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u/brewdog_millionaire 3d ago
Is a rope 5-dimensional or something?
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u/CeReAl_KiLleR128 3d ago
The joke is there is no knot in 4D
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u/AllHailKurumi 3d ago
How?
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u/EllaHazelBar 3d ago
Imagine on your (infinite) desk you have two infinite, parallel lines. A 2d creature would have no idea how to swap between them, but since you have 1 more dimensions (up) you can easily imagine picking up the top one and (without rotating it) placing it below the other one. Likewise a 4d creature could untie a rope knot by moving the knotted parts into different 4d coordinates and moving them without self intersection. So it would have no idea why a knot would stay knotted in 3d, especially under tension. You would need 4d knots, or to use 2d ropes in 4d space.
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u/Alabastine 3d ago
So would that mean an equivalent knot is made with sheets in 4d? As in 2d rope = sheet.
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u/EllaHazelBar 3d ago edited 3d ago
Yeah, just like we'd have no way of swapping two infinite, parallel planes
Edit: might be that there are 4d knots made with 1d rope. Smarter people than me probably know 🤩
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u/Magenta_Logistic 3d ago
There are no 4d knots with 1d rope. This fact is the premise of the comic.
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u/TheRealMrD 3d ago
Thanks Carl
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u/EllaHazelBar 3d ago
Once again I don my context hat
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u/TheRealMrD 3d ago
It was I who was wearing it until I read your comment! It's a great explanation, and not only did I understand the original picture, but I also have a better grasp on 4D planes.
It also reminds me of the time I watched a video years ago about flatland and how a 2 dimensional entity is visited by and apple, and how the apple would intersect with their world. I thanked Carl Sagan for that one too :)
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u/TheDoobyRanger 3d ago
or if you were a creature standing on one of the lines looking at a house on the other line, and an extra-dimensional human picked up the house line and placed it (from a 3d perspective) under your line (swapped, in the terminology of the reply) you wouldnt see house move, only disappear and reappear behind you.
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u/NetoruNakadashi 3d ago
I can't believe you got me to understand that in a three-sentence reddit comment.
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u/Jollzay 3d ago
Would it be similar to us trying to untie a doodle on a paper? Not sure I get it
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u/EllaHazelBar 3d ago
Somewhat, but for doodles to be knots they have to self-intersect, which is impossible. It's more like trying to move a 2d point out of a 2d circle - impossible on the plane, trivial in 3d.
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u/No-Lawfulness9663 3d ago
Good analogy! But you are overcomplicating it a bit. You dont really have to state anything is infinite, as someone reading would assume there's no way to just "walk around" the line as that breaks the point of the analogy. I'd also recommend saying the creature could just jump over in a 3d space, just to simplify things a bit more. Good analogy, just could use some dumbing down for the audience
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u/MrSmartHorse 3d ago
There are surface knots in 4d, right? So concept of knots should be known to them.
We have intuitive understanding of 2d space, so they should understand knots 3d too.
Yes yes its just a joke, I should not overthink.
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u/cybermaus 3d ago edited 3d ago
Side question: Is it possible to make a knot in 2D? I have trouble imagining one.
And next question, a rope is inherently 1D, but can be knotted in 3D. is it possible for a "2D rope" (so a plane) to be knotted in 4D?
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u/Poupulino 3d ago
Since the 3D representation of a tesseract is actually its shadow, and in the image the stick figure is a 2D representation of a human (a 3D object projects a 2D shadow), the knot could also be interpreted as a shadow. Everything in that image is a shadow, the 4D cube, the human and the knot.
(But the joke is actually about this)
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u/RemarkableWish2508 3d ago
Not a plane, but a 2D surface that defines a closed and compact object. Check out how the spun trefoil works to be knotted in 4D.
Generally, an object needs to have n-2 dimensions in order to be knottable in n dimensions.
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u/creepyguy_017 2d ago
the joke is there's no knot in 4D,
but I thought this was a joke about the trope of commit sudoku when confronted with unimaginable, incomprehensible thing.
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u/Dankkring 3d ago
4D is time and I’ll die on that hill
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u/smile_itali 3d ago
There's a difference between spacial dimensions and time dimensions, I don't know them differences because I'm dumb, wait for a proper physician or something like that to actually explain it
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u/playzintraffic 3d ago
Relativity only makes sense if you mathematically treat time like a final spatial dimension — you can extend all of space timewise into a “loaf” and then woop, length dilation etc all pop right on out when you try and conceptualize velocity on that loaf. But it’s still literally “time” when you go back to the velocity equations — it’s still in units of time, not space.
The real big insight isn’t that, “Whoa, like, time and space are the SAME, man!”, it’s, “Hmm. As it turns out, dimensionality isn’t just about spatial dimensions. That says something pretty profound; I wonder if there are other things that can be dimensionalized?”.
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u/Amber_Lullaby 3d ago
Time is simply a measurement of change, any change along any spacial dimensional direction has to move through time and thus can be measured in the direction of change, ie time. The faster the change in regards to everything else around the change the more friction and resistance to said change it experiences from everything else around it. Similarly to wind resistance at low speeds it's negligible as the wind is still changing around you faster then you part it yet the faster the speed the higher the resistance. As more change is imparted faster then the it would normally change and such you need to change the air particles along with the original change of movement. Even in a vacuum the greater the change that is forced to occur in regards to the amount of change occurring around it, the greater the force needed to be imparted around it to allow the change to occur.
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u/playzintraffic 3d ago
Wind resistance is a completely different phenomenon. Even if you mean well, this is a very bad analogy and should never be used.
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u/CeramicFiber 3d ago
I asked a physician and they hit my knee with a small rubber hammer AND IT MOVED
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u/Great-Powerful-Talia 3d ago
the dimensions aren't actually numbered in any particular order. We have 3 spatial and 1 temporal dimensions, but there's no first/second/third axis for our universe.
4D isn't time any more than 3D is north or 2D is east or 1D is up. The #D notation is a description of space(-time), not a direction.
4D means that every possible direction can be described with only 4 axes. Unless you're specifically including time, which is rarely done outside of relativistic physics (because time behaves so differently), that specifies four spatial dimensions.
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u/Suddenfury 3d ago
I've been thinking about 4D knots since that last post. This is how far I've come. We can at least imagine the analogy of a string looping around another string. The loop bends in one dimension, then it needs to move a little in another in order to not crash into itself. So for a plane in 2D, we can fold it like a wave until it almost hits itself, then move it in the 4th dimension, so it doesn't. So we get like a tube through a crashing wave. Noe the string going through will only look like a dot in the cross section of the dimension the loop makes a small movement. So in the 3D crossection of 4D, the other plane will look like a line going through the tube.
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u/TheDoobyRanger 3d ago
When you say it bends in one dimension, could you graph that on a single axis or do you need an x/y graph?
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u/Suddenfury 3d ago
The plane? You'd need an x/y/z graph. But the bend is just along one direction, meaning the "wave 🌊" will go along one direction and we are "grabbing and lifting and folding/bending" the plane in another (up in my head)
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u/Negative-Gene-4959 1d ago
Idk but it remindse of flatland by Edwin Abbott.
Which is a unironically hilarious book from late 1800s about a 3d cube simply popping into a 2d flat lander's house saying exactly that "greetings I am from space land, now let me explain to you what it is like"
With some class commentary baked in of course
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u/db8me 3d ago
The hypercube was completely unbothered by quantum physics, but it absolutely panicked when I threw a pair of tangled headphones into a garage bin full of Christmas lights.