How The Most Useless Branch of Math Could Save Your Life
There is an entire branch of math simply devoted to knots - and it has changed the world. We’ll rope you in. Head to brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
Special thanks to our Patreon supporters! Join the community to help us keep our videos free, forever:
ve42.co/PatreonDEB
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Huge thanks to Prof. Colin Adams for his excellent help guiding us through the world of knots.
Many thanks to Prof. Doug Smith, Dorian Raymer, Prof. David Leigh, and Prof. Dorothy Buck for helping us understand applications of knot theory.
Many thanks to Prof. Dan Silver & Prof. Jim Hoste for speaking with us about the history and tabulation of knots.
If you want to learn more about knots and play with them yourself, check out:
The amazing KnotPlot tool - knotplot.com/. Thanks to Rob Scharein for providing technical help as well!
A table of knots and all their invariants - knotinfo.math.indiana.edu/
The Knot Atlas for general info on knots - katlas.org/wiki/Main_Page
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Knot Theory Video References - ve42.co/KnotTheoryRefs
Images & Video:
Alexander Cutting the Gordian Knot by Donato Creti via Fine Art America - ve42.co/GordianCut
Indus Valley tablet via Quora - ve42.co/IndusValley
Pages from the Book of Kells via National Trust of Scotland - ve42.co/BookOfKells
Medieval Celtic designs from @thebookofkellsofficial via Instagram - ve42.co/KellsInsta
Chinese knotwork by YWang9174 via Wikimedia Commons - ve42.co/Panchang
Quipu cords by Pi3.124 via Wikimedia Commons - ve42.co/Quipu
Borromeo heraldry via Terre Borromeo - ve42.co/Borromeo
Birman/Jones letter via Celebratio Mathematica - ve42.co/JonesBirman
Molecular trefoil knot by M stone via Wikimedia Commons - ve42.co/TrefoilMolecule
X-ray structure of trefoil knot by Ll0103 via Wikimedia Commons - ve42.co/XrayTrefoil
Bacteria animation from Your Body's Molecular Machines by Drew Berry via the Walter and Eliza Hall Institute of Medical Research - wehi.tv
Topoisomerase and knots from Orlandini et al. Synergy of topoisomerase. PNAS, vol. 116, no. 17, 2019, pp. 8149-8154. - ve42.co/Orlandini2019
KnotProt 2.0: A database of proteins with knots and slipknots - ve42.co/Knotprot
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Special thanks to our Patreon supporters:
Anton Ragin, Balkrishna Heroor, Bernard McGee, Bill Linder, Burt Humburg, Dave Kircher, Diffbot, Evgeny Skvortsov, Gnare, Jesse Brandsoy, John H. Austin, Jr., john kiehl, Josh Hibschman, Juan Benet, KeyWestr, Lee Redden, Marinus Kuivenhoven, Mario Bottion, MaxPal, Meekay, meg noah, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Stephen Wilcox, Tj Steyn, TTST, Ubiquity Ventures
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Directed by Emily Zhang
Written by Emily Zhang and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Ivy Tello, Jakub Misiek, and Mike Radjabov
Filmed by Derek Muller, Raquel Nuno, and Emily Zhang
Produced by Emily Zhang, Han Evans, and Derek Muller
Thumbnail by Ignat Berbeci and Mike Radjabov
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound
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?
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
@@HeavenlyDevilGamingIn a way they made the joke funnier.
blud is way too mad@@HeavenlyDevilGaming
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...
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?
"Not knot" "Who's there?" The *Unknot*
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
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.
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!
@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.
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
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.
Hello internet, welcome to Knot theory
The mathematicians missed the opportunity to name it 'Notknot'.
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. 💯
@@HEN_Xy 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
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!
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 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!
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....
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......!
This is the most complicated video I've ever watched in this channel. I didn't Understand much but after seeing that our everyday knot can be so interesting to great scientific minds I get excited. 😯
Many of your videos i watch and enjoy your explanations yet only begin to grasp the concepts. Some I’m still clueless yet i love to know how much i don’t know about the world. Thank you for them all.
Very informative and entertaining!!
Nice
Nice
Nice
👍
Good
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!
This is amazing Im so glad I watched this till the end to see what it could be used for. It’s a lot to digest and I have a certain problem concentrating but I made it. Thank you for posting.
I have no idea how you make these subjects fascinating but it is working flawlessly
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?
@@NoNameUswrdont 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.
