instinctively do the first knot "backwards", meaning I usually just do a mirror of his granny knot. Probably [k]not going to be able to break that muscle memory after all these years of doing it one way, but it's interesting to note that doing the second knot anti-clockwise might help my boot technique. [which is usually just using longer laces and tying a third reversed knot anyway]
Color me highly skeptical of the idea that the square knot is "better" than the granny knot. The reef knot or square knot has several bad properties, including that it can capsize and separate (come untied spontaneously, by capsizing to a cow knot and a straight section), it doesn't hold well with different size or stiff ropes (many knots have this unfortunate property). And it's absolutely a terrible knot when used as a bend (to tie two ropes together).
@@eyesoars9212 Regardless of the square knot being bad at most non-shoe jobs, that doesn't mean another knot can't be even worse. In fact there are probably hundreds of knots you could theoretically tie in shoelaces that would be even worse than even the granny knot in one way or another. The granny knot is definitely worse; if I ever happen to tie the bottom half of a shoelace knot backwards then the top (which I always tie in the same direction out of habit) will come undone potentially as often as once every couple minutes, regardless of how tightly I tie it, until I fully untie and retie the bottom half, after which the knot often lasts the entire day. The difference in symmetry makes the difference between a stable knot and a self-loosening knot and this is a well-known effect. In fact before I knew about the granny knot, I would fairly often tie my left shoe as a granny knot and my right shoe as a square knot, and for many years I wondered why one shoe came untied so much more often than the other. This stopped after I learned about the difference and switched to using the Ian knot (actually a method, it's still the same knot) which is slightly more comfortable to tie as a square knot and that helps a bit to remember. You can also tell the difference because the two twists being in the same direction tends to cause the granny knot to take on an overall twist, with the free ends oriented perpendicular instead of in-line. And of course shoes are a very specific application of knots, and other than capsizing the problems you named simply don't matter. Unless I suppose maybe you glued two different sizes of highly stiff cord to the different sides of your shoes and tie a zeppelin bend to hold them together, instead of using a single flexible lace with a shoelace knot like everyone else.
@Am1kke Thank you for pointing this out. When he was explaining it, I was like "Derek was obviously never in the Scouts! LMAO" The clockwise/counter-clockwise distinction doesn't make any sense without saying what direction the first crossing was in. Another annoyance with this is how wrong the thumbnail is. It shows a loop (the UN-KNOT) and says that it's a KNOT and then shows a standard "pretzel" shape and says that it is NOT a knot, even though it is really a trefoil with one end cut (or not taped together). It's like whoever created the thumbnail either didn't understand what the video was about or just deliberately showed misleading and incorrect information in order to get people to click the video...
Your shoelace knot also depends on the orientation of the first crossing. I start in the opposite way that you do for the simple reason that the "granny knot shoelace" will sit paralell to your shoe while the sailors knot sits perpendicular. Good to know its also stronger :)
Dude everything aside, its from a wannabe physicist or a human who is just curious how things work… your explanation and videos are so much intriguing and interesting even for a drunk person like me right now.. i love your videos keep posting such videos. I think you should work with someone who isnt aware of everything but wants to ask so many questions on how things work and you explaining things to them and this would even lead to a discovery or a disaster but i think its still worth it!
Derek got it wrong in the very beginning. The two ways of tying your shoe don’t have to do with clockwise or counterclockwise. It has to do with if you do the second crossing in the same direction or not. So like if you did the first crossing clockwise, do the loop part counter clockwise to keep the knot balanced and torques low. You can also do the first crossing counter clockwise if you want instead, as long as you do the opposite on the loop part. It will be just as strong.
I caught this just before bed and ended up dreaming about the 3 types of knots. I’m now a knot theory devotee. In an ocean of mindless content this channel is so refreshing! Hands down one the best TH-camrs. Thanks so much!!
Thank you, Derek and the Veritasium team, for making 'exotic' mathematical topics so clear, interesting, and engaging. Your videos on knot theory and invariants, as well as the previous one on p-adic numbers, are truly enlightening.
The reef knot is one of the easiest knots to untie one handed. Grabbing one end and giving it a sharp jerk turns the other end into a hitch which slides off thestanding end. It's why it's used to reef sails; you can keep to the old adage: one hand for the ship, the other for you.
The way I have always been keeping headphones/cables from knotting is this: I double them like you showed, but instead of then coiling them, I just keep doubling them over until they are as compact as I want. I think the reason this works as well as it does is that there are basically no loops being made for the free ends to go through and form a knot. Yes, this doesn't hold them together, but that is hardly ever a problem, because even if they do unwrap and get tossed around, usually do not get get tangled. I've tested this a bit before commenting here, and it definitely works. Another thing I noticed is that when cables are looped around like that, more often than not, it's the loops going through each other that causes the tangling, not just the free ends.
A way I've learned: grab one end, and then throw up rocker horns (index finger and pinky raised). Wrap the cord in a figure 8 between those two fingers. Finish by taking the end in your palm and circling the middle a few times. Somehow they never tangle.
I also use your successive doubling technique, but only until the step BEFORE where the multiple strands are too short and bulky to form a simple overhand knot. The eye-ometer serves here. Then I tie an overhand knot with the multistrands. Keeping this knot confined in some way, as the vid suggests, also helps. It depends on the stiffness of the cable.
Yachtsman here. If you have the tail of a sheet coming out of a block or winch, you never "coil" it into loops. That inevitably tangles if you disturb the coil or throw the coil away behind you as you loose the block. Instead you lay it in a figure 8 , either over the block or a hook. Never bothered to check WHY, but when you pick up the figure 8 and throw it out to run the sheet through the block, it CAN NOT tangle.
@@uncletiggermclaren7592 That is because the twists of each side of the eight are in opposite directions, and when you throw it out they cancel. I have a method of coiling cable or rope in a circle but with opposite twists in alternating coils, but it is too hard to describe in words. It works well with heavier stuff like mains extension leads.
Working as a sound tech we deal with very long XLR cables, usually around 20 to 50 feet but sometimes much longer. Over 100 feet we use spools, but lower than that we have to coil them up by hand a specific way, we can't just leave them uncoiled and confined as you suggest. We also have to straighten them out as we coil otherwise they'll twist and want to spring back forming sloppy coils. We take the lose end and wrap it around the entire coil and finish it off with a simple trefoil to keep it in place. Once that's done we stack them into confided bins, but they not always full leaving space and sometimes the trefoil can come undone and cause knots. Thanks to this video I'm going to try and do the opposing trefoil thing and see if that works better. Math is improving my life lol.
I once gave a talk about the basics of knot theory to colleague math students who previously knew nothing about them, and it was my best received talk ever. Knots are fun.
For everyone that has their shoelaces untie throughout the day... I can't recommend enough learning to turn your knot into the square knot. It'll feel weird at first, but will change everything. The easiest way to do this is to switch the direction of the first tie to the opposite way. So, if you feed the end one way on the first tie, instead switch it to the mirrored version by feeding the opposite end through using mirrored hand motions. Then, tie your normal second knot because that is the more complex one.
I posted virtually the same comment before seeing yours. Derek didn't really make clear that the issue occurs between the "substrate" and the loopy part.
i love that I never know in which rabbit hole I am going to fall into when I watch your videos but it`s always incredibly fascinating! Thank you for your valuable content!
Next thing you know, you're studying Marlinspike Seamanship and ordering your very own copy of the Ashley Book of Knots. It's a deep rabbit hole, indeed!
@threeriversforge1997 i have a laminated card with 40 knots drawn on it, never thought I'd see the Marlinspike anywhere else. Also i like to flex on younger boy scouts by tying sheepshanks behind my back
I've always found untying knots of my ear phones fun and relaxing, I honestly miss doing it since we have bluetooth earphones now. This is just soooo facinating! I never thought I'd actually love something about Mathematics! Absolutely loved this!
I was in telecom and after pulling miles of cat5 cable on a single job, you got an absolute mess at the end. I was the only person that could figure out how to untie that crap. I wasn't sure how I could do it, I just sort of had a feeling.
