Rubik's Tesseract

[cubinator]

For those that don't know about this already, this thread is about 4-dimensional analogues to Rubik's Cube and other twisty puzzles. I am (obviously) a speedcuber, but I have yet to successfully solve a 4-dimensional twisty puzzle. I tried the Magic Cube 4D phone app several months ago, and got pretty far along in solving it, but I got lost at the part in the instructions regarding 4-color pieces. At that point I drifted away from such puzzles. Today I decided to try the computer version of the app, and I discovered that it allows one to select from a plethora of hyperdimensional twisty puzzles, not just the 3x3x3x3 simulated by the phone version. I decided to try my hand at the 2x2x2x2, as it should be much simpler. I managed to get 5 pieces aligned, but now I'm stuck. Unfortunately, even though it only has one type of piece, it happens to be the one piece I least understand . This is a cool brainteaser for anyone who wants to have their mind bent (or should I say 'extruded'?).

[Wjolcz]

Just looking at it gives me a headache. No wonder I never completed a single wall of the 3D Rubik's cube.

I remember seeing a 4D platformer. I think it was on xkcd? Does anyone know what the title of the game was?

EDIT: was it this one?: http://miegakure.com/

Edited March 14, 2016 by Veeltch

[cubinator]

@Veeltch Yeah, that's the one from xkcd.

A little off-topic but I'd like to see a real 2d game sometime, where your field of view is a line instead of a plane. Nothing 3d or anything, not a single object outside the 2-dimensional plane of reality.

Edited March 14, 2016 by cubinator

[lajoswinkler]

That's the 3D shadow of a 4D object. You will never be able to witness a true tesseract.

[cubinator]

2 minutes ago, lajoswinkler said:

That's the 3D shadow of a 4D object. You will never be able to witness a true tesseract.

I know, and I've even tried to visualize what it would be like if I somehow was pulled into the fourth dimension and survived. At first I wouldn't be able to see anything, my vision is limited to a 3D space parallel to our universe. If I was tilted a little towards Earth, I would be able to see a planar field of view where Earth would look like a 2-dimensional planet: The planet is a disc, with the surface being the outer edge, and the molten interior visible on the inside. If I was tilted further so that I was looking at the center, I would be able to see the inner and outer core, the mantle, and the lithosphere--but only in a single 2-dimensional 'slice' at a time. I wouldn't be able to see the whole volume the way I can see a whole area.

That said, this puzzle acts the same way mathematically you could expect it to work if you managed to build a real 4D tesseract. While it is technically a 3D projection of a 4D object shown on a 2D screen, it is effectively a 4D puzzle.

[cubinator]

I finally finished solving it yesterday! I didn't do it all in one go, I progressed slowly but steadily for a few weeks. I was pretty stumped by the last 3 pieces for a while! But now I finally managed to figure it out! That was an interesting experience, to say the least.

[0111narwhalz]

Do you have any algorithms to share?

[cubinator]

1 hour ago, 0111narwhalz said:

Do you have any algorithms to share?

Only the ones from Superliminal.

http://superliminal.com/cube/solution/solution.htm

I found they work pretty well. The page labeled "Still Stuck?" has a couple of other algorithms that may be helpful.

[Bill Phil]

It's missing a cell...

[stargazer1235]

More importantly, can you transmit complex mathematical equations and theorems through it using Morse code. 

[RainDreamer]

Sorta unrelated question to OP: if you have now managed to beat a 4d tesseract...can you still be called cubinator?

[cubinator]

15 hours ago, Bill Phil said:

It's missing a cell...

The 8th cell is in the 4th dimension, not visible to the 3D slice we project it upon. To view it, we can rotate the tesseract 4-dimensionally. Similar to the way we can't view all six faces of a cube at once, we can't view all eight cells of the tesseract at once, at least not with this projection.

11 hours ago, stargazer1235 said:

More importantly, can you transmit complex mathematical equations and theorems through it using Morse code. 

Only if there is a very special watch on the other side of the tesseract. Unrelated:

Spoiler

Has anyone decoded what actually was being said in Morse through the watch? I wonder if there's an easter egg there?

9 hours ago, RainDreamer said:

Sorta unrelated question to OP: if you have now managed to beat a 4d tesseract...can you still be called cubinator?

I deal with cubes much more often than tesseracts, so I will keep the name.

[Kozak]

Solved it. took 12 hours total. having no previous knowledge of how to solve them. and no google.

[cubinator]

Just now, Kozak said:

Solved it. took 12 hours total. having no previous knowledge of how to solve them. and no google.

What was your method? Was it edges-corners-hypercorners or was it a different method like layer-by-layer? I haven't seen a LBL method for the hypercube, but that would be cool.

[Kozak]

Just now, cubinator said:

What was your method? Was it edges-corners-hypercorners or was it a different method like layer-by-layer? I haven't seen a LBL method for the hypercube, but that would be cool.

That time is a blank in my mind... it melted my brain... I'm pretty sure it was layer by layer and just solve like that.

[cubinator]

1 minute ago, Kozak said:

That time is a blank in my mind... it melted my brain... I'm pretty sure it was layer by layer and just solve like that.

Cool. You should submit your log file and get your name on the Hall of Fame!

