How Knot To Hang A Painting
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- Опубликовано: 13 апр 2025
- Subscribe to Up and Atom! / @upandatom or start with Jade's video on quantum tunnelling: • What is Quantum Tunnel...
You've got a painting and two nails. Can you use both nails to hang the painting so that if either nail is removed, the painting falls? That's the puzzle: in this week's guest video, Jade's going to solve it with maths.
Thanks Tom. It was awesome to be a part of this :)
Was gonna come up with a pun but I can see there's already a bundle.
great video. I was a subscriber before this video.
good video 9/10
That was a great video and really easy to follow even if you don't know anything about. Only thing that was a bit to fast was the undoing the 3 knots at once maybe slow it down there or show them one after another (but that is just nitpicking^^)
Thanks for this, very cool.
Great video. I'm going to subscribe right now.
Yes, I regret not changing the end card to say "Things You Might Knot Know". Thank you so much, Jade!
You have disappointed me m8 ngl
Surely, you mean "I regret *knot* changing the end card"
Tom you missed the opportunity for a great pun twice. Congrats
Tom Scott Knot theory and String theory, well it seems our universe is knitted!
Have you uploaded these in the wrong order, because the pun at the end seems to be about the video last time.
Guessing they were originally gonna call this string theory but that was already taken
Knot theory is older!
@@MattMcIrvin Guess they were originally gonna call it knot theory, but that was taken
that's knot what happened.
Mn M that joke was strung together very well, my friend!
@@zacjohnson452 I have to knot in agreement
Solution: forget the string, put the painting on top of the tacks. Boom. Solved.
Damn
Outside-the-box - the only realm mathematics simply cannot penetrate ;)
That was my solution too 😂
Easy as that
Not a valid solution.
"and next week, a video that may leave you breathless"
*points camera at water*
is that a threat?
next video: "fishermen who can hold their breath for 10 minutes"
so........ yes
test
Everyone who watched that next video was drowned.
This proven by the fact I didn't watch it and I'm alive. I don't know anyone alive who watched it.
Damn right it's a threat!
Sounds like something 47 would say
String theory: who are you?
Knot theory: I'm you, but I actually exist.
string theory: vibrates angrily
But that's just a theory
@@jeanchachalo695 a game theory
string theory: bull strings out of your ass
@@LaraOlina a _quantum_ theory
This was the perfect example of how math is not about making easy stuff hard, but to make seemingly impossible stuff possible.
It is more like making simple things hard in order to make impossible things hard.
teacher: impossible
Great, now I can hang up all my paintings incorrectly!
depress
meep
On the plus side, easier for when you have to move house
@@DewMan001 I like the way you think
only easier if you don't mind leaving a pin in the wall, otherwise you still need to remove both.
1) Place both pins into the wall
2) Rest the painting atop the pins
3) Throw out the string
This was my thought too 😂
oops, step three is unnecessary You do not need a string at all.
4) use the pins and string as a hunting bolo and use the painting as fuel.
Mathematically you could balance the painting on one pin and them removing the other pin obviously would do nothing
What if you have 3 pins, and want the painting to fall if ANY of these 3 pins are removed?
oh wow that was way more complicated than I ever thought it would be
yesh this is secretly a test for adhd, if you zoned out you have it 😀
I mean I've been doing jobs badly for a long time
Tom, you sly dog. Tricked me into watching somebody else's video.
I mean, I’m not complaining
When you changed the pins to strings I could tell the solution was going to be linked (pun intended) to the Borromean Rings somehow, but I couldn't figure out how the heck you were going to map that onto pins that couldn't change shape or be closed. So not only is this just a cool video but it also helped me understand why the Borromean Rings are even a thing. Thanks for that.
Up and Atom has some great videos and she's super animated and passionate so is a pleasure to watch.
For anyone curious, this configuration has a name. A Brunnian Link is a nontrivial link that, if a knot is removed, becomes a set of trivial, unlinked knots. This particular configuration of this link is the simplest solution, and is called the Borromean Rings.