Fun Fact: So when detangling yarn many people tend to pass one (or both) of the ends under loops they seem to be tangled in but most of the time the tangling is an unknot. so the better way is to first try to shake and carefully loosen up everything to untangle it into the unknot it is and resort to the passing under loops strategie, only when it is so tangled that you cannot loosen it up properly or loosening it up / shaking it a bit, doesn't give you any progress.
This reminds me of getting the mooring lines sorted out last minute on a sailing trip and the skipper shouting “ pull the loops apart don’t pull the ends!”
I can't help but watch every one of your videos... you're like the math version of watching a run clearner clean a rug. I don't understand how you do it, but I love the process.
Certainly one of the best animations on this topic out there. Great work Derek & Team! Shall these videos be forever available for humans who seek knowledge.
What a wonderful video! I gained tremendous respect for these people who worked just for their curiosity, when they could be doing the equivalent of watching Netflix on their couch and eating snacks. It's because if their tireless efforts that we enjoy the discoveries and treatments that we do today. This is why going out of your boundaries and discovering the unknown matters, this is why exploring the cosmos and sending probes to the moon, sun, Mars, and beyond matters, even for developing countries. Well done Derek and team!! 👏
Yes but a lot of these Victorian thinkers had independent income so could do this full time. But I was intrigued that Tait complained he didn't have enough leisure time (and thanks Derek - I appreciate the pronunciation from British perspective). I wonder what he was doing for the rest of the time!
@@roginkresearchers like these dont earn enough for the work they put in, because their work rarely IMMEDIATELY becomes productive. In this capitalistic society, if ur work is not immediately productive, ur gunna struggle to find someone to pay u. Professors get by teaching students but for how many hours they work, their pay isnt that great. Its definitely a passion job.
@@vwlz8637 True the title 'professor' isn't quite as prestigious as it once was. Of course it depends on which university employs you, and your discipline. Sure, the humble PhD student has to scrape by, but when you get to Prof status, in most Western universities you will have a comfortable salary, a job for life, and generous pension when you retire. Regardless, that has nothing to do with these Victorian thinkers. They weren't employed by universities - or anyone else. They mostly had property and earned income from that.
@@vwlz8637 oh yeh, communist societies I'm sure are waaaayyy more hospitable to mathematicians working on things with no immediate application. funny how everyone rags on how capitalism doesn't allow for this sort of thing, and yet pretty much all great mathematicians come from capitalist societies. clearly it isn't as inhospitable as you think it is.
Good video. As a former rescue squad member, I think a video explaining the mechanical differences and advantages/disadvantages of each knot would be rather interesting. Also: if you have p coloration, you might want to see your doctor.
I’ve had an (unspoken) interest in knot-theory for a good couple of years, and not to discredit or mock anyone, but i’m so glad that someone ”bigger” finally brought this subject forward so i don’t feel quite so stupid for having an interest in this 😂😅❤
I've always loved knot theory! I have never fully understood how it works, but I love the idea of thinking so deeply about things many people find so trivial, while it can be so interesting!
@31:36 I stiffened knowing the mistake you were about to broadcast as good practice... never do this with any type of cable, but especially cable that contains un-braided stranded wire Ie. Earbuds 3 destructive actions take place when you twist stranded wire onto itself, or even wrapped around a center bobbin. Ie. An extension cord spooled around your hand and elbow. 1. The individual wires that make up stranded wire are equal in length (for many reasons) but as you twist the cable, each individual wire inside the protective insulator is rotating longitudinally, and when you un-twist your cable the inner wires do not completely return to their factory position, so over time they begin to bunch around each other tighter and tighter. since the wires closest to the outside are effectively getting shorter faster, having a farther distance to move with each rotation, they will begin to knot inside the cable first, snapping away from the ends while the inner wire continue to become stiffer, and exerting force on the cable ends in the opposite direction as the outer wires. After a while you will notice that even when you spool out the cable it begins to look wavy as if it had been curled. Since there is less wire making contact with each snapped strand, the resistance slow rises at each end of the cable dropping the voltage... In the case of extension cords you will notice that this makes the plug act like a heating element. With earbuds you will notice that over time the volume decreases, until shortly before one side stops working they only operate at 25%-50% of original volume. You can actually measure it, check output when new, then twist and untwist them 180 times @6 months worth of simulated use, and measure the difference. 2. Friction, you ever had to cut a wire or piece of metal in half, and had only your hands, you folded it several times at a certain point... well a twist is essentially a rotational fold and each crossing point is a fold location since copper is a soft metal, each time you force one side of wire to cover a longer distance than the other side what happens is the two opposing forces pinch the atoms together at that spot forcing them to rub against each other with much more force than they would see during normal use. To figure out how much farther a side has to pinch and stretch to accomplish a twist, take the diameter of the wire then find the circumference for 180 degrees, now using that distance as your radius, double it to find the diameter of the twisted wire, now find the circumference using that diameter for 180 degrees and that is the distance of travel between the shortest side, and longest side. 3. With stranded wires, the insulation is usually not as tough as cable with less strands of thicker gauge, simply for the same reason we use stranded wire in applications where we want the cable to remain easily pliable. So the insulation is easier to damage inside the cable after repeated use, and the insulation be it enamel for earbuds or pliable vinyl in romex, with enough twist, you can find yourself with a cable that is in a permanent state of "dead short" and the big danger being it quickly melts the conductor ending the short, so it gets set aside, and you forget or a coworker uses the cord, plug it in making it live, the rolls the cord out loop by loop and when they get to the place where the damage is, the movement causes their hand to complete the circuit at the damaged location. I tell people all the time the two best ways two best ways to store any cable is do not twist or loop decide on a convenient length and fold the cord back and forth like an accordion then pinch the centers together and tie with a piece of scrap wire or bread tie depending on size of cable. The second way is essentially the same as the first, but instead of a back and forth stacking of the cable, start a spiral on a flat surface with then roll it around itself so that it has no rotation perpendicular to the length like it does when looping, now continue that rolling, until you have four to five passes on the flat spiral. Now start your next roll on top of the first roll at the same size make the same number of passes you did on the first spiral layer, repeat until you have a roll of cord 4-5 passes wide and about the same number of layers high. you will almost certainly be left with a cable end on each side or both ends meeting at same place. You can now place a tie around the finished coil. I almost always use two so that it retains its shape for storage... It I am unclear you can visualize it as being rolled the same way windings on a transformer are.
31:30 Problem with that is twisting will cause the coaxial cable to short out. Never twist a cable or coil it extremely tightly. Honestly, the best way is similar to what you said earlier - use a small container, but also loosely fold the cable back and forth, and then use a twist tie or similar to keep the coiled portion closed enough so the ends cannot find their way through in storage.
Exactly, I was going to suggest that to my dad who still uses wired headphones but then remembered disadvantages from co-axial cables from my Computer network class. 😅
@@chetanuniyal3428 To be fair, if it was a rope or a necklace or something, this would be ideal (barring screwing up the links in the necklace or what not).
@@Qermaq yeah for a rope it would be perfect, Not so much for the necklace though, it's metal so too rigid and considering the quality of jewelery these days, the locks can snap anytime.
@@chetanuniyal3428 Right it absolutely depends on how the necklace is constructed. If it's not chain, or if it's a fine enough linkage, it would be ok. Otherwise you risk tangling and possibly warping the links.
Thompson, Lord Kelvin's thinking on knots and atoms feels a bit like string theory. This is a beautiful subject! Thank you for making it approachable to the rest of us. Excellent work as always.
Correct. When tying the square knot, a good practical method is to choose one of the strands to be your working end. Now, if this working end goes over (under) in the first overhand knot, then it must also go over (under) in the second overhand knot. After the knot is tied, the two strands are coming out together from the "side loops", that is, both go under on one side and both go over on the opposite side. Obviously, this is much harder to put into words then to just show it with a bit of rope 😅
@@clayz1you've said the same as the guy in the video, which is wrong. The first knot will give you two ends, obviously, one pointing towards you and the other pointing the other way. After that knot you have to keep those ends on the same side, moving them in a paralel way towards the center, without crossing the first knot. Then you only go over the first knot when you tie your second knot, and you've got a perfect, beautiful square knot
@@clayz1 you can tie a square knot in two ways: starting left over right, ending right over left is one way. Starting right over left, ending left over right is the other way and results in the mirror image of the first way. One way is clockwise, the other way is counter clockwise around the loop. The same is true for granny knots, only the first and second trefoil are both in the same direction in stead of different directions.
