Rubik's Cubes in Less Than 3 Dimensions!

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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
Music:
Hip Hop Rap Instrumental (Crying Over You) by christophermorrow
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Опубликовано:

2 июн 2024

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Комментарии : 293

@meep_poggerson Год назад

In 3 dimensions, there's cubers. In 2 dimensions, there's squarers. In 1 dimension, there's liners. In 0 dimensions, there's ers.

@Player-ux4ke Год назад

In -1 dimension, there's sre

@trendygaming795 Год назад

In -2 dimensions there are srenil

@Player-ux4ke Год назад

@@trendygaming795 in -3 dimensions, there's srebuc

@meep_poggerson Год назад

@@Player-ux4ke lol

@Player-ux4ke Год назад

@@meep_poggerson do you think thats the end? NO! 4D is tesseracters meanwhile -4D is sretcaresset

@WafflerWhite 2 года назад

1:37 I like how it's just minecraft blocks. 2:33 the memes makes the whole video better.

@RowanFortier 2 года назад

Thank you 🙏 I tried super hard on this video :)

@Flightkitten Год назад

we call minecraft blocks "cubes"

@Parshovvv Год назад

@@Flightkitten actually minecraft blocks are just called blocks

@popipom18 7 дней назад

Wouldn’t a 2d rubik’s cube be a Rubik’s Square?

@NYUSmanChannel Год назад

For those who asking what is easier than 1×1 rubik's cube. The answer is 0d and 1d rubik puzzle. 😎👍

@person4119 Год назад

Everything’s easier than the 1x1 it’s the hardest puzzle smh

@geeteevee7667 Год назад

@@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

@lennystudios3.14 Год назад

@@geeteevee7667 yeah but it’s so difficult I can’t solve it

@WolfWarrior01 Год назад

@@geeteevee7667r/Woooosh, its a joke in the entire cubing community

@DaLou1e Год назад

@Gigachad I can confirm this

@RyanKennelly03 2 года назад

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

@wingdinggaster6737 Год назад

Factorial actually does function in the negative, look it up on youtube

@want-diversecontent3887 Год назад

@@wingdinggaster6737 Not negative integers, since it goes to infinity

@wingdinggaster6737 Год назад

@@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)

@BleachWizz Год назад

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.

@codycodycodycodycody Год назад

''Rukik''

@GFJDean35 Год назад

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.

@goktuggokbulut4424 Год назад

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.

@RowanFortier Год назад

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 🤯

@petros_adamopoulos Год назад

@@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.

@Nico2718_ Год назад

I never thought that by watching a rubik's cube video I would find out about complex shapes. That's insane, thanks! 💪🤣

@Peteboi64932 Год назад

Thanks for telling me about the factorial function because I didn’t know about the factorial until now. But thanks!

@Watchfa 9 месяцев назад

1:46 Minecraft carpet texture 😂

@WebStrike445 Год назад

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?

@RowanFortier Год назад

Absolutely

@drippymissouri Год назад

Only in odd dimensions, like 1d and 3d, because in 2d, -2×-2 = 4 and not negitice

@marcusmelander8055 Год назад

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.

@marcusmelander8055 Год назад

I haven't finished watching the video idk why I responded

@familiamarquez3219 Год назад

Or complex numbers. What would a 3+4i×3+4i cube look like?

@kikag13 Год назад

This is so cool

@demonsrun3281 Год назад

I was looking forward to the net of a cube in 2-dimensional space and how it would function as you solved it

@theaceraichu Год назад

You can have fractional dimensions and have fractal puzzles, idk but could be cool. for example, a serpinski triangle is roughly 1.585

@Marvin-ho1vo Год назад

1.585 what? Apples? Bananas

@molybd3num823 Год назад

@@Marvin-ho1vo 1.585D

@johnpeace1149 Год назад

Nice thoughs about other dimensions.

@Kyungo_ 9 месяцев назад

U cant rotate a one dimension line in a one dimension space *Proceeds to die☠️*

@elidoz7449 Год назад

you could try a fractal, those can have non integer dimensions

@TechSY730 Год назад

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.