A Brunnian link can theoretically be done with any amount of circles. Interesting solutions include the common braid (which is Brunnian), or if you have ever seen loom bands in use, those are merely sequences of Brunnian links
thanks!
NERD!
Kill me if you actually have a degree in this
i came up with the solution before seeing the explanation using that knot, and it worked!
*Tries to balance painting on top of pins*
"Does this count?"
69 likes... congrats👏👏👏😂
I know this is a science theory video but my brain is still going "why would anyone want their painting to fall?"
Maybe, Banksey-like, you want to destroy a piece of art immediately after it's been auctioned.
Maybe a rube-goldberg machine?
obviously to mess with someone else
I think it might have maritime applications: moor a boat at two points, and removing one thing sets the boat entirely free.
Awkwardly enough, in my brain this is how nuclear launch keys work, removing one key makes the system shutdown the same way one pin gets pulled and things still fall down
It would be a great party trick to memorize how to do this with like 7 pins and shock everyone
This is much easier to get a handle on than the OTHER kind of string theory. Well done!
Was I able to solve the problem? I’m a frayed knot.
You sir have out punned yourself kudos 🎉🎉😄
I was knot expecting that!
Struck a chord with that one.
Am I knot getting the joke here
And the prize for the best pun goes to... It's a tie!
7:51 when both version of her said mathematics, I got scared
Klapaucius Fitzpatrick it was adorable, but math is most definitely not😂
@@aspnnn That means that you haven't got deep enough into mathematics in order to appreciate them, and it's the fault of the educative system.
@@GRBtutorials I actually have had some of the most amazing math teachers who genuinely care about what they are teaching and do it very well, but math just isn't my cup of tea. I definitely agree it is important, but I just automatically correlate math with tests and homework:/ I guess I am just coming at it from the wrong perspective.
"Mathematics 😈" AAAAHHHHHHH 😱😱😱
mathemathematicsmatics
Solution: Place the pins 1 string width apart so a knot in the string can't pass between them.
This one's really clever, and a knot at the end of the string would mean you aren't relying on tension between the pins to hold the string. AND unlike the "rest it on both pins" it uses the string. And technically there's a knot involved too.
Such a good idea why can I never come up with these :D
I like your solution. Mine would be to tie a knot around the pins and just slip the string throug the holes in the painting. That way the string stays at the wall, but the painting will slip off.
The comments here are just trying to create memes and rambling over some mini tangents. Can we quickly appreciate what a nice intro to "problem abstraction and reformulation" and knot theory this was!? I have a PhD in engineering and I am used to certain more sophisticated mathematical tools like tensor calculus, but I have never looked at knot theory - this was really neat!
Knot theory belongs to a branch of pure mathematics called abstract algebra, which is one of the few biggest branches of pure mathematics. Abstract algebra can look less complicated than applied calculus on the outside but it is actually very complex and sophisticated once you go deep enough into. And also very fun and refreshing since it doesn't look like anything like the mathematics the vast majority of people have learnt in high school or in science majors.
@@cheungch1990 Isn't knot theory a branch of geometric topology?
I stopped at 0:47.
My answer: Put the two pins very close together, place a loop in between and tie a knot in the loop above the pins. Since the knot wont fit through the gap between the pins, it wont fall unless one is removed.
Exactly my idea as well!
Haha I was looking for this! Nice to not be the only one 😂
now scale it to 3, 4, 5 etc.
@@The1wsx10 if the wall is not flat but the inside of a tube, the knot could be balanced between 3 and maybe even 4 pins whilst still satisfying the conditions. With 5 it'll get very hard though :D
Cheeky
When you changed the pins to strings I could tell the solution was going to be linked (pun intended) to the Borromean Rings somehow, but I couldn't figure out how the heck you were going to map that onto pins that couldn't change shape or be closed. So not only is this just a cool video but it also helped me understand why the Borromean Rings are even a thing. Thanks for that.
The pins are effectively closed. Gravity means the string can't slide up and off the pins, so the upward pointing pin, the wall behind it, and the higher gravitational potential above it form a loop that encloses any strand of string that goes above it. If gravity isn't strong enough in your room you could use screw eyes instead of pins and get the same effect.
