Rubik's Cubes in Less Than 3 Dimensions!

[@meep_poggerson]

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]

In -1 dimension, there's sre

[@trendygaming795]

In -2 dimensions there are srenil

[@Player-ux4ke]

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

[@meep_poggerson]

@@Player-ux4ke lol

[@Player-ux4ke]

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

[@RyanKennelly03]

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]

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

[@want-diversecontent3887]

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

[@wingdinggaster6737]

@@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]

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.

[@sketchimationsREAL]

''Rukik''

[@nyoesman_channel]

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

[@person4119]

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

[@geeteevee7667]

@@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]

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

[@WolfWarrior01]

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

[@DaLou1e]

@Gigachad I can confirm this

[@WafflerWhite]

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

[@RowanFortier]

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

[@Flightkitten]

we call minecraft blocks "cubes"

[@shovmm123]

@@Flightkitten actually minecraft blocks are just called blocks

[@popipom18]

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

[@GFJDean35]

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]

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]

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]

@@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.

[@LordAxolotlOfficial_YT]

what the heck are these calculations

[@Hla_Perm]

Finally found a reason to convince my mom that cubing videos aren't a waste of time, I learn.... try to learn..... actually try to understand some complex stuff. I am still in 7th grade like what is this gibirrish..... at least I understood factorial and that's good enough for me

[@Adam46221]

This isn't gibberish

[@WebStrike445]

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]

Absolutely

[@drippymissouri]

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

[@marcusmelander8055]

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]

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

[@familiamarquez3219]

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

[@Peteboi64932]

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

[@Kyungo_]

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

[@orangeaedan]

5:05 little correction. It would have -1D stickers. You can’t technically talks about stickers since it needs -2 sticker. It would be a point with a line going away from it in the negative direction.

[@deltainfinium869]

You know something I haven't seen explored yet? Additional time dimensions. So far, all the rubiks cubes you've been referring to work within 1 time dimension (ours). A 3x3x3 is actually a 3+1 dimensional cube (+1 being the 1 time dimension). So theoretically you could have a 3+2 dimensional cube which would have 2 different time axis that work independently. I really don't know how this would work, though.

[@Nico2718_]

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

[@theaceraichu]

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]

1.585 what? Apples? Bananas

[@molybd3num823]

@@Marvin-ho1vo 1.585D

[@Watchfa]

1:46 Minecraft carpet texture 😂

[@MortisGod_FS]

ikr 😂 sorry for replying after a whole year has passed

[@hanumands50]

i'm not that sure but i remember hearing that fractals are somehow related with "rational" dimensions, like .3 or 2.5 like you said but positive. So maybe there could be some kind of cube with infinite stikers but they are contained within themselves idk

[@dacgamer5741]

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

[@elidoz9522]

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

[@TechSY730]

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.

[@Anonymous41726]

Dang I went on a whole quest to figure this out, when this video gave me all the info I needed

[@quadruplay9788]

you can use hadamard's gamma function to extend the factorial function to complex numbers including negative integers

[@DuckieAM_viewing_chanel]

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

[@Kpop0_0Love]

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(????)*

[@demonsrun3281]

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

[@xuefeili5311]

If there was negative dimensions what will the r ubik's cube be called

[@petros_adamopoulos]

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]

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]

4:40 had me cracking up

[@MarioLopez-tp2gi]

btw 0d would be

[@itzecuber]

Such a nerd Thank you for your content

[@rina-i9a]

you can just use the (3^d)-1 formula, d=dimension (-1 is for excluding core) 3d= 26 pieces + 1 core, 54 bidimensional stickers, 6 faces 2d= 8 pieces + 1 core, 12 unidimensional stickers, 4 faces 1d = 2 pieces + 1 core, 2 nulidimensional stickers, 2 faces 0d = 0 pieces + 1 core, 0 necunidimensional stickers, 0 faces -1d = -0.6̄ pieces + 1 core, -0.2̄ necbidimensional stickers, -2 faces -2d = -0.8̄ pieces + 1 core, -0.1̄4̄8̄ nectridimensional stickers, -4 faces -3d = -0.9̄6̄2̄ pieces + 1 core, -0.0̄7̄4̄ necquadridimensional stickers, -6 faces

[@A_literal_cube]

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

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

[@energyーy]

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

[@junebugrobotics]

-1d: 3÷3

[@vasileiospanagiotisdouzeni7213]

0d: 3:3

[@NaySantos-y2o]

-2d 3÷3÷3

[@vasileiospanagiotisdouzeni7213]

-3D:3÷3÷3÷3

[@johnpeace1149]

Nice thoughs about other dimensions.

[@anime_erotika585]

Mathematicians when they solve some problem: fuck it, negative

[@wPelniSwiadomy]

The music is too loud. It's a shame, because you talk about very interesting things.

[@bernardfinucane2061]

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]

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

[@turtleninja16tn66]

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.

