The Four Dimensional Rubik's Cube | Melinda's 2x2x2x2

Prepare yourself for an out-of-this-world experience with the first ever physical analog of a four-dimensional twisty puzzle - the 2x2x2x2! This crazy looking thing adds an extra dimension to the classic 2x2x2 (with a few extra complications)! In this video, I take you through how this puzzle works and attempt to explain exactly what it is! Can Chris Solve? will follow shortly!
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Canonical Moves: • Melinda's 2x2x2x2 - Ca...
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HAVE A FANTASTIC DAY!

[@alvin_row]

Just as a heads up, it's not like it has "many" solved states. It's all the same, you're just "rotating it", but since we live in a 3d space, we have to do all these weird moves to see from other (4d) perspectives. Don't know if that's understandable.

[@MelindaGreen]

That's a very good way to put it.

[@Konomi_io]

noticed this and commented about it but it seems live you've beaten me to the punch lol

[@liamhenderson7367]

7:33. Imagine a 4d being seeing this. According to them we would just be rotating the cube saying they’re all different solved states. 😂

[@aidenbagshaw5573]

I like to imagine a 2D being rotating a 3D cube and talking about how it has 24 solved states.

[@pauljmorton]

I feel like all those solved states are just various 3D representations of the one 4D solved state. They're just cube rotations?

[@MelindaGreen]

Exactly right.

[@maxmuller445]

Correct

[@Daansaes]

I think that if we were seeing the puzzle on a 4-dimensional hyperspace the 8 pieces of each colour would be touching on the solve state, because the different solve states in 3d are different projections of the 4d "model" in 3d, like when you draw a cube in a piece of paper. Sorry for my lame English.

[@MelindaGreen]

Daniel Antonio Sánchez Esteve Look at the solved face in the very center. You can see how it is complete with all 8 hyper-stickers touching each other. That's the 4D equivalent of the 2x2 grid of flat stickers on each face of the original puzzle. 4D faces and stickers are 3-dimensional, in the same way that the original puzzle's faces and stickers are 2-dimensional.

[@Ykulvaarlck]

to those of you who don't understand: this isn't actually a 4 dimensional puzzle but rather a 3d puzzle that is equivalent to what the 4 dimensional puzzle would be like. it's like taking a rubiks cube and splitting it into 3 layers and then telling you the rules of how you can manipulate those 3 separate layers.

[@MelindaGreen]

It's a bit more literal than that, but you are correct that the logical puzzle nature of twisty puzzles is not quite the same as the mechanism that implements it.

[@JoelDowdell]

The maker of the puzzle actually acknowledges the fact that it's not "really" four dimensional. Obviously the puzzle exists in only 3 spatial dimensions and 1 time dimension. Not 4 spatial dimensions and 1 time. It is called 4D because if you stay within the canonical moves, it has the same topology as a hypothetical 2*2*2*2 would have. (When talking about this puzzle 4D does not mean 3D + time, it means four dimensions that act the same way that the 3 of space do + a fifth dimension that acts like our time dimension does. All of this is hypothetical) Since 4D space is kinda large, when we "squish" it into 3D space, so it has take up more space. In fact, ignoring the 4D space between the 3D components, the real 2^4 would have 64 mini 1*1*1 cubes in it. Similarly, the 2^3 cube has 24 individual 1*1 squares, and some 3D space in between. In 3D we have faces of the 2^3, each of which is a square. In 4D we have cells (I think) each of which is a cube. all these cubes are squished into octohedrons, then sliced up and stuck to bits of other colors' octohedrons, one of each color, except for the "opposite" color.

[@BenziLZK]

Well...... We're watching a 4D rubik's cube, In a 3D reality, On a 2D screen Inside our 1D brain.......

[@swarley2500]

Technically your screen is not 2D There must be some bumps or scratches in it right?

[@maxmuller445]

Technicly the human brain is an (close to) 2.x dimensional fractal with overal positive curvature

[@killmeister2271]

1D brain?

[@MrRyanroberson1]

studies find that the human brain is closer to 8 dimensional in the matrix of it, and at the very least it's 3d

[@RetjeeeTv]

Benzi LZK lol

[@gamerwizard69]

this is a really interesting take on putting the 4th dimension in our restricted 3rd dimension!

[@MrRyanroberson1]

the way you say "can chris solve" sounds like "cankerous solve" lol

[@offbrandgeorge]

...this finally helped me understand the 4th dimension...I've had this phenomenon stuck in my head for a year now and this finally helped me understand it all...Thank You

[@maranto15]

That'a so cool!! I really want to just play around with it!