'Removing a pin' doesn't have to mean literally removing a pin - it could just mean helping the string overcome gravity to pass above it.
You've created a mechanical OR gate.
And?
Or would it be an AND gate? It only hangs if both are true.
You mean AND gate. I suppose it would be OR in negative logic, but who thinks like that?
@@PurpleViking221 clearly it's a knot gate...
@@PurpleViking221 Depends how you frame the problem (pun not intended).
If the condition is "pin N is *present*", it's an AND: "painting is hanging" = "pin 1 is present" AND "pin 2 is present".
If the condition is "pin N is *removed*", it's an OR: "painting is hanging" = "pin 1 is removed" OR "pin 2 is removed".
Edit: See Yadobler's comment for a fuller explanation, cause this also depends on how you define the output too.
The X shape string support is the best for *framed pictures and mirrors.*
Because the movable cross point in the crossed X string allows adjustment.
would you mind explaining in more details? or a phrase I can search for. because I tried and nothing came up
*I CLAIM INTERNET BRAGGING RIGHTS!*
It took me way too long but I finally got there, even if I don't have any theory to back it up that I'm guessing I'm going to learn as soon as I watch the full video.
I knew the solution would need to have the string "on the outside" of both nails, so that if you take one out the other one is not inside the string's "inside area" anymore. I also suspected that you would need to come up with something fancy where one nail would be inside the string area twice, so if you remove it the other one is free and if you remove the other one it will be "twice inside", and so really outside. Kinda like multiplying negatives.
So the solution goes, supposing you put the nails side by side, from the left corner of the painting, string above the left nail, then carried to below the right nail, turn over the right nail and straight over the left, then from below the left nail carry it above the right nail and straight down to the right corner of the painting.
Oh, the satisfaction!
I love when Tom gets guest videos, because I get to learn about a bunch of great creators I never would have found out about.
This was really interesting! My initial idea was to put the two pins directly next to eachother, then tie the middle of the string into a knot that was thick enough to get caught and not fall through the gap between them.then, it could rest on top of the pins but would fall if either was taken out.
engineer vs mathematician
My solution of using around half the required tension on each pin is similarly engineer-y.
Awesome video Jade! I've never even heard of knot theory even though it sounds so fundamental. I still remember the rabbit going around the tree before the burrow knot from Scouts so assuming my Nobel Prize isn't far away?
I had to tie bowlines around my waist cos I could never remember the order of the rabbits and trees
Medlife Crisis I can tie my shoes
You can't have knot heard of it.
Guys. Learn your bowline. It's actually very easy to learn (just spend a couple minutes practicing every day for a week or so) and very useful in a pinch. It's also extremely versatile and can be used in place of most other, more specialised knots (many of which are bowline variations anyway, like the sheet bend to join two lines).
That knot is how you tie a tie XD
Everyone in the UK learns that because of high school
Hey that's Cherry the Chicken, one of my artworks🐔! Good work Cherry my feathery friend.
Timmy: I wish we were string so we could study knot theory!
Cosmo and Wanda: *Poof*
2:28
I see they brought in Poof, too.
If Tom Scott can’t solve a puzzle then I am totally screwed.
@@ragnkja That's not very strange.
Even trying to use the solution in practice I can't make it work 😂I feel dumb XD
I managed to solve it with 2 pins quite easily. I think my framework generalizes to 3+ pins, but it's damn hard to think of a move sequence that will cancel itself out.
My solution uses "holes" between the pins as a reference. When braiding the string, you start at the bottom. Valid moves when braiding the string are moving through the left, middle, or right "hole". After a move like that, you are at the top (above all pins). You can now make another move, going through the left, middle or right hole.
You need to end up on the bottom to attach to the picture frame at the end.
The rules are:
Holes are numbered 1, 2 and 3.
Going through the same hole twice is the same as not going through it at all.
Removing a pin means merging two holes into one. One of the ways to do this is to add 1 to all digits that match the pin's number.
For 2 pins, the solution is 123123 - it does not contain any doubled up hole numbers, and each number appears at least once.
