Rubik's Cubes in Less Than 3 Dimensions!
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- Опубліковано 28 тра 2024
- The classic 3x3x3 Rubik's Cube is a 3-dimensional twisty puzzle. Some of you may be familiar with the 4-dimensional Rubik's Cube, but what about puzzles in lower dimensions? This video will explore twisty puzzles in 2D, 1D, 0D, and beyond!
Chapters:
0:00 Intro
0:26 Dimensional Analogies
1:50 2 Dimensions
3:27 1 Dimension
4:52 0 Dimensions
5:23 Negative Dimensions
7:07 Complex Dimensions
7:33 Complex Polytopes
8:24 Outro
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In 3 dimensions, there's cubers.
In 2 dimensions, there's squarers.
In 1 dimension, there's liners.
In 0 dimensions, there's ers.
In -1 dimension, there's sre
In -2 dimensions there are srenil
@@trendygaming795 in -3 dimensions, there's srebuc
@@Player-ux4ke lol
@@meep_poggerson do you think thats the end? NO! 4D is tesseracters meanwhile -4D is sretcaresset
For those who asking what is easier than 1×1 rubik's cube. The answer is 0d and 1d rubik puzzle. 😎👍
Everything’s easier than the 1x1 it’s the hardest puzzle smh
@@person4119 bruh the 1x1 is always solved because there’s no mechanism lmao. But is is the hardest puzzle to scramble because it can’t be scrambled
@@geeteevee7667 yeah but it’s so difficult I can’t solve it
@@geeteevee7667r/Woooosh, its a joke in the entire cubing community
@Gigachad I can confirm this
if we ignore the factorial (which doesn't make sense in negative dimensional space), you could make it so negative dimensional Rukik's cubes are fucntionally similar to their positive counterparts, but have 1 dimensional lower stickers, which would be one higher in magnitude.
eg: a -2d cube would have -3d stickers and look like a square surrounded by 3 cubes on each side...
I don't think it would affect how it operates as a puzzle though
Factorial actually does function in the negative, look it up on youtube
@@wingdinggaster6737 Not negative integers, since it goes to infinity
@@want-diversecontent3887 but it does pass through integers, so you could have a cube with non-integer dimensionality (look up fractal dimensional on youtube, theres a good 3b1b video on the topic)
n! = n.(n-1)!
0! = 0.(-1!)
can't divide by 0 so -1! switches places.
1/-1! = 0 this is weird so just do as √-1, let it be.
now watch it:
-1! = -1.(-2!)
1/-2! = -1.(1/-1!)
moving on...
1/-3! = -2.-1.(1/-1!)
1/-4! = -3.-2.-1.(1/-1!)
so the reciprocal of negative integer factorials can be all written based on the reciprocal of negative one factorial regardless of it existing or not. which I think is pretty fun.
''Rukik''
1:37 I like how it's just minecraft blocks.
2:33 the memes makes the whole video better.
Thank you 🙏 I tried super hard on this video :)
we call minecraft blocks
"cubes"
@@Flightkitten actually minecraft blocks are just called blocks
Wouldn’t a 2d rubik’s cube be a Rubik’s Square?
Woa, I did not expect to hear about the gamma function in a cubing video. As a math nerd it is one of my favs, shows up as the solution to a lot of interesting integrals.
Hi Rowan in your video you mentioned negative integer dimensions that don't give a value because of the vertical asymptote but how about the values (could be non-integer) that will give you a positive integer on the graph assume that the negative 2.137469... dimension gives you a positive integer value such as 9 which will then be 9 pieces on each side of the cube on that dimension.
Hmmm that's interesting. Some negative numbers squared are equal to positive numbers, yeah. But I'm not sure at all what that would mean for the number of pieces or anything 🤯
@@RowanFortier Maybe what he means is that some negative numbers have an integer factorial, such as -2.13824709508197...! = 7.
I think an approach worth trying is to work out the generalized formula for the amount of pieces, configurations, etc, given any number of dimensions.