I bet every time knot theorists get together for a conference they'll be sporting some of the most impressive tie knots you'll see. I'd hope there's a little competition at each conference to identify the most practical, creative and/or aesthetic tie knot
I'm only halfway through watching, but I'd love to see a follow-up about common knots and practicality. I'm mostly intrigued about friction and benefits to knots. I assume many fishing knots benefit almost exclusively from friction, but it's a very significant force on their effectiveness.
It's amazing how mathematicians are able to take such abstract concepts like knots and mathematically describe them such that you can perform operations on them and write code to discover them.
At the end of the day everything is mathematics. Reality itself is just math happening so it makes sense that anything even knots can be represented mathematically.
@@vectoralphaSecYes of course, but being able to take what you observe and describe it rigorously with mathematics is not trivial at all. Then taking it to a point where you can write algorithms, and proofs is even harder.
Working with paracord while i watch this. Ive been so obsessed with learning new knots lately so this vid hits the spot, and may explain why people like me find them so fascinating.
Have any lingering questions about knots? Want to hear more knot stories that didn’t make the cut? Derek and Emily (the writer/director of this video) will be hosting a livestream for our Patreons next week! Join our Patreon for more info and a link to the stream - ve42.co/VePatreon
HI DEREK
🎉
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
Veritasium inspires me.. My parents said if i get 50K followers They'd buy me a professional camera for recording..begging u guys , literally
Begging...
Why is it called a unknot instead of a notknot?
Veritasium's graphic designer would have become a physicist by now. It must take a lot of understanding on their part to learn the concept first and then visualize how to demonstrate it. It is just mind-blowing.
And the animator too
This
They might even be the same person
@@dburitto the face you see is Derek Muller.
the animator is Fabio Albertelli, he also does graphical design (so probably also doing the graphical design for the videos).
don't think they are the same person.
Fabio Albertelli is well educated in science so he can work with the knowledge he already posseses.
It's not _that_ complicated though...
I'm in awe at someone having the patience and skill to visually tie thousands of knots and distinguish duplicates. Thanks for another great story wonderfully told.
It is truly mind numbing stuff. Source: I tried to figure it all out a few decades ago.
My headphone wires form the most complicated knot in the world
I did not expect a video about Knots to be that interesting.
@@cartoonsinkannada1186 especially if you put them in your pocket/on your table un-knotted
And all that work without having an aim or purpose in mind at first. Just to broaden humanity's knowledge.
As a Ph.D. student in algebraic topology, I am glad to see that different areas of topology are finally getting the attention they deserve.
So you deal with stuff like mobious strips, klein bottles and 4-D toruses
Very cool! I'm a graduate student in math learning algebraic topology. I'm working through Hatcher's right now. Its interesting enough right now, so we'll see if I end up focusing on algebraic topology.
As a non-Ph. D student in anything, topology and knot theory is, and has been, a very popular subject on science and mathematics themed channels for a very long time. It isn't "finally" getting the attention the subject deserves - you have only just now discovered it, apparently. Those are two very different situations.
@@watcherofwatchers I have not "just now discovered knot theory", however, I was merely trying to say that I am happy people are presenting it to the general public so more people can learn about these fields of mathematics.
@@watcherofwatchersAs a non-phd student in anything, you should let them talk
I don’t think I’ve ever watched a video that I completely understood while, at the same time, I had no idea what you were talking about. It’s like a miracle. Fascinating subject!
Def check out Hannah Fry's stuff!
Although I wouldn't in a hundred years choose to study knots, it never fails to inspire me how people take up these causes, pushing esoteric fields forward for nothing more than a pure love of the game until eventually their discoveries can be tied to other fields to make important scientific advances. Science really is humanities most collaborative sport.
The wonders of a deterministic universe
People think its intelligent design, but it actually is thermodynamics, entropy, and life trying a better hand at making more "complex life" for energy dissipation
@@anthonymartial2832 I've heard that theory before, that life is an outcome that naturally extends from energy dissipation/entropy maximization, although for me it's still mostly theory. I don't think we've gathered enough information to know yet whether life is as prevalent in the universe as that theory would suggest. But it is a fascinating idea though.
@@anthonymartial2832what if thermodynamics is by design?
@@anthonymartial2832 Them's fightin' words, podnuh.
@persona2grata why knot study knots?
My earphones discover all 352,152,252 knots half a second after entering my pocket.
lmao
Yes, but if you dig deeper, you'll find its just a simple unknot which is proving to be elusive to untangle.
@@supertubemindway to ruin the joke
@@idkwhattoputhere0770In a way they made the joke funnier.
blud is way too mad@@idkwhattoputhere0770
Math is so incredible. People just study a phenomenon and it reveals a language that describes the world in ways we didn't know of before. Wonder what fields of maths exist that we have yet to study
I wonder if there is any phenomenon which just gives random meaningless solutions the closer you study it
Every natural phenomenon can be reduced to mathematical precision. Plato and his world of Ideas are the true foundation of the world. 💯
@@THE-ONE-MXy el caos es un cuento chino?
Maths is all definitions so fields are potentially infinite. Knots being an actually studied one is especially tied to its relevance in physics.
@@sledgehammered1765 chaos theory
The mathematicians missed the opportunity to name it 'Notknot'.
Who's there
The unknot
@@P3TEY the not so knot
😂ya
@@P3TEY The unknot who?
*italian voice* the ona two tri
Fun fact: making sure you're doing a square knot instead of a granny knot is also very important in surgery. They are taught to alternate the way they secure off the suture.
I wonder if surgeons are better at tying their shoes.
My understanding is the suture knot is similar to a square knot but with an additional 'under' at the first step so right over left and under and under, left over right and under. I read it was supposed to reduce scaring but looking how it performs it appears to lift the added knot mass off the surface perhaps making for easier removal. I suspect surgeons use a granny suture knot based on biological sex and age under... just for giggles.
@@tumekeehoa3121
The start of the 'surgeon's knot' is three twists so that it holds tension better while we get the next layer in place- or at least that was the explanation given to me. There's a lot of different types and thickness of suture material, but it's common for it to be smooth and springy, and you need to make sure it knots tightly around the blood vessel and not as a pointless loop with no tension.
Are you a Boy Scout too?
just untangled it not without breaking it as much as you can until you can’t
Derek has been killing it with the math videos lately
@repentandbelieveinJesusChrist2😂
@repentandbelieveinJesusChrist2repent for your illogical blasphemy and math will save your soul!
Abacus 2:77,232,917-1
@repentandbelieveinJesusChrist2 AMEN!
Just to avoid potential confusion for those folks moving to a squar knot for tying their shoes, its actually isnt just clockwise or counter clock wise, it depends on how the first overhand knot you make is tied, whether its the left side going over then under or vice versa. It also depends on if you make the loop on the left or right side. So check to look if it actually appears like a squar knot to confirm.
Bingo! It was so frustrating the Derick didn't say this. Now people that were tying their shoes correctly may end up listening to his advice and getting granny's.
I cringed every time :(
I'm left-handed, and was congratulating myself because my second knot was correct, then realized that my first wasn't. I have a reverse granny!
I find the simplest way to remember is to the first half "forwards" and the second half "backwards." a/k/a right-over-left, then left-over-right.
THIS!
0:51 “it’s knot pure math”
I’m so glad that veritasium is making more and more math videos.
Repent to these nuts in your mouth@repentandbelieveinJesusChrist2
@repentandbelieveinJesusChrist2Jesus is a femboy and screams uwu all over the place
@repentandbelieveinJesusChrist2this literally has nothing to do with religion nor does it deny it. In fact, it's kind of like admiring the beautiful universe God created and its intricacies.