[@alexdavidson1021]

Marie I

[@mrsar6700]

120$ xD i buy one

[@jessicah8749]

U can make one.... with magnets and paper

[@jackolopecuber7112]

The first ever hyper-pop.

[@LukeLane1984]

When I first saw this I was unsure of how this would represent a 2x2x2x2, but after thinking about it a little while in the shower, it kind of clicked in my brain. Quite cleverly made.

[@keithdoherty3608]

I really like that concept

[@dezaviercrite4211]

2x2x2x2... So not catchy! How about, "The 2x2 Tesseract?"

[@CanChrisSolve]

Dezavier Crite I would recommend contacting Melinda! You can find a link to her channel below and she should have contact information from there!

[@poghole]

More like the 2x2^2

[@ByteSizedGamer]

KJDL CUBER 2x2^3 tecnically.

[@kameronpeterson3601]

or 2(2x2)

[@colinbergmann5750]

The Twosseract

[@williamross6477]

4th dimensionally speaking, wouldn't there only be one solved state, just in different orientations? So the simple rotation, arbitrary juxtaposition and gyro rotation moves are essentially just 4th dimensional X, Y and Z moves?

[@MelindaGreen]

Yes, there is only one solved state. Simple rotations and the gyro move make no changes to the puzzle state. Some of the arbitrary juxtapositions are pure rotations, but others are twists that change the puzzle state.

[@higgledypiggledycubledy8899]

This is a super clever design, I really want to try it out some day. It hurts my brain. But in a good way.

[@leofreitasa9933]

wow! This is a pretty cool representation of a hyper cube! If you think that the 4th dimension is time, we are speaking of 4 spacial dimensions, our universe is made of 3 dimensions but we can simulate the 4th dimension, you can simulate a cube in a 2d plane, and you can simulate a hyper cube in a 3d plane, it's almost the same thing. if i said something wrong, english is my second language ;)

[@nikhillingem]

Technically not 4-dimensional...

[@noahnaugler7611]

Jake Hay but just about the best analogue you can fabricate. None of them are technically 3 dimensional when you watch them on KZbin anyways

[@ramiel555]

obviously, considering we live in 3-dimensional space, it CAN'T be 4-D, it's just a name

[@nikhillingem]

ramiel555 well yes that’s what I was implying lol

[@Greennoob2]

Jake Hay it’s 4D represented in 3D. The only way we have of seeing 4D so yeah, it’s 4D

[@shemishtamesh]

Jake Hay if you want to get technical, it does move in time so it is four dimensional.

[@roryadie9158]

You got a like because your cat is adorable :)

[@ThatBiohazardGuy]

Really like the way she implemented this.

[@nabranestwistypuzzler7019]

The “turns” that have different pieces on the outside are actually just hypercube rotations in the 4 dimensions. When you’re just doing x rotations on a 3-Dimensional Twisty Puzzle, it’s rotating it in 2 dimensions. When you add y & z moves, it’s in 3 dimensions.

[@creeksidecubing1009]

11:12 moment of terror, lol!

[@amberblyledge7859]

This makes me happier than trying to explain 4 dimensional cubes IN 2 DIMENSIONS. People trying to explain teseracts with slides at school, or gifs on the computer.

[@Konomi_io]

3:41 you say the puzzle has a number of solved states, its just the same state but rotated differently in 4d space. its like how is you turn a 3d cube so orange is on the top instead of yellow, it looks different but its the same state, but this time its in 4d

[@alexismandelias]

The struggle to make this a 10 minute video is real

[@jonni2734]

Really cool puzzle! Good video!

[@ka20na0k5]

A tesseract!!?!???!

[@MelindaGreen]

Yes

[@ka20na0k5]

Melinda Green R u the one who sent this to him....

[@inigo8740]

Kanakjyoti Hariharan yes she is

[@logansmith6342]

That's sick !

[@bigwonghong]

actually its not 2 2x2s its 8 of them and the 4th dimension is another direction that we cannot access (because were 3d)

[@notusknot3002]

You’re not a mathematician? B-but you can solve a Roubrix cube!

[@neroforte6183]

GCubes not all cubers are good at math, its just a cubing stereotype. And its spelled as "Rubiks", not "Roubrix".