Starting with the positive ones and trying to extrapolate to negative and non-integer dimensions. Doesn't matter if the cube is realizable, imaginable, or not, just to see if it makes sense mathematically.
I have always been thinking what if a cube went into the negatives, like a -2x-2 would it be like a black hole or rip in space time?
Absolutely
Only in odd dimensions, like 1d and 3d, because in 2d, -2×-2 = 4 and not negitice
If you increase the length of a 1d line, the length increases that amount. A 2d square has an area that decreases with the square of the side length, that is, the area is the side length squared. A 3d cube has a volume whose side length increases with the cube of the side length. Notice how each time, the equivalent measure of area/volume/whatever is proportional to the side length to the power of the dimension.
If we want to expand the idea of dimensions to negatives, for example, a -2d square, we need to think of an object whose area is proportional to the inverse of the square side length, aka the side length to the power of -2. How you'd do that, and what that'd look like, who knows, but it's a good starting place for creating something negative dimensional.
As for black holes, totally correct, since anything with a side length of 0 in any negative dimension would have to have 1/0 area.
I haven't finished watching the video idk why I responded
Or complex numbers. What would a 3+4i×3+4i cube look like?
I never thought that by watching a rubik's cube video I would find out about complex shapes. That's insane, thanks! 💪🤣
Thanks for telling me about the factorial function because I didn’t know about the factorial until now. But thanks!
U cant rotate a one dimension line in a one dimension space
*Proceeds to die☠️*
Nice thoughs about other dimensions.
I was looking forward to the net of a cube in 2-dimensional space and how it would function as you solved it
you could try a fractal, those can have non integer dimensions
Well, it depends on your definition of "dimension".
(Even if you already know this, this comment may be useful for later readers)
If we are talking about topological dimension (the "usual" meaning of dimension, the max number of directions you can have and stay orthogonal), then fractals still have an integer one of those.
Like the Sierpinski Triangle still has a topological dimension of one.
However, by "how much does it grow if you increase scale by 2x", Hausdorff dimension, you do get non-integers for many fractals.
Like the Sierpinski triangle will have a Hausdorff dimension of log(3)/log(2) ≈ 1.585.
But what matters for how we build a rubix cube/square/whatever, we are interested in the number of unique independent directions, which for fractals would still be an integer.
This is so cool
You can have fractional dimensions and have fractal puzzles, idk but could be cool. for example, a serpinski triangle is roughly 1.585
1.585 what? Apples? Bananas
@@Marvin-ho1vo 1.585D
1:46 Minecraft carpet texture 😂
Carykh made a 2d rubik’s cube-like puzzle callled LoopOver where you move squares that you guessed it, loop over. if i sound confusing, watch Cary’s video
In 0 dimensions, there are pointers.
In 1 dimension, there are liners.
In 2 dimensions, there are squarers.
In 3 dimensions, there are cubers.
In 4 dimensions, there are tesseracters.
Mathematicians when they solve some problem: fuck it, negative
bros now gonna invent a 1.5 dimensional cube 💀
what is the song called for the 1d dimensional cube?
If you have a 2.5 dimensional cube, is that enough to do rotations in? :P
Hm... how could we interpret that? There’s fractal dimension of fractals, but that doesn’t seem to fit nicely with like, finite numbers of pieces? I don’t see a clear way to give this a good meaning..
The 4 4 complex polytope is the same as a 4d cubes isn't it? It has the same graph. Maybe some additional properties of this object could be used to makes rules reducing the way a 4D cube can be turned.
No. It’s made of complex lines, whereas the hypercube is made of 8 cubes
Topologically speaking, that is mathematically, the Rubik's cube is really 2-dimensional, I mean it.
You can "spherify" it (such round versions do exist), and then pieces are just tiles whose movements are restricted to the surface of a sphere (called a 2-sphere).
At no point do you need to "solve" anything inside that sphere, so.