@repentandbelieveinJesusChrist2you managed to comment the least interesting topic for this comment section.
@repentandbelieveinJesusChrist2 i want to enter jesus' gates 🥵😫😩😳
When it comes to avoiding knots in headphones, my easy way that I have used for years is to simply not allow the endpoints into the storage case. If it is a zippered pouch, just leave the earbuds and the plug hanging outside the zipper. You can just grab the entire length of cable and shove it in the zipper pouch as a massive wad if you want, just leave the ends outside the zipper, and you will have no knots. Same story if you put them in your pocket. Just leave the ends sticking out of the pocket and you get no knots.
You sir are legendary. I read ur comment when this video reach exactly 3:46 minutes. I tried this today when you post this, an entire day I follow ur instructions (I have a retro tape walkman) trying to have a walk the entire day in my town, visiting a caffe, meeting friends, work outside, bringing 4 cassette album from 2 legendary musician Daft Punk and Santana. And not a single accident of tangled knots occurred. Bless you for ur wisdom. Now I can resuming to watch this video to completion. Much love from Indonesia. 🎉🎉
I was going to comment something like "imagine not using wireless"
But although I myself use wireless, even as the annoying internet troll that I often am, I just simply cannot deny the absolute genius of this.
Proof: As was explained, if the knot does not involve the ends it is an unknot!!
Or maybe you find not.
@@kephalopod3054 I think what you meant to say was:
"Or maybe you find KNOT"
I'll show myself out now....
My great aunt (Mary Gertrude haseman) was one of the founders of knot theory (after tait) (incidently her brother got his ph.d under Hilbert). She worked out a subset of 12 crossings in the early 1900w. After ph.d she became a housewife and knots were ignored until around the 80s mostly
broooo thats so crazyyy
Wow I've heard about her , so cool man😁
hey I have a question
is someone willing to answer it?
@@αβγδεdont ask to ask
Do you ever have Impostor Syndrome or feel pressure to do better or on par with your ancestors? Very cool family tree you've got there but I know I would've felt depressed trying to live up to it.
People from Gordion: That's knot how you're supposed to do it.
Alexander: I do knot care.
AMAZING
This video changed my life. I don’t have to double knot my shoes now. I tied them the other way and they didn’t come undone all 12 hours running around at work. Amazing.
Bro same. Now i dont have to tie my shoe every 100m 😂
Same here 😂
both methods are just double-knots, and nobody here knots their shoes this way at all
My knots wont open since 2021,
i just slip in and out of the shoes.
I have won in life.
I have demonstrated to a friend that his shoes are tied wrong and how to correct it, but he refuses to tie them correctly. 😫
Knot theory, and particularly the Alexander- and Jones polynomials, were my first foray into mathematics research in 2013. So happy to see algebraic topology getting a spotlight on your channel, and the incredible applications!
Oh man, I got excited when Conway showed up. It's fascinating every where and every time he shows up. In this one he just pops in, does something in an afternoon that no one had done before and then we don't hear from him anymore. I'm very grateful for all the footage we have of him.
He was a true polymath albeit mainly in math
I said out loud "Yeah! Conway! Let's go!"
He died of Covid :(
Conway is one of the most brilliant minds to ever walk the earth 🙌
@@TheQuicksilver115 his game of life, for me, put the lid on the coffin of Creationism
We need a follow-up video on what all this knot theory means regarding conquering the practical, real-world, problem of detangling a mess of wire/rope/line the most efficient way possible.
My initial reaction was "So what? I wear slip-on shoes.". I then became slightly interested by the mathematics underlying knot theory and ended up floored by the practical applications of this area of study. An excellent video as always.
I recommend spray on shoes.
Velcro
There is a certain demographic that I hope never finds this extended tribute to knots
It's me. I'm the demographic. 😡
I don't like this cuz u have a tails avatar and know exactly what u mean
hah, tough job you'll have trying to stop boat owners from learning this one, your hopes are for naught
they have known this for decades
The boy scouts 😱
Knot
0:00 Intro
0:24 Knot Theory
1:17 What is a knot?
3:40 Knot equivalence problem
4:32 Other famous knots in history
5:20 Vortex theory of the atom
8:25 On Knots paper (the first seven order of knottiness)
9:52 Reidemeister Moves
10:51 Haken’s Unknot Theorem (and upper bound and crossing number)
13:01 Knot invariant
14:13 Tricolorability
16:37 p-colorability (and polynomials)
21:34 Perko pair
22:32 n-crossings knots
24:21 Molecular knots
28:31 How You Should Knot Your Shoes :)
29:40 Doug Smith & Dorian Raymer experiments
32:00 Knot Theory's Potential
33:15 Outro (and video sponsor Brilliant)
Bro please tell me how to knot my shoe clockwise or anti clockwise
28:31 ^_^@@himx_3
thanks!
Thanks
You forgot @ 6:37 the bong on the windowsill
This is why everyone should have a copy of the Ashley Book of Knots in their library. Study 'marlinspike seamanship' for even a few days, and you quickly see how important knots are, and how seemingly complex knots are often just simple knots built upon each other. Clifford Ashley was documenting knots before knots were cool!
20:50 In grad school I took a class with Jozef Przytycki on Graph Theory and Knots, and he was also on my oral exam committee. It's so cool to see him pop up in a Veritasium video!
This has to be one of the best, if not THE best, video on knot theory on TH-cam. Amazing job as always, Veritasium!
That's awesome
In southern India, everyday women create knot diagrams called 'Kolam' in their front porches . The more complicated the knotting the more skilled the person drawing it. This video is when I realized that many such Kolams are actually super complicated, challenging to create, un-knots! So cool to know there is a whole sub branch of math around this!
Unknowingly it sounds like these women have been practicing Reidemeister moves on a daily basis in attempts to create ever more complicated knot diagrams!
And instead of the p-colourability, these Kolams care more about the areas between the loops which are denoted by simple points. The points are actually laid out first and the knot emerges as a line diagram around them .
Are you a math professor?
That's super interesting. Now I have to go read more about what those women are doing and what they know.
But also, the description in your last paragraph sounds just like how my knot theory research represents the knots with graphs (graph theory kind), nodes representing the loops and the lines represent crossings. I wouldn't be surprised if someone in math academia lifted the ideas from the Kolams.
@@nichiyes26 exactly what I thought
Thanks for sharing... 🇮🇳❤
bro whattt......!
Very informative and entertaining!!
Nice
Nice
Nice
👍
Good
Another way to prevent cords from tangling is to loop them like normal, but leave enough uncoiled to then feed it through the middle, out around the outside, through the middle, over and over, making sure to space each loop so all of the coiled cord is wrapped with that extra length you started with. I do this for computer cable management, headphones wires, chargers, etc… it has never failed me and it puts less strain on the wire than Veritasium’s stiffening method
As a knitter and never heard of this is so fascinating. As someone who hated math but use basic arithmetic for knitting; but this field of math wants me advanced my math knowledge and thinking.
right! i do crochet but when he mentioned slip knots I pointed at the screen and said "oh I know that one!"
zzz
@@sniearrsI guess crochet (other than any terminating knot) is just one big unknot!
@@OstrolphantI was just thinking that. Crochet, many knots but also unknot.
Ayye what up my knitta
I’ve been a rock climber for over five years and this was a great video. I’ve spent a lot of time wondering about knot mechanics. and you spent a lot of time explaining knots, and I really appreciate that. I learned a lot.
I too, learned a knot.
when I was six and extremely bored, I had a habit of tying hair bands into as many knot combinations as I could think of. I also realized that they behaved differently than if I tied a knot with a normal string, and I've always been curious to find out why. This was super informative and kept my attention the whole way through, great video!
So if you never broke the bands I guess they would all be unknots?
E
Facts@@EEEEEEEE
@@circuit10 Nope. Imagine pinching the band flat, now it's double the width and has two free ends.
Insanely good video: quantity of material, interconnected concepts, clarity, and engagingness. A standard-setter.
