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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."
Heck with solving it. There are some things that just aren't worth solving. Now where can I find a software rendered four dimensional analog of a hammer and nail?
A programmer is a machine for converting coffee into code.
it took me long enough to finish the real thing.
I can't even figure out the regular one. Hell, I am lucky I can tie my shoelaces in the morning!
The ultimate network admin tool needs HELP!
Apply a screwdriver to it; reassemble in the proper order.
Um, though that may be a little hard with the program, I'll admit.
Maybe if I apply the screwdriver to the ~~++5#Q%NO CARRIER
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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. Anyone have any clue how long it would take a computer to solve your standard rubics cube through brute force?
YOU SUCK BALLS!
and there is also a running competition for the most efficient solution.
duh...just peel off the stickers.
Can someone plz send me a link to a trainer for this. Thx. also no-cd version much appericated.
I'm going to get good and liquored up and play with my new 4-d rubik's cube. Who wants to come?
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
What, you have to step into the future to solve it? :-D
More than mere navel gazing.
That's what you get when you mess with the timeline!
Neat game. It's been around a while. I've been able to solve 7 random twists. The first thing you have to do is start with a ordered cube and see what happens when you twist it different ways. Not consistently, though. The trick is to figure out what the last move probably was, reverse it, the one before it, reverse that, and so on. After 3 random twists, you might be able to make a bad guess and recover from it. After 7, one wrong turn is a good reason for starting over. Never was able to solve a regular 3d rubiks cube puzzle though.
or is that page black text on a dark brown background? Some people...
Just a word of warning to the foolish and brave. Before you tackle the 4^4 hypercube, make sure you buy an ergonomic mouse and mousepad. My guess is you'll probably develop super-carpal tunnel syndrome before you even you match one side of the damn cube. Also be sure to stockpile a few extra mouses, there's no knowing how many of them you'll be throwing against the wall.
The 1980s certainly seemed the nadir of American animation...
Lawrence Person (lawrencepersonh@gmailh.com (remove all "h"s to mail)
http://www.lawrenceperson.com/
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Any idea how long it will take to have lego's solve it?
Free Instant Site Inclusion
I suspect that this could be solved in a reasonable amount of time with a heuristic search algorith, such as ACO or a genetic algorithm using the number of matches as a heuristic.
Obviously, brute force, even at a massively parallel execution, is completely out of the question.
I memorized the solutions to the Rubik's Cube so everyone would think I was smart! Haha, fooled them!
Now I just get drunk and masturbate a lot.
I solved a Rubiks' Clock on the way home from the swapmeet I bought it at. That's it, right? Like the Rubik's Cube, but about time...
Go to Options->Solve
it's not really a cube is it? i mean, that implies n^3 but this is n^4 so is it really a rubiks quartic?
-1: flamebait should really be -1: inciteful
I don't know. It looks like a more complex 3D version that's just real togh to build with plastic.
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.
--= Isn't it surprising how badly I spell ?
I've found a very sparce selection of downloadable Go games for GNU/Linux, (GNU Go is the only one I know of). I'm surprised there's not more renderings of this awesome ancient game.
:)
Still, when you got a four-demensional rubik's cube goin' on, life is pretty good
SEO Copywriter. Just Say ON
Right. If I could bend my arm in a fourth spacial dimension, I could steal your liver without making a single incision.
The software is just a 2 dimensional representation. I find it almost impossible to solve the normal cube in the software version and I can solve a physical cube in under 5 minutes. A 4D cube might be interesting but not a 2D representation of one. I like the 4x4x4 and 5x5x5 cubes at rubiks.com.
Jason
ProfQuotes
mice/trackballs do I need to install to solve this thing? Alternatively, can I use mouse and keyboard? Ah heck I might as well be playing Counter-strike.
"I just can't sit while people are saying nonsense in a meeting without saying it's nonsense" J Watson, Sci Am 288:(4)51
Still I love this program. I'm a big fan of rubik's cubes and of geometry of higher dimensions.
Komi
The ultimate goal of science is to unify all forces of nature to a single law that can be silk-screened onto a T-shirt.
1) Click OPTIONS
2) Click SOLVE
Two clicks... anyone do better?
I am NOT a man!
I am a free number!
Well it's not news, and it's not even close to new, but it sure is nerdy :)
Did anyone not have a cube?
- Adam L. Beberg - The Cosm Project - http://www.mithral.com/
Not to be a troll or anything, (please don't see it this way)
I thought that People lived in the Fourth Dimention, hence why time plays such an important factor on us. We are just able to see and manipulate in the third. It would be a being that lives in the Fifth Dimention (whatever the hell that might be) that could see and manipulate the fourth. It's a bit late for me so my brain is a bit clouded for this Quantum Physics stuff.