On a lighter note, and this is literally true
3D-cube : Hi, my name is 3x3x3, what's yours?
0D-cube :
That's true. You can call a 3D cube a 2D sliding puzzle embedded on the surface of a sphere.
Also if you're going by the exponents, then:
3^3 = 3x3x3
3^0 = 1
3^(-1) = 1/3 🤔
what if negative dimensions was deleted space.
Imagine a rubix anticube (yes, -3d, anticube)
And it was just a void in the shape of a cube, with certain "void colors" like the eyes detecting not how much light is there, but how much light was taken away.
I doubt you could touch it though.
Hey Rowan what is that shape called that looks like a diamond at 8.09
It’s not a kite
hey, can you help me scramble my 3?
3x3x3? no. my THREE.
2d rubixcube stickers look like unconnected minecraft glass panes
4:40 had me cracking up
btw 0d would be
I subbed
the 0d rubics cube is like a 3d 1x1x1 rubics cube tbh
What about interlocking 2d Circle Puzzles
0th dimensional Rubik's Cube has -1st dimensional stickers
3:48 you put red yellow and blue and its the puzzle to swap place with every line with another
If u split a -1 dimensional line into 2, youll get 2 lines taht is the same size of the first
Formula: log2(n) = -1
Dimensional calculations: 1/2^-1 = 2
Scale^dimention = mass
yes the stickers of a stickered rubik's cube is a minecraft carpet block
1:49
3D rubiks cube is 0D 1D 2D all together zero is the center of the cube. One is the edges of the cube. Two is is the individual parts and that makes the rubiks cube.
This reminds me of stuff I would have mused about during highschool. Pretty fun!
The fact I've actually heard of a lot of these things before is funny to me
wow
why 3D sticker on video are shown as a purple carpet from minecraft?
a square is my favourite three dimensional cube
Square is 2d bruh
What if we make them out of Venn diagrams? instead of it being a straight line, we just used curved lines instead
that could actually make a functional 2D puzzle, but it would not be a rubik’s square
4d rubiks cube
You solve inside and outside 💀
So true 💀
You said that non integer number dimensions make no sense
Have you heard of fractal dimension
You're welcome meep_poggerson for making your comment went popular
The 4D cube is called a tesseract
Indeed
I feel like a Rubio puzzle in hyperbolic space should be doable
…wait. COMPLEX NUMBERS LETSS GOOO
the video bar kinda looks like an unequal 9 (1d 9x9)
-1 dimensional rubix cube: just nothing
In 2d you can rotate something around a dot.
If there is a 10d Rubik's cube the stickers are 9d also if there a 9d Rubik's cube the stickers are 8d also if there is a 8d Rubik's cube the stickers are 7d also if there is a 7d Rubik's cube the stickers are 6d also if there is a 6d Rubik's cube the stickers are 5d also if there is a 5d Rubik's cube the stickers are 4d also if there is a 4d Rubik's cube the stickers are 3d and also the 3d Rubik's cube the stickers are 2d if there is a 2d Rubik's cube which is a 2d Rubik's square but the stickers are 1d if there is a 1d Rubik's cube which is a 1d Rubik's line but the stickers are 0d if there is a 0d Rubik's cube which is a 0d point but the stickers are -1d
Message to the creator: there is already a 2 dimensional Rubik's cube called loop over by Cary huang, he is also the creator of Bfdi with his brother Michael huang
message to amypotter8519: I know of loopover, but it is not a 2d rubik's cube. it's a completely different puzzle on a different geometry and topology. please watch the video again
Couldn't you just disassemble the 3x3x3 into the 3x3 ,the 3, and the 0 cubes? You just first remove the front and back layers. And you are left with the visible core and 1d lines for stickers
Sure, I guess. But then it still exists in 3D space, while trying to look like lower dimensions
"you cant scramble 2d rubiks cube without mirroring"
loopover:
How about 4d rubix cubes
5:20 Like a 1 by 1
4:51 *3*
How about -1d
0:52 Wait a second, you're not trying to sneak in bits of group theory without actually saying, are you? 😉
Nah, I don't know anything about group theory yet 💀
Make a -9d rubix cube
The good old 3:28
What is easier thana 0d cube and 1d cube well it is actually a 10d cube
4D: 3X3X3X3
3D: 3X3X3
2D: 3X3
1D: *3*
0D: 3:3
-1D: 3:3:3(?)