If you remove the left pin, it becomes
223223 => 33 => empty.
If you remove the right pin, it becomes
133133 => 11 => empty.
Now, I can't think of a solution for three pins, because this method does not give you an algorithm to think of such a braiding. It's just a framework that really helps to think about it.
I came up with a solution that doesn't work as knots, but does drop the painting (but not the string) if either pin is removed - tie the string into a loop, thread it through the holes on the painting, and hook one end over each pin. Provided the string (knot and all) can pass freely through the holes of the painting, removing either pin lets it do exactly that, allowing the painting to slide to the floor.
That was my solution too.
I guess you can still model this with knots by representing the painting as two entangled knots
Had the same Idea before I got tied up in all the knots.
yep, a far simpler solution
yea... so much about this video is messy. There are easier solutions, there was a lack of cause for seeking the intended solution, etc.
Me:
*Doesn't know how to solve it*
*Watches Video*
*Goes away more confused*
Knot just me, then? (I'll get my coat...!)
yep secretly a test for adhd😂
I thought this video would be about how paintings are hanged or framed in a museum in a way that does not damage them over time.
The knot pun in the title makes more sense now that I've seen it.
how to solve it
“get rid of everything in it, so then it’s just nothing.”
"now, after we've cleared everything up, we go backwards"
Sorry, can't watch the video im a little tied up.
Knot a problem, come back when you are untangled.
Giggity
kinky
I literally need to hang a bunch of paintings in my house and this didn't help me at all...
* This did knot helo me
You could accept that they will always be crooked. It would make your life easier, and keep dinner guests entertained for a short time.
instructions unclear, accidentally got involved in shibari
'accidentally'
😲
@@productofmytime exidentali
Lucky you
Had to Google Shibari, luckily I was at home
My solution would be to simply let me do hanging of the painting, it will eventually end up on the floor even with zero pins removed.
I noticed that the meaning of X-1 is actually *tied* to the previous X. What I mean by that is you can represent String1 going under String2 by X, if next time the same string goes over again, then that becomes X-1; and if it goes under, then X-1.
So a string going over or under another string can still represent X depending on what previous sequence was. (See @5:20, string goes over, then under, which is physically different, but has same notation ie X)
I had a completely different idea.
I would hang the picture in the middle of the string and pin each end directly through the fabric (or tie a loop around the pin).
LIKE: (PIN) ----() Picture() ---- (PIN)
If one pin is pulled the string zips through the holes of the painting and remains on the other pin while the painting falls.
Tada :D
Or do you think thats outside the rules ?
Or you could make the string into a loop like the rules, and instead make the pins farther apart than the distance to the floor. :)
@@JNCressey It's not mentioned that these are the rules, though. Which is why the solution is so unsatisfying. It solves it according to unmentioned rules.
I like how you think!
@@jorgis123 Well, it's a solution using knot theory to abstract the problem, and it is actually mentioned that in knot theory, a knot is basically a loop, so that is a rule.
I think the only thing that is more implicit is, that the string on the painting and the painting itself are one object that always drops together (I'd assume since the painting doesn't interact with anything, it doesn't matter if you use one knot to represent both, or link the purple knot to another knot that represents the picture, so they just used one).
If you take away that more implicit rule, it could potentially open up at least another solution, but I am not sure if that is valid in the ruleset of knot theory.
That is knot allowed
As people have said, there are lots of simpler solutions (such as the string going from one pin through the painting to the other pin, or hanging by a pincer grip that requires both pins close together to maintain) because the problem, or the rules for the desired solution, weren't clearly enough defined. Nevertheless, it was an interesting video, and the explanation of the basics of knot theory was very clear and concise.
ah thanks for explaining the "pincer grip" thing, I couldn't figure out what those people were on about
I immediately thought of the Sheepshank knot or maybe the Borromean ring... Turns out they are all essentially the same solutions
This was soooo amazing. Not because of the result but because of the great way you showed how to work on difficult tasks systematically. Great job
"if you want to win a Nobel prize you better start knoting!" Furries: I am something of a scientist myself
And that's why I couldn't take the video seriously, at all.
