Lace Knot Trick – Numberphile


Unbeknownst to many, there are two ways of tying your shoelace. You see, the first step is usually like this. In the second step, you can either do it like this, in which case, you see, the knot becomes kind of perpendicular to the direction of the lace at the end. Or, you can do exactly the mirror image of what you have just done. And it is slightly wrong, actually, when you do this. But that’s a nice way to do it. When you do that, in this case, the knot becomes kind of parallel, if you see what I mean, to the shoelace. What did I do? So, there are two ways of doing it, right? You can do, start from, like, this, or the other direction. So let’s do it in this direction, in some sense. Now, that determines one of the orientations. So, one way to do it is to, from my point of view, the right hand, and pull it over, and then do this, which produces a perpendicular knot. The other way is to make the loop with my left hand, and then turn it over and through, and then make the knot, in which case the knot becomes parallel to the shoelace. That’s quite interesting. Now, it turns out that these two things have a difference. And I’d like to show one of the differences. Which is also a nice trick to know in practice, in daily life. Let’s make a knot by first doing this, and then, secondly, by doing that. If you think of this as a mirror, this is not symmetric with respect to this mirror. Because you see, this strand goes under this loop, whereas this one goes over this loop. It’s kind of more like a, you know, rotation symmetry. Whereas if I put them in this configuration, that’s symmetric, in the sense that they’re both going under. And you can see that it is symmetric. Now, Brady: “So which one matches which shoelace?” I think this one matches the parallel one, and the rotation one matches the perpendicular one. I’m not entirely sure about this. You explore. Okay. So, let’s make a tight knot with this. And this is a fairly tight knot. This was the symmetric one. And, you know, if you wanted to undo this knot, you have to go in, and it’s really a bothersome. But there is actually a nice trick to undo this knot. Let me show it to you first. I hold it like this. It comes straight off. What did I do? Let’s do it in slow motion and in detail. Again, this is the symmetric one. And when I close it, it’s like that. You grab those two or those two. It doesn’t matter which one, let’s. And when you pull them taut, you get the straight line. And it turns out that the knot, the entire knot, can slide across the, along the straight line. And it just comes off the end and undoes itself. So this kind of symmetric knot is quite fragile. Or, if you like, if you knotted it like this, as far as it’s somewhere in the middle, it’s quite tight, and it’s, it’s secure. But if you want to untie it, you don’t have to go in and mess around with just undoing that, I need to, a little bit. You can pull it off, slide it off completely. Whereas, if you made the other rotational knot, which one is it? It’s I think this one. Brady: “This is a the asymmetric.” Asymmetric one. And this one goes over, this one goes under. It’s not symmetric with respect to the similar. That’s a very secure knot. You can’t really undo it. The only way to undo it is to actually go in. So it’s useful to know, by the way. You know, what is this thing? It certainly has a lot of crossings. But again we’re looking for the minimal number of crossings, so we try to untangle this and open it up as much as we possibly can. And if you’re patient enough and do that

100 Comments

  • The animations for the symmetrical (square knot) and asymmetrical (granny knot) are reversed.

  • This guy has a lot of Free time…

  • If Morgan Freeman is unavailable, this man can narrate my life movie.

  • Tadashi sensei is rapidly becoming my favourite guest on Brady's channels.

  • Wait… so I should stop using loops? Yeah… I'll try to remember to try this tomorrow. Reaf knot, no loops. I'll have a lot of spare lace to tuck in my socks or something, but it'll hold better than with the loops in it. Experiments! ^_^

  • Reef knot versus granny knot.  Any other names?

  • It's somewhat ironic that the square knot is the more secure by normal everyday application, compared to the "granny" knot, but standing alone they flip and the "granny" is more secure. I get why, I just found it interesting.

  • This guy make me wonder about even the most mundane things in my life. Sometime back it was the coffee cup. Now the shoe lace.

  • I was tought the symetrical knot to be a "medical knot" because of its flatness.

  • we call the symetric knot a reef knot and the asymetric one a granny knot.

  • knot videos always make the sailors come out of the woodwork. where do they come from? is there some kind of secret sailor social network where these get posted so sailors can show up and lecture everyone about knots?

  • Looks like you should spend some time on a boat, learning some about the different knots.

  • I'd really like to see a video on Ian's knot for shoelaces. I consider it the best shoelace knot, and maybe there are some interesting differences between it and the traditional knots.