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 🥵😫😩😳
17:34 I lost track on the 5-colorable with this image showing only 4 colors
I really enjoyed this video. Knots have fascinated me from childhood. I figured out on my own how to tie certain knots that amazed and frustrated others. I especially liked making varieties of slip knots because people would be trying to figure it out, and I would pull and the complex knot would vanish like a magic trick. And I would laugh and evil laugh. I was a weird kid.
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. 😫
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
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.
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
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
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
Thanks for what you do. This is insanely informative and well presented.. Very informative and entertaining!!.
The square knot you showed towards the end is (at least in Germany) used in Firefighting. Its main Use is to connect two ropes together because it pulls itself tighter when pressure is applied
when you realise there is not an impostor at 27:49...
You might like Polymatter, did a video on the economy of Delaware and gift cards the other day.
He has a research team, come on!
@@savagepro9060 I really love how he finds out these facts all by himself while his research teams claims all the credit
I don't know how someone can make a half hour long video about knots and still make it entertaining but he does it anyway, also toilet gang
Essential craftsman has a good video o knots and string for construction use but this is far more detailed
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
Thank you for making such good videos guys it’s like my attention span length is getting better than ever
Your video was literally amazing. Thank you for sharing such incredible knowledge. After watching your video, I got interested in the relationship between the knot theory and materials in chemistry. So I tried to find some more about it, but it was hard. Could you recommend some good resources/researches/websites/articles or whatever related to it? Thank you in advance!
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
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 KZhead. Amazing job as always, Veritasium!
That's awesome
Ending the video with this quote was immensely satisfying and tied (!) everything together so elegantly.
Absolutely! Well noticed by you and that's a great pun noticed by me
That ending quote was quite inspirational - a great mood lifter and motivator to pursue knowledge
People from Gordion: That's knot how you're supposed to do it. Alexander: I do knot care.
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
Your E comments are getting E-nnoying.@@EEEEEEEE
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
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.
For the shoe tying thing it's about the direction of tension applied to the knot vs the direction the knot tightens or loosens upon
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.
@@7890tom7890a 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
As always, I learn so much from your videos. Thank you for sharing!
Excellent video as always. I'm pretty much always learning something new in every video you make, thank you for that. Now about the tying you shoelaces bit......The clock-wise or counter-clock-wise way isn't really the point. Let me explain. When tying your shoelaces what you essentially are doing is tying a two knots. But by not pulling any further at the point where the loops are about as long as the remainder of the shoelaces you end up with the laces in a nice looking bow. Continue to pull the loops all the way until the end of the laces are through and you'll have made either a granny knot or a square knot, and are left with long shoe laces again. Whether you'l have to go clock-wise or not when tying the bow-bit actually depends on the first knot you've tied. Like you explain in the video around 29:15, in essence you wanna ty a square knot because that doesn't loosen up as easy. When tying a normal square knot you go Left over Right and then Right over Left, or vice versa. As long as you counter the first knot when making the second knot you'll end up with a square knot. So depending on how you tie the first knot, let's say the base for the bow-part, you need to go clock-wise or counter-clock-wise with the bit that forms the bow-part in order to get a square knot at the end. If during your day you have to tie your she's again you'll will have made a granny knot the first time which loosens up while you are walking. Once again thanks for the all you have taught me in all of your videos.
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!
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.
One of the most interesting videos I've seen in a long time. Frankly, the math goes WAY over my head. I'm not nearly studied enough to understand the polynomial equations, at least. Still, the premise is so intriguing for the fact that it proves with math that there are true answers to a seemingly impossible question. And, honestly, if there was ever an application for which quantum computers are best suited, this may just be the one. But what would be even more exciting is if they can't solve for very large prime knots. Because the equations which form them could become the basis of future encryption the way large prime numbers are today.
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.
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.
Its honestly incredible how much your videos have improved in recent years
Thank you for the continuation of education!
I’m actually working in this area of study right now! There’s more to it as well: in 1996 one Dr. Kauffman invented virtual knot theory to generalize knot invariants to knots embedded in surfaces of arbitrary genus, allowing for knots whose gauss codes (the invariants he was studying) could not exist in 3-dimensional Cartesian space. In short, This is an exciting field of mathematics, precisely because it’s so novel.
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?