Ok that was epic
1:55 was really satisfying watching the string turn into a straight triangle and back again 🤷♀️
-Looks at video title
-Gets angry
-Video plays in background as I try to think up a good comment
-Has no idea what the video actually contained
-Rewatch
Tom you genius, you've doubled your views
That's not how views work.
I did google it to verify before posting. It was a bit confusing sorry :(
I'll go to my room
@@paradox9551 they used to work like that so it makes sense
"Views" don't matter; watch time does.
@Liam Walton, and your comment still sucks. Not fair, I say.
The more I watch physics and mathematics video, the more I feel like my brain is far more smooth than average
Same!
We too can tell that by your English.
Me building a solution relying on the weight of the painting.
The video: the painting is just a joining of the ends, and is unimportant.
Calculus: i sleep
Tying some strings together: now we're talkin'
*This is knot very useful*
Oh no you didn't!!
I just realised the title is "knot" not "not" after reading this comment.
Technically knot a knot
WoW! Bob McCoy on a non Inside Edition video... I did *knot* know that was even possible.
I did knot understand the video because I was too busy staring into space.
Noone:
Nobody:
Literally not a soul:
Tom Scott: Here's how to hang a picture so it falls
Every painting I hang falls, as if by......I'm going to say _intuition._
Knots are a major part of my career and I will need to watch this video many more times before it makes sense to me.
RIP to everyone else who was really stoned and just curious about framing/hanging paintings.
Thanks YT for bringing me a video that gives me flashbacks of 1970's daytime Open university on the TV.
This is a nice introduction to knot theory, but the method I used to solve the puzzle, topologically, seems easier by far. In that case, I establish the area within the inital loop as the "inside", and the area external to the loop as the "outside". The problem then becomes one of rearranging these boundaries so that both pins are situated on the "outside". It only takes one true fold of the loop to meet those conditions.
Wow, a video showing a new math theory that I was actually able to comprehend. Very well explained :)
The problem was deconstructed in a very understandable way! I’m actually glad Tom is taking a break so these excellent channels can get the exposure they deserve.
this is just the thing i messed around with as a child. turns out there's an entire theory about it
Tom: She’s going to solve this puzzle
Me: :D
Tom: With maths
Me: D:
Based idiot
I watched the whole thing and I still don’t really understand. Like, I literally understand the concept, but I totally couldn’t explain it back or hang the chicken the right way. 🤣
Her translating the over/under to the clockwise/counterclockwise wrapping around the pin was simultaneously where I lost it and the thing that dragged me back in. I think this knot math is something people probably start taking a class in and then either drop it or persevere out of love.
Unless you're a genius it will take you some time to understand each individual step. The video is only about 8 minutes. I would estimate that if you read a well summarized written version with examples and clear definitions, you could more or less comprehend it in 2 hours.
There's an entire group of human beings that are infinitely smarter than me, and it's hard to be reminded of that...
I'm fairly confident that I will never have any use for this knowledge.
And yet I still watched it till the end
Did I just fall in love?
W....with math?
Who needs to learn trigonometry in high school when I can just learn braid notation instead?
False choice, and why don't you find any value in trigonometry?
If you'd learnt braid notation but not trigonometry in high school, I'd bet a lot of money that you'd be saying the exact opposite on a video like this about trigonometry. Novelty and presentation really make this, and lots of similar, excellent videos exist about trigonometry
I was just joking - trigonometry's great.
What was bad about trigonometry?
I need to study for my trigonometry test tomorrow but I’m watching this video instead 😂
Rest the picture on the two pins (like a minimal shelf), if you remove either of them the pic will fall
Thinking outside the box, I love it!
That's exactly what I thought 😂 What's all this complicated string nonsense
That wouldn't be "hanging" the picture.
From Merriam-Webster: "hang - v. to fasten to some elevated point *without support from below"*
That's too simple! Genius.
Solution doesn't extend to three or more pins, and relies on the pins being somewhat horizontally aligned. The important part as noted was that it gives a framework that works with any number of pins arranged in any way.