I was very surprised when Derek, a scientist, missed a very important piece of the shoe tying equation. You would only tie your shoes (bows) clockwise if you first tied the base knot counter clockwise, otherwise you are just tying a "lefthanded" granny knot. Clockwise or counter clockwise makes no difference, a proper knot involves one of each. Eg. left over right + right over left = good knot. You can't just finish correctly if you've started wrong in the first place.
It's possible he presumed a certain start condition for the sake of clarity. A,B or B,A but not A,A or B,B
Exactly! When I learned about square vs granny knots, it was actually easier for me to flip the base knot than the final knot motion.
Thanks, I was looking for this comment. Might be confusing otherwise.
I knew the difference between a granny knot and a square knot as a kid. In college, a girlfriend pointed out that I was tying my shoes with a granny knot - that was a real blow to my manhood. I couldn’t seem to change how I tied the top knot, but it was relatively easy to change the bottom knot and now I try my shoes with a square knot even though I did not change how I actually tie the bunny ear part.
@@faroukhashim3862except that's only clearer if everyone else assumes the same starting position. And that can be pretty bad communication if you don't make the starting position clear
A week or so after people watch this, they're not going to remember the details of the diagrams or the animations, but they'll remember that he said that clockwise knots stay together better than anticlockwise knots. That's not a great lesson to teach, IMHO, not without the clarification
Veritasium always makes a knot into my brain with his genius explanations, but I did not expect it to be literally about knots.
E
But maybe your brain is actually an unknot.
@@vigilantcosmicpenguin8721 lol this would explain why I don't know understand your comment
As a budding molecular biologist, I know think that it is essential and indeed impossible to venture into the field without having a thorough grasp of knot theory first. Thanks Veritasium, truly eye-opening.
these videos are cool because at the beginning i understand nothing and by the end i still understand nothing but it's cool that there are people that do.
I seriously love this channel, seems like these videos take a LOT of effort to build but the quality and completeness and depth is unmatched all in one place.
Its honestly incredible how much your videos have improved in recent years
The fix for turning your granny knots into reef knots is really simple. When you start to tie your shoes, pay attention to which lace you place over the other. This is a habitual action and people do it the same way every time. If your habit is to start by placing your left lace over the right, simply reverse that step, go right over left instead. Then just finish tying your knot the same way you always do. Your hopeless granny knot will become a perfect reel knot. It may take a few times of consciously reversing that initial step, but it will quickly become your new habit and your shoes will never come untied again.
E
I'm not a matematician with fine expertise on knots... but i know something about storage of audio matherial.
I could clearly hear those hearbud's chord screaming for mercy!
The first thing you want to avoid is twisting cables, that's why it is most commonly stored in circular or "8" shape takeing care to gently twist it between your finger while coiling up so the core is kept straight. To prevent further mess there are chord holders or just use some tape. Confineing in a restricted area as a bag is a good advice anyway.
Tip to get used to tying shoe laces stronger: don't change the complex movement that finishes the tying, but the first simple knot. The effect is the same
Happy side effect of the secure knot is that the loops stay perfectly perpendicular to the shoe so it's also prettier
The added advantage is that when you untie your shoe laces, as long as they're not too short, the 1st knot can often remain tied for next time, so you don't have to remember to tie the 1st part 'backwards' relative to what you've spent all your life doing - just tie the 2nd part which requires the more complex movement as you've always done.
@@richardjones38 sadly my laces are short(or I have to undo them in hiking boots) but after a short amount of time, even though the first knot still feels "backwards" I do it without thinking it
I find the easiest way to tie a square knot in my shoe laces is to use the "bunny ears" method, where the second knot is just an overhand knot of two loops. Then, tying your shoes is just two overhand knots. Make sure to tie the two overhand knots in opposite directions, and you've got your square knot.
@@manolismarinakis8444 I spent a couple of months trying to teach myself to tie the 2nd part of the knot 'backwards', but still regularly kept tying it the way I always have. This was when wearing boots in the winter, so I had to re-tie both parts each time. Then when the summer came around and I wore lighter shoes I noticed I often left the 1st part tied without even thinking. I guess my Vans just had the right length laces, so reversing the 1st part if the knot effectively 'lasts longer' between my forgetting and tying it the way I've always done. Once I wear boots in the winter again it'll be interesting to see how often I forget and tie it the old way!
So, the version where the bow tends to aligne lengthwise with the shoe is the less secure one?
As a contractor and a math enthusiast, I quickly learned that isolating the two free ends of a long extension cord would make any wrapping process into an unknot. Many of us know the braid, which I believe is a type of sailor’s way of keeping a rope from tangling. I also knew IT people who’d use similar strategies for long cat-5 cables. It would be interesting to me to see how tradespeople and sailors had long ago “discovered” these theories by trial and error.
Incidentally, I’ve tied my shoes with a square knot since I was a teenager, and my young kids know the difference between the granny and square. When they try to teach their friends they’re usually met with blank stares. 😂
Chain Sinnet ;)
Great video as usual from this channel, but sometimes he does make some more controversial proposals. His idea at 31:23 of twisting the headphone cables are kind weird to me. It is the last thing i would do at work to avoid knots in a electrical cable. Just imagine how much the wires inside the cable will suffer with everyday twist and untwist.
The control of the ends of the cable and a good "snug space" to keep it should be the main priorities, to which each of us will add their own learned experience.
@@estranhokonstathe practicality within certain contexts is questionable when other properties need to be preserved, like stress on an electrical cable, nonetheless, whatever works with the minimal applied work/force is the definition of mastery in a given domain. Some task may require these higher level of application, so judge each task as individual and use as little skill as required to achieve the desired outcome. A simple metaphor I use is Jimi Hendrix's guitar playing style, effect the maximum amount of change, with the minimum work required, the graph at the end of the video (the knots in a box experiment) outlines a representation of the point of diminishing returns.
@@Saturn_Enslaveda rudimentary explanation I believe is required at this point in order for most of the others to be able to keep up and utilize the information with which you were projecting for them to necessarily come up with the plan for them to have the same kind of outcome that is beneficial to themselves that previously wasn't necessarily beneficial to them based on the Simplicity of the explanation of such programming however there are ones that will be able to interpret to them later down the road I'm sure so hopefully the commentary at this point is in a complete loss but will be remembered and click in someday.
Huh in the Boy Scouts around here every kid learns and teaches the difference between square and granny knots at the most basic levels. It's all over the literature and even symbology in scouts, I thought it was pretty universal. Although, turns out that tying the 'sheet bend' is much stronger in many circumstances, there are some where it can not be used and the square knot can still shine.
Making something as potentially boring as knot-theory interesting is no small feat. You, sir, are simply a truly gifted educator.
Knot theory is interesting. It may have important connections with quantum field theory and unifying physics.
except those are not knot
Nevertheless, I fell asleep very quickly while watching this video.
Knot theory is anything except boring ffs
he’s not an educator he’s a salesman
“This is easily the largest number we have ever shown in a video” wow that’s how you convey scale right there 🤯
The research for your videos must be absolutely insane! Not to mention figuring out and understand those scientific papers to really break it down for us
31:24 For every twist you introduce, you also introduce forces that will eventually snap the thin conductor inside. That's why you should not coil an electrical cable, or a braided climbing rope, like you coil a 3- or 4-strand rope. For your headphones, just doubling and redoubling them to a convenient length and then putting a clothespeg on them is just as efficient and gives you more use from them before you break them. 😊
A method I use is to wind my headphones in a figure eight. I don't remember where I heard about this, but since doing this, I can carry around my headphones in one of my backpack pockets without them getting tangled.
Twisting. Exactly, not tying. Tying produces knots. Twisting don't.
over under roadie wrap
@MmmVomit i use wireless and don't worry about a knotted mess of wires whatsoever.
Or you can learn to properly coil cables, something pretty much every audio technician get taught.
By introducing opposing twists, the cable doesn’t accumulate axial torque. It saves the cable from trouble and it greatly reduces knotting, since most of it in headphones is from the coil twisting, not the ends going through the loop.
