Four-Dimensional Rubik's Cube Craziness

roice writes "Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."

this is news?

[Anonymous Coward]

mc4d-src-2_1-1.rpm 17-Jun-2001 15:22 140k
mc4d-src-2_1.tgz 17-Jun-2001 15:22 139k
mc4d-src-2_1.zip 17-Jun-2001 15:21 181k
mc4d-src-2_2.zip 03-Mar-2002 17:40 183k
mc4d-win32-bin-2_0.exe 17-Jun-2001 15:19 186k
mc4d-win32-bin-2_1.exe 17-Jun-2001 15:21 187k
mc4d-win32-bin-2_2.exe 03-Mar-2002 17:41 416k

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Re:damn it....

[Waffle Iron]

you know how long I've been working on my three dimensional one? over a year. Perhaps I'm stupid, but that thing is impossible to solve.

Maybe somebody subjected you to one of my favorite old tricks. Take one corner off of a solved cube and rotate it so that the colors don't match the rest of the cube. Reassemble in this orientation. Presto: unsolveable cube.

Re:damn it....

[cioxx]

Perhaps I'm stupid, but that thing is impossible to solve. Anyone have any clue how long it would take a computer to solve your standard rubics cube through brute force?

A regular computer would solve it in less than 10 seconds. Really a messy scramble of the 4D cube took only 6 seconds to solve. And it wasn't even backtracking.

http://www.kinnetica.com/cioxx/hypercube.png [kinnetica.com]

Re:damn it....

[deadsaijinx*]

thank you, that side eventually led me to my answer [t-online.de]

Re:Is this actualy 4D ?

[cascino]

Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.
The 4th dimension is whatever you define it as. There's no "true" 4th dimension. Einstein had the idea that time could be treated in a fashion similar to that of the spatial dimensions, and so, in his work, he defined the 4th dimension as the temporal dimension.
However, for this program's purposes, it's assumed that we're talking about the 4th *spatial* dimension. You can (kinda) visualize it if you think of the progression of first 3 dimensions: a line (1st d) can be rotated 90 degrees to itself to form a square (2nd d) which can be rotated 90 degrees to itself to form a cube (3rd d). The 4th dimension is thus hypothesized as the space defined by a cube rotated 90 degrees to itself.
(Granted, I'm no mathematician, so if someone has a better understanding, please correct me.)

Re:Not complete

[bad_fx]

That would be like having regular 3D rubik's cube and not be able to turn the white face.

Not quite. It's like having a physical 3D rubik's cube and not being able to see all 6 faces at the same time. You can however turn a physical cube around so you can see the hidden face. It's a similar idea in this one. The way to see the hidden "face" is given in the FAQ:

Q: I can turn a real cube around so that I can see the hidden faces, can
I do something similar to see the invisible eighth "face"?
A: Yes. If you hold down the control key and click either mouse button
on any part of a "face", the puzzle will "rotate" in 4D until that "face"
is in the center. That "rotation" will bring the invisible face into the
same position as the one you clicked on. The "face" on the opposite side
of the puzzle will "rotate" out until it turns inside-out and becomes the
invisible "face". This "turning inside-out" motion is very typical of 4D
"rotations". Notice that control-clicking either mouse button on the
central "face" does nothing because it's already in the center.

Re:Is this actualy 4D ?

[Jonathan the Nerd]

If you've ever read the story "And He Build a Crooked House" by Robert Heinlein, it contains a very good description of what a four-dimensional hypercube would look like. Imagine a small cube in the middle, six cubes surrounding it (one on each side, squashed together so that they share faces), and one big cube on the outside. Alternately, imagine two intersecting cubes (one corner of each cube is in the middle of the other cube), where each face of one cube is connected to each face of the other cube by another cube. Confused yet? So am I! Read the story, it's quite interesting.

This puzzle uses the first model mentioned above, except that you can only see seven cubes at once (the outer cube is hidden so that it won't block the view of the others). If you rotate the model (with Shift-left or Shift-right click), the outer cube comes into view.

You were close...

[bazmonkey]

The best way to solve a given cube is called "God's algorithm" to us Rubik's geeks (I can average about 50 s. solving a cube, which is ok, but not phenomenal). It's 18 moves [www2.vo.lu]. The method behind it is far too complicated for a person to do without a computer to assist, but using a rather simple method [olympus.net], a person can very easily solve a cube in around 65 moves, but slowly. The record-breaking solution times are closer to a hundred moves, but rather than remembering a move-efficient but thought-intensive way to solve it, one remembers many more algos that whose situation can be recognized much more quickly.