[Kozak]

7 minutes ago, cubinator said:

Cool. You should submit your log file and get your name on the Hall of Fame!

Nah. (no not because i cheated, it would be obvious if i did.)

I don't really want to be on a wikipedia page  seems kinda boring.

[Bill Phil]

Look up a tesseract net. It's pretty cool.

[0111narwhalz]

So, I'm approaching this from the other side:

After being terribly incompetent with the mundane 3³, I've decided to try a bottom-up method. I've worked my way up from looking at the 3⁴ and going "durr" to being able to solve three-twist puzzles with reasonable confidence. But I'm not sure if this is sustainable up to the 40-odd twists the program generates for the "full" function.
What are your thoughts?

Incidentally, what do you think about the 5-D version? 
I think there's even a 7-D program, if you can believe that.

[cubinator]

3 hours ago, 0111narwhalz said:

So, I'm approaching this from the other side:

After being terribly incompetent with the mundane 3³, I've decided to try a bottom-up method. I've worked my way up from looking at the 3⁴ and going "durr" to being able to solve three-twist puzzles with reasonable confidence. But I'm not sure if this is sustainable up to the 40-odd twists the program generates for the "full" function.
What are your thoughts?

Incidentally, what do you think about the 5-D version? 
I think there's even a 7-D program, if you can believe that.

You probably won't be able to solve the full scramble just by reversing the moves like in low-count puzzles, just like you wouldn't be able to do that on a 3D puzzle either for a full scramble. Those few twists do help, though, with recognizing the kinds of patterns that appear in the hypercube and learning how the pieces can be moved around and manipulated.

Yes, there is a 5D one, and yes, there is a 7D one. There is no such thing as too far, apparently.

[monstah]

Whoa.

Sorry to dig up the nearly-year-old thread, but I just ran into it and... memories.  

See, I have played that Rubik's Tesseract over a decade ago. I could even beat it, although it took quite some time (I've never been a speedcuber, but this was just painstaking). Anyway, for some new content on the thread: I know also of this 4D maze game! It was a good mind blower, although I don't know if the Java works anymore.

[cubinator]

On 2/13/2017 at 11:19 AM, monstah said:

Whoa.

Sorry to dig up the nearly-year-old thread, but I just ran into it and... memories.  

See, I have played that Rubik's Tesseract over a decade ago. I could even beat it, although it took quite some time (I've never been a speedcuber, but this was just painstaking). Anyway, for some new content on the thread: I know also of this 4D maze game! It was a good mind blower, although I don't know if the Java works anymore.

Cool! I downloaded it and it works fine, but I'm still figuring out how to play. 

[0111narwhalz]

5 hours ago, cubinator said:

Cool! I downloaded it and it works fine, but I'm still figuring out how to play. 

I looked at a few of the "notes" pages and messed about in the 3D maze, and it started to make a bit more sense. Still don't know what the end looks like, or even if it's any different from the rest of the tiles.

[monstah]

9 hours ago, cubinator said:

Cool! I downloaded it and it works fine, but I'm still figuring out how to play. 

 

3 hours ago, 0111narwhalz said:

I looked at a few of the "notes" pages and messed about in the 3D maze, and it started to make a bit more sense. Still don't know what the end looks like, or even if it's any different from the rest of the tiles.

The end is a yellow hypercube, like the start is a grey one.

Here's the revelation that allowed me to play it:

• First play the 3D version for awhile. It's boring and simple, and you'll think, 'duh, I got this'. BUT, abstract away from the actual 3D maze you're building in your head, and look at the picture moving. Look how it reacts to your inputs. How turning right "makes world go in the picture" on the right side and "go out the picture" on the left one and vice-versa, and how this distorts what your're seeing (but keep in mind that it's still a 2D projection of a 3D world)
• Realize that what you're seeing is an image of what the camera in the maze is seeing (heh, I sound like a monk doing guided meditation). As in, you could rotate the picture left or right (like, turning your monitor for example) without changing the 3D avatar's relation to the maze.
• Now, turn the 4D. What you're seeing is the 2D projection of a 3D projection of a 4D maze. Now, just like the previous step, you can rotate the 2D projection, but also the 3D projection. And there are keyboard inputs for rotating this 3D projection, without actually moving or reorienting in the maze! This is key to understanding what you're seeing.
• NOW. Setup the rotation inputs for WASDQE, in such a way that opposite rotations are opposite keys (that is; instead of left-right being A-D and the other weird axis being Q-E, put left-right on A-E and the other one on Q-D). Now, play around rotating the cube (i.e., the 3D projection). Remember step one? When you abstracted the "world go in picture" thing? At some orientation of the image-cube, the commands will match exactly what happens on screen. You press W, world goes in on top, out on bottom. You press D, world goes in on bottom, out on top. Press, E, world goes in on the top right, out on the bottom left. Moving becomes intuitive
• You still gotta be able to intuit what's actually going on in the 4D world, but once you can move about it's easy enough to learn what the hell it is you're looking at.

[Camacha]

On 14/03/2016 at 9:14 PM, lajoswinkler said:

That's the 3D shadow of a 4D object. You will never be able to witness a true tesseract.

I have always felt these 4D representations are a hoax.