I never knew knots would be so complicated and diverse in use! It is great to learn about their different uses and I am excited to see what the future could bring for knots!
ok
Hello internet, welcome to Knot theory
thanks for the head up, michael stricuvagzki chalapel trovuatskyee
A buddy of mine is studying knots in projective spaces, called like “knots in the shadow world”; he explained that you can’t necessarily get a well defined projection onto the plane for them (over/under crossings could be the same so you don’t really get a “drawing” of the knot in way that works well).
Is the idea to see how much additional information you need to specify to recover the original knot from its projection?
This is a good start. I suppose there need be one more input to determine if: over/under. The knot(plot) thickens...
It reminds me of the vague bits I know of in spectral matrix theory.
Does this have anything to do with virtual knot theory? There's similar things going on where they draw knots on non-simply connected surfaces of genus 1+2, which can't be "translated" to the plane without virtual crossings.
@@Kaiveran I’m not sure tbh, but I suspect not.
OMG it is uncredible that something so "common" like a knot would help us to develop ENORMOUS changes in science and technology like that. That's the reason I love science.
It's not whether you counter clockwise or clockwise tie the knot. It depends on the first step and whatever way you cross the strings, it must be the opposite in the second step.
Plus if you've been tying granny knots your whole life, it's easier to reverse the first step. It's a tad clumsier to reverse the bow.
@@YoeyYutchExactly what I did in my very late twenties after realising why my shoelaces didn’t want to stay in place across the shoe. ("Have I been doing it wrong for twenty years? Yes, I have.") When you learn to tie your shoes, it's going to be mostly random if you happen to start doing it wrong or not.
Also use this technique for 10 years
Upvote
and you know you succeeded if the two loops are parallel to the laces.
I have no idea how you make these subjects fascinating but it is working flawlessly
I’m surprised that knot theory - a branch of math that is “knot” so easy to understand- can be explained so well!
Mad respect
"Hey, what is @veritasium's new video about?"
"Knot Theory."
"Cool, neither is mine."
I've started to lace my shoes like this ~2 years ago when I realized its symetry and aesthetism, but never paid attention to its tightness. Thank you for this great video, as always !
I really liked how this video shows the benefits of "knowledge for knowledge's sake". That something with no obvious practical application can be worked on for centuries, and suddenly a breakthrough happens that turns the previously "useless" knowledge into something potentially world changing.
I've been telling my students since forever that "no knowledge is wasted"
This is amazing. I am extremely happy, that this video found me today.
I've loved knots since childhood. I was tieing knots and drawing them in my album for hours, I've tried to compare and replicate them.
Is there any books abouts knots? I really want to explore its mathematic and scientific side
My all-time favorite knot to tie is the trucker's knot. My dad showed me how to form 2 trucker's knots in series when a lot of tension was needed over a long pull length. It's effortless to tie. It secures a load, and it can easily be untied even after great tensions are applied.
One of my favorite books about knots is The Rigger's Apprentice by Brion Toss. It contains lots of useful knots and nice illustrations too.
This is such an inspiring example of the value of pure science and long-term benefits of pure intellectual curiosity. I wish this kind of story could land in the hearts of more people. The survival of our great grandchildren's civilization may depend on supporting today what seems to be pointless navel gazing.
The knot in my back after sitting for 8 hours at work has got to be a new discovery
FOR TYING SHOE LACES:
You don't need to loop the other way for more security. You can just go around twice. Loop around twice. Not double knotting, but looping twice. It has more friction.
The shoes tying direction changes depending on how you tie the first half of the knot. The upper one must be a different direction than the lower one to form a square knot. This is one of the first things even amateur freshwater sailors learn - you do not want the rigging that holds your big strong sails and heavy pipes they are attached to unwinding because you tied a granny knot. Besides that great video!
Figured I'd look to see if anyone else picked up on this.
As someone who always went clockwise, [I never learned the "bunny ears" method either] I never realized that it was supposed to be "better". But as it turned out, I had to slow down and pay attention to notice that I also instinctively do the first knot "backwards", meaning I usually just do a mirror of his granny knot.
Probably [k]not going to be able to break that muscle memory after all these years of doing it one way, but it's interesting to note that doing the second knot anti-clockwise might help my boot technique. [which is usually just using longer laces and tying a third reversed knot anyway]
Color me highly skeptical of the idea that the square knot is "better" than the granny knot. The reef knot or square knot has several bad properties, including that it can capsize and separate (come untied spontaneously, by capsizing to a cow knot and a straight section), it doesn't hold well with different size or stiff ropes (many knots have this unfortunate property). And it's absolutely a terrible knot when used as a bend (to tie two ropes together).
@@eyesoars9212 Regardless of the square knot being bad at most non-shoe jobs, that doesn't mean another knot can't be even worse. In fact there are probably hundreds of knots you could theoretically tie in shoelaces that would be even worse than even the granny knot in one way or another. The granny knot is definitely worse; if I ever happen to tie the bottom half of a shoelace knot backwards then the top (which I always tie in the same direction out of habit) will come undone potentially as often as once every couple minutes, regardless of how tightly I tie it, until I fully untie and retie the bottom half, after which the knot often lasts the entire day. The difference in symmetry makes the difference between a stable knot and a self-loosening knot and this is a well-known effect.
In fact before I knew about the granny knot, I would fairly often tie my left shoe as a granny knot and my right shoe as a square knot, and for many years I wondered why one shoe came untied so much more often than the other. This stopped after I learned about the difference and switched to using the Ian knot (actually a method, it's still the same knot) which is slightly more comfortable to tie as a square knot and that helps a bit to remember. You can also tell the difference because the two twists being in the same direction tends to cause the granny knot to take on an overall twist, with the free ends oriented perpendicular instead of in-line.
And of course shoes are a very specific application of knots, and other than capsizing the problems you named simply don't matter. Unless I suppose maybe you glued two different sizes of highly stiff cord to the different sides of your shoes and tie a zeppelin bend to hold them together, instead of using a single flexible lace with a shoelace knot like everyone else.
I found it hard to believe he made the error once, let alone twice! It's an odd error to make in a maths video
@Am1kke Thank you for pointing this out. When he was explaining it, I was like "Derek was obviously never in the Scouts! LMAO" The clockwise/counter-clockwise distinction doesn't make any sense without saying what direction the first crossing was in.
Another annoyance with this is how wrong the thumbnail is. It shows a loop (the UN-KNOT) and says that it's a KNOT and then shows a standard "pretzel" shape and says that it is NOT a knot, even though it is really a trefoil with one end cut (or not taped together). It's like whoever created the thumbnail either didn't understand what the video was about or just deliberately showed misleading and incorrect information in order to get people to click the video...
Your shoelace knot also depends on the orientation of the first crossing. I start in the opposite way that you do for the simple reason that the "granny knot shoelace" will sit paralell to your shoe while the sailors knot sits perpendicular. Good to know its also stronger :)
Dude everything aside, its from a wannabe physicist or a human who is just curious how things work… your explanation and videos are so much intriguing and interesting even for a drunk person like me right now.. i love your videos keep posting such videos.
I think you should work with someone who isnt aware of everything but wants to ask so many questions on how things work and you explaining things to them and this would even lead to a discovery or a disaster but i think its still worth it!
Derek got it wrong in the very beginning. The two ways of tying your shoe don’t have to do with clockwise or counterclockwise. It has to do with if you do the second crossing in the same direction or not. So like if you did the first crossing clockwise, do the loop part counter clockwise to keep the knot balanced and torques low. You can also do the first crossing counter clockwise if you want instead, as long as you do the opposite on the loop part. It will be just as strong.
I was thinking the same thing! Glad someone else mentioned it!
He very clearly explains this in the video.
I caught this just before bed and ended up dreaming about the 3 types of knots. I’m now a knot theory devotee. In an ocean of mindless content this channel is so refreshing! Hands down one the best TH-camrs. Thanks so much!!
bro got converted
Thank you, Derek and the Veritasium team, for making 'exotic' mathematical topics so clear, interesting, and engaging. Your videos on knot theory and invariants, as well as the previous one on p-adic numbers, are truly enlightening.