    Plus people need to know about Ian's knot and start tying their shoes the fastest way 🙂

  • I love Tadashi-san!

  • Is this a Tadashi fan service video? lol

  • I'm not a theorist; not a knot theorist and I do not think that's actually a knot.

  • This would be more useful if I tied my shoes more than once in its lifetime since I usually just slip them on tied.

  • the pictures with laces at 1:06 and 1:23 should be swapped 🙂

  • At 00:23 he activates my "hey siri" LoL

  • that lace wouldnt even work at all dislike 🙁

  • Hey, boy scouts, this is the difference between a square knot and a granny knot! But if you're a boy scout, you already knew that.

  • Is there any way you can make Numberphile videos available for download? I don't want to "steal" them by downloading them without the owner's permission.

  • I'm a simple man, I see Tadashi, I like and favorite the video. :3

  • Knot to be picky here, but what did that have to do with numbers?

  • Having experience neither as a Boy Scout nor as a sailor, knots are interesting and complicated to me.

    I was playing with the knots as demonstrated but found I could slide one end out of the other with either knot … the mirrored version was easier, but either worked. Interestingly, the mirrored version was more resistant to pulling on the looped section of rope (equally, pulling the two short ends apart).

    Fascinating stuff!

  • there are a few tricks to change to tie a parallel knot without doing the complete mirror knot (which is very weird and more difficult than you'd think) you can either just flip the underlying knot, or, rather than tying it by going over the loop through the hole, you instead go under the hole and through the hole (it's a small change from what you probably already do). It's fairly hard to explain, but either of these two I found much easier than learning to switch hands. Although, if you wanna relearn to tie your shoes, learn the half second method that Matt Parker showed in a previous video.

  • symmetric double = reef/wreath knot
    asymmetric double = granny knot

  • I tie my shoes completly different than these two.

  • One is a square-knot and the other is a granny-knot.

  • Did he honestly portray the reef knot as less secure than the granny knot? Wtf.

  • WOW !!! Awesome

  • And of course he wears loafers.

  • His symmetric knot is basically a square knot, you can do it by going; Right over Left and Left over Right and you'll have it symmetrical every time. (you can also reverse it: Left over Right and Right over Left) : )

  • I did not receive a notification when this video was published 🙁

  • Isn't this a square knot?

  • Terry Moore did a great TED Talk about tying your shoes, look up "TED Talk How to tie your shoes" it's a great watch.

  • That's basically a reef knot, lays flat, is easy to undo and is ideal for joining ropes, of different thickness's.

    It is (or was when I was young) the first knot you learned at "Cubs".

  • VIDEO SUGGESTION!
    Can you please make a video talking about and explaining the mathematical and statistical background of "game theory" assuming that we know the logical and theoritical side of it! It is a commonly used thing today, yet nobody fully understands the core ideas in it. Thank you!

  • Speaking of secure knots: The symmetric knot, known as a square knot, is actually more secure when used to join two strings together and then pulling on them. In the case of the knot with rotational symmetry this can "walk along the string" and open.

  • Could you do a video on turning a sphere inside out?

  • Oh, this is not the genuine lace knot trick!

    Listen to this:
    1. Make the knot that appears second at 2:06 at right part of the screen; that would be the "mirror" one (not the "rotational", which there appears at the left).
    2. Take the right end of the lace – here it is coloured with blue – and pass it through the lower loop with direction from you to the front of the loop.
    3. This (blue end of the lace) devides the upper loop in two – left gap (in blue) and right gap (in red).
    4. Take the blue end of the lace appearing behind and at the right side of the knot and pass it through the left gap, again in direction from you to the knot.
    5. Pull two ends of the lace to tighten the knot.
    6. Surprisingly the knot disappears!

    I learned this trick 30 years ago as a kid.

  • I want this guy to narrate my life

  • I think some magicians are gonna be pissed.

  • The asymmetric knot will untie itself when tied with two slips as you do for shoelaces. It's a granny knot and generally useless. The other, the square knot with two slips will not come apart unless you manipulate it into a lark's head knot and pull it apart. This cannot be done while your shoes are tied and most uses of a square knot also do not allow it. Academically, it is interesting, however the conclusions drawn are the reverse of what is practical.

  • Safety warning: this video contains very, very poor information.

    The symmetric one is called a square knot or a reef knot. The asymmetric one is called a granny knot.