[@U.Inferno]

Dimensions convert linear units into dimensional units, so 3d is x^3 where x is the width. 2d is x^2 and 1d is x^1. x^0 for 0d just resolves to 1 so it's just the 0 dimensional unit. Negative Dimensions, then would be x^-1 or x^-2 and so forth, which all reduce to 1/x or 1/x^2. So a Negative dimensional 3×3×3 would have 1/27 "cubes" (vs the 27 pieces of a normal cube; 8 corners, 12 edges, 6 centers + core). What does that even *mean*? No clue. But that's what it would look like

[@hiscool1525]

bro it stops being a cube past 3d

[@ŁŁŁŁŁŁŁŁŁŁŁŁŁŁŁz]

Rubik's square

[@itraknmsandminecraft8094]

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

[@LukasPratz]

What about interlocking 2d Circle Puzzles

[@SwagridCubing]

a square is my favourite three dimensional cube

[@nyoesman_channel]

Square is 2d bruh

[@stolenmonkey7477]

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

[@zacharyandjulianbrownell6171]

In my opinion, I sometimes call rubix cubes all sides same distance and stuff 3^3 1 dimension: 3^1 (3) 2 dimensions: 3^2 (9) 3 dimensions: 3^3 (27) 4 dimensions: 3^4 (81) 5 dimensions: 3^5 (243) 6 dimensions: 3^6 (729) 7 dimensions: 3^7 (2.1K) *From this point, my hands are getting tired so I won't put the "3^" thing further.* 8 dimensions: 6.5K 9 dimensions: 19.6K 10 dimensions: 59K 11 dimensions: 177.1K 12 dimensions: 531.4K 13 dimensions: 1.5M 14 dimensions: 4.7M 15 dimensions: 14.3M 16 dimensions: 43M Part 2 at 10 likes (I'm checking either daily or weekly)

[@kikag13]

This is so cool

[@soapycanthandle]

-1 dimensional rubix cube: just nothing

[@bigoofersrock]

The 4D cube is called a tesseract

[@RowanFortier]

Indeed

[@blockman_games17]

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

[@Trashywasnthere]

Poo Lover

[@MemeAnt]

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

[@Bartexz]

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

[@MaxwellCatAlphonk]

2d rubixcube stickers look like unconnected minecraft glass panes

[@Tomasu82]

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

[@charleskids-e2i]

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.

[@lunae-moon]

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

[@aquaragegod]

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

[@spencerdumlao1654]

It’s not a kite

[@galoomba5559]

It's the complex polygon 2{4}3, which has the vertices and a subset of the edges of a 4D polytope called a triangular duotegum.

[@aquaragegod]

@@galoomba5559 thx for that info after a year tho lol

[@camerontheninja9592]

I mean, one of the images vaguely looked like an Alexander's Star I guess. But I was probably very misunderstanding.

[@bagelnine9]

(2:49) That's offensive to flatlanders.

[@pepsi9145]

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

[@modahabbab]

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

[@brainboy53]

I subbed

[@JustAPersonWhoComments]

If people have a 0x0 cube, that means everyone has it, but they can’t see it

[@learnwithammad8074]

5:20 Like a 1 by 1

[@drdca8263]

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..

[@ghostagent3552]

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

[@chri-k]

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

[@Complexitor37]

What about non integers?

[@SpaceUK45]

i don't think we'd want a NaND cube

[@chenhou946]

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

[@Player-ux4ke]

You're welcome meep_poggerson for making your comment went popular

[@Mr_Joe_theidiot]

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

[@RowanFortier]

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

[@Mr_Joe_theidiot]

@@RowanFortier oh, i see, thanks for clarifying!

[@technobecian]

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

[@damianzieba5133]

Non euclidean rubik's cube? You are genius!

[@dipp4416]

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]

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

[@lukatolstov5598]

In 2d you can rotate something around a dot.

[@Planty567]

How about 4d rubix cubes

[@SanityInAnAmazonBoxShorts]

The good old 3:28

[@Dracosiriusmalfoyblack538]

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

[@amypotter8519]

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]

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

[@Garfield_Minecraft]

4d rubiks cube You solve inside and outside 💀

[@RowanFortier]

So true 💀

[@RobotBlueSpark]

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

[@Scrolte6174]

0:34 Huh?

[@dex.16]

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

[@_Caden]

What about, say, 2.5 dimensions?

[@geckoanims]

How the f-

[@mohamedazadabdulrahman3226]

there's squaravotsquarers

[@NaySantos-y2o]

half squares crying in the corner

[@panthererousse]

14.5884572681 pieces (excluding core) and 25.9807621135 stickers

[@robvdm]

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

[@elesystemic6742]

4 dimension was a tesseract!

[@cooarha82we]

Make a -9d rubix cube

[@cooarha82we]

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

[@vskrautar080808]

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

[@TechSY730]

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

[@RowanFortier]

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

[@Internetontheperson]

4:51 *3*

[@ExDixionconderoga]

A 0d is like the 1x1x1

[@Red_bananas]

Him: Or can you? *vsauce music intensifies*

[@Dexuz]

I hold the world record in solving a 3

[@romanashinn7096]

The 2 dimensional cube is basically a floppy cube

[@nick.100]

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

[@xantheiron1272]

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

[@r3gret2079]

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

[@HalValla01]

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

[@xirolyfe]

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.

[@soulsofspirit9729]

…wait. COMPLEX NUMBERS LETSS GOOO

[@effperm]

the 3

[@RowanFortier]

yes

[@nyoesman_channel]

@@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"

[@thomaskierstead6864]

How about -1d

[@hollykirk1466]

R u voice actor of Lollipop BFB

[@RowanFortier]

No, idk what that is

[@matheussboldrimsoares5856]

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

[@Steven-ig6tw]

What about the? -infinity. Dimension.