It is such a missed opportunity that a zero loop knot isn’t called a “not” or a “not knot”
Surprised this doesn’t have more likes
The reef knot is one of the easiest knots to untie one handed. Grabbing one end and giving it a sharp jerk turns the other end into a hitch which slides off thestanding end. It's why it's used to reef sails; you can keep to the old adage: one hand for the ship, the other for you.
Can you tie it one handed effectively? I can sort of loop two ropes and end up with a reef, but it won’t keep the rope taut, so it’ll be tied slack.
The way I have always been keeping headphones/cables from knotting is this: I double them like you showed, but instead of then coiling them, I just keep doubling them over until they are as compact as I want. I think the reason this works as well as it does is that there are basically no loops being made for the free ends to go through and form a knot. Yes, this doesn't hold them together, but that is hardly ever a problem, because even if they do unwrap and get tossed around, usually do not get get tangled. I've tested this a bit before commenting here, and it definitely works. Another thing I noticed is that when cables are looped around like that, more often than not, it's the loops going through each other that causes the tangling, not just the free ends.
A way I've learned: grab one end, and then throw up rocker horns (index finger and pinky raised). Wrap the cord in a figure 8 between those two fingers. Finish by taking the end in your palm and circling the middle a few times. Somehow they never tangle.
I also use your successive doubling technique, but only until the step BEFORE where the multiple strands are too short and bulky to form a simple overhand knot. The eye-ometer serves here. Then I tie an overhand knot with the multistrands. Keeping this knot confined in some way, as the vid suggests, also helps. It depends on the stiffness of the cable.
@@flamencoprof Cool, I guess that would work better
Yachtsman here. If you have the tail of a sheet coming out of a block or winch, you never "coil" it into loops. That inevitably tangles if you disturb the coil or throw the coil away behind you as you loose the block.
Instead you lay it in a figure 8 , either over the block or a hook. Never bothered to check WHY, but when you pick up the figure 8 and throw it out to run the sheet through the block, it CAN NOT tangle.
@@uncletiggermclaren7592 That is because the twists of each side of the eight are in opposite directions, and when you throw it out they cancel. I have a method of coiling cable or rope in a circle but with opposite twists in alternating coils, but it is too hard to describe in words. It works well with heavier stuff like mains extension leads.
Working as a sound tech we deal with very long XLR cables, usually around 20 to 50 feet but sometimes much longer. Over 100 feet we use spools, but lower than that we have to coil them up by hand a specific way, we can't just leave them uncoiled and confined as you suggest. We also have to straighten them out as we coil otherwise they'll twist and want to spring back forming sloppy coils. We take the lose end and wrap it around the entire coil and finish it off with a simple trefoil to keep it in place. Once that's done we stack them into confided bins, but they not always full leaving space and sometimes the trefoil can come undone and cause knots. Thanks to this video I'm going to try and do the opposing trefoil thing and see if that works better. Math is improving my life lol.
The best edu video I have seen, in terms of clarity, visual and explanation. I am now a fan. Let the fans multiply to blow the universe!
I once gave a talk about the basics of knot theory to colleague math students who previously knew nothing about them, and it was my best received talk ever. Knots are fun.
Same .....it was so fun to research and know soo much complicated simple knots can be and seeing people's mind get blown hearing about the same.
For everyone that has their shoelaces untie throughout the day... I can't recommend enough learning to turn your knot into the square knot. It'll feel weird at first, but will change everything. The easiest way to do this is to switch the direction of the first tie to the opposite way. So, if you feed the end one way on the first tie, instead switch it to the mirrored version by feeding the opposite end through using mirrored hand motions. Then, tie your normal second knot because that is the more complex one.
Left over right, right over left
Okay, but I do the loops in my shoe laces first, then the cross over knot, so which way should I switch them?
@@Nubivagance0314 do the first cross unnaturally, the reverse of what you usually do
I posted virtually the same comment before seeing yours. Derek didn't really make clear that the issue occurs between the "substrate" and the loopy part.
@@Nubivagance0314what's the point of doing the overhand knot on top of the slip knot
i love that I never know in which rabbit hole I am going to fall into when I watch your videos but it`s always incredibly fascinating! Thank you for your valuable content!
Next thing you know, you're studying Marlinspike Seamanship and ordering your very own copy of the Ashley Book of Knots. It's a deep rabbit hole, indeed!
@threeriversforge1997 i have a laminated card with 40 knots drawn on it, never thought I'd see the Marlinspike anywhere else.
Also i like to flex on younger boy scouts by tying sheepshanks behind my back
¡La forma en que enseñas el análisis de velas es muy clara! Gracias por los videos educativos.
I've always found untying knots of my ear phones fun and relaxing, I honestly miss doing it since we have bluetooth earphones now. This is just soooo facinating! I never thought I'd actually love something about Mathematics! Absolutely loved this!
I was in telecom and after pulling miles of cat5 cable on a single job, you got an absolute mess at the end. I was the only person that could figure out how to untie that crap. I wasn't sure how I could do it, I just sort of had a feeling.
30:29 Derek masterfully sneaking in an alibi for all those baggies he’s stashing
Funniest comment I’ve seen so far in this video
Came looking for this comment 😂😂😂
Fun Fact:
So when detangling yarn many people tend to pass one (or both) of the ends under loops they seem to be tangled in
but most of the time the tangling is an unknot.
so the better way is to first try to shake and carefully loosen up everything to untangle it into the unknot it is and resort to the passing under loops strategie, only when it is so tangled that you cannot loosen it up properly or loosening it up / shaking it a bit, doesn't give you any progress.
This reminds me of getting the mooring lines sorted out last minute on a sailing trip and the skipper shouting “ pull the loops apart don’t pull the ends!”
I can't help but watch every one of your videos... you're like the math version of watching a run clearner clean a rug. I don't understand how you do it, but I love the process.
Certainly one of the best animations on this topic out there. Great work Derek & Team! Shall these videos be forever available for humans who seek knowledge.
What a wonderful video! I gained tremendous respect for these people who worked just for their curiosity, when they could be doing the equivalent of watching Netflix on their couch and eating snacks. It's because if their tireless efforts that we enjoy the discoveries and treatments that we do today. This is why going out of your boundaries and discovering the unknown matters, this is why exploring the cosmos and sending probes to the moon, sun, Mars, and beyond matters, even for developing countries. Well done Derek and team!! 👏
Yes but a lot of these Victorian thinkers had independent income so could do this full time.
But I was intrigued that Tait complained he didn't have enough leisure time (and thanks Derek - I appreciate the pronunciation from British perspective). I wonder what he was doing for the rest of the time!
@@roginkresearchers like these dont earn enough for the work they put in, because their work rarely IMMEDIATELY becomes productive. In this capitalistic society, if ur work is not immediately productive, ur gunna struggle to find someone to pay u.
Professors get by teaching students but for how many hours they work, their pay isnt that great. Its definitely a passion job.
@@vwlz8637 True the title 'professor' isn't quite as prestigious as it once was. Of course it depends on which university employs you, and your discipline. Sure, the humble PhD student has to scrape by, but when you get to Prof status, in most Western universities you will have a comfortable salary, a job for life, and generous pension when you retire.
Regardless, that has nothing to do with these Victorian thinkers. They weren't employed by universities - or anyone else. They mostly had property and earned income from that.
@@vwlz8637 oh yeh, communist societies I'm sure are waaaayyy more hospitable to mathematicians working on things with no immediate application. funny how everyone rags on how capitalism doesn't allow for this sort of thing, and yet pretty much all great mathematicians come from capitalist societies. clearly it isn't as inhospitable as you think it is.
30:06
"Longer agitation time leads to a higher chance of knotting"
Can confirm.
real
Not calling the unknot a notknot was not the best choice.
Why not?
@@quatcilovad knot really.
@@quatcilovadthats knot what he meant
Maybe you meant:
"Knot calling the unknot a notknot was knot the best choise"
@@leokinglv1970 Dokn’t go there.