Um, though that may be a little hard with the program, I'll admit.
No it won't, we just have to wait for someone to come up with a software implimented 4 dimensional hammer...there's probably already one written for emacs...
If Mr. Edison had thought smarter he wouldn't sweat as much. --Nikola Tesla
Now if someone would only release a patch to stop that infernal beeping when you click in the wrong place on the window. xset and setterm seem to have no effect.
wasn't there a place where hot and sultry female villians are willing to perform, erm, certain acts, in return for a rubix cube like that? Maybe this is the updated version of the intergalactic somethingoranother - beware if women on the street starts to act suspiciously intimate once you start solving this thing!
My life in the land of the rising sun.
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. The method behind it is far too complicated for a person to do without a computer to assist, but using a rather simple method, 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 (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.
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."
I didn't find it particularly hard to play, but some people do. I think it's a good way to practise thinking about things abstractly.
Anyway, find a friend, and play a few games, see how you do. The rules are slightly different, you play until you fill the board, and the person at the end with the most numbers of three in a row wins.
Gotta love that.
:)
But it would be much more interesting to peel somebody out of the third dimension, flip them over, and put them back in. To them, it would appear as if the universe had just been mirrored left to right, but to everybody else, it would appear that that person had been mirrored left to right... IOW, his heart would be on the wrong side, if he was left handed he's now right handed, etc.
He'd have a hell of a time reading anything, as all the text in the world is now backwards (to him at least).
I dont recall the name, but a friend of mine actually had a book on solving the original in 15 minutes or less, and it actually seemed to have a solid strategy base behind it.
it was written by some math professor who spend a whole summer obsessing (much like the rest of america at the time) with the cube...
at any rate, i wish id read the damn book.... for some reason, since i work with computers, people expect me to be able to solve puzzles like that in real time, while concurrently explaining how to fixed their botched aol 3.0 installations....
gah
Realware, by Rudy Rucker, is a fun bit of sci-fi that involves things like that happening.
"...always new atoms but always doing the same dance, remembering what the dance was yesterday." -Richard Feynman
Here is a neat Java applet of the 3D version.
and they even publish their source code for download.
./configure && make under FreeBSD nor Debian.
I guess you haven't tried to get it compiled? No luck with a straight
bash$
I used to play with lego's when I was a kid, but I sort of grew out of them once I started playing with my computer. I guess you could call it LEGOS for grownups :)
:)
So, you're probably wondering what I did with all my LEGO's, right? Well, I gave my Lego's to my grandmother, who organized the lEGO's by color and then sold the leGO's at a garage sale.
I guess that's the story of my legO's.
Oh yeah, LeGo's, lEgO's, LEGOS'! Ha!
If you pop off a corner of a solved Rubiks cube, rotate it 120 degrees, and pop it back on, it becomes unsolvable. You should try it on someone you hate, or someone you know who won't murder you repeatedly. >.>
This statement is false.
I could steal your liver without making a single incision.
"But I'm using it."
- Meaning of Life
The line must be drawn here. This far. No further.
My problem with this is that it rotates so fast, that I can't figure out what the effect of a rotation is supposed to be. The speed also makes learning by observing it solving itself useless ... just some flashes and 0.25 seconds later it's done. Any way to slow it down?
---------
There is inferior bacteria on the interior of your posterior.
Popular? Do people still play with this? I haven't even seen one in the last 15 years or something (I'm in Europe). My impression was that after the initial 'craze' everyone got collectively sick of it somewhere in the mid-eighties and it kind of faded away. It was an interesting puzzle though, not that I ever really tried to solve it.
JP
Puzzled by the cube? Try renting two (relatively low-budget, unknown) sci-fi flicks. - Cube: Buncha people, trapped in a buncha cubes, with a buncha deadly traps. - Cube 2: Hypercube: 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).
http://www.chmodoplusr.com/
You are a bitch to the corporation that makes LEGOs.
Tim
Omnia vestra castrorum habetur nobis.
Stuff that, I'm having trouble enough reading the
black text upon the black background.
Heck, It was just too easy.. solved it in less than a minute.
But I won't submit my entry into the hall of fame, otherwise the FBI will come looking for this "human computer" that can perform 10^30 trops, and exceeds export regulations :P
If you're not using firefox, you're not surfing the web, you're suffering it.
---
Another way of viewing the 3D Rubik's cube (for the mathematicians out there) is as a group on 6 generators, meaning that any reachable configuration could be gotten by merely repeating the same 6 operations in some order (I believe the 6 generators being rotating the two outer 3x3x1 squares 90 degrees clockwise along any of the 3 axes).