@thescratchguy428 11 месяцев назад

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.

@pepsi9145 Год назад

what is the song called for the 1d dimensional cube?

@bernardfinucane2061 Год назад

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.

@RowanFortier Год назад

No. It’s made of complex lines, whereas the hypercube is made of 8 cubes

@drdca8263 Год назад

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..

@turtleninja16tn66 Год назад

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.

@blockman_games17 4 дня назад

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

@petros_adamopoulos Год назад

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 :

@RowanFortier Год назад

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 🤔

@MarioLopez-tp2gi 11 месяцев назад

4:40 had me cracking up

@MarioLopez-tp2gi 11 месяцев назад

btw 0d would be

@brainboy7123 Год назад

I subbed

@aquaragegod 11 месяцев назад

Hey Rowan what is that shape called that looks like a diamond at 8.09

@spencerdumlao1654 11 месяцев назад

It’s not a kite

@dacgamer5741 Месяц назад

hey, can you help me scramble my 3? 3x3x3? no. my THREE.

@JasinPlayzYT 9 дней назад

the 0d rubics cube is like a 3d 1x1x1 rubics cube tbh

@itraknmsandminecraft8094 Год назад

0th dimensional Rubik's Cube has -1st dimensional stickers

11 месяцев назад

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

@DuckieAM_viewing_chanel 10 месяцев назад

3:48 you put red yellow and blue and its the puzzle to swap place with every line with another

@MaxwellCatAlphonk 4 месяца назад

2d rubixcube stickers look like unconnected minecraft glass panes

@LukasPratz Месяц назад

What about interlocking 2d Circle Puzzles

@stolenmonkey7477 Год назад

The fact I've actually heard of a lot of these things before is funny to me

@user-ve3ub4qh2j 4 месяца назад

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.

@A_literal_cube Год назад

yes the stickers of a stickered rubik's cube is a minecraft carpet block 1:49

@technobecian Год назад

I feel like a Rubio puzzle in hyperbolic space should be doable

@bigoofersrock Год назад

The 4D cube is called a tesseract

@RowanFortier Год назад

Indeed

@Player-ux4ke 4 месяца назад

You're welcome meep_poggerson for making your comment went popular

@anime_erotika585 Год назад

Mathematicians when they solve some problem: fuck it, negative

@Bartexz 11 месяцев назад

why 3D sticker on video are shown as a purple carpet from minecraft?

@MemeAnt Год назад

You said that non integer number dimensions make no sense Have you heard of fractal dimension

@SwagridCubing 2 года назад

a square is my favourite three dimensional cube

@NYUSmanChannel Год назад

Square is 2d bruh

@dipp4416 Год назад

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

@RowanFortier Год назад

Sure, I guess. But then it still exists in 3D space, while trying to look like lower dimensions

@ghostagent3552 Год назад

What if we make them out of Venn diagrams? instead of it being a straight line, we just used curved lines instead

@U20E0 Год назад

that could actually make a functional 2D puzzle, but it would not be a rubik’s square

@robvdm Год назад

This reminds me of stuff I would have mused about during highschool. Pretty fun!

@lukatolstov5598 8 месяцев назад

In 2d you can rotate something around a dot.

@Garfield_Minecraft Год назад

4d rubiks cube You solve inside and outside 💀

@RowanFortier Год назад

So true 💀

@amypotter8519 4 месяца назад

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

@RowanFortier 4 месяца назад

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

@modahabbab4576 5 месяцев назад

the video bar kinda looks like an unequal 9 (1d 9x9)

@soulsofspirit9729 6 дней назад

…wait. COMPLEX NUMBERS LETSS GOOO

@Tomasu82 10 месяцев назад

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

@yustrianiachian6984 11 месяцев назад

wow

@Kpop0_0Love 11 месяцев назад

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(????)*

@sullivanbell2397 Год назад

-1 dimensional rubix cube: just nothing

@elesystemic6742 Год назад

4 dimension was a tesseract!