[@charlieharrison]

I think it's a joke

[@vpertys]

roobliksxs*

[@baconwizard992]

A robux cube XD

[@Mrb3cubed]

Begone, cancerous jokester...

[@MrRyanroberson1]

5:35 technically that is essentially the same as the 180 long move, if you just reorient the cubes properly. in fact, all of the canonical moves map to each-other since they are all designed to mimic the behavior of a normal 2 cube.

[@MelindaGreen]

Not quite. It's a 90 degree twist of the central face.

[@danielbbg6199]

tho easy to cheat, it seems challenging to do it as you are supposed :D

[@albind8622]

That looks so interesting!

[@kiraPh1234k]

I would like to see you solve it with only the rotation, 90 twist, axial twist and 180 twist. (The gyro move is still allowed as it is just a rotation through the 4th dimension which you need for full solution) But any moves that you are mixing like the juxtaposition and especially the solving like a 2x2x2 stage are only mathematically correct. They are not possible without taking the puzzle apart though, even in the 4th dimension.

[@MelindaGreen]

A simpler minimal ruleset leads to a simple proof that this is the true 2^4 puzzle. It consists of only the arbitrary juxtaposition and a gyro. The juxtaposition nicely matches a natural definition of a 4D twist which is that you can twist any 2x2x2 half puzzle any way you like and then snap it back on. For the two outer faces, you can therefore reach all 24 possible moves for each of them. Adding a gyro lets you do the same for any other face pairs by first moving them to the outside. Solving a puzzle this way is clearly enough to prove that the puzzle is isomorphic to the virtual MagicCube4D puzzle.

[@arfrck2222]

Where can you get one of these

[@luciuskessler7821]

Buying only one can make a two person 2x2 competition

[@AndrewTyberg]

How coincidental that I just uploaded this video (kzbin.info/www/bejne/iHbJi2ycf9JrsMU) the day before Haribo's video came out!

[@killmeister2271]

sue him

[@yosltsum]

If you don't follow the rules of this puzzle, the universe will implode.

[@derrickdunn7643]

Yay......a video

[@alvin55531]

Can't wait till they make the 3x3x3x3 version of this puzzle xD

[@michaeljones7465]

This theory is sound enough for beginners & works with the principle of tesseracts.

[@adirmugrabi]

all the kings men couldn't put it back together again

[@alexj136]

The many different 'solved states' correspond to different viewing angles on what is a single state in full 4D.

[@MelindaGreen]

Exactly.

[@kellymiller9976]

You should do a can Chris solve on the chromium cube

[@MelindaGreen]

I second the suggestion! The Little Chop is notoriously difficult.

[@Batwoman550]

Where can I get one??

[@CanChrisSolve]

Follow the link in the description to liminalcube and you can find Melinda’s contact information there!

[@polyhedralparadise8623]

Yes! Awesome! Where do you get one?

[@mrsar6700]

120$ ... i buy one if you want one i can Helio you is very easy

[@Daniel-ye4uz]

This is like the coolest thing I've ever seen. How can I buy one?

[@CanChrisSolve]

Daniel Apsley Follow the link to Melinda’s channel in the description below! 😊

[@zlac]

Daniel Apsley You can also play a simulated version with MC4D, up to 4D 10x10 I think. Also, there's a software called MC7D that goes up to 7D 5x5.

[@chuckleshelicopterwigwamjo7315]

False advertising, it only has three spatial dimensions

[@Brawler_1337]

Chuckles Helicopter Wigwam Jones Of course it only has three spatial dimensions; we live in a world that can only support three dimensions. However, this is a topological _analogue_ for the 2x2x2x2 puzzle in the fourth dimension. Magic Cube 4D allows you to play with that version of this puzzle, and there was a KZbinr who looked at both that and this puzzle and worked out how the two relate to one another.

[@nayutaito9421]

So why is this the same as 2x2x2x2 tesseract?

[@doritodog6242]

Can someone tell me how to lube this cube?

[@norielsylvire4097]

I need this

[@karacthweatt3155]

IS THIS A COOKIE-CUTTER VERSION OF CARL'S BASEMENT?

[@fgvcosmic6752]

-This isnt even a good representation of 4D- Edit: after seeing the "gyrorotation" thing i change my mind. Pretty good

[@MrSerkanSaral]

That's a weird baby you got there.