Using this group, you could do various things like find the odds that a random arrangement of stickers is actually solvable (take the size of the group divided by the number of possible arrangements). Are there computations involving this for the 4D cube on the web anywhere?
So it seems you can invent a whole hierarchy of n-dimensions Rubik's puzzle... for n >= 3. But is it possible to invent a 2-dimensional version? Just for people like me who could never figure out the 3D
-- http://matteo.vaccari.name/
Now I have. Thanks.
I found this great 1-D Rubik's Cube, here, I can embed it here on this page:
.
.
The interface is simple: just look at it. Quantum mechnaics dictates that observing it changes it's state so just assume it's solved.
Here is a magnified version:
If you still have trouble with it, my book will be coming out pretty soon.
THE WORLD IS GOING TO END!!!! eventually.
...the web page was easier to read.
When I'm King, there'll be a law against web pages using a black font on a near black background.
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). 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.
I wonder how many possible combinations of the cube are solvable (if you put the pieces together in all possible combinations?)
Furthermore, any solvable combination will just be a permutation of any other solvable combination (i.e. you don't have to take the cube apart to create another solvable combination from one). So all these "solvable" states can be collapsed into 1.
So then I wonder how many unique combinations there are, of which only one is solvable. The answer is left as an exercise to a reader who is much more motivated than I am.
Hi! I've managed to take a funny story and turn it into a mind-boggling math problem.
-CausticPuppy "Of all the people I know, you're certainly one of them." -Somebody I don't know
I put 3D-Homer back together in only 27 turns...this 4D bull should be no problem!
****--- A fortune cookie once told me the meaning of life...so I ate it. ---****
Shouldn't this be called Rubik's Tesseract?
That is, if we can get a a licensing deal with Erno. . .
Only after a few minutes my mind is already going nuts!
:-)
What a crazy game!
I played with this back in 98 or 99 (perhaps even before). It's based on the HyperCube obviously. That being a point streched perpendicular to itself is a line, a line stretched perpedicular to itself is a 2D plane (rectangle), a rectangle stretched perpedicular to itself is a 3D plane (cube), and so on and so on. It's infinite. But I'm sure most of you already knew that. Regardless, I wonder if they made any changes since last time I played with it?
Rivendahl
... there is nothing that has not already been thought
Give me a week and I'll have it solved by last month.
>
> How am I supposed to go to sleep with that stuff in my head? Now I'll have to watch some porn or something...
Time for my bastardly deed for the day:
"Oh, Rubie! (clackclackRubik!clack) Yeah, Rubie, that's it! (Rubik!clackclack) Twist it there Rubie! Oh, Rubie, (Rubik!Rubik!) let me send you to the Fourth Dimension, Rubie! (RubikrubikrubufRUUUUUUUUUUUUBIK!!!!!!!!!)"
I'm not interested in 4D. Let me know when they get to 5D, so I can get my Rubik's Tesseract.
--
"Outlook not so good." That magic 8-ball knows everything! I'll ask about Exchange Server next.
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.
I actually know one of the people on the hall of fame, a young man named Douglas Li. A couple of months after he completed his solution, he and I competed together on Michigan's all-star high school math team for ARML (American Regions Math League). He's quite good with mathematics in general, and both he and I scored about par for the course in the individual portion of the competition.
What I'll never forget, though, is that on the bus ride from Michigan to Iowa, he would take particular challenges on his Rubik's cube. Before the trip, he disassembled and oiled his cube so that he could make moves more quickly. He could solve any 3x3x3 in under 30 seconds by examining all faces of the cube, then pretty much spinning it on autopilot. He took a little longer for a 5x5x5. A rubik's dodecahedron actually gave him a run for his money, but after about 45 minutes of puzzling, he got it.
The most interesting thing he accomplished, though, was creating an image of a rose, with stem, on one of the faces of a 5x5x5. We suggested that he use it to ask a girl to prom. No word yet on whether he did, but if so, that's surely worthy of the hall of fame, don't you think?
Anonymous Luddite: "What do you think of the dehumanizing effects of the Internet?"
Andy Grove: "Not Much."
Your room temperature example illustrates a 3D function quite well, but I'm not sure it helps anyone's conception of a 4D object. A 2D function is a surface (e.g. a sail), which is not the same thing as a 3D object (e.g. a solid cube).
Since this is a discrete example, probably the easiest visualization is a spreadsheet. A simple 3x3x3x3 discrete cubic object is just 81 rows with the 4 columns ranging from -1 to 1. If you added a 5th column without increasing the number of rows, you would have a 4D function.
I'm not sure how this representation is matched to the Rubik's cube example. The first thing is that the row with all 0s is not used as it is not on the 4D surface. Then I guess you could have an ID that represents the state of the surface point. Depending on whether the point is on the center of the face (3 0s), an edge (2 0s), a corner (1 0s), or a 'hypercorner' (no 0s), the ID would represent the set of colors and orientation of the piece. Finally you need a way to describe the effect of all possible moves on the spreadsheet.