Good video. As a former rescue squad member, I think a video explaining the mechanical differences and advantages/disadvantages of each knot would be rather interesting.
Also: if you have p coloration, you might want to see your doctor.
Clever but too clever for the sheeples.
I’ve had an (unspoken) interest in knot-theory for a good couple of years, and not to discredit or mock anyone, but i’m so glad that someone ”bigger” finally brought this subject forward so i don’t feel quite so stupid for having an interest in this 😂😅❤
jasuxi
I wouldn't use the word "stupid", but same!
I've always loved knot theory! I have never fully understood how it works, but I love the idea of thinking so deeply about things many people find so trivial, while it can be so interesting!
You should really make a video on how you make videos. Each time I'm most stunned how easy it is to follow the logic. Chapeau!
I'm a teacher and this is a problem I'm struggling with each and every day. And I'm not even a native speaker.
@31:36 I stiffened knowing the mistake you were about to broadcast as good practice... never do this with any type of cable, but especially cable that contains un-braided stranded wire Ie. Earbuds
3 destructive actions take place when you twist stranded wire onto itself, or even wrapped around a center bobbin. Ie. An extension cord spooled around your hand and elbow.
1. The individual wires that make up stranded wire are equal in length (for many reasons) but as you twist the cable, each individual wire inside the protective insulator is rotating longitudinally, and when you un-twist your cable the inner wires do not completely return to their factory position, so over time they begin to bunch around each other tighter and tighter. since the wires closest to the outside are effectively getting shorter faster, having a farther distance to move with each rotation, they will begin to knot inside the cable first, snapping away from the ends while the inner wire continue to become stiffer, and exerting force on the cable ends in the opposite direction as the outer wires. After a while you will notice that even when you spool out the cable it begins to look wavy as if it had been curled. Since there is less wire making contact with each snapped strand, the resistance slow rises at each end of the cable dropping the voltage... In the case of extension cords you will notice that this makes the plug act like a heating element. With earbuds you will notice that over time the volume decreases, until shortly before one side stops working they only operate at 25%-50% of original volume. You can actually measure it, check output when new, then twist and untwist them 180 times @6 months worth of simulated use, and measure the difference.
2. Friction, you ever had to cut a wire or piece of metal in half, and had only your hands, you folded it several times at a certain point... well a twist is essentially a rotational fold and each crossing point is a fold location since copper is a soft metal, each time you force one side of wire to cover a longer distance than the other side what happens is the two opposing forces pinch the atoms together at that spot forcing them to rub against each other with much more force than they would see during normal use. To figure out how much farther a side has to pinch and stretch to accomplish a twist, take the diameter of the wire then find the circumference for 180 degrees, now using that distance as your radius, double it to find the diameter of the twisted wire, now find the circumference using that diameter for 180 degrees and that is the distance of travel between the shortest side, and longest side.
3. With stranded wires, the insulation is usually not as tough as cable with less strands of thicker gauge, simply for the same reason we use stranded wire in applications where we want the cable to remain easily pliable. So the insulation is easier to damage inside the cable after repeated use, and the insulation be it enamel for earbuds or pliable vinyl in romex, with enough twist, you can find yourself with a cable that is in a permanent state of "dead short" and the big danger being it quickly melts the conductor ending the short, so it gets set aside, and you forget or a coworker uses the cord, plug it in making it live, the rolls the cord out loop by loop and when they get to the place where the damage is, the movement causes their hand to complete the circuit at the damaged location.
I tell people all the time the two best ways two best ways to store any cable is do not twist or loop decide on a convenient length and fold the cord back and forth like an accordion then pinch the centers together and tie with a piece of scrap wire or bread tie depending on size of cable. The second way is essentially the same as the first, but instead of a back and forth stacking of the cable, start a spiral on a flat surface with then roll it around itself so that it has no rotation perpendicular to the length like it does when looping, now continue that rolling, until you have four to five passes on the flat spiral. Now start your next roll on top of the first roll at the same size make the same number of passes you did on the first spiral layer, repeat until you have a roll of cord 4-5 passes wide and about the same number of layers high. you will almost certainly be left with a cable end on each side or both ends meeting at same place. You can now place a tie around the finished coil. I almost always use two so that it retains its shape for storage... It I am unclear you can visualize it as being rolled the same way windings on a transformer are.
31:30 Problem with that is twisting will cause the coaxial cable to short out. Never twist a cable or coil it extremely tightly. Honestly, the best way is similar to what you said earlier - use a small container, but also loosely fold the cable back and forth, and then use a twist tie or similar to keep the coiled portion closed enough so the ends cannot find their way through in storage.
Exactly, I was going to suggest that to my dad who still uses wired headphones but then remembered disadvantages from co-axial cables from my Computer network class. 😅
@@chetanuniyal3428 To be fair, if it was a rope or a necklace or something, this would be ideal (barring screwing up the links in the necklace or what not).
@@Qermaq yeah for a rope it would be perfect, Not so much for the necklace though, it's metal so too rigid and considering the quality of jewelery these days, the locks can snap anytime.
@@chetanuniyal3428 Right it absolutely depends on how the necklace is constructed. If it's not chain, or if it's a fine enough linkage, it would be ok. Otherwise you risk tangling and possibly warping the links.
Thompson, Lord Kelvin's thinking on knots and atoms feels a bit like string theory.
This is a beautiful subject! Thank you for making it approachable to the rest of us. Excellent work as always.
Respect to the guy who used his several computers to find 300+ million knots instead of mining bitcoin in 2020
It doesn't matter wether you tie shoe laces clockwise or counter clockwise around the loop. It all depends on the direction of the first trefoil.
Correct. When tying the square knot, a good practical method is to choose one of the strands to be your working end. Now, if this working end goes over (under) in the first overhand knot, then it must also go over (under) in the second overhand knot. After the knot is tied, the two strands are coming out together from the "side loops", that is, both go under on one side and both go over on the opposite side. Obviously, this is much harder to put into words then to just show it with a bit of rope 😅
Just take care that the bows are lying flat after tying and not at an angle to the laces.
If not ... repeat until they do ;)
@@clayz1you've said the same as the guy in the video, which is wrong. The first knot will give you two ends, obviously, one pointing towards you and the other pointing the other way. After that knot you have to keep those ends on the same side, moving them in a paralel way towards the center, without crossing the first knot. Then you only go over the first knot when you tie your second knot, and you've got a perfect, beautiful square knot
I keep it real simple and just tie the second knot in the direction that's uncomfortable to tie.
@@clayz1 you can tie a square knot in two ways: starting left over right, ending right over left is one way. Starting right over left, ending left over right is the other way and results in the mirror image of the first way. One way is clockwise, the other way is counter clockwise around the loop. The same is true for granny knots, only the first and second trefoil are both in the same direction in stead of different directions.
I bet every time knot theorists get together for a conference they'll be sporting some of the most impressive tie knots you'll see.
I'd hope there's a little competition at each conference to identify the most practical, creative and/or aesthetic tie knot
I'm only halfway through watching, but I'd love to see a follow-up about common knots and practicality. I'm mostly intrigued about friction and benefits to knots. I assume many fishing knots benefit almost exclusively from friction, but it's a very significant force on their effectiveness.
I'm here because of reverse 1999 latest story chapter about knots
Two Veritasium videos in the same week? Is this heaven?
fr
It's amazing how mathematicians are able to take such abstract concepts like knots and mathematically describe them such that you can perform operations on them and write code to discover them.
At the end of the day everything is mathematics. Reality itself is just math happening so it makes sense that anything even knots can be represented mathematically.
@@vectoralphaSecYes of course, but being able to take what you observe and describe it rigorously with mathematics is not trivial at all. Then taking it to a point where you can write algorithms, and proofs is even harder.
Absolutely fascinating! This is why I love Math, and why I love this channel. Thank you Veritasium, for all of these stellar videos.
Working with paracord while i watch this. Ive been so obsessed with learning new knots lately so this vid hits the spot, and may explain why people like me find them so fascinating.