And for the previous posts asking how long it takes a computer to do it... it's very, very low. Under a second. Many people can do it, manually (a computer just has to give the moves, it can ignore the time required to actually turn the cube) in under 20 seconds [speedcubing.com] (For the people out there in disbelief, Dan Knights has a video of him actually doing it in 17, it's for real. I won't post the link, because I'm not going to be responsible for slashdotting his site).

There's a huge difference between a computer solving it "brute force", and a person or computer solving it through established algorithms. By brute force, just twirling the cube until the solution popped up, it would take on average however long it takes your computer to process half of the possible combinations. That's quite a long time. However, a computer solving a cube how we would, focusing on time rather than least amount of moves, could easily solve more than one a second.

Not "Cubey",

[teamhasnoi]

Information on the "Rubik, The Amazing Cube" television show

Premiered on ABC: September 10, 1983-September 1, 1984.

The series ran for 1 year, and had a total of 12 episodes. It was
originally broadcast as "The Pac-Man/Rubik, The Amazing Cube Hour"
on Saturday mornings in colour with each Rubik segment lasting
22 minutes.

The Plot
--------

Rubik is discovered by a young boy (Carlos) who brings the colourful cube
to life - after he aligns all the cube's sides - an sets out on a magical
adventure tour along with his brother and sister, Renaldo and Lisa.
The series was rebroadcast in the spring of 1985 as a mid-season replacement.
Ruby-Spears Enterprises produced the series.

Voices
------

Rubik: Ron Palillo
Carlos: Michael Saucedo
Renaldo: Michael Saucedo
Lisa: Jennifer Fajardo
Ruby Rodriguez: Michael Bell
Marla Rodriguez: Angela Moya

Episode List
------------

"Rubik, The Amazing Cube," "Rubik And The Lucky Helmet," "Back Packin'
Rubik," "Super Power Lisa," "Rubik And The Mysterious Man," "Rubik And The
Pooch-Nappers," "Rubik And The Buried Treasure," "Rubik And The Science
Fair," "Honolulu Rubik," "Rubik's First Christmas," "Rubik In Wonderland"
and "Saturday Night Rubik."

Movie References

[HeXetic]

Puzzled by the cube? Try renting two (relatively low-budget, unknown) sci-fi flicks. - Cube [imdb.com]: Buncha people, trapped in a buncha cubes, with a buncha deadly traps. - Cube 2: Hypercube [imdb.com]: Buncha people, trapped in a hypercube, with less deadly traps but more confusion as to wtf is going on. Both movies are fairly puzzling in their own right, with that sort of "unknown" sci-fi ending that is commonly found in lower-budgeted movies (e.g. Pi).

Hofstadter's the best source for rubik weirdness

[aziraphale]

Douglas Hofstadter wrote a couple of excellent columns on Rubik's cube and variations on the theme for his Metamagical Themas column in Scientific American back in the eighties (you can buy his collected columns in this book [amazon.com]). In particular, he talks about the various ways you can modify the basic 3x3x3 cube concept - for example, 4x4x4 cubes, 3x3x3 tetrahedra, alternate colour schemes, and so on (along the way, investigating the spark of inspiration that encourages people to try out different variations on a theme - something he refers to elsewhere in his books as 'conceptual slippage' - this hypercube would be a 'slip' along a different axis to those hofstadter explores - I'm sure he'd appreciate it :) ). He goes into plenty of detail about the mathematical approaches you can use to solving the cube, and some intriguing analogues to subatomic physics that crop up in the maths of rubik... anybody wanting an introduction to the kinds of topics the people behind this hypercube are exploring could do worse than to read those articles.

There's also some excellent stuff in that book on Lisp, quantum mechanics, chaos theory, Alan Turing, and nuclear war... great selection of articles by an extremely interesting mind.

Re:nooo

[tsvk]

Haha, it only took me a minute to solve the 3D version!

Bah, as long as one minute? You are slow.

Check out this site [speedcubing.com], especially the multimedia section. There are videos of guys that solve the cube in less than 20 seconds!

Nope...

[Jerf]

Those are only descriptions of a hypercube that is projected onto a three-dimensional space or intersected with a three-dimensional space.

A real hypercube looks like a hypercube, not a cube with lines or anything else... of course you need to be five-dimensional to perceive the whole thing at once.

In general you need N+1 dimensions to perceive an N-dimensional object; for example, we can only fully perceive two dimensional objects all at once. Three dimensional objects we only see a particular side of, and generally only the surface. A four-dimensional being could potentially see the entire three dimensional object all at once, just as we perceive two-dimensional objects all at once. A two-dimensional being only sees one dimension around him, and can only see a certain side of, say, a square.

Note that there's nothing magical about any of this, or particularly unbelievable; if you're having trouble believing it's this simple your mind has been corrupted by bad sci-fi, probably Star Trek.