Tom Scott is the best channel for discovering the rest of the edutainment side of youtube!
Love it! 💚
I studied math. I never saw this info before... neither was I able to solve it....
But after seeing this video... the info seems so bassic. I am glad you teached me this!
I bet a lot of magic tricks can be made with this info. :)
So, the goal is anti-redundancy?
As in, “let’s design something with as many points of failure as possible,”
Thank you! I am very confused and understand nothing!
misteryA555, right?!??! Imagine her as a teacher? FML
lmao mood
At 1:03, I know that's what it's actually called, but I'm still disappointed there wasn't a string theory joke in there.
Similar answer, but symmetric so that the string hangs from the outside of both pins: xxy⁻¹y⁻¹x⁻¹x⁻¹yy. Brute forced that answer, but learned the notation from this excellent video!
This is what algebra sounds like to foreigners
I cannot think of a more complicated way to explain that... imagine if this lady tried to explain how to rig a sailboat
Even that's really simple. I've done it on a small scale.
Changes pins into string
Minutes later: The strings are too hard to keep track!
I mean.. last week's video also left me breathless
When you thought you were Learning quantum physics for a minute
There is a trivial solution to the question at 0:46: tie the string in a loop, thread it through both holes and put the loops over the pins. Of course she's asking for a solution where the painting and the string both fall. How many of us paused the video and solved it; how many went just-tell-me-the-answer?
I was ready to fall asleep until Jade mentioned now you know how to solve it with any amount of pins. OK, well played it is interesting.
Im knot a kneblin
I'm a knome
And you’ve been knomed
Next video: How Knot To Tie A Noose with Rusty Cage
(family friendly content version)
This is one of my favorite videos ever! It’s so geeky but you feel like you can understand it. I think people should watch this video when they ask why we need math in the real world.
Finally after binge watching both channels youtube brings my heroes together.
Kudos algorithm!
Respect for those hand drawn 3 little pigs that only had 2 seconds air time
Pin both tips of the string to the wall and pass the string through the holes in the painting to hang it, making a \_/ shape with the string.
EXACTLY. That's it haha, exactly my thought. That's the problem with abstracting math, there are always other ways :) Liked the actual awnser though
Tom Scott and Up and atom in the same video???
I must be dreaming
On second thoughts, I’ll just put the painting on a stand...
This went from a fun puzzle to a math problem where the solution is just arranging it into the borromean rings. How.
Magnificent way to bridge the distance between common reality and the abstract world of Mathmatics! Just brilliant!
Put the two pins in the wall, put the painting above that, then shove the string on top of the painting.
"knot theory"
The internet broke me. I can't take it seriously with that name.
Do you mind to explain?
@@randomguy263 trust me when i say you don't want to know
@@nobodys_winds6580 Furries
@@nobodys_winds6580 Okay, you asked for it: when canines copulate, the male's penis expands at the base in what known as a knot and this locks the pair together. In furry porn and werewolf/pack dynamics fanfiction, this feature is used in sex scenes. So this word has a strange sexual connotation for people familiar with the shenanigans of these internet circles. I'm sorry.
Like a fox
Tie the string into a loop. Fold the string, and feed through both holes. There should be two strings of the loop running through each hole. Then put the 2 ends of the loop over each pin respectively. When you pull either pin the string will pull out of the painting; the string will remain hanging but the painting will fall
This was absolutely fascinating.
This is an amazing video because it’s so smart and far beyond my mental capacity, but I still can’t get over how they slowed down the 60fps footage at 7:44
This is Knot my favorite form of Physics! It's too Loopy!
How long did it take me to solve this one? Well, how long is a piece of...
Oh, never mind.
Pre-watching prediction: Tie the pins together so removing one removes the other
hakairyu1 wait that’s absolute genius
Harvard we got an excellent candidate for you.
Ah the elegant simplicity.
Same here.
I was kinda lost until the physical example was given. Then I understood the diagrams instantly.
Make a closed loop of thread. Hook over one pin, thread through the two holes in the picture and hook onto the other pin. Meets challenge. Appreciate scaling potential of mathematical solution. Bravo.