    Contrary to what Tadashi suggested in the video, the reef knot is considered by knot experts to be vastly superior to the granny knot. In fact, the granny knot is such an inferior knot most people consider ever tying it to be a mistake, and when you learn knots possibly the first thing you learn, apart from never tying overhand knots, is how insecure the granny knot is.

    I teach sailing as a job, often times we avoid teaching the reef knot entirely to students and replace it with something like a sheet bend, because of the horrible danger posed in the possibility an inexperienced sailor might accidentally tie a granny knot when trying to tie a square knot and someone could end up dead or seriously injured.

    Other things Tadashi suggests in this video, like that the square knot is difficult to undo unless you pull it off like he showed, is totally false. The square knot is a good knot because it does the two things every good knot should do: it is easy to untie when you want to untie it, but it is not prone to fail when you don't want it to untie.

    The granny knot on the other hand is just the opposite: it is prone to slipping–i.e. failing, becoming undone or deformed when you don't want it to–and at the same time it jams: becomes impossible to undo when you do want to undo it. This combination makes it very dangerous. Talk to any paramedic about how many granny knots they've had to cut off of shoes in an emergency. You don't want to have an emergency where you need to remove a shoe and perhaps don't have a knife on you and you've mistakenly tied a granny knot.

  • In Finnish, the symmetric knot is called "Merimiessolmu", which translates literally as "seaman knot" or "seamans knot". On the other hand, the rotated one is called "Ämmänsolmu", which translates as "womans knot", or literally "[disrespectful expression meaning aged woman]s knot". The reason for the latter name is presumably because the rotated knot is not secure an may easily become loose. Maybe the art of tying knots was a manly job in the old times, requiring lots of skill and knowledge which was difficult for women to achieve… 😉

  • If magic teleporting shoes existed, which got left behind if and when you used them, then as the centuries pass, the probability of the shoes ending up in an inaccessible place approaches 1.

  • I saw who was featured in this video and upvoted before watching.

  • Topologists…

  • I always tie my shoelaces like Matt Parker does.

  • I tried to do it with my shoelace, but it became a mobius strip. What did I do wrong?

  • Don't pay attention to these cretins numberphile, they're just practicing their basketball trash talk and pay no attention to content. I've been using square knots my whole life and never knew that! I enjoyed your vid.

  • Dr. Tadashi's 3D visualization skills are uncanny

  • Ah! Mr sparkle!

  • Honorary Dr. Haran….

  • The symmetric knot is called the square knot.

  • The two cartoon examples at 1:05 and 1:20 are swapped.
    After the symmetric knot in the cartoon you tie a assymmetric knot and v.v.

    The symmetric knot makes it ""parallel"
    and the assymetric makes it "perpendicular"

  • You should do a video on Normal numbers.

  • how could i contact cliff stoll? i recently got a klein bottle

  • The "asymmetric" knot (known in Boy Scout parlance as a "granny" knot) is a quite poor knot. It comes undone trivially, while the symmetric knot (called a square knot) doesn't. If you use a granny knot to tie your shoelaces, you will soon be tripping over them as they untie themselves.

    The square knot won't actually slip, because in practice, tension on the knot comes from both strands entering the knot, while the ends are loose, rather than having the tension come from only one strand, as Tadashi shows in the clip. I say "in practice", because of the tension on the knot were to be in a different configuration, you would choose a different knot.

  • What we see in comments is a classic example of a bike-shed effect. Everyone who knows anything about such a trivial thing had to put their 2 pence in.

  • Huh. That's interesting.

    If I'm not misreemembering the vocabulary–and we totally ignore the single-pull loops:

    1. Both kinds he discusses are spare knots.

    2. The parallel/symetrical one is a reef knot (often also called a square not, but I don't think us land folks are careful enough with our vocabulary to confidently assign that name with that knot and think it should be used with a number of knots with similar characteristics). My book on knots calls it the most over-used and least secure of all the common knots.

    3. The perpendicular/non-symetric knot is the thief-knot, possibly because it's a pain in the neck to undo.

    And now I know why my left shoe insists on untying itself. I thought it might be something like that, but now I know and can experiment.

    THANKS!

  • Why you didnt color halves in different colors? It would be better, i think

  • I realized the you sometimes recommend books at the end of some videos. It would be nice if you make a video recommending books about maths, physics, science !

  • Hey, could you do a "reaction" or rather a statement video to the Gödels incompleteness theorems? I think it would be a great topic to discuss about. 🙂

  • This is boring

  • And yet in the shoelace application the proper symmetrical / square (aka reefknot ) version is superior because it does not fall undone.