-2D: 3:3:3:3(??)
-3D: 3:3:3:3:3(???)
-4D: *3:3:3:3:3:3(????)*
4 dimension was a tesseract!
The 2 dimensional cube is basically a floppy cube
Did anyone else miss understand and click cause you though he was gonna talk about a 2x2 cube and a 1x1 cube and some how explain the negative versions
fractal rubix cube?
bro it stops being a cube past 3d
Many people still use 3x3 to refer to the 3d puzzle.
A 0d is like the 1x1x1
What about, say, 2.5 dimensions?
How the f-
there's squaravotsquarers
half squares crying in the corner
14.5884572681 pieces (excluding core)
and 25.9807621135 stickers
How about -all?
the 3
yes
@@RowanFortier when you said minus d
In my head: "oh, 2d is 3×3, 1d is 3, 0d is 1, so -1d is 1/3, -2d is 1/3×3"
A 1x3x3 its a 2d 3x3 but without top and bottom stickers.
3d: 3x3x3
2d: 3x3
1d: 3
0d:
-1d: �̴̡̨͇̮̼̖̜̗͍̻͈̻̪͕̙̠̦͕̙̠̼̘̤͉̗̟̯̩̗̖̆̐̉̈̔̌̔̄̓͌̈̔̒͗̋͆͋̀́̿̾̚͜͝͝͠ͅ�̶̪̇̅̈̈́̌̓͑͆͆̈̅̂͋̕͘̕͝͝
-1d: 3÷3
0d: 3:3
-2d 3÷3÷3
-3D:3÷3÷3÷3
What about the? -infinity. Dimension.
For 2D rubik's cube just use the scramble picture
Swapping places of the one-dimensional lines on the one-dimensional cube
And you look like doctor strange
R u voice actor of Lollipop BFB
No, idk what that is
wouldn't a 2D 3x3 just be a 3x3x1?
2d shapes like squares don't have volumes, but rather areas. the volume of a square would be 0 due to the lack of depth. a 2d can be considered a 3x3x0 in terms of volume, but simplified to just 3x3 because depth doesn't exist in a 2d world.
Wait, whats a -3 dimensions
0:34 Huh?
Wow I can solve those way easier than a 3d cube.
In 3 dimensions, that's a square
i love how he just explains us how to use a 'normal' rubiks cube
It’s for the dimensional analogies
¿Who was interested in the negative dimensions?
1:45 purple carpet?
*MINECRAFT CONFIRMED*
yes 💀
My poor head
0:34 In 3 Dimensions it’s a *square*
In 2 dimen-
*Huh*
2*2*2*2
in no one going to notice that at time 3:11 the colour scheme is wrong
Loop Over By Carkh: am i a joke to you
The one piece!!!
Negative is so there is no Negative rubix cube.
also fun fact, carykh actually made a 2D rubix cube that is playable (on a website)
idk if it's still playable, but he made a video on it
Yeah I love loopover! It is a very good puzzle that is more like a 15-puzzle on the surface of a torus. An actual 2D Rubik's Cube is like the one I showed in the video
@@RowanFortier oh, i see, thanks for clarifying!
The -3x-3x-3 should look like a normal Rubik’s cube but it would become outside-in inside-out which that you prototype is not gonna work as that is completely incorrect as to these correct facts
So what about -3.7980122+2.4480521i dimensions? Huh? HUH?
Why are you calling the center the "core" and the edges the "centers"??
because a piece with 0 colours is a core, and a piece with 1 colour is a center