@hiscool1525 11 месяцев назад

bro it stops being a cube past 3d

@jensentota Год назад

3d: 3x3x3 2d: 3x3 1d: 3 0d: -1d: �̴̡̨͇̮̼̖̜̗͍̻͈̻̪͕̙̠̦͕̙̠̼̘̤͉̗̟̯̩̗̖̆̐̉̈̔̌̔̄̓͌̈̔̒͗̋͆͋̀́̿̾̚͜͝͝͠ͅ�̶̪̇̅̈̈́̌̓͑͆͆̈̅̂͋̕͘̕͝͝

@junebugrobotics Год назад

-1d: 3÷3

@vasileiospanagiotisdouzeni7213 Год назад

0d: 3:3

@Four4bfdi Год назад

-2d 3÷3÷3

@vasileiospanagiotisdouzeni7213 Год назад

-3D:3÷3÷3÷3

@Internetontheperson Год назад

4:51 *3*

@SanityInAnAmazonBox 11 месяцев назад

The good old 3:28

@learnwithammad8074 11 месяцев назад

5:20 Like a 1 by 1

@romanashinn7096 11 месяцев назад

The 2 dimensional cube is basically a floppy cube

@Planty567 9 месяцев назад

How about 4d rubix cubes

@xX_TF_CNS_SyntaxCNS_Stere0_Xx Год назад

i love how he just explains us how to use a 'normal' rubiks cube

@RowanFortier Год назад

It’s for the dimensional analogies

@dex.16 7 месяцев назад

"you cant scramble 2d rubiks cube without mirroring" loopover:

@nick.100 Год назад

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

@TechSY730 Год назад

0:52 Wait a second, you're not trying to sneak in bits of group theory without actually saying, are you? 😉

@RowanFortier Год назад

Nah, I don't know anything about group theory yet 💀

@chenhou946 11 месяцев назад

Many people still use 3x3 to refer to the 3d puzzle.

@cooarha82we Год назад

Make a -9d rubix cube

@thomaskierstead6864 Год назад

How about -1d

@xantheiron1272 11 месяцев назад

For 2D rubik's cube just use the scramble picture

@TheRepublicOfDixionconderoga 11 месяцев назад

A 0d is like the 1x1x1

@matheussboldrimsoares5856 4 месяца назад

A 1x3x3 its a 2d 3x3 but without top and bottom stickers.

@tomansager1 Год назад

1:45 purple carpet? *MINECRAFT CONFIRMED*

@RowanFortier Год назад

yes 💀

@vskrautar080808 Год назад

Swapping places of the one-dimensional lines on the one-dimensional cube And you look like doctor strange

@cooarha82we Год назад

What is easier thana 0d cube and 1d cube well it is actually a 10d cube

@HalValla01 Год назад

wouldn't a 2D 3x3 just be a 3x3x1?

@xirolyfe Год назад

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.

@effperm 2 года назад

the 3

@RowanFortier 2 года назад

yes

@NYUSmanChannel Год назад

@@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"

@_Caden Год назад

What about, say, 2.5 dimensions?

@dergecko92 Год назад

How the f-

@mohamedazadabdulrahman3226 Год назад

there's squaravotsquarers

@Four4bfdi Год назад

half squares crying in the corner

@panthererousse 11 месяцев назад

14.5884572681 pieces (excluding core) and 25.9807621135 stickers

@Steven-ig6tw 5 месяцев назад

What about the? -infinity. Dimension.

@r3gret2079 Год назад

Wow I can solve those way easier than a 3d cube.

@BleachWizz Год назад

fractal rubix cube?

@thomaskierstead6864 Год назад

How about -all?

@Peridot216 4 месяца назад

0:34 In 3 Dimensions it’s a *square* In 2 dimen- *Huh*

@hollykirk1466 10 месяцев назад

R u voice actor of Lollipop BFB

@RowanFortier 10 месяцев назад

No, idk what that is

@beybruhs6700 Год назад

in no one going to notice that at time 3:11 the colour scheme is wrong

@Scribbledbucket 2 месяца назад

Wait, whats a -3 dimensions

@penguincute3564 Год назад

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