[@stevenwatson9678]

Serkan that's his wife tho

[@LoreLibrary-Official]

This is so easy....smash it and assembled it

[@MelindaGreen]

It's good to solve it in 3 stages. First is literally what you said. Learn to reassemble it to understand it's topology. Second is to solve the "bandaged" version where you don't use the gyro move to scramble or solve. It's still 4D but it's like a cube where you can make 90 degree turns on two opposite faces, but only 180 degree twists on the others. Third phase is the full unbandaged puzzle using the gyro during scramble and solve, probably by reducing to the bandaged version and from there like you've already learned in the previous stage.

[@Random-bw2km]

Now where's the 3x3, 4x4, etc?

[@peytoncali6398]

KITTYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

[@congress7914]

Uhh I think I made a 3x3 tesseract puzzle kinda

[@alexandrachirino639]

Couldn't you just take it apart every cube and then just putting it back together?

[@MelindaGreen]

Yes, and it's a very good thing that it's easy to do that because it's helpful to search for algorithms by trying them on a solved puzzle. It's no different from how you can reassemble regular twisty puzzles, but without the risk of damage.

[@slevtubeyey2144]

That cat looks pissed

[@CanChrisSolve]

slevtube yey Trust me, she always looks like that!

[@pymxpvp8082]

yesterday is my birthday!!!

[@alexanderniedland5943]

*was

[@killmeister2271]

*will be

[@johnarken1810]

You have central vacuum.

[@StefanReich]

Question. Where are there these triangular shapes coming from? The 2x2x2 has square faces, as does the 2x2. Not sure I get your concept.

[@MelindaGreen]

You are right that in 4D, the natural puzzle pieces each have 4 cubical "stickers" that sort of surround a section of 4-space. This is analogous to the way that in 3D there are 3 square stickers that sort of surround a section of 3-space. I squished the pieces into this shape out of physical convenience, and is valid because it preserves the topology of the underlying puzzle.

[@condizionatore5356]

I'm CONFUSED

[@vilmernyberg193]

cant you just pick all the pieces apart

[@MelindaGreen]

You can do that with a regular 3x3 too.

[@ShadowaOsu]

820pp with hd balance

[@charlieharrison]

There should be a 3x3x3x3 to satisfy Russian Derpy

[@pimasters3147]

Charlie Harrison there is and I have solved it! Very hard.

[@lilyyy411]

KITTY!!!

[@zlac]

You still didn't solve it? It's been 4 days, noob!:P

[@shdbdn2052]

4th

[@The_NSeven]

Rock da Cuber Dimension

[@transArsonist]

Man do you know how to start a video

[@prsm3]

i think only ones who know how the fourth dimensional works are watching this video.

[@caleborg5688]

u do know u can download a 4-d rubiks cube online right?

[@gazinggoat5869]

Can Chris Solve who or whom?

[@killmeister2271]

*whomst

[@gazinggoat5869]

That's actually correct! You have won the grand prize! Please just send me some common info and I'll get your prize out to you. I'll need your Social Security number, date of birth, Mother maiden name, and your physical address. Cant wait to get you your prize!

[@regen-Q]

Oh god

[@cozimfrench]

That is not a four dimension 2by2by2 that is a 4by2by2

[@alankritgaur]

I thought that the 4th dimension was time

[@h-Films]

how exactly is this 4d?

[@envasgdandmore3135]

EnvasGDAndMore!

[@joobin814]

Naisu

[@phamdinhhoang1998]

there is no unsolved state

[@a-ds-player5961]

I’m confused

[@aerosair6298]

Literally magnet blocks, not much of a puzzle if you ask me

[@ethandevenney1898]

How did they trap the essence of time in space into a state of physical being?

[@europa_bambaataa]

where to buy

[@raideno4488]

Serum..serum!!..oh god...I mean i know that you don't dedicate ur time into solving cubes,not rubiks cubes because rubik's brand sucks, and the way of a cuber but seriously?? You have no cube knowledge, btw either that kid used beginners method, or CFOP frenchic method,the faster method.

[@creeksidecubing1009]

That cat looks BAD!

[@alexanderniedland5943]

You can’t have a four dimensional object, the fourth dimension is time

[@Abhiously]

Mr. Rubric depends on who you ask lol. in this "case", its just another physical dimension

[@Kino-Imsureq]

basically 16x16x1 cube lol

[@Tbone-kt7sb]

It’s a 2x2x4

[@TheRealDrae]

2x2x2x4, but yes. He seems to not realise it's two of the 2x2x2x2s.