Try the following bit of code...
:link, :link * { color: #0000EE !important } :visited, :visited * { color: #551A8B !important }'; if(document.createStyleSheet) { document.createStyleSheet("javascript:'"+styles+"' "); } else { newSS=document.createElement('link'); newSS.rel='stylesheet'; newSS.href='data:text/css,'+escape(styles); document.documentElement.childNodes[0].appendChild (newSS); } })();
If you copy and paste that into a bookmark, that book mark will have the function of removing all colors from a page. Any page.
The 4D cube page has TERRIBLE coloration. This helps.
Rudy
javascript:(function(){var newSS, styles='* { background: white ! important; color: black !important }
1. 2.
The colours, the horrible colours!
Blue links and black test on a dark grey background. What was this guy thinking?
"People who do stupid things with hazardous materials often die." -- Jim Davidson on alt.folklore.urban
How am I supposed to rearrange the stickers now?
(C) Kaki Sain, 2011. By reading this, you have illegally copied my property to your brain.
I second this comment on Hofstadter's Metamagical Themas column (although I'm more a fan of his colleague Egbert B. Gebstadter's row called Thetamagical Memas)
I remember a disappointed follow up by Hofstadter written (I believe) as one of the Post Scripta that follow the reprints of the columns in the book, that the world in general didn't follow down the primrose path to further cube-notion slipping: he laments that many cubes have been melted down for their plastic, etc, and comments (in 1985, when the reprints came out) that humans have made themselves "collectively sick of the cube."
Hofstadter is always worth checking out if you've never heard of him, but you need to look at about either exactly one or any three different titles by him to begin to understand the breadth and depth of what motivates him. And he just so happens to be a kind and generous guy in person too, if you've ever met him.
It took me long enough to learn how to do the original in under a minute... now I have to learn this?
SlicerAce Solving Rubik's Cube in 34 seconds
Hofstadter is definitely an amazing author. I'm about 200 pages into "Godel, Escher, Bach -- an Eternal Golden Braid", and it's hands down the best book I've ever written. It won a Pulitzer, IIRC.
It's rare that someone has such a grasp of both conteptual material and language as to be able to explain concepts such as addressed in GEB, and to relate them to each other. Hofstadter addresses the concept of "Strange Loops" (self-referential structures), using Bach and Escher to explain the importance of Godel's work (and using Godel and Bach to explain Escher's art, and using Escher and Godel to describe Bach's music).
This book uses self-reference to explain the self-referential works of all three minds, all in a way which manages to be both astoundingly lucid and refreshingly amusing for a 700-page text addressing such complex topics.
I feel that this book will be as good (or better) of a read the second time through -- of course, the second time through I'll be taking more notes, and looking for more puzzles as well as a deeper understanding of the meaning of the text. Much like a work by Escher, Hofstadter's "Godel, Escher, Bach" has surprises for the attentive observer on many levels.
Somebody get that guy an ambulance!
I'm so tired of the physics-illiterati mangling the fourth demension (time).
/pet peeve
For those just tuning in, the universe is 4-dimensional. Every possible location in the universe can be described using 4 dimensions; the 3 with which you are familiar, and time. You are where you are at this particular time. Therefore, your location is 4-dimensional. Change any one of those ordinates, and it's a different place in space-time, which is how we currently understand the universe.
There are 4D rides at Universal Studios here in Florida. Yeah, right. They manipulate time, or can control your passage through it. Now this Rubik's cube takes the 4th dimension into account? How? How must time be manipulated so that it affects the outcome of the challenge? Just going forward in time as usual is not a manipulation.
I remember in the old NES days everyone would say "I have a Nintendo" NOT "I have a Nintendo entertainment system". The reason for this was obvious -- the Nintendo corporation didn't sell anything else in the US (or not anything that kids knew about) and they had their name emblazened on the box. It seems this should apply to Lego as well since, as far as I know, they don't make anything other than plastic pieces which plug together (and now the Mindstorm computers). So if one says "I have some Legos", it's obvious they are refering to Lego blocks.
you call that challenging? Wait until the command-line version of the game comes out! :)
like i said
It's a DIY because they sell blank black cubes and have all sorts of sticker sets, like flags, coloured happy faces, and whatever. That way they don't have to deal with manufacturing each model, stocking inventory for each, end-of-line sales for unpopular ones... they just pack in the sticker set.
Rubik's sells cube lube. "If the only lube you've ever purchased is cube lube, you might be a geek."
(C) Kaki Sain, 2011. By reading this, you have illegally copied my property to your brain.