  • The animations at 1:07 and 1:21 are backwards and need to be swapped.

  • funny, i NEVER have tied my shoe laces in ANY of those ways ^^

  • I think any boy scout with knot experience will disagree with this conclusion.
    Reef/Square knots generally hold better and ARE easy to undo after being loaded.
    Granny knots are noted for slippage and are diabolical to undo after being loaded.

  • Well I have slip on shoes so no need to worry.

  • dude, that trick not he tied is just a simpler form of tying a neck tie. big over small big behind small big goes under, big goes through loop

  • 1:45 THAT IS NOT A KNOT!

  • As Tadashi says @ 2:20, "I'm not entirely sure about this. You explore." So I did.

    The symmetric knot results in parallel laces and the non-symmetric knot results in the perpendicular laces. So the animations at 1:00 are backwards. Also, this confirms many of the comments below that the symmetric knot is less likely to work loose, as I've noticed in the past that if my "ears" don't come out parallel, my shoelaces eventually will be untied.

  • Hmmm. I now wonder if my shoelaces keep getting undone because I knot them the symmetric way.

  • No comment on the super punny name of the video? Lace knot trick (Let's not trick)

  • He sounds like the game show host from the episode in which the simpsons visit Japan.

  • I have been tying my shoes the wrong way my whole life…. started tying them asymmetrically and no double knot required!

  • This is apparently one example where the theoretical diverges from the practical. The "symmetrical" knot, aka the reef knot or square knot, is much better for tying one's shoelaces because (under ordinary circumstances) tension will not be exerted in the direction which will pull the knot through and undo it in the fashion shown. Furthermore, the direction in which the tension will be exerted will have the effect of tightening the square knot. The same cannot be said of the "asymmetrical" knot, aka the granny knot, which will loosen when tension is applied in the relevant direction.

    I confess that I use a square knot because it's simpler to tie, but the sheet bend is superior to both the square knot and the granny knot for shoelace tying (and honestly for most other applications as well) because it combines the best features of both: can't be pulled through and is self-tightening under ordinary circumstances.

  • As many have already said the symmetrical, square knot, is the preferred knot. In the real world it is not a knot unless you can untie it as easily as you tie it. The square knot turns into two half-hitches when you straighten one side.

  • One is a square knot, the other is a magicians knot. That's boy scout stuff.

  • I actually already to this knot!

  • When we tie knots for first aid (bandaging, spine board transfer etc) we use square knots bc they are strong yet quick to untie.

  • I don't tie my shoes normally. I never learned the normal way…

  • A Boy Scout or sailor or climber would tell you the symmetric version is a square knot, the asymmetric version is a granny knot. The square knot is preferred as it is more stable under load (tension from the shoe) and won't jam (is easier to untie). My preferred shoelace knot is a square knot with the entire loops used throughout the entire second crossing. In other words, the second crossing is made using the loose ends doubled into loops. It is very secure and pulls open nicely.

  • This guy needs Matt Parker's help

  • HES A WITCH

  • That is interesting

  • "it is knot symetrical"

  • what's wrong with a linemen's splice!? or the bujt crimp?

  • those look like liberal arts shoes, what are you doing in the math department?

  • this is a square knot vs a granny knot (with bytes)

  • The symmetrical reaf knot is better on a shoo. As the tension is different than in the example. You can not do the slide thing when the knot is on a shoo. If you are double knotting, then it is because you are using asymmetric knot, the bow will fall at 90°. Just change the way you do it: left then right or right then left.

  • Seamen always use the symetrical knot & never the non-symetrical one …

  • If you are in the United States Army this is a huge problem. The standard is the square knot, but you never get it on the first try. You always have to do a Granny knot and correct it. It's part of rappelling out of a helicopter.

  • 1:50
    This is KNOT symmetric

  • So basically what he's trying to say is that always make sure the second knot you tie on your shoes is the opposite way so just in case if second knot comes undone, and if you end up with those annoying 2 knots overlapping, you can easily untie the two knots. Genius

  • The animations in the first part were mismatched, not that anyone else cares…

  • 0:33 Of course, instead of learning to tie the second knot like a left-handed in order to produce the "parallel to the shoelace" knot, you can just tie the first knot like a left-handed (which is way easier) and continue with the second one as usual. Same result.

  • One's granny knot and one is a reef knot, all sailors know the reef knot is the better one Tadashi has it backwards

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