[@ryanlowe0]

we live in a 3 dimensional universe (string theory and such notwithstanding), so yes physically its a 2x2x4 3 dimensional construct. you need to use your imagination to picture the two 2x2x2 cubes being next to each other in a 4th dimension..

[@TheRealDrae]

Pff, nerd. For a normal person it's still 2x2x2x4.

[@shemishtamesh]

Jakub Komorowski-Marcjan It's not the same, the 2x2x4 have six faces but the 2x2x2x2 have 12 faces.

[@potatohunter7751]

no... it has inner pieces. how blind do you have to be to realize that

[@8bitcubing184]

so its just a 2x2x4? pls help

[@mrsar6700]

8bitcubing is a representation of a 4D cube yup is incredible

[@ramen6236]

It's not a twisty puzzle though is it?

[@l-fun4056]

Oh.....I’m early

[@carlmwaamba9846]

If it was 4th dimensional you would be breaking the laws of physics. If it was to be 4D it would look all weird and trippy but this is just a cuboid with magnets. (a 4D cube is called a tesseract as far as I remember or just a hyper cube If you want to look it up because its weird as shit)

[@zlac]

you can project a normal 3D rubiks cube on a 2D plane very easily as it's only the surface of the cube that you're dealing with. This is a 3D "projection" of a 4D rubiks cube and it works just like it's suppose to. It only works because it's a 2x2x2x2 so there are only 4-color pieces (like there are only 3 color pieces on a 3D 2x2x2) 3x3x3x3 would have to have a one-color cube for each color INSIDE the cube(s), it would have to have 2 color pieces and 3 color pieces; that's just not possible to project in actual real world (at least not possible that we know of, there could always be someone extremely smart that'll do it...)

[@carlmwaamba9846]

zlac I was being literal as in you can't have a real 4D object in a 3D space, I'm not talking about projections so go away and stop correcting me because you didn't quite understand what I was getting at you bully

[@zlac]

By your comment, it looks like you're underestimating the awesomeness of being able to have a working 3D model of a 4D puzzle, even though it's "just a cuboid with magnets"... It is also self evident that it is not literally 4D. Nobody claimed it is literally 4D so go away, YOU bully...

[@carlmwaamba9846]

zlac yeah nobody except the title and the person in the video so go away *YOU* bully

[@zlac]

It literally says in the description: "first ever physical analog of a four-dimensional twisty puzzle" If you don't know what analog means... take some courses or something, god damn...

[@idkbigoofs890]

Isn’t it just a 2x2x4?

[@yellowmarkers]

no

[@yellowmarkers]

@sean winter still isnt just a regular 2x2x4, like the comment was asking

[@EranB]

well it's not really 4D.. we live in a 3D world, meaning that 4D is basically impossible. just as we can create a 3D illusion in a drawing, it may be possible to make a 4D illusion in the real world. however a real 4D object is impossible, so this cube is not 4D.

[@MelindaGreen]

It's not geometrically 4D but it is topologically identical to the 4D 2x2. What that means is that it has the same 16 corner pieces with the correct 4 colors each (one for each dimension), and they connect to each other in the correct graph. You can prove that if you stick to the canonical moves, then you can perform every twist of the geometrical 4D puzzle with this one, though some twists are more difficult to perform than others, which creates an additional challenge.

[@EranB]

@@MelindaGreen How would you know what a real 4d 2x2 would look like? i understand what you were going for with the four colors on each corner piece and only corner pieces, but the fourth color is hidden hidden and at every given moment only 3 are visible. it's a nice project, but a 4th dimension simply doesn't exist and there is no way to tell (currently) what a 4d 2x2 would look like.

[@haydnmclennan4739]

sooo... it's a 2x2x4??

[@aidanjacobs6082]

That looks like a 6th dimensional cube Or maybe 10th

[@Mickaleb]

you cant have a 4d puzzle in a 3d word

[@MelindaGreen]

It surprised me too but it turns out you can.

[@idkbigoofs890]

Melinda Green I don’t understand it. How?

[@MelindaGreen]

Topologically it is identical to the virtual MagicCube4D equivalent. For each basic move in one puzzle there is a corresponding move in the other. This is easiest to see by noticing that you can move each of the outer 2 faces into all 24 possible orientations (these are the 4D twists of those 3D hyper-faces). The gyro move lets you put any pair of opposite faces in those outer positions without changing the puzzle state. Therefore you can perform any twist on any face. See my intro video where I break this down more slowly.

[@mrsar6700]

Is a representation you can’t imagine that but some persons can