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
@@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.
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.
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.
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.
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
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.
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.
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.
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 🤔
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
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.
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.
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
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.
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
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
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
A 1x3x3 its a 2d 3x3 but without top and bottom stickers.
Год 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
I think you should've look into methodology of dimensions before diving into this They are just things to define things Wanna make a negative dimension? Just call it a negative dimension Arguing can a dimension be whatever is like arguing if the Y value is defining height/extent/longitude or is it latitude/width OR EVEN DEPTH?!?! Y is whatever you define as This thought process is pointless if you ask me :p
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 -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
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.
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
Thanks for telling me about the factorial function because I didn’t know about the factorial until now. But thanks!
4:40 had me cracking up
btw 0d would be
5:20 Like a 1 by 1
(2:49) That's offensive to flatlanders.
Wow I can solve those way easier than a 3d cube.
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
-1D cube iria gerar um buraco negro
my brain:
if 3d=3x3x3, 2d=3x3 and 1d=3
then maybe 0d = 3/3 (=1)
and -1d = 1/3
-2d = 1/9
-3d = 1/27
Great intuition , but how can you make a half peice?
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''
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
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?
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.
what the heck are these calculations
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.
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?
The music is too loud. It's a shame, because you talk about very interesting things.
bro it stops being a cube past 3d
Rubik's square
U cant rotate a one dimension line in a one dimension space
*Proceeds to die☠️*
hey, can you help me scramble my 3?
3x3x3? no. my THREE.
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
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.
0th dimensional Rubik's Cube has -1st dimensional stickers
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.
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 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
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.
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 🤔
1:46 Minecraft carpet texture 😂
ikr 😂 sorry for replying after a whole year has passed
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
3d: 3x3x3
2d: 3x3
1d: 3
0d:
-1d: �̴̡̨͇̮̼̖̜̗͍̻͈̻̪͕̙̠̦͕̙̠̼̘̤͉̗̟̯̩̗̖̆̐̉̈̔̌̔̄̓͌̈̔̒͗̋͆͋̀́̿̾̚͜͝͝͠ͅ�̶̪̇̅̈̈́̌̓͑͆͆̈̅̂͋̕͘̕͝͝
-1d: 3÷3
0d: 3:3
-2d 3÷3÷3
-3D:3÷3÷3÷3
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(????)*
I never thought that by watching a rubik's cube video I would find out about complex shapes. That's insane, thanks! 💪🤣
a square is my favourite three dimensional cube
Square is 2d bruh
If people have a 0x0 cube, that means everyone has it, but they can’t see it
The 4D cube is called a tesseract
Indeed
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)
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
In 3 dimensions, that's a square
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.
The fact I've actually heard of a lot of these things before is funny to me
I mean, one of the images vaguely looked like an Alexander's Star I guess. But I was probably very misunderstanding.
why 3D sticker on video are shown as a purple carpet from minecraft?
negative dimensions doesn't make much sense
2d rubixcube stickers look like unconnected minecraft glass panes
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.
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
you can use hadamard's gamma function to extend the factorial function to complex numbers including negative integers
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
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
0:34 In 3 Dimensions it’s a *square*
In 2 dimen-
*Huh*
So what about -3.7980122+2.4480521i dimensions? Huh? HUH?
"you cant scramble 2d rubiks cube without mirroring"
loopover:
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
Poo Lover
3:48 you put red yellow and blue and its the puzzle to swap place with every line with another
-1 dimensional rubix cube: just nothing
You're welcome meep_poggerson for making your comment went popular
yes the stickers of a stickered rubik's cube is a minecraft carpet block
1:49
What about interlocking 2d Circle Puzzles
can’t you just put stuff inside out for -demensions
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
A 1x3x3 its a 2d 3x3 but without top and bottom stickers.
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
the video bar kinda looks like an unequal 9 (1d 9x9)
bros now gonna invent a 1.5 dimensional cube 💀
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
In 3 dimensions that's a square
My poor head
…wait. COMPLEX NUMBERS LETSS GOOO
I think you should've look into methodology of dimensions before diving into this They are just things to define things Wanna make a negative dimension? Just call it a negative dimension
Arguing can a dimension be whatever is like arguing if the Y value is defining height/extent/longitude or is it latitude/width OR EVEN DEPTH?!?! Y is whatever you define as This thought process is pointless if you ask me :p
I hold the world record in solving a 3
Many people still use 3x3 to refer to the 3d puzzle.
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"
My Brain cant compherhand hypercubing.
For 2D rubik's cube just use the scramble picture
The 2 dimensional cube is basically a floppy cube
in no one going to notice that at time 3:11 the colour scheme is wrong
the 0d rubics cube is like a 3d 1x1x1 rubics cube tbh
Him: Or can you?
*vsauce music intensifies*
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..
What about the? -infinity. Dimension.
I know what y'all are thinking. *wat*
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
Negative is so there is no Negative rubix cube.
T H R E E
your favorite puzzle is 3x3x3x3?
my favorite one, is 3
el mio es el 3x3x3x3x3x3x3x3x3x3 adivina cual es esa dimension
Such a nerd
Thank you for your content
Loop Over By Carkh: am i a joke to you
Meanwhile in dimension -1.5:
Mathematicians when they solve some problem: fuck it, negative
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
What is easier thana 0d cube and 1d cube well it is actually a 10d cube
lol 3id cubes arent possible
cary made a 2D cube
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
How about 4d rubix cubes
4 dimension was a tesseract!
Gomez from FEZ is fucking *_LIVID_*