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Facts@@EEEEEEEE
Only at 13:10 so idk if they are already get to this, but I’m thinking that if you just label one crossing as 1, the next as 2, so on and so forth; sort of treating it like a sequence of crossings. you can eliminate the number of crossings by going through the three rightamiester wtv processes to reduce each crossing to simply a non overlapping line that connects the two crosses next to it. Once you’ve done that to each crossing you should know how many true crossings you have, and as they’re already all in a sequence, you can just go along the sequence to mark the type of crossing they are to determine wether they are different knots from another. Edit: example Triknot - triquetra would have 3 true crossings and you could label them binarily as 101, or 010 depending on if you start at the top of a crossing or the bottom. To simplify maybe always start on the top of a crossing but I haven’t thought about all the difference and if there are any, could be beneficial to consider both startings as possible in any knots to be compared. if any two knots have the same number of crossings and their binary sequence can be matched up identically, than they are the same knot. I wonder if a top starting knot sequence could match up with a bottom starting knot sequence but then each knots opposite start couldn’t match to eachother, that certainly couldn’t make sense if all crossings were true but I’m not trying to think about allat
that graph showing how many knots that certain prople discovered kept blowing my mind over and over again when more people were added
30:06 "Longer agitation time leads to a higher chance of knotting" Can confirm.
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?
the square vs granny thing also applies to tying a jacket around the waist. if you do the overhands in the same direction you get a granny knot that works loose. i did this for years and had to keep tightening the knot. but if you do the overhands in opposite directions you get the square/reef knot which won't work loose.
I will save this to watch later. It is late, and I am knot following along very well.
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
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."
A lot of people are here to see the actual shoe knot explanation at 28:40. My addition to this is that, you can still do a counterclockwise motion and end up with a square knot instead of a granny knot, but to get this, your first half-hitch / overhand knot needs to be done the opposite way as how Derek has it in the video. In his half-hitch, the end pointing to the right is going over and then under, but if you invert this, then once you get to the second part of the knot, it is now when you can do a counterclockwise motion and get a square knot. Knots can be mirrored, so it isn't really the best explanation to tell it as an absolute that "you have to do it clockwise to get a square knot", because that is not necessarily true, but for this, something else in the process of making the knot needs to change to mirror it properly.
Reminds me of the lesson on DNA supercoiling and gyrase I had in bio class recently
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.
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.
I find kelvins early interpretation of atoms as different knots very interesting due to its surface level similarities to string theory.
24:57 This here... This RIGHT HERE is the key to the future... To EVERYTHING
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.
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 😂😂😂
btw: The trick to tying shoelaces with a secure and proper square knot doesn't require relearning a clock or counterclock bow. The (slippery reef) square knot doesn't care which way the bow is rotated as long as it is the opposite of the initial (marlin hitch) overhand knot. If your shoelaces are sloppy granny knots, continue using your same familiar bow tying technique. Simply tie your initial overhand knot the other way round. / sailor
As someone who tied their shoes wrong for 25 years, I found switching the rotation of my bows very difficult. Trying to work against that somewhat complex muscle memory just didn't go well. Instead, I found it much simpler, as others have pointed out, to change how I do the simpler base knot. After about a week of focusing on the new base knot (maybe 10 tyings), I was back to normal speed with an improved knot. In short, if your laces aren't working and you do the first crossing right over left, switch it to left over right (or vice versa) then do the harder part the same. I've passed along to multiple people and has even worked for people with dexterity issues (arthritis/amputated digits).
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.
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.
Haha I’ve been using that headphone trick since I figured it out in high school and was very happy about it! Cool to know there’s so much intricate theory behind it!
The Tricolouribility move to solve some part of the knot problem was just genuinely genius
25:28 No, the most complex knot ever created is my bedsheet twisted and tangled up when I need to use it.
What a rollercoaster of emotions this video has been.
I move for a series of trading cards that catalog all of the prime knots as shown in this video. You can get the unknot and trefoil knot cards as Commons, and a 17-crossing knot as a Super-Rare. Trade them at your local comic-book store.
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.
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.
Great video! Interdisciplinary studies is where it's at!
I use the slip knot and trailer knot far more often then i should but they do work quite well
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.
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 wrote a paper on this in 96 comparing unnotched and DNA and not a DNA amylase cutting up the DNA making a trefoil and the you talked about from the other guy the first noted molecule chemist put together what a fun paper
To tie a square knot, you take the two ends and go right over left and then left over right. Or you go left over right and then right over left. Technically, when you were showing the counter-clockwise vs clockwise generating a granny vs square, it was because you started with left over right on your leg and then did another left over right (counter-clockwise). If you start tying your shoes right over left, you can then do a counter-clockwise (left over right) to generate a square knot. So it is more about how you start the knot... the second part just has to be the opposite.
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"
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...
16:42 my p-colorability depends on how much water I drink
There’s a way to coil headphones that reduces knotting and doesn’t twist it, which helps increase their longevity. Coil it like you would an audio cable, by twisting over and then under and repeating